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Acidities of arylamnines and arylammonium ions Dolman, Douglas 1966-12-31

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THE ACIDITIES OF ARYLAMINES AND ARYLAMMONIUM IONS by DOUGLAS DOLMAN B . S c , U n i v e r s i t y of B r i t i s h C o l u m b i a , 1962 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of C h e m i s t r y We a c c e p t t h i s t h e s i s as c o n f o r m i n g t o the r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA M a r c h , 1966 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d s t u d y . I f u r t h e r a g r e e t h a t p e r  m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h i s r e p r e s e n t a t i v e s „ I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i  c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f T h e U n i v e r s i t y o f B r i t i s h C o l u m b / a V a n c o u v e r 8, C a n a d a D a t e //nOyLcX The University of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of DOUGLAS DOLMAN B.Sc, The University of B r i t i s h Columbia, 1962 IN ROOM 261, CHEMISTRY BUILDING THURSDAY, MARCH 10, 1966, AT 3:30 P.M. COMMITTEE IN CHARGE Chairman: I. McT. Cowan A. V. Bree G. H. Dixon C. A. McDowell D. E. McGreer R. E. Pincock . R. Stewart External Examiner: J . T. Edward Department of Chemistry M c G i l l University Research Supervisor: R; Stewart THE ACIDITIES OF ARYLAMINES AND.ARYLAMMONIUM IONS ABSTRACT In order to study quantitatively the acidity of very weak acids and at the same time the effect of a polar aprotic solvent on the basicity of hydroxide ion a Hammett H_ acidity function based on the ionization of 24 substituted anilines and diphenylamines has been established in the system dimethylsulfoxide-water- tetramethylammonium hydroxide. The basicity of hydro xide ion is increased dramatically as the solvent is changed from water to dimethylsulfoxide. The H_ of a 0 , 0 1 1 molar solution of tetramethylammonium. hydroxide ranges from 12 in water to 26 in 9 9 . 6 mole % dimethylsul- foxide-water, an increase in. basicity of fourteen powers of ten. The increase in basicity is due to the increased activity of the hydroxide ion brought about by the reduc tion in its solvation in the poor anion-solvating solvent, dimethyl sulfoxide and indicates the extensive solvation enjoyed by the hydroxide ion in water. The PKTTA values of the indicator acids vary from 1 3 . 8 4 for 2V4-dinitrodiphenylamine to 2 5 . 6 3 for 3 - chloroaniline. From a plot of log versus Hammett substituent constants ( cT) for six monosubstituted di- . phenylamines a rho ( p ) value of 4 . 0 7 is found. The magnitude of substituent effects on the acidity of aniline appears to be quite similar. The acidities of a l l the substituted diphenylamines do not follow the above men tioned correlation with Hammett o" constants; the pKy^ values of 4-amino-, 4-methoxy-, 4-methylsulfonyl-, and 4-nitrodiphenylamine are a l l less than expected from the Hammett <5 constants for the substituents in these com pounds. The 4-nitro substituent exerts a particularly large acid-strengthening effect on the acidities of ani line and diphenyl amine; the decreases in pKjj^ being approximately 8 . 4 and 6 . 8 pK units, respectively. The pK^values of 17 compounds other than those in dicators used to establish the H_ function have been deter mined with the aid of the H_ function. Most of these com pounds are alkyl-substituted 4-nitroanilines. Alkyl groups ortho to the amino group of 4-nitroaniline cause a decrease in the pKy^ (an increase in acidity). Simi larly, N-methyl-, N-ethyl-, and N-isopropyl-4-mitro-a n i l i n e are a l l stronger acids' than 4 - n i t r o a n i l i n e i t s e l f . An explanation f o r the ef f e c t s of a l k y l substituents on the a c i d i t y of 4 - n i t r o a n i l i n e i n terms of the solva t i o n of both the ionized and unionized amines i s advanced. A Hammett H 0 a c i d i t y function based on the protonation of 17 diphenylamines i n 20 volume % ethanol-aqueous s u l  f u r i c acid has been established. The H 0 value for the most a c i d i c s o l u t i o n studied i s -6.97 for 11.2 molar s u l  f u r i c , a c i d . This a c i d i t y function d i f f e r s from that based on the protonation of azobenzenes i n the same solvent system; the l a t t e r a c i d i t y function diverges to more, ne gative H 0 values.as the s u l f u r i c acid concentration i n  creases. The pKgj^ j. values f o r the protonation of the diphenyl amines vary from 1.36 for 4-methoxydiphenylamine to -6.21 for 4,4'-dinitrodiphenylamine. A plot, of log Kgjj^. versus Hammett, <T constants for f i v e mono-substituted diphenyl amines y i e l d s a rho (p) value of.3.36. The yKgj^. values for 4-methoxy-, 4-m.et.hyl-, 4-methylsulfonyl-, and 4-nitro- diphenylamine are a l l less (morenegative) than expected from the Hammett substituent. constants. Substituent e f f e c t s on the b a s i c i t i e s of a n i l i n e and diphenylamine are the same. This i s evident from the fact, that a plot of the pKgH-j- values of 11 diphenylamines versus the pKgm- values of the corresponding a n i l i n e s y i e l d s a good straight l i n e with slope 1.01. The b a s i c i t i e s of several n i t r o - s u b s t i t u t e d diphenyl amines appear to vary regul a r l y and do not r e f l e c t the presence of a strong i n t e r a c t i o n between the n i t r o group and s u l f u r i c a c i d . A plot of the a c i d i t y versus the b a s i c i t y ( p K ^ versus pKgjjj.) for nine diphenylamines yields, a straight l i n e with slope 1.30. In a s i m i l a r plot for 33 substituted a n i l i n e s and diphenylamines two types of behaviour are observed. Those a n i l i n e s and diphenylamines without an ortho or para h i t r o group f a l l about the l i n e with slope 1.30 while those amines with at l e a s t one n i t r o group i n the ortho or para p o s i t i o n f a l l on a d i f f e r e n t , curved l i n e with a slope of less than unity. GRADUATE STUDIES Field of Study: Chemistry Topics in Physical Chemistry Topics in Inorganic Chemistry Topics in Organic Chemistry Spectroscopy and Molecular Structure Chemical Kinetics Physical Organic Chemistry Organic Reaction Mechanisms Linear Algebra J. A. R; Coope A. Bree W. R. Cullen N. Bartlett H. C. Clarke J. T. Kwon J. P. Kutney F. McCapra A. I. Scott C. Reid E. J. Wells L. W. Reeves K. B. Harvey G. B. Porter D. G. L. James R. Stewart R. Pincock Ri C. Thompson i ABSTRACT S u p e r v i s o r : P r o f e s s o r R. Stewart In o r d e r t o s t u d y q u a n t i t a t i v e l y the a c i d i t y of v e r y weak a c i d s and at the same time the e f f e c t of a p o l a r a p r o t i c s o l v e n t on the b a s i c i t y of h y d r o x i d e i o n a Hammett H _ a c i d i t y f u n c t i o n based on the i o n i z a t i o n of 24 s u b s t i t u t e d a n i l i n e s and d i p h e n y l a m i n e s has been e s t a b l i s h e d i n the system d i m e t h y l s u l f o x i d e - w a t e r - t e t r a m e t h y l a m m o n i u m h y d r o x i d e . The b a s i c i t y of h y d r o x i d e i o n i s i n c r e a s e d d r a m a t i c a l l y as the s o l v e n t i s changed from water to d i m e t h y l s u l f o x i d e . The H _ of a 0.011 molar s o l u t i o n of tetramethylammonium h y d r o x i d e ranges from 12 i n water t o about 26 i n 99.6 mole % d i m e t h y l s u l f o x i d e - w a t e r , an i n c r e a s e i n b a s i c i t y of f o u r t e e n powers of t e n . The i n c r e a s e i n b a s i c i t y i s due t o the i n c r e a s e d a c t i v i t y of the h y d r o x i d e i o n brought about by the r e d u c t i o n i n i t s s o l v a t i o n i n the poor a n i o n - s o l v a t i n g s o l v e n t d i m e t h y l s u l f o x i d e and i n d i c a t e s the e x t e n s i v e s o l v a t i o n e n j o y e d by the h y d r o x i d e i o n i n w a t e r . The PKJJA. v a l u e s of the i n d i c a t o r a c i d s v a r y from 13.84 f o r 2 , 4 _ d i n i t r o d i p h e n y l a m i n e t o 25.63 f o r 3 - c h l o r o - a n i l i n e . From a p l o t of l o g KJJA. v e r s u s Hammett s u b s t i t u e n t c o n s t a n t s ( C T ) f o r s i x m o n o s u b s t i t u t e d d i p h e n y l a m i n e s a rho ( P ) v a l u e of 4 .07 i s f o u n d . The magnitude of s u b s t i t u e n t i i e f f e c t s on the a c i d i t y of a n i l i n e appears t o be q u i t e s i m i l a r . The a c i d i t i e s of a l l the s u b s t i t u t e d d i p h e n y l a m i n e s do not f o l l o w the above mentioned c o r r e l a t i o n w i t h Hammett 0~ c o n s t a n t s ; the p K H A v a l u e s of 4 - a m i n o - , 4 - m e t h o x y - , 4 - m e t h y l s u l f o n y l - and 4 - n i t r o d i p h e n y l a m i n e are a l l l e s s than e x p e c t e d from the Hammett C T c o n s t a n t s f o r the s u b s t i t u e n t s i n these compounds. The 4 - n i t r o s u b s t i t u e n t e x e r t s a p a r t i c u l a r l y l a r g e a c i d - s t r e n g t h e n i n g e f f e c t on the a c i d i t i e s of a n i l i n e and d i p h e n y l a m i n e ; the d e c r e a s e s i n pKjj^ b e i n g a p p r o x i m a t e l y 8.4 and 6 .8 pK u n i t s , r e s p e c t i v e l y . The pKjj^ v a l u e s of 17 compounds o ther than those i n d i c a t o r s u s e d t o e s t a b l i s h the H _ f u n c t i o n have been d e t e r m i n e d w i t h the a i d of the H _ f u n c t i o n . Most of these compounds are a l k y l - s u b s t i t u t e d 4 - n i t r o a n i l i n e s . A l k y l groups o r t h o t o the amino group of 4 - n i t r o a n i l i n e cause a decrease i n the p K H ^ (an i n c r e a s e i n the a c i d i t y ) . S i m i l a r l y , N - m e t h y l - , N - e t h y l - , and N - i s o p r o p y l - 4 - n i t r o a n i l i n e are a l l s t r o n g e r a c i d s than 4 - n i t r o a n i l i n e i t s e l f . An e x p l a n a t i o n f o r the e f f e c t s of a l k y l s u b s t i t u e n t s on the a c i d i t y of 4 - n i t r o a n i l i n e i n terms of the s o l v a t i o n of both the i o n i z e d and u n i o n i z e d amines i s advanced . A Hammett H Q a c i d i t y f u n c t i o n based on the p r o t o n a t i o n of 17 d i p h e n y l a m i n e s i n 20 volume % e t h a n o l - a q u e o u s s u l f u r i c a c i d has been e s t a b l i s h e d . The H n v a l u e f o r the most a c i d i c i i i s o l u t i o n s t u d i e d i s -6 .97 f o r 11.2 molar s u l f u r i c a c i d . T h i s a c i d i t y f u n c t i o n d i f f e r s f rom t h a t based on the p r o t o n a t i o n of azobenzenes i n the same s o l v e n t sys tem; the l a t t e r a c i d i t y f u n c t i o n d i v e r g e s t o more n e g a t i v e H Q v a l u e s as the s u l f u r i c a c i d c o n c e n t r a t i o n i n c r e a s e s . The pK B I j+ v a l u e s f o r the p r o t o n a t i o n of the d i p h e n y l a m i n e s v a r y from 1.36 f o r 4 -methoxydiphenylamine t o -6 .21 f o r 4 , 4 * - d i n i t r o d i p h e n y l a m i n e . A p l o t of l o g Kgjj+ v e r s u s Hammett 0~ c o n s t a n t s f o r f i v e m o n o - s u b s t i t u t e d d i p h e n y l a m i n e s y i e l d s a rho (p) v a l u e of 3 .36 . The pKgjj+ v a l u e s f o r 4 -methoxy- , 4 - m e t h y l - , 4 - m e t h y l s u l f o n y l - , and 4 - n i t r o d i p h e n y l a m i n e are a l l l e s s (more n e g a t i v e ) than e x p e c t e d from the Hammett s u b s t i t u e n t c o n s t a n t s . S u b s t i t u e n t e f f e c t s on the b a s i c i t i e s of a n i l i n e and d i p h e n y l a m i n e are the same. T h i s i s e v i d e n t from the f a c t t h a t a p l o t of the PK3JJ+ v a l u e s of 11 d i p h e n y l a m i n e s v e r s u s the pKgH+ v a l u e s of the c o r r e s p o n d i n g a n i l i n e s y i e l d s a good s t r a i g h t l i n e w i t h s l o p e of 1 . 0 1 . The b a s i c i t i e s of s e v e r a l n i t r o - s u b s t i t u t e d d i p h e n y l a m i n e s appear t o v a r y r e g u l a r l y and do not r e f l e c t the presence of a s t r o n g i n t e r a c t i o n between the n i t r o group and s u l f u r i c a c i d . i v A p l o t of the a c i d i t y v e r s u s the b a s i c i t y (pKjj^ v e r s u s pKgH+) f o r n i n e d i p h e n y l a m i n e s y i e l d s a s t r a i g h t l i n e w i t h s l o p e 1 . 3 0 . In a s i m i l a r p l o t f o r 33 s u b s t i t u t e d a n i l i n e s and d i p h e n y l a m i n e s two t y p e s of b e h a v i o u r are o b s e r v e d . Those a n i l i n e s and d i p h e n y l a m i n e s w i t h o u t an o r t h o or para n i t r o group f a l l about the l i n e w i t h s l o p e 1.30 w h i l e those amines w i t h at l e a s t one n i t r o group i n the o r t h o or para p o s i t i o n f a l l on a d i f f e r e n t , c u r v e d l i n e w i t h a s l o p e of l e s s than u n i t y . V TABLE OF CONTENTS Page INTRODUCTION 1 A . D e f i n i t i o n s of A c i d and Base 1 B . The A c i d D i s s o c i a t i o n C o n s t a n t . . . . 2 C . Hammett A c i d i t y F u n c t i o n s 5 D . O t h e r Methods of M e a s u r i n g A c i d i t i e s . . 19 E . F i r s t and Second D i s s o c i a t i o n C o n s t a n t s of D i b a s i c A c i d s 21 OBJECTS OF PRESENT RESEARCH 24 METHODS OF APPROACH 26 EXPERIMENTAL 27 A . P r e p a r a t i o n and P u r i f i c a t i o n of I n d i c a t o r s 27 B . P u r i f i c a t i o n of S o l v e n t s 27 C . P r e p a r a t i o n of S o l u t i o n s 29 D . S p e c t r a l Measurements i n the D i m e t h y l s u l f oxide - Water System 31 E . S p e c t r a l Measurements i n 20 Volume % E t h a n o l - Aqueous S u l f u r i c A c i d . . . . . . . . 34 F . Treatment of the S p e c t r a l Data . . . . 35 RESULTS 39 A . The System DMSO-Water-Tetramethylammonium H y d r o x i d e . . . . . . . . . . . . 39 B . The System "20 % E t h a n o l - A q u e o u s S u l f u r i c A c i d 52 C . P r o b a b l e E r r o r i n H and pK V a l u e s . . . . 55 DISCUSSION 61 A . V a l i d i t y of the H_ F u n c t i o n 61 B . I n t e r p r e t a t i o n of S o l v e n t B a s i c i t y . . . . 65 C . V a l i d i t y of the H Q F u n c t i o n 73 D . Comparison of the H Q F u n c t i o n f o r D i p h e n y l  amines w i t h o ther H Q F u n c t i o n s . . . . 77 E . C o r r e l a t i o n of S t r u c t u r e w i t h A c i d i t y . . 82 F . A c i d and Base S t r e n g t h s of N i t r o - s u b s t i t u t e d A r o m a t i c Amines . . . . . . . . . . 105 G . Comparison of the A c i d i t y and B a s i c i t y of A n i l i n e s and D i p h e n y l a m i n e s . . . . . . 118 v i SUGGESTIONS FOR FURTHER WORK 127 Appendix A : P r e p a r a t i o n and P u r i f i c a t i o n of I n d i c a t o r s 132 Appendix B: S p e c t r a l Data f o r the I n d i c a t o r s 145 Appendix C: I o n i z a t i o n R a t i o Data . . . . 150 BIBLIOGRAPHY 159 v i i LIST OF TABLES Page I The pKjj A Values of the Indicators Used to Es t a b l i s h the H_ A c i d i t y Function .. .. .. .. . . . . 41 II H_ Values for the System DMSO-Water- Tetramethylammonium Hydroxide (0.011 M) 42 III Summary of PK H A Values of Various Amine Acids 49 IV Values of pKgji+ for the Diphenylamines Used to Es t a b l i s h the H Q A c i d i t y Function 54 V H D Values for the System "20 % Ethanol"- Aqueous S u l f u r i c Acid .. .. .. 56 VI The pKjjA Values of Some Alkyl-substituted Anilines and Diphenylamines 95 VII The p K H A Values of Some Nitro-substituted Diphenylamines .. .. .. .. I l l VIII Values of pKgji+ a n d P KHA for Anilines and Diphenylamines 122-3 IX Absorption Maxima and Molar Ab s o r p t i v i t i e s of the Indicators in 95.6 % Ethanol 145-6 X Absorption Maxima and Molar A b s o r p t i v i t i e s of Diphenylamines i n 20% Ethanol .. 147 XI Absorption Maxima and Molar A b s o r p t i v i t i e s of Indicator Anions in DMSO-Water .. 148-9 XII Experimental Values of Log [A-] / [HA] for the Indicators used to Determine the H_ Values in DMSO-Water-Tetramethylamnionium Hydroxide (0.011 M) 150-3 XIII Experimental Values of Log [ A ~ ] / [ H A ] for Various Indicators in DMSO-Water-Tetramethyl- ammonium Hydroxide (0.011 M) .. .. 154-5 v i i i XIV E x p e r i m e n t a l V a l u e s of Log [BH+] / [B] f o r the S u b s t i t u t e d D i p h e n y l a m i n e s Used t o Determine the H Q V a l u e s i n 20 Volume P e r c e n t E t h a n o l - A q u e o u s S u l f u r i c A c i d 156-8 ix LIST OF FIGURES Page 1 H_ Acidity Function for the System: DMSO- Water-Tetramethylammonium Hydroxide (0.011 M) 44 2 Plot of Log [Al/M Versus H_ for the Indicators Used to Establish the H_ Scale 45-47 3 Plot of Log [Ai/flA] Versus H_ for Various Amines 50,51 4 HQ Acidity Function for the System: "20 % Ethanol"-Aqueous Sulfuric Acid .. .. 57 5 Plot of Log DBH^ /lB] Versus H Q for the Indicators Used to Establish the HQ Scale .. .. 58,59 6 H Q Acidity Functions in Sulfuric Acid Media 78 7 Hammett Correlation of the Acidity of Substituted Diphenylamines 84 8 Plot of PKHA o f Anilines and Diphenylamines Versus pK R A of Phenols 91 9 Hammett Correlation of the Basicity of Substituted Diphenylamines .. .. .. 102 10 Plot of PKBH+ o f Anilines Versus pKg|j+ of Diphenylamines 104 11 Correlation of the Basicity of Substituted Diphenylamines and 41-Nitrodiphenylamines 108 12 Plot of PKHA Versus PKBH+ f o r Diphenylamines 119 13 Plot of pKjj^ Versus pKBH+ for Anilines and Diphenylamines .. .. .. .. .. 120 X ACKNOWLEDGEMENT I would l i k e t o thank P r o f e s s o r R. Stewart f o r h i s guidance and encouragement throughout t h i s work. I would a l s o l i k e t o thank the N a t i o n a l R e s e a r c h C o u n c i l f o r generous f i n a n c i a l a s s i s t a n c e . 1 INTRODUCTION A . D e f i n i t i o n s of A c i d and Base The e x i s t e n c e of a c i d s and bases has been r e c o g n i z e d f o r a l o n g t i m e . The q u e s t i o n of what e x a c t l y i s an a c i d or 1: a base h a s , however, r e c e i v e d a v a r i e t y of answers . A r r h e n i u s d e f i n e d an a c i d as a substance t h a t i o n i z e s i n aqueous s o l u t i o n to produce a hydrogen i o n and a base as a substance 2 3 t h a t i o n i z e s t o produce a h y d r o x i d e i o n . B r o n s t e d and Lowry d e f i n e d an a c i d as a p r o t o n donor and a base as a p r o t o n a c c e p t o r . Lewis'* broadened the concept of an a c i d w i t h h i s d e s c r i p t i o n of an a c i d as a molecule or i o n capable of c o o r d i n a t i n g w i t h the unshared e l e c t r o n p a i r of a b a s e . 5 U s a n o v i t c h d e f i n e d an a c i d as any substance capable of g i v i n g up c a t i o n s or of c o m b i n i n g w i t h a n i o n s , and a base as any substance capable of g i v i n g up a n i o n s or of c o m b i n i n g w i t h c a t i o n s . These d e s c r i p t i o n s v a r y c o n s i d e r a b l y i n s c o p e . The d e f i n i t i o n of A r r h e n i u s r e s t r i c t s a c i d s and bases t o aqueous s o l u t i o n , w h i l e that of U s a n o v i t c h i s independent of s o l v e n t and c o v e r s a wide v a r i e t y of s u b s t a n c e s . The l a t t e r d e f i n i t i o n has even been e x t e n d e d to o x i d i z i n g and r e d u c i n g agents by a l s o d e f i n i n g as a c i d s those s u b s t a n c e s t h a t combine w i t h e l e c t r o n s and as bases those s u b s t a n c e s t h a t g i v e up e l e c t r o n s . 2 A B r o n s t e d a c i d i s a s p e c i a l type of Lewis a c i d s i n c e the p r o t o n from a p r o t o n donor c o o r d i n a t e s w i t h the l a e l e c t r o n p a i r of a base . B r o n s t e d a c i d s have r e c e i v e d by f a r the g r e a t e s t a t t e n t i o n s i n c e i t i s p o s s i b l e t o d e s c r i b e these a c i d s i n q u a n t i t a t i v e thermodynamic t e r m s . B . The A c i d D i s s o c i a t i o n C o n s t a n t The a c i d i t y of a B r o n s t e d a c i d i n aqueous s o l u t i o n i s e x p r e s s e d i n terms of the e q u i l i b r i u m HA + nH 90 - A " + H + (1) aq ^ aq aq where " a q " denotes t h a t the s p e c i e s are h y d r a t e d . HA i s an a c i d w i t h any net charge and A"~ i s the base conjugate t o HA • w i t h one u n i t l e s s p o s i t i v e c h a r g e . The e q u i l i b r i u m i s e x p r e s s e d by the r e l a t i o n * (A") (H + ) K' - _ (2) ( H A ) ( H 20) n i n which the s u b s c r i p t " a q " has been o m i t t e d . In d i l u t e aqueous s o l u t i o n the q u a n t i t y ( H O ) i s a lmost c o n s t a n t and Q e q u a l t o u n i t y so t h a t the e x p r e s s i o n can be r e w r i t t e n * The f o l l o w i n g s y m b o l s , [ ] , ( ) , and f w i l l be u s e d to r e f e r t o c o n c e n t r a t i o n , a c t i v i t y , and a c t i v i t y c o e f f i c i e n t , r e s p e c t i v e l y , on the molar s c a l e . As u s u a l , a l l a c t i v i t y c o e f f i c i e n t s t e n d t o u n i t y as the s o l v e n t c o m p o s i t i o n tends toward t h a t of the pure s o l v e n t ^ * 3 . (A") (H+) IC,. = K ' ( H 9 0 ) n = (3) m 2 (HA) 7a The c o n s t a n t K „ . i s known as the a c i d d i s s o c i a t i o n c o n s t a n t HA Because i n d i v i d u a l a c t i v i t i e s can be d e t e r m i n e d f o r uncharged s p e c i e s o n l y , d i r e c t measurement of thermodynamic d i s s o c i a t i o n c o n s t a n t s u s u a l l y i n v o l v e s m e a s u r i n g the c l a s s i c a l d i s s o c i a t i o n c o n s t a n t [A-] m K c = (4) [HA] as a f u n c t i o n of i o n i c s t r e n g t h and e x t r a p o l a t i n g t o i n f i n i t e d i l u t i o n . Kortum, V o g e l and Andrussow have s u r v e y e d methods of d e t e r m i n i n g a c i d d i s s o c i a t i o n c o n s t a n t s i n aqueous s o l u t i o n . For the sake of convenience a c i d d i s s o c i a t i o n c o n s t a n t s are o f t e n e x p r e s s e d i n terms of pK u n i t s , where P K H A " - l 0 g V ( 5 ) so t h a t one pK u n i t c o r r e s p o n d s t o a change of one power of t e n i n K. The s m a l l e r the v a l u e of pK , the s t r o n g e r the a c i d . I t s h o u l d a l s o be mentioned t h a t the b a s i c i t y of B r o n s t e d bases i s o f t e n e x p r e s s e d i n terms of the p K ^ of t h e i r c o n j u g a t e a c i d s . 4 S i n c e measurements of a c i d d i s s o c i a t i o n c o n s t a n t s r e q u i r e e x t r a p o l a t i o n of K c t o i n f i n i t e d i l u t i o n , measurements must be made i n s o l u t i o n s of low i o n i c s t r e n g t h . I f e q u a t i o n (3) i s r e w r i t t e n as (HA) p K „ . - l o g - l o g G O (6) H A (A~) then i t can be seen t h a t there i s a l i m i t t o the type of a c i d f o r which pKjj A can be d e t e r m i n e d a c c u r a t e l y . In e q u a t i o n (6) the l a s t q u a n t i t y i s j u s t the pH of the s o l u t i o n (or at l e a s t approximates the p H , s i n c e the d e f i n i t i o n of pH i s now an o p e r a t i o n a l o n e ^ c ) . Now c o n s i d e r a v e r y weak a c i d w i t h a of 20 i n a s o l u t i o n w i t h pH of 10. I f the c o n c e n t r a t i o n of HA i s 1 0 - 3 m o l a r , then from e q u a t i o n (6) (and n e g l e c t i n g any d i f f e r e n c e between a c t i v i t y and c o n c e n t r a t i o n ) the c o n c e n t r a t i o n of A~ -13 i s 10 m o l a r . T h i s i s much too s m a l l t o be measured and so the d i r e c t measurement of pKjj A f o r t h i s a c i d i s i m p o s s i b l e . There are many a c i d s t h a t do not show a p p r e c i a b l e i o n i z a t i o n i n the u s u a l pH r a n g e , and on w h i c h , t h e r e f o r e , i t i s i m p o s s i b l e t o make a c c u r a t e measurements i n d i l u t e aqueous s o l u t i o n . Many of these a c i d s i o n i z e i n e i t h e r s t r o n g l y a c i d i c or s t r o n g l y b a s i c m e d i a , and i t i s of i n t e r e s t t o use these o b s e r v a t i o n s t o make e s t i m a t e s of the d i s s o c i a t i o n c o n s t a n t s of the a c i d s i n aqueous s o l u t i o n . T h i s a l s o p r o v i d e s 5 some q u a n t i t a t i v e knowledge of the a c i d i t y of these m e d i a . C . Hammett A c i d i t y F u n c t i o n s By f a r the most p o p u l a r approach t o t h i s problem 8 9 i s t h a t d e v e l o p e d by Hammett and Deyrup ' . E q u a t i o n (6) may be r e w r i t t e n as [HA] f . - P K „ A = l o g — - l o g ( H + ) - £ - (7) H A [A ] f HA and the f o l l o w i n g d e f i n i t i o n made f . - H = - l o g ( H + ) - ^ - ( 8 ) f H A For two a c i d s , HA^ and HA , i n the same s o l u t i 2 on [HAJ [ H A 2 ] f f - l o g ^ — ^ - l o g 1 + l o g -*- ^ f - 1 2 [ A l ] M f A - f H A 2 ( 9 ) The s u c c e s s of the Hammett t rea tment depends on the l a s t q u a n t i t y i n e q u a t i o n ( 9 ) b e i n g z e r o o r , i n o ther words , on the r a t i o f A - / f „ A i n a g i v e n s o l u t i o n b e i n g independent of A HA the i n d i c a t o r a c i d . In t h i s c a s e , the f u n c t i o n H i s a l s o independent of the i n d i c a t o r . T h i s has become known as the 10a Hammett a c t i v i t y c o e f f i c i e n t p o s t u l a t e . In the event t h a t t h i s p o s t u l a t e h o l d s , e q u a t i o n ( 9 ) r educes t o P * H A I - P K H A 2 - l o , L J - l o g L _ J ( 1 0> and the r e l a t i v e p K ' s f o r two a c i d s t h a t are p a r t i a l l y i o n i z e d i n the same s o l u t i o n can be o b t a i n e d by m e a s u r i n g the two q u a n t i t i e s on the r i g h t s i d e of e q u a t i o n (10) . T h i s i s u s u a l l y done s p e c t r o p h o t o m e t r i c a l l y so t h a t c o n c e n t r a t i o n s -4 -6 of i n d i c a t o r a c i d , about 10 t o 10 m o l a r , t h a t do not measurably change the medium can be u s e d . I f the Hammett p o s t u l a t e h o l d s , then the r e l a t i v e p K ' s o b t a i n e d from e q u a t i o n (10) f o r two a c i d s s h o u l d be the same when measured i n a s e r i e s of s o l u t i o n s of v a r y i n g a c i d i t y . C o n s e q u e n t l y , such c o n s t a n c y i n the r e l a t i v e p K ' s i s g e n e r a l l y taken as e x p e r i m e n t a l p r o o f t h a t the q u a n t i t y l o g f ^ A^-/ f / i~ f«/i i s a c t u a l l y z e r o . A l H A 2 G i v e n the thermodynamic f o r one of the i n d i c a t o r s , then u s i n g the r e l a t i v e p K ' s , the thermodynamic pK f o r the second i n d i c a t o r can be o b t a i n e d . The procedure HA can be a p p l i e d t o a t h i r d a c i d HA i f b o t h H A Q and HA are p a r t i a l l y i o n i z e d i n the same s o l u t i o n . By a c h o i c e of i n d i c a t o r a c i d s w i t h s u i t a b l y spaced p K ' s the i o n i z a t i o n c o n s t a n t s of a c i d s w i t h a wide range of p K ' s can be d e t e r m i n e d depending upon the range of s o l v e n t a c i d i t i e s a v a i l a b l e . I t s h o u l d be s t r e s s e d t h a t i f the Hammett p o s t u l a t e h o l d s r i g o r o u s l y the P ^ J J A ' s d e t e r m i n e d u s i n g t h i s procedure are the thermodynamic ones f o r i o n i z a t i o n of the a c i d s i n aqueous s o l u t i o n . 7 From the same measurements of [HA] / [A"] t h a t are u s e d t o determine the p K ' s of the i n d i c a t o r a c i d s , the Hammett a c i d i t y f u n c t i o n , H , can be d e t e r m i n e d f o r the s o l u t i o n s i n which the measurements were made. Thus from e q u a t i o n s (7) and (8) [HA] H - pK - l o g (11) H A [A~] F o r an a c i d t h a t obeys the Hammett p o s t u l a t e i t can be seen from e q u a t i o n (11) t h a t the pKjj A of the a c i d i s e q u a l t o the v a l u e of H f o r the s o l u t i o n i n which i t i s h a l f i o n i z e d . A l s o a p l o t of l o g [HA] / [A -] v e r s u s H g i v e s a s t r a i g h t l i n e w i t h u n i t s l o p e . As was mentioned e a r l i e r , HA has been u s e d t o r e f e r to a c i d s of any charge t y p e . The symbol f o r a Hammett a c i d i t y f u n c t i o n i s g e n e r a l l y w r i t t e n w i t h s u b s c r i p t i n d i c a t i n g the charge on the base c o n j u g a t e t o the i n d i c a t o r a c i d used t o determine the H f u n c t i o n . Thus H r e f e r s t o the o i o n i z a t i o n of a c i d s such as ammonium i o n s w i t h one p o s i t i v e charge and H_ r e f e r s t o the i o n i z a t i o n of n e u t r a l a c i d s such as a c e t i c a c i d . Much of the e a r l i e r work on a c i d i t y f u n c t i o n s was 9 11 done i n s t r o n g l y a c i d i c media such as aqueous s u l f u r i c a c i d ' 12 P a u l and Long have r e v i e w e d the work t h a t had been done up 13 t o 1956 and Deno has p u b l i s h e d a b i b l i o g r a p h y of a c i d i t y 8 f u n c t i o n s r e p o r t e d from 1957 t o 1962. A r n e t t ^ ^ has r e v i e w e d the b a s i c i t i e s of o r g a n i c compounds o b t a i n e d u s i n g a c i d i t y f u n c t i o n s and o ther methods. In r e c e n t y e a r s i t has become q u i t e o b v i o u s t h a t 12 the t r a d i t i o n a l H Q s c a l e , d e r i v e d l a r g e l y u s i n g p r i m a r y amine i n d i c a t o r s , does not e n j o y w i d e s p r e a d q u a n t i t a t i v e a p p l i c a b i l i t y t o the p r o t o n a t i o n of o r g a n i c b a s e s . T h i s i s shown by the f a c t t h a t p l o t s of l o g [BH +]/[B ] v e r s u s H .. 14,15 _. . .. „. 16 . 17 . , _ 18 f o r amides a l i p h a t i c e t h e r s , p y r r o l e s , i n d o l e s , 19 and a z u l e n e s do not have u n i t s l o p e as i s r e q u i r e d by e q u a t i o n (11) f o r p r o t o n a t i o n e q u i l i b r i a governed by H . I n s t e a d , i t appears t h a t o r g a n i c bases f a l l i n t o many s e p a r a t e c l a s s e s a c c o r d i n g to s t r u c t u r a l d i f f e r e n c e s , the i o n i z a t i o n e q u i l i b r i a of each c l a s s d e s c r i b i n g i t s own s e l f - c o n s i s t e n t a c i d i t y f u n c t i o n . T h u s , s e p a r a t e H o a c i d i t y f u n c t i o n s have been d e r i v e d f o r the p r o t o n a t i o n of 20 21 22 23 24 amides ' ' , p r i m a r y amines , t e r t i a r y amines and i n d o l e s " ^ i n a c i d media . The d i s p a r i t y between the H Q f u n c t i o n s i n s u l f u r i c 23 24 a c i d f o r p r i m a r y and t e r t i a r y amines emphasizes the n e c e s s i t y of u s i n g i n d i c a t o r s of o n l y one s t r u c t u r a l type i n d e v e l o p i n g a s c a l e . Thus i n 90% s u l f u r i c a c i d , H Q based 23 on the p r o t o n a t i o n of p r i m a r y amines i s -8.93 , w h i l e H Q 24 based on t e r t i a r y amines i s -11.14 . The d i f f e r e n c e between 9 the two s c a l e s d e c r e a s e s as the c o n c e n t r a t i o n of s u l f u r i c a c i d d e c r e a s e s s i n c e e v e n t u a l l y the two s c a l e s must become i d e n t i c a l w i t h pH i n d i l u t e aqueous s o l u t i o n (see e q u a t i o n (8)) The d i f f e r e n c e s among the H s c a l e s d e s c r i b e d by o the v a r i o u s t y p e s of base stem from changes , d e p e n d i n g on the s t r u c t u r e of the b a s e , i n the a c t i v i t y c o e f f i c i e n t s 2 2 , 2 5 , 2 6 , 2 7 of b o t h the uncharged bases and t h e i r p o s i t i v e l y charged c o n j u g a t e a c i d s 1 5 > 2 2 > 2 5 > 2 6 » 2 8 > 2 9 » 3 0 on p a s s i n g from d i l u t e aqueous s o l u t i o n t o s t r o n g a c i d m e d i a . In s h o r t , the p r o s p e c t of t h e r e b e i n g o n l y one H Q f u n c t i o n f o r a g i v e n s o l v e n t system has not m a t e r i a l i z e d and i n s t e a d s e v e r a l H f u n c t i o n s , each d e t e r m i n e d by the o p r o t o n a t i o n e q u i l i b r i a of one narrow f u n c t i o n a l c l a s s of b a s e s , have emerged. T h i s does n o t , however, i n v a l i d a t e the u s e f u l n e s s of a c i d i t y f u n c t i o n s i f c a u t i o n i s e x e r c i s e d i n t h e i r u s e , e s p e c i a l l y i n i n t e r p r e t a t i o n s of k i n e t i c c o r - , . . 31,32 r e l a t i o n s ' . One f a c t o r t h a t can c o m p l i c a t e the use of a c i d i t y f u n c t i o n s i n s t r o n g l y a c i d media i s the b e h a v i o u r of u n s a t u r a t e d s u b s t i t u e n t s such as the n i t r o and c a r b o x y l g r o u p s . T h i s i s of p a r t i c u l a r importance f o r the H q s c a l e s f o r 23 . ^ 4 . . 24 . . p r i m a r y and t e r t i a r y amines i n which e v e r y i n d i c a t o r p o s s e s s e s at l e a s t one n i t r o s u b s t i t u e n t . Deno and P e r r - 27 i z z o l o have shown t h a t the b e h a v i o u r of the a c t i v i t y 10 c o e f f i c i e n t s of a v a r i e t y of o r g a n i c m o l e c u l e s i n c l u d i n g n i t r o b e n z e n e and b e n z o i c a c i d i s s i m i l a r from 0 t o 60% s u l f u r i c a c i d . Beyond 60% s u l f u r i c a c i d the l a t t e r two compounds and o t h e r s c o n t a i n i n g the same groups show markedly d i f f e r e n t b e h a v i o u r from h y d r o c a r b o n s such as benzene . The a c t i v i t y c o e f f i c i e n t s of compounds c o n t a i n i n g the n i t r o and c a r b o x y l groups decrease r a p i d l y as the medium approaches h i g h (90%) s u l f u r i c a c i d c o n c e n t r a t i o n s , i n c o n t r a s t t o the b e h a v i o u r of the a c t i v i t y c o e f f i c i e n t s of benzene and c h l o r o b e n z e n e . In f a c t , n i t r o b e n z e n e d i s s o l v e s t o the 27 e x t e n t of 98% i n 96.7% s u l f u r i c a c i d , as compared t o a s o l u b i l i t y of 0.0098 moles/1000 grams of s o l u t i o n i n 33 35.8% s u l f u r i c a c i d . T h i s i s i n s p i t e of the f a c t t h a t 34 n i t r o b e n z e n e i s l e s s than 1% p r o t o n a t e d i n 97% s u l f u r i c a c i d 27 Deno and P e r r i z z o l o have sugges ted t h a t the g r e a t i n c r e a s e i n s o l u b i l i t y of n i t r o b e n z e n e at h i g h 3 3 s u l f u r i c a c i d c o n c e n t r a t i o n s i s due to f o r m a t i o n of a hydrogen bonded s p e c i e s such as ( I ) . Haldna and c o - 35,36 workers have p o s t u l a t e d the e x i s t e n c e of a s i m i l a r s p e c i e s f o r ni t romethane i n g r e a t e r than 85% s u l f u r i c a c i d . They a l s o suggest t h a t i n m i x t u r e s of 35 t o 85% s u l f u r i c a c i d the n i t r o m e t h a n e m o l e c u l e e x i s t s as a h y d r a t e of the p r o t o n a t e d f o r m . 11 I 37 A r n e t t and Anderson have f o u n d t h a t almost a l l weak bases b e a r i n g an u n s a t u r a t e d f u n c t i o n e x h i b i t b e h a v i o u r 33 s i m i l a r t o n i t r o b e n z e n e and b e n z o i c a c i d i n s u l f u r i c a c i d s o l u t i o n s . Such i n t e r a c t i o n s of s u b s t i t u e n t s w i t h a c i d media would p r e c l u d e a c c u r a t e e s t i m a t i o n of the p K ' s of such compounds from measurements of t h e i r i o n i z a t i o n e q u i l i b r i a 24 i n these s o l u t i o n s . A r n e t t and Mach have s u g g e s t e d t h a t n i t r o a n i l i n e s might be such weak bases because " o f the a b i l i t y of the n i t r o group t o be s t r o n g l y s o l v a t e d i n medium s t r e n g t h a c i d " . U n t i l r e c e n t l y , a c i d i t y f u n c t i o n s i n a c i d i c media have o c c u p i e d the a t t e n t i o n s of most workers i n t h i s f i e l d . In the p a s t f i v e y e a r s , however, t h e r e has been a c o n s i d e r a b l e amount of work done i n b a s i c m e d i a . T h i s has accompanied an i n c r e a s e d i n t e r e s t i n the e f f e c t s of p o l a r a p r o t i c s o l v e n t s 38 on r e a c t i o n s 12 B a s i c s o l u t i o n s have been u s e d t o s t u d y the i o n i  z a t i o n s m a i n l y of n e u t r a l a c i d s . The a p p r o p r i a t e a c i d i t y f u n c t i o n f o r t h i s type of e q u i l i b r i u m HA - H + + A " (12) i s the H_ f u n c t i o n where IV] H - p K H A + l o g — (13) [HA] A r e v i e w of H a c i d i t y f u n c t i o n s i n b a s i c s o l u t i o n s 39 i s t o be p u b l i s h e d i n the near f u t u r e There a r e , i n g e n e r a l , t h r e e methods of p r o d u c i n g s o l v e n t systems w i t h c o n t i n u o u s l y v a r i a b l e b a s i c i t y , and H a c i d i t y f u n c t i o n s have been d e t e r m i n e d f o r a l l t h r e e t y p e s . The most o b v i o u s , and f i r s t s t u d i e d , s o l v e n t system type i s t h a t c o n s i s t i n g of a p r o t i c s o l v e n t and a s a l t of i t s conjugate b a s e . The b a s i c i t y of the system i s v a r i e d by c h a n g i n g the c o n c e n t r a t i o n of the b a s e . Some systems 40 41 ,42 of t h i s type t h a t have been s t u d i e d are l i t h i u m , sodium , 41 40 p o t a s s i u m , and benzyl t r imethylammonium h y d r o x i d e i n 43 43,44 43,45 water , and l i t h i u m , sodium , and p o t a s s i u m methoxide i n m e t h a n o l . At low c o n c e n t r a t i o n s of base ( l e s s than 0 .1 molar) 42,46 t h e r e i s a d i r e c t r e l a t i o n s h i p between H_ and base 13 c o n c e n t r a t i o n of the form H _ = B + l o g [OR -] (14) i n which B i s a c o n s t a n t and depends on the s o l v e n t . As the c o n c e n t r a t i o n of base c o n t i n u e s t o i n c r e a s e , however, the H_ i n c r e a s e s beyond t h a t e x p e c t e d from t h i s s i m p l e 40 42 44 r e l a t i o n s h i p ' 5 . T h i s r e s u l t s from r e d u c t i o n of the amount of f r e e s o l v e n t p r e s e n t t o s o l v a t e an i n c r e a s i n g amount of b a s e . The thermodynamic a c t i v i t y of f r e e h y d r o x i d e or a l k o x i d e i o n s i s p r o b a b l y v e r y much g r e a t e r than t h a t of the s o l v a t e d s p e c i e s . 41 The data of Schwarzenbach and S u l z b e r g e r f o r H_ i n aqueous s o l u t i o n s of sodium and p o t a s s i u m h y d r o x i d e have 47 been i n t e r p r e t e d by Y a g i l and Anbar i n terms of the e q u i l i b r i u m HA + 0 H ( H o 0 ) ~ - A~ + (n + l ) H o 0 (15) ^ n z They d e r i v e d e q u a t i o n (16) t o e x p r e s s H _ as a f u n c t i o n of the h y d r o x i d e and " f r e e " water c o n c e n t r a t i o n s . T h i s i s based on the assumption t h a t the r a t i o of a c t i v i t y c o e f f i c i e n t s , f A - f H 2 0 1 > / f H A f O H - i S z e r 0 " H p K w + l o g [OH ] - (n + 1) l o g [H 20] (16) In the above e q u a t i o n p K w r e f e r s t o the i o n p r o d u c t of water and the c o n c e n t r a t i o n of water i s th'at not bound by the h y d r o x i d e i o n ( " f r e e " w a t e r ) . B e s t agreement w i t h the 14 e x p e r i m e n t a l r e s u l t s was o b t a i n e d f o r n e q u a l to 3 o r , i n o t h e r words , f o r the assumption t h a t h y d r o x i d e e x i s t s as a t r i - h y d r a t e d s p e c i e s . 42 P r e v i o u s l y , Edward and Wang i n a s i m i l a r t rea tment of t h e i r data on H i n s o l u t i o n s of sodium h y d r o x i d e had c a l c u l a t e d H_ as a f u n c t i o n of base c o n c e n t r a t i o n and water a c t i v i t y r a t h e r than " f r e e " water c o n c e n t r a t i o n . They p r o p o s e d t h a t the a c t i v i t y c o e f f i c i e n t r a t i o f T T . f n t i - / f - i s a f u n c t i o n of water a c t i v i t y such t h a t HA un A ^ H A ^ O H - l o g - r l o g (H„0) (17) f A " Thus they u s e d the e q u a t i o n H_ - pKw + l o g [0H~] - (-r+p+1) l o g (H 2 0) (18) t o attempt t o c a l c u l a t e H _ . In t h i s case the q u a n t i t y p , though analogous t o n , i s not n e c e s s a r i l y the h y d r a t i o n number of the h y d r o x i d e i o n but r a t h e r the d i f f e r e n c e i n h y d r a t i o n numbers between the l e f t and r i g h t s i d e s of e q u a t i o n (15) . Over the range of base c o n c e n t r a t i o n s measured (0 t o 4 .5 molar) good agreement between c a l c u l a t e d and o b s e r v e d H _ v a l u e s was o b t a i n e d f o r (-r+p+1) e q u a l to 3 . 2 . S o l u t i o n s of c o n t i n u o u s l y v a r i a b l e b a s i c i t y can a l s o be produced w i t h b i n a r y s o l v e n t systems i n which one s o l v e n t i s i t s e l f q u i t e b a s i c . Members of t h i s type of 15 system t h a t have been s t u d i e d are aqueous s o l u t i o n s of , , . 4 8 , 4 9 ... . . . 50 . 0 . u ,51 h y d r a z i n e , e t h y l e n e d i a m m e , and 2 - a m i n o e t h a n o l The t h i r d type of s o l v e n t system a l s o uses a b i n a r y s o l v e n t sys tem, one of the p a i r b e i n g a h y d r o x y l i c s o l v e n t such as water and the o ther b e i n g a p o l a r a p r o t i c s o l v e n t such as d i m e t h y l f o r m a m i d e . These s o l u t i o n s themselves are not p a r t i c u l a r l y b a s i c so t h a t base must be added, g e n e r a l l y as the conjugate base of the h y d r o x y l i c member. A l t h o u g h the b a s i c i t y can be v a r i e d by c h a n g i n g the base c o n c e n t r a t i o n i t can be v a r i e d j u s t as e f f e c t i v e l y by c h a n g i n g the c o m p o s i t i o n of the b i n a r y s o l v e n t p a i r . A t c o n s t a n t base c o n c e n t r a t i o n , the b a s i c i t y of t h i s type of s o l v e n t system i n c r e a s e s as the p r o p o r t i o n of the p o l a r a p r o t i c component i n c r e a s e s . S t u d i e s of H_ f u n c t i o n s have been made on aqueous t e t r a m e t h y l e n e s u l f o n e ( s u l f o l a n e ) s o l u t i o n s c o n t a i n i n g 40 tetramethylammonium h y d r o x i d e and phenyl t r imethylammonium 52 h y d r o x i d e , aqueous p y r i d i n e c o n t a i n i n g t e t r a m e t h y l  ammonium h y d r o x i d e ^ , aqueous d i m e t h y l s u l f oxide (DMSO) 40 c o n t a i n i n g tetramethylammonium h y d r o x i d e , m e t h a n o l - 53 d i m e t h y l s u l f o x i d e c o n t a i n i n g sodium methoxide , and e t h a n o l - 54 d i m e t h y l s u l f o x i d e c o n t a i n i n g sodium e t h o x i d e A v a r i e t y of i n d i c a t o r a c i d s have been used i n s t u d y i n g H_ a c i d i t y f u n c t i o n s . These have i n c l u d e d a c i d s 16 i n which the a c i d i c p r o t o n i s a t t a c h e d t o c a r b o n , n i t r o g e n 41 and oxygen. Schwarzenbach and S u l z b e r g e r u s e d i n d i g o M d e r i v a t i v e s (II) as a c i d s but o b t a i n e d r e s u l t s s u g g e s t i n g a g r e a t e r i n c r e a s e i n b a s i c i t y when s u b s t i t u t e d g l u t a - c o n d i a l d e h y d e d i a n i l s (III) were u s e d . They s u g g e s t e d t h a t the l a t t e r compounds i o n i z e d not by s i m p l e p r o t o n l o s s but r a t h e r by a p r o c e s s i n v o l v i n g h y d r o x i d e 42 a d d i t i o n . Edward and Wang s u g g e s t e d , however, t h a t the d i f f e r e n c e i n b e h a v i o u r i s due t o d i f f e r e n c e s i n h y d r a t i o n of the two conjugate b a s e s . U s i n g t h i o a c e t a m i d e as the i n d i c a t o r a c i d , these workers o b t a i n e d r e s u l t s i n sodium h y d r o x i d e s o l u t i o n s s i m i l a r t o those o b t a i n e d u s i n g the i n d i g o compounds. 17 The m a j o r i t y of H _ s t u d i e s have u s e d s u b s t i t u t e d a n i l i n e s (IV) and d i p h e n y l a m i n e s ( V ) 4 0 ' 4 4 , 4 8 ' 5 1 ' 5 2 and 4 f t c o CZA v a r i o u s carbon a c i d s such as f l u o r e n e (VI) d e r i v a t i v e s and s u b s t i t u t e d d i p h e n y l - and t r i p h e n y l m e t h a n e s (VII) as i n d i c a t o r s . // \\ -NH; // \N v V I V I I R o c h e s t e r has d e t e r m i n e d an H_ s c a l e i n s o l u t i o n s of sodium methoxide i n methanol u s i n g h i n d e r e d p h e n o l s as a c i d s and has found t h a t t h i s s c a l e does not r i s e as 44 r a p i d l y as the s c a l e o b t a i n e d by R i d d and More O ' F e r r a l l u s i n g s u b s t i t u t e d a n i l i n e s and d i p h e n y l a m i n e s . S i m i l a r 56 r e s u l t s have been o b t a i n e d by Stewart and B u c k l e y i n m e t h a n o l - d i m e t h y l s u l f o x i d e s o l u t i o n s c o n t a i n i n g sodium methoxide . 1 8 Until further work is done on the dependence of H _ on the structure of the indicators, and in view of the dependence of H q scales on indicator structures, i t is advisable to use acids of only one type in determining an H _ scale. As an indication of the basicities of the solutions that have been studied, the H _ values for the most basic solution in some of the systems will be mentioned. An aqueous solution of 1 0 molar potassium hydroxide has 4 1 an H of 1 7 . 3 , 2 . 3 8 molar benzyltrimethylammonium hydroxide has an H _ of 1 6 . 2 4 ® , and 4 molar sodium methoxide 4 4 in methanol has an H _ of about 1 7 . 1 . A solution of 4 0 9 5 mole % hydrazine in water has an H of 1 9 . The effect of polar aprotic solvents' on hydroxide iOn: basicity is very pronounced. The H of a 0 . 0 1 1 molar tetramethylammonium hydroxide solution is 1 9 . 2 in 9 5 mole % aqueous tetramethylene- 4 0 sulfone (VIII) and 1 8 . 6 in 7 0 mole % aqueous dimethyl- 4 0 sulfoxide (IX) as compared to approximately 1 2 in aqueous solution. 1 H3C - S - C H 3 VIII IX 19 57 In a r e c e n t communication , S t e i n e r and G i l b e r t r e p o r t e d measurements made i n d i m e t h y l s u l f o x i d e c o n t a i n i n g s m a l l amounts of water or m e t h a n o l . The base was added i n the form of the p o t a s s i u m s a l t of the conjugate base of d i m e t h y l s u l f o x i d e . The p K ^ v a l u e s of a s e r i e s of h y d r o  carbon a c i d s , the weakest b e i n g t r i p h e n y l m e t h a n e w i t h a p K ^ of 27.2, were d e t e r m i n e d based on the v a l u e of 18.4 f o r the p K H A of 4 - n i t r o a n i l i n e o b t a i n e d by Stewart and 40 O ' D o n n e l l . I t would appear t h a t s o l u t i o n s w i t h H_ of about 30 can be o b t a i n e d i n t h i s s y s t e m . D . Other Methods of M e a s u r i n g A c i d i t i e s Some of the e a r l i e s t measurements of the a c i d i t i e s of v e r y weak a c i d s were made by Conant and 58 5Q Wheland and by McEwen . They s t u d i e d the e q u i l i b r i u m e s t a b l i s h e d between one weak a c i d and the p o t a s s i u m s a l t of another i n e t h e r s o l u t i o n . The p o s i t i o n of the e q u i l i b r i u m was d e t e r m i n e d HA-L + K+Ag - K % + HAg (19) c o l o r i m e t r i c a l l y . T h i s t e c h n i q u e has been used w i t h modern 60 s p e c t r o p h o t o m e t e r s by S t r e i t w i e s e r and c o - w o r k e r s and by 57 S t e i n e r and G i l b e r t K i n e t i c measurements of hydrogen i s o t o p e exchange have been u s e d t o compare the s t r e n g t h s of weak a c i d s . For 20 t h i s approach t o be v a l i d i t i s e s s e n t i a l t h a t the r a t e of a t t a i n m e n t of e q u i l i b r i u m i s d i r e c t l y r e l a t e d t o the p o s i t i o n of e q u i l i b r i u m and t h a t i o n i z a t i o n i s the r a t e - d e t e r m i n i n g p r o c e s s i n hydrogen exchange r e a c t i o n s ^ . 62 S h a t e n s h t e i n and c o - w o r k e r s have s t u d i e d hydrogen i s o t o p e exchange of weak h y d r o c a r b o n a c i d s i n l i q u i d ammonia w i t h 6 0 , 6 1 , 6 3 p o t a s s i u m amide. S t r e i t w i e s e r and h i s s t u d e n t s have made s i m i l a r s t u d i e s i n c y c l o h e x y l a m i n e w i t h l i t h i u m 6 0 c y c l o h e x y l a m i d e as b a s e . They have shown t h a t the e q u i l i b r i u m a c i d i t i e s of, a s e r i e s of f l u o r e n e d e r i v a t i v e s (VI) d e t e r m i n e d i n t h i s system by the method of Conant and 58 Wheland g i v e a f a i r c o r r e l a t i o n w i t h the r e l a t i v e r a t e s of h y d r o g e n - t r i t i u m exchange i n methanol c o n t a i n i n g sodium 64 methoxide I t i s n e c e s s a r y t o be c e r t a i n i n i n t e r p r e t i n g i s o t o p e exchange r a t e s t h a t i o n i z a t i o n of the p r o t o n a c t u a l l y d e t e r m i n e s the r a t e of i t s exchange . F o r the exchange of the methyl hydrogens of t o l u e n e i n the c y c l o  hexylamine s o l v e n t system there i s a k i n e t i c i s o t o p e , 63b e f f e c t , k / k , g r e a t e r than 10 >. . Hydrogen exchange i n H D t h i s system o b v i o u s l y i n v o l v e s b r e a k i n g of the c a r b o n - hydrogen bond i n the r a t e - d e t e r m i n i n g s t e p . On the o t h e r hand, i n d i m e t h y l s u l f o x i d e w i t h p o t a s s i u m t - b u t o x i d e as base the k i n e t i c i s o t o p e e f f e c t , k D / k T » i s a p p r o x i m a t e l y u n i t y and t h e r e f o r e , p r e s u m a b l y , k / k i s a l s o a p p r o x i m a t e l y H D 21 65 u n i t y . I t appears t h a t i n t h i s system the b r e a k i n g of the c a r b o n - h y d r o g e n bond i s n o t , or i s o n l y p a r t i a l l y , r a t e - d e t e r m i n i n g i n exchange r e a c t i o n s . C o n s e q u e n t l y , r e l a t i v e r a t e s of hydrogen exchange i n t h i s medium cannot r e a d i l y "be taken as a measure of a c i d i t y . E . F i r s t and Second D i s s o c i a t i o n C o n s t a n t s of D i b a s i c A c i d s The p r e s e n t knowledge of f i r s t and second d i s s o c i a t i o n c o n s t a n t s f o r a c i d s of the type H - Z - H , i n which both a c i d i c p r o t o n s are a t t a c h e d t o one c e n t r a l atom, i s l i m i t e d . Some v a l u e s t h a t are known i n c l u d e pK-^ and pK^ f o r E^S, 7 .1 and 13.1 r e s p e c t i v e l y , and f o r I ^ S e , 3.9 and 10.0 66 r e s p e c t i v e l y . There i s a d i f f e r e n c e of about 6 pK u n i t s between the p K ' s f o r the f i r s t and second d i s s o c i a t i o n s of these two a c i d s . The f o l l o w i n g p r o c e s s e s NH* - H + + NH_ 4 3 (20) NH - H + •+ NH~ >J 2 must a l s o be c o n s i d e r e d as the f i r s t and second i o n i z a t i o n s of an a c i d of the type H - Z - H . The pK, and pK of the ammonium 67 68 i o n are 9 .25 and an e s t i m a t e d 35 r e s p e c t i v e l y . The d i f f e r e n c e here i s about 25 pK u n i t s . 40 Stewart and O ' D o n n e l l have d e t e r m i n e d the a c i d d i s s o c i a t i o n c o n s t a n t s f o r a s e r i e s of n i t r o - s u b s t i t u t e d 22 a n i l i n e s and d i p h e n y l a m i n e s u s i n g Hammett H _ a c i d i t y f u n c t i o n s i n a v a r i e t y of m e d i a . The d i s s o c i a t i o n c o n s t a n t s f o r the c o r r e s p o n d i n g ammonium i o n s of many of these compounds had been d e t e r m i n e d p r e v i o u s l y u s i n g the H Q s c a l e . A p l o t of pK (as o r d i n a t e ) v e r s u s p K Q (as a b s c i s s a ) f o r the 1 ^ 69 ammonium i o n s gave a l i n e w i t h s l o p e of about 0.6 T h i s means t h a t s u b s t i t u e n t s have a l a r g e r e f f e c t on the a c i d i t y of ammonium i o n s than on the a c i d i t y of the c o r r e s p o n d i n g n e u t r a l amines . Such an e f f e c t i s s u r p r i s i n g s i n c e the o p p o s i t e might have been p r e d i c t e d . I o n i z a t i o n of the n e u t r a l amine produces an a n i o n c a p a b l e of d i s p e r s i n g i t s n e g a t i v e charge over an a r o m a t i c r i n g ; t h i s i s not p o s s i b l e f o r the p o s i t i v e charge of the a n i l i n i u m i o n . I t would be e x p e c t e d t h a t s u b s t i t u e n t s on the r i n g s h o u l d have a c o n s i d e r a b l e e f f e c t on the charge d e l o c a l i z a t i o n and c o n s e q u e n t l y on the energy of the a n i o n . One would expec t t h i s t o be r e f l e c t e d i n a g r e a t e r e f f e c t of s u b s t i t u e n t s on the e q u i l i b r i u m (21) than on e q u i l i b r i u m (22) . 23 -NH, H++ V N H ; ( 2 2 ) 24 OBJECTS OF THE PRESENT RESEARCH T h i s work was u n d e r t a k e n t o s t u d y s o l u t i o n s of g r e a t e r b a s i c i t y than had been p r e v i o u s l y s t u d i e d u s i n g the method of Hammett. The b i n a r y s o l v e n t system w a t e r - d i m e t h y l - s u l f o x i d e c o n t a i n i n g tetramethylammonium h y d r o x i d e appeared t o h o l d c o n s i d e r a b l e promise f o r g r e a t b a s i c i t y s i n c e i t had been shown t h a t a s o l u t i o n of 70 mole % d i m e t h y l - 40 s u l f o x i d e has an H_ of 18.6 . As the r e m a i n i n g 30 mole % of the water i s removed the b a s i c i t y would be e x p e c t e d t o c o n t i n u e t o r i s e . I t had a l s o been found t h a t the r a t e of r a c e m i z a t i o n of ( + ) - 2 - m e t h y l - 3 - p h e n y l p r o p i o n i t r i l e (X) as c a t a l y s e d by methoxide i o n i s a c c e l e r a t e d by a f a c t o r of g a p p r o x i m a t e l y 10 upon c h a n g i n g the s o l v e n t from methanol 70 t o d i m e t h y l s u l f o x i d e . I t s h i g h d i e l e c t r i c c o n s t a n t , 71 48 .9 at 2 0 ° , and i t s a b i l i t y to d i s s o l v e a wide v a r i e t y 72 of compounds a l s o commend d i m e t h y l s u l f o x i d e f o r such a s t u d y . C H 3 X F u r t h e r m o r e , the d i s s o c i a t i o n c o n s t a n t s of the and d i p h e n y l a m i n e s used as i n d i c a t o r s would be from t h i s s t u d y . I t was hoped t h a t t h i s would a n i l i n e s o b t a i n e d 25 p r o v i d e some i n f o r m a t i o n on s u b s t i t u e n t e f f e c t s on the a c i d i t y of amines . The d e t e r m i n a t i o n of the d i s s o c i a t i o n c o n s t a n t s of the conjugate a c i d s of a s e r i e s of d i p h e n y l a m i n e s as w e l l as of the d i p h e n y l a m i n e s themselves was a l s o u n d e r  taken t o examine f u r t h e r the l i n e a r r e l a t i o n s h i p between pK and pK of a n i l i n i u m and diphenylammonium i o n s o b s e r v e d 1 2 6 9 by Stewart and O ' D o n n e l l f o r the n i t r a t e d a n a l o g s / 26 METHODS OF APPROACH The i o n i z a t i o n of a n i l i n e s and d i p h e n y l a m i n e s i s accompanied by a marked change i n e l e c t r o n i c a b s o r p t i o n s p e c t r a . The a n i o n s e x h i b i t s t r o n g l i g h t a b s o r p t i o n i n the v i s i b l e or near u l t r a v i o l e t r e g i o n s w i t h maxima at wavelengths at which the u n i o n i z e d compounds t r a n s m i t a l l , or a lmost a l l , the i n c i d e n t l i g h t . T h i s p r o v i d e s a c o n v e n i e n t means f o r f o l l o w i n g the i o n i z a t i o n e q u i l i b r i a of these amines . The i o n i z a t i o n of these amines i n s t r o n g a c i d media can a l s o be s t u d i e d t h i s way, s i n c e , on p r o t o n a t i o n , the l o n g wavelength a b s o r p t i o n of these amines d i s a p p e a r s . A l l i n d i c a t o r s used i n t h i s work showed v i r t u a l l y i n s t a n t a n e o u s s p e c t r a l changes upon a d d i t i o n of base t o t h e i r s o l u t i o n s i n d i m e t h y l s u l f o x i d e - w a t e r m i x t u r e s . The s p e c t r a of the u n i o n i z e d amines c o u l d be r e g a i n e d by n e u t r a l i z i n g the base w i t h a c e t i c a c i d . These two o b s e r v a t i o n s , i n s t a n t a n e o u s and r e v e r s i b l e s p e c t r a l changes , were u s e d as c r i t e r i a of i o n i z a t i o n by p r o t o n l o s s f o r a l l a c i d s . 27 EXPERIMENTAL A . P r e p a r a t i o n and P u r i f i c a t i o n of I n d i c a t o r s Some of the compounds were o b t a i n e d from commercial s o u r c e s ; the o t h e r s were p r e p a r e d by known methods. I n f o r  mation on t h e i r p r e p a r a t i o n and p u r i f i c a t i o n i s t o be found i n the appendix A . M e l t i n g p o i n t s were d e t e r m i n e d i n c a p i l l a r i e s u s i n g a B u c h i m e l t i n g p o i n t a p p a r a t u s and are u n c o r r e c t e d . S u b l i m a t i o n p r o v e d t o be a most u s e f u l t e c h n i q u e both i n p u r i f y i n g compounds and i n r e c o v e r i n g p r o d u c t s from r e a c t i o n m i x t u r e s . In s e v e r a l cases i t was the o n l y p r a c t i c a b l e method of p r o d u c t r e c o v e r y s i n c e r e a c t i o n c o n d i t i o n s were so d r a s t i c as to produce l a r g e amounts of t a r r y m a t e r i a l s . S u b l i m a t i o n s were c a r r i e d out at t empera tures near the m e l t i n g p o i n t s of the compounds and under o i l pump p r e s s u r e . B . P u r i f i c a t i o n of S o l v e n t s D i m e t h y l s u l f o x i d e (DMSO) was s t i r r e d i n a c l o s e d v e s s e l over powdered c a l c i u m h y d r i d e f o r at l e a s t two days and then d i s t i l l e d under r e d u c e d p r e s s u r e . F r a c t i o n s c o n t a i n i n g the f i r s t 15 t o 20% and the l a s t 10 t o 15% of the d i s t i l l a t e were d i s c a r d e d . N i t r o g e n gas was u s e d i n 28 the l e a k . A P e r k i n t r i a n g l e was used t o cut f r a c t i o n s a l l o w i n g n i t r o g e n t o be i n t r o d u c e d d i r e c t l y on top of the d i s t i l l e d DMSO i n the c o l l e c t i o n v e s s e l s . These f l a s k s were s e a l e d w i t h ground g l a s s s t o p p e r s which were f u r t h e r s e a l e d w i t h masking tape and then t r a n s f e r r e d t o a d r y box w i t h n i t r o g e n atmosphere . In t h i s way the DMSO was p r o t e c t e d from a t m o s p h e r i c m o i s t u r e and oxygen. The DMSO o b t a i n e d i n t h i s manner was shown t o c o n t a i n l e s s than 0.01% water by t i t r a t i o n w i t h K a r l F i s c h e r r e a g e n t . When the DMSO was t o be used t o make s o l u t i o n s c o n t a i n i n g more than 90 mole % DMSO i t was f u r t h e r p u r i f i e d 73 by a s i m p l i f i e d zone f r e e z i n g method . T h i s c o n s i s t e d of c o o l i n g the v e s s e l i n an i c e - w a t e r bath u n t i l 75 t o 85% of the DMSO had f r o z e n and then d e c a n t i n g the r e m a i n i n g l i q u i d . The s o l i d was m e l t e d and the procedure r e p e a t e d . D e c a n t i n g of the l i q u i d was done i n the d r y box under n i t r o g e n atmosphere . Water t h a t was u s e d f o r p r e p a r i n g DMSO-water m i x t u r e s was d i s t i l l e d , b o i l e d and then c o o l e d w i t h n i t r o g e n b u b b l i n g t h r o u g h i t . Tetramethylammonium hydroxide was o b t a i n e d from Eastman O r g a n i c C h e m i c a l s e i t h e r as a 10% aqueous s o l u t i o n or as the c r y s t a l l i n e p e n t a h y d r a t e and was used w i t h o u t f u r t h e r p u r i f i c a t i o n . 29 S u l f u r i c a c i d was Baker and Adamson Reagent grade m a t e r i a l . C o n s t a n t b o i l i n g e t h a n o l (95.6% e t h a n o l ) was p r e p a r e d from commercial 100% e t h a n o l by a d d i t i o n of the amount of water c a l c u l a t e d t o g i v e the a z e o t r o p i c c o m p o s i t i o n f o l l o w e d by d i s t i l l a t i o n . A f t e r a f i r s t f r a c t i o n of a p p r o x i m a t e l y 5%, the next 60% was c o l l e c t e d and u s e d f o r measurements w i t h s u l f u r i c a c i d . C . P r e p a r a t i o n of S o l u t i o n s S t o c k s o l u t i o n s of DMSO-water were p r e p a r e d and s t o r e d i n o r d i n a r y l i q u i d r e a g e n t b o t t l e s s t o p p e r e d w i t h rubber serum s t o p p e r s w i t h a f l a p t h a t c o u l d be bent down over the l i p and neck of the b o t t l e f o r m i n g an a i r t i g h t s e a l . The membrane of the serum s t o p p e r c o u l d be p e n e t r a t e d many t imes w i t h o u t l o s i n g i t s s e a l . Care was taken t h a t the s o l u t i o n s d i d not s p l a s h a g a i n s t the rubber s t o p p e r s . The b o t t l e and s t o p p e r were weighed, t r a n s f e r r e d t o the d r y box and then a c a l c u l a t e d amount of DMSO i n t  r o d u c e d i n t o the b o t t l e w i t h a l a r g e s y r i n g e . The s t o p p e r e d b o t t l e was then removed from the dry box and weighed a g a i n . F i n a l l y , the r e q u i r e d amount of water was added - a g a i n by s y r i n g e - ahd-a t h i r d w e i g h i n g made. From the three w e i g h i n g s the e x a c t c o m p o s i t i o n of the s o l v e n t c o u l d be c a l c u l a t e d . 30 S o l u t i o n s c o n t a i n i n g more than 97 .5 mole % DMSO were p r e p a r e d i n a s i m i l a r manner from DMSO and a s o l u t i o n of about 50 mole % DMSO. I n d i c a t o r measurements i n the DMSO-water system were done u s i n g a c o n s t a n t c o n c e n t r a t i o n of b a s e , 0.011 molar tetramethylammonium h y d r o x i d e . I n t r o d u c t i o n of the base i n a 10% aqueous s o l u t i o n a l s o i n t r o d u c e s water i n t o the system and thus produces an upper l i m i t of a p p r o x i m a t e l y 97 mole % on the amount of DMSO p r e s e n t i n the s y s t e m . T h i s upper l i m i t can be ex tended t o about 99 .5 mole % DMSO by u s i n g tetramethylammonium h y d r o x i d e p e n t a h y d r a t e and i n t h i s case base was i n t r o d u c e d i n t o the DMSO-water m i x t u r e s by way of a s t o c k s o l u t i o n of the l a t t e r compound i n DMSO. A sample of the tetramethylammonium h y d r o x i d e p e n t a h y d r a t e was ground i n a m o r t a r , weighed i n t o a s t o p p e r e d f l a s k and an a p p r o p r i a t e amount of DMSO added. The mix ture was shaken and warmed t o cause d i s s o l u t i o n . There was always a s m a l l amount of u n d i s s o l v e d m a t e r i a l ( p o s s i b l y carbonate ) and t h i s was removed by f i l t r a t i o n through a s i n t e r e d - g l a s s f u n n e l . The c l e a r s o l u t i o n was t r a n s f e r r e d t o a g l a s s reagent b o t t l e and s t o p p e r e d w i t h a serum s t o p p e r . A l l the above o p e r a t i o n s , except the warming, were c a r r i e d out i n the dry box under n i t r o g e n atmosphere . 31 Samples of the base s o l u t i o n were t i t r a t e d w i t h s t a n d a r d i z e d h y d r o c h l o r i c a c i d u s i n g p h e n o l p h t h a l e i n i n d i c a t o r . A s o l u t i o n of about 0 .12 molar base c o u l d be p r e p a r e d i n t h i s way. The water c o n t e n t of the s o l u t i o n was d e t e r m i n e d by K a r l F i s c h e r t i t r a t i o n i n methanol - a c e t i c a c i d . C o r r e c t i o n was made f o r the water formed from n e u t r a  l i z a t i o n of the b a s e . S o l u t i o n s p r e p a r e d i n t h i s manner were i n i t i a l l y c o l o r l e s s but t u r n e d y e l l o w a f t e r one or two weeks. A f t e r t h r e e weeks t h e r e was a s l i g h t drop of about 4% i n base c o n c e n t r a t i o n , presumably due t o d e c o m p o s i t i o n caused by 74 75 a t t a c k by h y d r o x i d e i o n on the tetramethylammonium i o n j ' C o n s e q u e n t l y , measurements u s i n g the s o l u t i o n were made w i t h i n two weeks of i t s p r e p a r a t i o n . I t i s i n t e r e s t i n g t h a t no e t c h i n g of g l a s s c o n t a i n e r s , s y r i n g e s or a b s o r p t i o n c e l l s by s o l u t i o n s of h y d r o x i d e i o n i n DMSO was e v e r n o t i c e d d u r i n g t h i s work d e s p i t e t h e i r g r e a t b a s i c i t y . D . S p e c t r a l Measurements i n the D i m e t h y l s u l f o x i d e - W a t e r  System A l l measurements of s p e c t r a were made i n 1 cm s i l i c a c e l l s u s i n g a Bausch and Lomb Model 502 r e c o r d i n g s p e c t r o p h o t o m e t e r . The i n s t r u m e n t was e q u i p p e d w i t h c o n s t a n t - temperature c e l l h o l d e r h a v i n g a l i q u i d c a p a c i t y of 300 m l . 32 Water from a b a t h t h e r m o s t a t e d at 2 5 ° C was pumped t h r o u g h the c e l l h o l d e r . S i n c e many of the a n i o n s used i n t h i s work, e s p e c i a l l y the more b a s i c ones , r e a c t e d r e a d i l y w i t h 76 oxygen, the procedure d e v e l o p e d p r e v i o u s l y by O ' D o n n e l l was u s e d t o p r o t e c t them from oxygen. The s o l u t i o n s were p r e p a r e d i n 1 cm s i l i c a a b s o r p t i o n c e l l s f i t t e d w i t h a s i l i c o n e rubber d i s c i n the ground g l a s s n e c k . The d i s c s were of the type used as i n j e c t i o n septums i n gas chromatography. They c o u l d be p i e r c e d many t imes w i t h s m a l l gauge s y r i n g e n e e d l e s w i t h o u t l e a k i n g and were i n e r t t o DMSO. In p r e p a r i n g a s o l u t i o n , the c e l l was f i r s t f i t t e d w i t h a s i l i c o n e d i s c and then two s y r i n g e n e e d l e s i n s e r t e d t h r o u g h t h i s . N i t r o g e n was p a s s e d i n through one of the n e e d l e s so t h a t the c e l l was f l u s h e d c o n t i n u o u s l y w i t h n i t r o g e n . N e x t , 30 m i c r o l i t e r s of a s o l u t i o n of i n d i c a t o r a c i d (2 - 2 5 x 10 molar ) i n DMSO was added from a 50 m i c r o l i t e r s y r i n g e f i t t e d w i t h a Chaney a d a p t e r . The c o n c e n t r a t i o n of s t o c k s o l u t i o n was so chosen as t o produce an absorbance near 0 .7 t o 0 .8 i n the f i n a l s o l u t i o n when the i n d i c a t o r was c o m p l e t e l y i o n i z e d . A p p r o x i m a t e l y 2 ml of DMSO-water s o l u t i o n was then added w i t h a 5 ml s y r i n g e a l s o f i t t e d w i t h a Chaney a d a p t e r . 33 In the case of a n i o n s r e a c t i v e w i t h oxygen i t p r o v e d p r o f i t a b l e t o bubble n i t r o g e n t h r o u g h the s o l u t i o n f o r about two minutes at t h i s p o i n t . T h i s was s i m p l y a c c o m p l i s h e d by l o w e r i n g the t i p of the n i t r o g e n i n l e t s y r i n g e needle below the l i q u i d l e v e l . The s y r i n g e n e e d l e s were then removed from the s i l i c o n e d i s c , the c e l l t r a n s f e r r e d t o the c e l l compartment of the s p e c t r o p h o t o m e t e r and a l l o w e d to e q u i l i b r a t e f o r at l e a s t 10 m i n u t e s . F i n a l l y the base was added w i t h a t h i r d s y r i n g e e i t h e r as a 10% aqueous s o l u t i o n or as a 0 .12 molar s o l u t i o n i n DMSO; the amount added b e i n g s u f f i c i e n t t o b r i n g the c o n c e n t r a t i o n of tetramethylammonium h y d r o x i d e i n the c e l l t o 0.011 m o l a r . The spectrum of the s o l u t i o n was taken i m m e d i a t e l y and r e t a k e n at l e a s t once a f t e r an i n t e r v a l of 3 or 4 minutes to i n s u r e t h a t the i n d i c a t o r s o l u t i o n was s t a b l e . In the few cases where the a n i o n appeared t o r e a c t i n some manner, the absorbance of the s o l u t i o n was o b t a i n e d by e x t r a p o l a t i o n of the r e a d i n g s o b t a i n e d at a p p r o p r i a t e time i n t e r v a l s t o the time of a d d i t i o n of the b a s e . In g e n e r a l , however, the spectrum showed no change f o r at l e a s t 10 t o 15 m i n u t e s . E x c e p t f o r the a d d i t i o n of 30 m i c r o l i t e r s of i n d i c a t o r s o l u t i o n i n DMSO, a b l a n k s o l u t i o n was p r e p a r e d i n the same manner as d e s c r i b e d above u s i n g the same 34 DMSO-water s t o c k s o l u t i o n . T h i s s o l u t i o n was u s e d i n the r e f e r e n c e beam of the s p e c t r o p h o t o m e t e r . The f i n a l c o m p o s i t i o n of the s o l u t i o n was c a l c u  l a t e d from the volumes of added components and t h e i r d e n s i t i e s . The d e n s i t y data f o r the DMSO-water m i x t u r e s at 77 2 5 ° C were those of Cowie and Toporowski E . S p e c t r a l Measurements i n 20% E t h a n o l - a q u e o u s S u l f u r i c A c i d An attempt was made t o determine the d i s s o c i a t i o n c o n s t a n t s of the ammonium i o n s of s u b s t i t u t e d d i p h e n y l a m i n e s i n aqueous s u l f u r i c a c i d . D i p h e n y l a m i n e i t s e l f p r o v e d s u f f i c i e n t l y s o l u b l e i n water f o r s p e c t r a l measurements i n 1 cm c e l l s . However s e v e r a l o ther d i p h e n y l a m i n e s , i n c l u d i n g the c h l o r o - , t r i f l u o r o m e t h y l , m e t h y l s u l f o n y l - and 3 , 4 ' - d i n i t r o - s u b s t i t u t e d compounds, were so i n s o l u b l e as to p r e c l u d e measurements i n 1 cm c e l l s and , i n s e v e r a l c a s e s , i n 10 cm c e l l s . I t was d e c i d e d , t h e r e f o r e , t o 7 8 79 adopt the procedure of J a f f e and c o - w o r k e r s ' who s t u d i e d the b a s i c i t i e s of azobenzenes i n "20% e t h a n o l " - a q u e o u s s u l f u r i c a c i d s o l u t i o n s . The amines p o s s e s s e d s u f f i c i e n t s o l u b i l i t y i n t h i s medium c o n t a i n i n g a p p r o x i m a t e l y 19 volume % e t h a n o l . The s o l u t i o n s were p r e p a r e d i n the f o l l o w i n g way. Two ml of a s o l u t i o n of an amine (1 - 3 x 1 0 - 4 molar) i n c o n s t a n t b o i l i n g e t h a n o l (95.6%) was p i p e t t e d i n t o a 10 ml 35 v o l u m e t r i c f l a s k which was then f i l l e d t o the mark w i t h aqueous s u l p h u r i c a c i d of the a p p r o p r i a t e s t r e n g t h . The s t o p p e r e d f l a s k was then suspended i n a water b a t h thermos- t a t e d at 2 5 ° C f o r at l e a s t 10 m i n u t e s . A t h i g h a c i d c o n c e n t r a t i o n s heat was e v o l v e d on a d d i t i o n of the a c i d to the e t h a n o l and the t h e r m o s t a t e d s o l u t i o n s had to be topped o f f w i t h more a c i d due t o the c o n t r a c t i o n of the volume of the s o l u t i o n on c o o l i n g . The s o l u t i o n was then t r a n s f e r r e d t o a 1 cm s i l i c a c e l l and the spectrum of the s o l u t i o n taken a f t e r f u r t h e r e q u i l i b r a t i o n i n the c e l l h o l d e r . A l l s p e c t r a were i n v a r i a n t w i t h t i m e . A b l a n k s o l u t i o n p r e p a r e d i n the same manner (except f o r the absence of amine i n the e t h a n o l ) u s i n g the same a c i d s t o c k s o l u t i o n was used i n the r e f e r e n c e beam. The c o n c e n t r a t i o n of the a c i d i n each s o l u t i o n was d e t e r m i n e d v o l u m e t r i c a l l y by t i t r a t i o n of a b l a n k s o l u t i o n w i t h 0.1 molar sodium h y d r o x i d e . F . Treatment of the S p e c t r a l Data In the DMSO-water system the l o n g e s t wavelength a b s o r p t i o n maxima f o r most of the a n i o n s showed s o l v e n t dependence; these g e n e r a l l y s h i f t e d to l o n g e r wavelength as the f r a c t i o n of DMSO i n c r e a s e d . The s h i f t f o r most of the a n i o n s of the a n i l i n e s and d i p h e n y l a m i n e s was about 5mu on p a s s i n g from 10% t o 90% i o n i z a t i o n . 36 In the s u l f u r i c a c i d media the p o s i t i o n of the a b s o r p t i o n maxima of the n e u t r a l d i p h e n y l a m i n e s s h i f t e d about 3 or 4 nyjk on p a s s i n g from 10% t o 90% i o n i z a t i o n f o r the n i t r o d i p h e n y l a m i n e s and not at a l l f o r the o t h e r s . The s h i f t was t o l o n g e r wavelength as the a c i d c o n c e n t r a t i o n i n c r e a s e d . The e q u a t i o n s f o r H Q and H_ can be w r i t t e n as H D = p K B H + - l o g (23) and H_ = pK^ + l o g — - (24) H A [HA] r e s p e c t i v e l y . S i n c e t h e r e are such l a r g e changes i n a b s o r p t i o n s p e c t r a f o r a n i l i n e s and d i p h e n y l a m i n e s on 80 i o n i z a t i o n the f o l l o w i n g e x p r e s s i o n s can be used t o c a l c u l a t e the r a t i o s [BH*] / [B ] and [A -] / [HA] f rom the s p e c t r a l data [BH+] 6 B - e (25) L>] £ " £ B H + = (26) [HA] eA- - € where £ B i s the molar a b s o r p t i v i t y of the n e u t r a l amine at i t s wavelength of maximum a b s o r p t i o n ^ B H + i s t h e m o ^ a r a b s o r p t i v i t y of i t s c o n j u g a t e base at the same wavelength 37 and £ i s the molar a b s o r p t i v i t y , at the same w a v e l e n g t h , of a s o l u t i o n i n which the i n d i c a t o r i s p a r t i a l l y i o n i z e d , £ A ~ i s the molar a b s o r p t i v i t y of the a n i o n at i t s wavelength of maximum a b s o r p t i o n £ H A i s the molar a b s o r p t i v i t y of the n e u t r a l amine at the same wavelength £ i s the molar a b s o r p t i v i t y , at the same w a v e l e n g t h , of a s o l u t i o n i n which the i n d i c a t o r i s p a r t i a l l y i o n i z e d . S i n c e , as was n o t e d p r e v i o u s l y , the a b s o r p t i o n maxima s h i f t e d w i t h change i n s o l v e n t c o m p o s i t i o n £ g , EA~> and £ were measured at the a b s o r p t i o n maximum f o r each s o l u t i o n . 23 T h i s method has been u s e d by J o r g e n s o n and H a r t t e r t o c o r r e c t f o r medium s h i f t s . I t was f e l t t h a t t h i s method would b e s t c o r r e c t f o r these s h i f t s . A l s o , s i n c e f o r any g i v e n i n d i c a t o r a l l the measurements were made u s i n g the same c o n c e n t r a t i o n of i n d i c a t o r the absorbance (A) r a t h e r than the molar a b s o r p t i v i t y (Q was u s e d . The molar a b s o r p t i v i t y (GA - ) ° f a n a n i o n w a s o b t a i n e d i n a s o l u t i o n the H_ of which was a l e a s t 2 u n i t s h i g h e r than the pK of the i n d i c a t o r . In the case of 3 - c h l o r o - , 3-HA t r i f l u o r o m e t h y l - and 3 - c y a n o a n i l i n e i t was n e c e s s a r y t o use a s o l u t i o n of p o t a s s i u m t - b u t o x i d e i n DMSO t o o b t a i n £ - f o r the a n i o n s . The t - b u t o x i d e i o n i s known t o be an e x t r e m e l y s t r o n g base i n DMSO, s i n c e i t appears t o be i n e q u i l i b r i u m w i t h 81 82 the conjugate base of DMSO i t s e l f 5 38 F o r 3 , 4 ' - d i n i t r o - , 4 - n i t r o - 3 ' - t r i f l u o r o m e t h y l - and 4 - n i t r o d i p h e n y l a m i n e the molar a b s o r p t i v i t i e s of the a n i o n s v a r i e d w i t h the s o l v e n t c o m p o s i t i o n so t h a t the e x t e n t of i o n i z a t i o n was d e t e r m i n e d by measur ing the d i s a p p e a r a n c e of the peak due t o the n e u t r a l amine r a t h e r than the appearance of the peak due t o the a n i o n . T h i s was p o s s i b l e s i n c e the a n i o n s absorbed l i t t l e at the wavelength of maximum a b s o r p t i o n of the n e u t r a l amines . S i m i l a r l y , i n the work i n a c i d s o l u t i o n s , the molar a b s o r p t i v i t y of a n e u t r a l amine (Eg) was o b t a i n e d i n a s o l u t i o n the H Q of which was at l e a s t 2 u n i t s above the pKgH+ of the i n d i c a t o r . In the case of 4 , 4 f - d i n i t r o d i p h e n y l - amine the molar a b s o r p t i v i t y (Eg) changed s l i g h t l y w i t h a c i d c o n c e n t r a t i o n so t h a t i t was n e c e s s a r y t o measure Eg over a range of s o l u t i o n s of from 0 t o 6 .5 molar s u l f u r i c a c i d and e x t r a p o l a t e t o the r e g i o n of i o n i z a t i o n . Appendix B c o n t a i n s s p e c t r a l data f o r the amines i n c o n s t a n t b o i l i n g e t h a n o l and f o r t h e i r a n i o n s i n DMSO- water m i x t u r e s . Appendix C c o n t a i n s the i o n i z a t i o n r a t i o data f o r the amines i n the DMSO-water and 20% e t h a n o l - w a t e r - s u l f u r i c a c i d s y s t e m s . 39 RESULTS A . The System DMSO-Water-Tetramethylammonium H y d r o x i d e From s p e c t r a l measurements on s o l u t i o n s of amine i n d i c a t o r s i n the m i x t u r e s of DMSO-water c o n t a i n i n g 0.011 molar tetramethylammonium h y d r o x i d e the r a t i o s of the c o n c e n t r a t i o n s of i o n i z e d t o u n i o n i z e d i n d i c a t o r (I [A "3 / [HA] ) are o b t a i n e d as d e s c r i b e d i n the p r e v i o u s s e c t i o n . From these r a t i o s are then o b t a i n e d the r e l a t i v e pK v a l u e s of the amine i n d i c a t o r s and the H v a l u e s f o r the s o l u t i o n s i n which the measurements were made. The r e l a t i v e pK v a l u e s were o b t a i n e d by Hammett 's 9 method of comparing i o n i z a t i o n r a t i o s of o v e r l a p p i n g i n d i c a t o r s i n the same s o l u t i o n . The q u a n t i t y l o g I was p l o t t e d against s o l v e n t c o m p o s i t i o n f o r each i n d i c a t o r and a smooth curve drawn t h r o u g h the p o i n t s f o r each p l o t . V a l u e s of l o g I between -1 and 1 c o r r e s p o n d i n g t o 10% and 90% i o n i z a t i o n , r e s p e c t i v e l y , were used i n the p l o t s . Where s u c c e s s i v e c u r v e s o v e r l a p p e d , d i f f e r e n c e s were taken at r e g u l a r i n t e r v a l s and the r e s u l t s a v e r a g e d . These averages gave the d i f f e r e n c e s between the pK v a l u e s of the i n d i c a t o r s . The r e f e r e n c e a c i d , the i n d i c a t o r f o r which the a c i d d i s s o c i a t i o n i s known, was 2 , 4 - d i n i t r o d i p h e n y l a m i n e . 40 40 Stewart and O ' D o n n e l l have d e t e r m i n e d v a l u e s of 13 .83 , 13.83 and 13.85 i n t h r e e s o l v e n t systems f o r i t s p K H A . The v a l u e 13.84 f o r the pK of t h i s compound was then used HA w i t h the r e l a t i v e pK v a l u e s of the r e s t of the i n d i c a t o r s t o c a l c u l a t e t h e i r thermodynamic PKjj A v a l u e s . T a b l e I c o n t a i n s a l i s t of the i n d i c a t o r s u s e d t o e s t a b l i s h the H_ s c a l e a l o n g w i t h t h e i r pK v a l u e s o b t a i n e d i n t h i s work. HA L i t e r a t u r e v a l u e s of pKjj^ are a l s o p r e s e n t e d f o r those compounds t h a t have been u s e d p r e v i o u s l y . The H _ v a l u e s f o r the DMSO-water m i x t u r e s were then c a l c u l a t e d from the pKjj A v a l u e s of the i n d i c a t o r s l i s t e d i n T a b l e I and the v a l u e s of l o g I o b t a i n e d from the smoothed c u r v e s mentioned above . T h i s was a c c o m p l i s h e d u s i n g e q u a t i o n (13) . [ A l [A"] H _ = PK + l o g — - (I - — ) (13) H A [ H A ] [ H A ] F o r a g i v e n s o l u t i o n , H_ i s g e n e r a l l y an average of v a l u e s o b t a i n e d from two or more i n d i c a t o r s . T a b l e II l i s t s the average H v a l u e s f o r the DMSO-water m i x t u r e s a l o n g w i t h the average d e v i a t i o n of the i n d i v i d u a l v a l u e s from the mean. A l s o , the i n d i c a t o r s t h a t were u s e d t o determine the H _ f o r a p a r t i c u l a r s o l u t i o n are g i v e n i n the l a s t column. The numbers i n t h i s column r e f e r to the numbers of the i n d i c a t o r s l i s t e d i n T a b l e I . 41 TABLE The pK V a l u e s of the I n d i c a t o r s Used HA t o E s t a b l i s h the H_ A c i d i t y F u n c t i o n I n d i c a t o r PjblA p K H A r e p o r t e d D i p h e n y l a m i n e s 1 2 , 4 - d i n i t r o (13. 84) 2 3 , 4 ' - d i n i t r o 14. 66 3 4 - n i t r o - 3 ' - t r i f l u o r o  methyl 14. 96 4 4 - n i t r o 15. 67 5 2 - n i t r o 17. 91 6 4 - m e t h y l s u l f o n y l 18. 80 7 3 - n i t r o 19. 53 8 3 , 4 ' - d i c h l o r o 19. 73 9 3 - t r i f l u o r o m e t h y l 20. 48 10 3 - c h l o r o 20. 73 11 4 - c h l o r o 21. 33 12 3-methoxy 22. 22 13 H 22. 44 14 4 - m e t h y l 22. 95 15 4-methoxy 23. 22 A n i l i n e s 16 4 - c h l o r o - 2 - n i t r o 17. 08 17 2 , 3 , 5 , 6 - t e t r a c h l o r o 19. 22 18 4 -cyano 22. ,68 19 3 , 4 , 5 - t r i c h l o r o 22. ,86 20 3 , 5 - d i c h l o r o 23. 59 21 3 , 4 - d i c h l o r o 24. ,60 22 3-cyano 24. ,64 23 3 - t r i f l u o r o m e t h y l 25. ,40 24 3 - c h l o r o 25. ,63 (13.84) 1 15.90* 17 15.68 57 a 17.22' 17.13 a b Stewart and O ' D o n n e l l , r e f . 40 L a n g f o r d and B u r w e l l , r e f . 52, as c o r r e c t e d i n r e f . 40 42 TABLE II H _ V a l u e s f o r the System DMSO-Water-Tetramethylammonium Hydroxide (0.011 M) Mole % DMSO H _ V a l u e A v e . Dev. from Mean I n d i c a t o r s 10.32 13.17 - 1 15.20 13.88 0.04 1,2 20.18 14.49 .02 1 , 2 , 3 23. 57 14.86 .01 2-4 26.95 15.22 .005 2-4 30.11 15.54 .005 2-4 33.42 15.87 .02 3,4 36.79 16.17 .005 4,16 39.86 16.48 .01 4,16 43.27 16.83 - 16 46.54 17.12 .02 5,16 49 .59 17 .42 .005 5,16 52. 55 17.73 .01 5,16 55.95 18.08 .02 5 ,6 ,16 58.56 18.34 .02 5 ,6 ,17 62.27 18.72 .01 5 ,6 ,17 64.20 18.92 .005 6-8 ,17 69 .09 19.41 .01 6 -8 ,17 71.35 19.65 .01 6 -9 ,17 73.69 19.90 .02 7-9 ,17 76.12 20.14 .005 7-9 78.36 20.38 .01 7-11 80.78 20.68 .005 9-11 83.14 20.97 .005 9-11 85.46 21.27 .01 9-11 88.79 21.61 .02 10-13 90.07 21.98 .005 12-14 ,18 ,19 92.47 22.45 .01 12-15 ,18 ,19 94.74 23.01 .01 13-15 ,18-20 95.77 23.32 .005 13-15 ,18-20 96.21 23.48 .01 14 ,15 ,18-20 97 .13 23.88 .02 20-22 97.89 24.25 .005 20-22 98.29 24.50 .01 20-23 98.71 24.84 .01 21-24 99.14 25.30 .01 21-24 99.59 26.19 .05 23,24 a Numbers r e f e r t o those i n t a b l e I 43 F i g u r e 1 i s a p l o t of H_ v e r s u s c o m p o s i t i o n of the DMSO -water-tetramethylammonium h y d r o x i d e sys tem. The v a l u e of H_ f o r 0.011 molar tetramethylammonium h y d r o x i d e i n water was c a l c u l a t e d from the e q u a t i o n H_ - p K w + l o g [OH"] (27) T h i s r e l a t i o n s h i p was f o u n d t o h o l d f o r s o l u t i o n s of sodium h y d r o x i d e of from 0.01 t o 1 molar c o n c e n t r a t i o n by 42 Edward and Wang . I f t h i s r e l a t i o n s h i p i s assumed t o h o l d go f o r tetramethylammonium h y d r o x i d e and the v a l u e 14.00 u s e d f o r p K w then the H f o r 0.011 molar h y d r o x i d e i o n i s 12.04. I t i s e v i d e n t from e q u a t i o n (13) t h a t a p l o t of l o g I v e r s u s H_ s h o u l d g i v e a s t r a i g h t l i n e w i t h u n i t s l o p e and i n t e r c e p t e q u a l to the p K R A of the i n d i c a t o r . F i g u r e 2 i s such a p l o t of l o g I ( l o g [A"[| / [HA] ) v e r s u s H_ f o r the i n d i c a t o r s i n T a b l e I . L i n e s of u n i t s l o p e w i t h i n t e r c e p t s e q u a l to the p K ^ v a l u e s of the i n d i c a t o r s have a l s o been drawn. The f i t of the e x p e r i m e n t a l v a l u e s of l o g I t o these l i n e s i s a measure of the p r e c i s i o n of the r e s u l t s and of the v a l i d i t y of the whole p r o c e d u r e . The pKjj^ v a l u e s of a number of compounds were determined from the H_ s c a l e u s i n g e q u a t i o n ( 1 3 ) . These were a c i d s t h a t were not used i n the e s t a b l i s h m e n t of the FIGURE I H_ ACIDITY FUNCTION FOR THE SYSTEM: DMSO-WATER - TETRAMETHYLAMMONIUM HYDROXIDE (O.OI I M) FIGURE 2 PLOT OF LOG [A~]/[HA] VERSUS H_ FOR THE INDICATORS USED TO ESTABLISH THE H_ SCALE THE NUMBERS REFER TO THE COMPOUNDS IN TABLE I H_ 13 14 15 '16 17 J I I 1 . L FIGURE 2 (CONT.) 18 48 H _ s c a l e and c o n s i s t e d m a i n l y of a l k y l - s u b s t i t u t e d 4- n i t r o a n i l i n e s . The pKjj A of an a c i d was taken as the i n t e r c e p t of a p l o t of l o g I v e r s u s H _ , t h a t i s , the H _ of the s o l u t i o n i n which the i n d i c a t o r i s h a l f i o n i z e d . These p l o t s are not a l l of u n i t s l o p e , e s p e c i a l l y f o r the s u b s t i t u t e d n i t r o a n i l i n e s . However, f o r f o u r d i c h l o r o a n i l i n e s the s l o p e s a r e , w i t h i n e x p e r i m e n t a l e r r o r , u n i t y . The a c i d s , t h e i r p K H A v a l u e s and the s l o p e s of the p l o t s of l o g I ( l o g [A"|] / [HA] ) v e r s u s H are l i s t e d i n T a b l e I I I and the above mentioned p l o t s are shown i n F i g u r e 3. The p l o t f o r 2 , 6 - d i - t - b u t y l - 4 - n i t r o a n i l i n e i s not a s t r a i g h t l i n e a l t h o u g h i t appears the p o i n t s approach a l i n e of u n i t s l o p e f o r v a l u e s of l o g I l e s s than z e r o . An e s t i m a t e was made of the p K H A of 4 - a m i n o d i p h e n y l - amine. An a c c u r a t e measurement c o u l d not be made because of the d i f f i c u l t y i n p u r i f y i n g t h i s compound and i t s r e a d i n e s s t o r e a c t w i t h the s l i g h t e s t t r a c e of oxygen i n the b a s i c m e d i a . A v a l u e of 24.2 was o b t a i n e d from a comparison of i t s i o n i z a t i o n r a t i o s i n t h r e e s o l u t i o n s w i t h those of 4 - m e t h o x y d i p h e n y l a m i n e . 49 TABLE I I I Summary of pR™. V a l u e s of V a r i o u s Amine A c i d s Compound p K H A Slope of p l o t of l o g I vs H _ 1. 4 - n i t r o a n i l i n e 18. 91 0 .92 2. 4 - n i t r o - 2 - m e t h y l a n i l i n e 18. 83 0 .91 3. 4 - n i t r o - 2 , 6 - d i m e t h y l a n i l i n e 18. 71 0 .89 4. 4 - n i t r o - 2 , 6 - d i - t - b u t y l a n i l i n e 17. 4 5. 4 - n i t r o - 3 , 5 - d i m e t h y l a n i l i n e 21. 16 1 .05 6. 4 - n i t r o - 2 , 3 , 5 , 6 - t e t r a m e t h y l - a n i l i n e 22. 66 1 .18 7. 4 - n i t r o - N , 2 - d i m e t h y l a n i l i n e 18. 58 0 .96 8. 4 - n i t r o - N - m e t h y 1 a n i l i n e 18.49 0 .99 9 . 4 - n i t r o - N - e t h y l a n i l i n e 18. 58 0 .95 10. 4 - n i t r o - N - i s o p r o p y l a n i l i n e 18. 66 0 .95 11 . 4 - n i t r o - N - t - b u t y l a n i l i n e 19. 64 1 .02 12. 4 - n i t r o - N - t r i p h e n y l m e t h y l - a n i l i n e 17. 98 0 .99 13. 2 , 3 - d i c h l o r o a n i l i n e 23. 14 1 .00 14. 2 , 4 - d i c h l o r o a n i l i n e 23. 46 1 .00 15. 2 , 5 - d i c h l o r o a n i l i n e 22. 71 1 .04 16. 2 , 6 - d i c h l o r o a n i l i n e 22. 40 1 .02 17. 2 , 2 ' - d i p y r i d y l a m i n e 19. 91 0 .85 a pKjjA taken as the H _ at h a l f i o n i z a t i o n FIGURE 3 PLOT OF LOGM/NA1 VERSUS H_ FOR VARIOUS AMINES o 51 52 B. The System "20% E t h a n o l " - A q u e o u s S u l f u r i c A c i d The PR,™* v a l u e s f o r the i o n i z a t i o n of the d i p h e n y l - DH ammonium i o n s i n t h i s medium were o b t a i n e d i n the same way (28) as the v a l u e s f o r the i o n i z a t i o n of the n e u t r a l amines i n the b a s i c medium. The r e f e r e n c e base was d i p h e n y l a m i n e . The P K B J J + v a l u e of i t s conjugate a c i d was found t o be 0.78 from a comparison of i t s i o n i z a t i o n w i t h t h a t of the c o n j u g a t e a c i d of 4 - n i t r o a n i l i n e i n aqueous s o l u t i o n s of h y d r o c h l o r i c a c i d . The f o l l o w i n g e q u a t i o n was used FB p K B H + - P K B R + = l o g I A - l o g 1^ + l o g ' A D (29) where the l e t t e r s " A " and ' ' D " r e f e r t o 4 - n i t r o a n i l i n e and d i p h e n y l a m i n e r e s p e c t i v e l y , and I' r e f e r s to the r a t i o (BH+3/[B]. E x p e r i m e n t a l l y i t was found t h a t l o g 1^ - l o g 1^ had a v a l u e of 0.217 - .004 f o r seven s o l u t i o n s of h y d r o c h l o r i c a c i d v a r y i n g i n s t r e n g t h from 0.03 t o 0.5 m o l a r . There appeared no tendency of t h i s q u a n t i t y t o v a r y , w i t h i n e x p e r i m e n t a l e r r o r , w i t h a c i d c o n c e n t r a t i o n . 53 S i n c e the l a s t term i n e q u a t i o n (29) must, by d e f i n i t i o n , be z e r o i n d i l u t e aqueous s o l u t i o n i t i s v e r y p r o b a b l y z e r o i n the h y d r o c h l o r i c a c i d s o l u t i o n s because of the c o n s t a n c y of the l o g I ' - l o g I ' t e r m . Thus the number A D 0.217 i s the d i f f e r e n c e i n pK D l J + v a l u e s f o r 4 - n i t r o a n i l i n e and d i p h e n y l a m i n e . T h i s d i f f e r e n c e combined w i t h the pKgjj+ v a l u e 84 85 of 1.00 f o r 4 - n i t r o a n i l i n e ' g i v e s a v a l u e of 0 .78 f o r the pK + of d i p h e n y l a m i n e . A v a l u e of 0 .79 has been B H 85 f o u n d by P a u l , a l t h o u g h i t i s r e c o r d e d as 0 .78 i n the 12 r e v i e w of P a u l and Long . The pKgH+ v a l u e s of a l l the s u b s t i t u t e d d i p h e n y l a m i n e s are based on a pKgjj+ v a l u e of 0 .78 f o r d i p h e n y l a m i n e . E q u a t i o n (23) was u s e d t o c a l c u l a t e H Q v a l u e s f o r the v a r i o u s a c i d s o l u t i o n s . As b e f o r e , two or more i n d i c a t o r s were g e n e r a l l y used t o c a l c u l a t e H Q f o r H ° - P KBH + " l 0 g 1 ' " ( 1' " T^ J I ( 2 3 ) each s o l u t i o n . T a b l e IV l i s t s the d i p h e n y l a m i n e s and t h e i r pkgH+ v a l u e s used t o c a l c u l a t e the H Q f u n c t i o n i n "20% e t h a n o l " - aqueous s u l f u r i c a c i d . 54 TABLE IV V a l u e s of pK_„+ f o r the D i p h e n y l a m i n e s on u s e d t o E s t a b l i s h the H Q A c i d i t y F u n c t i o n S u b s t i t u e n t s PKBH+ 1 4-methoxy 1.36 2 4 - m e t h y l 1.20 3 none (0.78) 4 3-methoxy 0.40 5 4 - c h l o r o 0.01 6 3 - c h l o r o - 0 . 4 5 7 3 - t r i f l u o r o m e t h y l - 0 . 7 8 8 3 , 4 ' - d i c h l o r o - 1 . 1 9 9 3 - n i t r o - 1 . 6 1 10 4 - m e t h y l s u l f o n y l -2 .54 11 4 - n i t r o - 3 ' - m e t h y l -2 .93 12 4 - n i t r o -3 .13 13 2 - n i t r o - 4 . 1 2 14 4 - n i t r o - 3 ' - c h i o r o - 4 . 1 5 15 4 - n i t r o - 3 ' - t r i f l u o r o m e t h y l -4 .47 16 3 , 4 ' - d i n i t r o - 5 . 1 9 17 4 , 4 ' - d i n i t r o -6 . 21 a T h i s v a l u e de termined i n aqueous s o l u t i o n s of HC1 55 T a b l e V l i s t s the mean H D v a l u e s d e t e r m i n e d f o r these s o l u t i o n s a l o n g w i t h the average d e v i a t i o n of the i n d i v i d u a l v a l u e s from the mean and a l s o the i d e n t i t y of the i n d i c a t o r s used t o c a l c u l a t e H 0 f o r each s o l u t i o n . F i g u r e 4 i s a p l o t of the data i n T a b l e V . F i g u r e 5 i s a p l o t of the e x p e r i m e n t a l v a l u e s of l o g I' ( [ B H + ] / [ B ] ) v e r s u s H Q . As b e f o r e , l i n e s of u n i t s l o p e w i t h i n t e r c e p t s e q u a l t o the p K B H + v a l u e s of the i n d i c a t o r s have a l s o been drawn f o r c o m p a r i s o n . The f i t of the e x p e r i m e n t a l p o i n t s t o the l i n e s i s a measure of the v a l i d i t y of the r e s u l t s . C . P r o b a b l e E r r o r i n H and pK V a l u e s With a l l a c i d i t y f u n c t i o n s i t i s d i f f i c u l t t o e s t i m a t e the u n c e r t a i n t y i n H v a l u e s and i n the pK v a l u e s of the i n d i c a t o r s used t o determine them. The f u r t h e r an a c i d i t y f u n c t i o n i s from the u s u a l pH range the g r e a t e r l i k e l i h o o d of e r r o r s because of the s tepwise procedure used to e s t a b l i s h i t . F o r example , i n s t r o n g l y b a s i c s o l u t i o n s any e r r o r e n c o u n t e r e d i n d e t e r m i n i n g the d i f f e r e n c e i n PK-HA v a l u e s between two o v e r l a p p i n g i n d i c a t o r s i s i n c o r p o r a t e d i n the p K H A v a l u e of the l e s s a c i d i c one and a l s o i n the H_ v a l u e s d e t e r m i n e d from i t s i o n i z a t i o n r a t i o s . E r r o r s can be m i n i m i z e d by u s i n g a l a r g e number of o v e r l a p p i n g 56 TABLE V H Q V a l u e s f o r the System "20% E t h a n o l " - A q u e o u s S u l f u r i c A c i d M o l a r i t y of H G V a l u e A v e . Dev. from I n d i c a t o r s 3 H2SO4 Mean 0.0163 1. 86 0.01 1,2 0.0339 1.56 .01 1,2 0.0567 1 .34 .00 1-4 0.0808 1.18 .005 1-4 0.163 0.87 .00 1-4 0.245 0.67 .01 1-4 0.406 0.41 .00 1-5 0.611 0.17 .01 3-6 0.763 0.03 .00 3-7 0.914 -0 .10 .00 3-7 1.26 - 0 . 35 .005 4-8 1.47 - 0 . 4 8 .005 4-8 1.72 -0 .63 .00 5-8 1.98 - 0 . 7 8 .00 5-9 2. 25 -0 .93 .01 5-9 2.49 -1 .07 .00 6-9 2.73 - 1 . 2 0 .005 6-9 3.07 -1 .40 .005 7 ,8 3.29 - 1 . 53 .00 7-9 3. 58 -1 .70 .01 7-10 3.76 -1 .81 .01 8-10 4 .14 - 2 . 0 3 .01 8-11 4 .38 -2 .17 .005 9-12 4 .62 -2 .32 1005 9-12 4.90 - 2 . 51 .01 9-12 5.15 - 2 . 6 5 .01 10-12 5.41 -2 .81 .005 10-12 5.66 - 2 . 9 7 .00 10-12 5.95 -3 .18 .03 10-14 6.47 - 3 . 52 .02 10-15 6.81 -3.. 75 .01 11-15 7.16 - 3 . 9 9 .005 12-15 7.64 -4 .33 .005 13^-16 8.14 -4 .69 .02 13-16 8.44 -4 .91 .03 13-16 8 . 8 7 -5 .20 .005 15-17 9.31 -5 .54 .00 16,17 9.81 -5 .91 .005 16,17 10.18 - 6 . 1 9 .005 16,17 10.65 -6 .54 - 17 11.22 -6 .97 - 17 a Numbers r e f e r t o those i n T a b l e IV FIGURE 5 PLOT OF LOG[BH+]/[B] VERSUS H G POP, THE INDICATORS USED TO ESTABLISH THE H 0 SCALE ( i ) (a THE NUMBERS R E F E R T J THE COMPOUNDS IN T A B L E T V 0 -2 59 60 i n d i c a t o r s so t h a t the H v a l u e f o r a g i v e n s o l u t i o n i s not dependent on the data f o r one i n d i c a t o r and by u s i n g i n d i c a t o r s of the same s t r u c t u r a l type t o ensure t h a t the Hammett a c t i v i t y c o e f f i c i e n t p o s t u l a t e i s obeyed as c l o s e l y as p o s s i b l e . The pK v a l u e s i n t h i s work are r e c o r d e d t o two d e c i m a l p l a c e s . T h i s i s v a l i d f o r the r e l a t i v e pK v a l u e s of i n d i c a t o r s t h a t are not more than one or two pK u n i t s a p a r t . The u n c e r t a i n t y i n t h i s case i s p r o b a b l y - .03 t o - .05 pK u n i t s . The u n c e r t a i n t y i n the thermodynamic pK v a l u e s , however, i s l i k e l y g r e a t e r than t h i s and the f i g u r e i n the second d e c i m a l p l a c e i s of l i t t l e s i g n i f i c a n c e T h i s i s p a r t i c u l a r l y t r u e of v e r y h i g h p K j ^ v a l u e s and of l a r g e n e g a t i v e v a l u e s of pKg H + . 61 DISCUSSION A . V a l i d i t y of the H _ F u n c t i o n The use of the Hammett procedure t o e s t a b l i s h an H_ f u n c t i o n f o r the i o n i z a t i o n of a r o m a t i c amines i n the DMSO-water system seems j u s t i f i e d . T h i s i s e v i d e n t i n the f a c t t h a t the p l o t s of l o g I v e r s u s s o l v e n t c o m p o s i t i o n gave p a r a l l e l c u r v e s f o r o v e r l a p p i n g i n d i c a t o r s . I t can a l s o be seen i n the good agreement i n H_ v a l u e s c a l c u l a t e d u s i n g d i f f e r e n t i n d i c a t o r s (Table II ) and i n the f i t of the e x p e r i m e n t a l p o i n t s f o r l o g I t o the l i n e s of u n i t s l o p e (F igure 2) . As shown i n T a b l e II and F i g u r e 2, a number of i n d i c a t o r s have i n g e n e r a l been used to determine H_ f o r each s o l u t i o n . T h i s procedure e n s u r e s t h a t the H _ s c a l e i s not too dependent on any one i n d i c a t o r . Both p r i m a r y and secondary amines have been used i n c o n s t r u c t i n g the H_ s c a l e and i t appears t h a t the i o n i z a t i o n b e h a v i o u r i n the DMSO-water system of b o t h types of amines i s d e s c r i b e d by one a c i d i t y f u n c t i o n . T h i s f a c t i s p a r t i c u l a r l y e v i d e n t i n F i g u r e 2 f o r the i n d i c a t o r s i o n i z i n g i n the r e g i o n of H_ from 21 .5 t o 2 4 . 0 . In t h i s range t h e r e are seven c l o s e l y spaced i n d i c a t o r s of which t h r e e are p r i m a r y amines and f o u r are s e c o n d a r y amines . 62 The p l o t s of l o g I v e r s u s H_ f o r both t y p e s of i n d i c a t o r are p a r a l l e l t o one another i n d i c a t i n g t h a t the i o n i z a t i o n of p r i m a r y and secondary amines i s governed by one H_ f u n c t i o n . The e x i s t e n c e of o n l y one H _ s c a l e f o r both p r i m a r y and s e c o n d a r y amines c o n t r a s t s w i t h the f a c t t h a t t h e r e are s e p a r a t e H Q s c a l e s t o d e s c r i b e the p r o t o n a t i o n of p r i m a r y and t e r t i a r y 2 3 > 2 4 a n d a l s o , q u i t e p r o b a b l y , 28 secondary amines i n s u l f u r i c a c i d m i x t u r e s . The d i f f e r e n t b e h a v i o u r i n a c i d i c and b a s i c media i s not u n r e a s o n a b l e i n view of c u r r e n t i d e a s on the s o l v a t i o n of ammonium i o n s . The f a c t t h a t i o n i z a t i o n s of the ammonium i o n s r e s u l t i n g from p r i m a r y , secondary and t e r t i a r y amines are d e s c r i b e d by d i f f e r e n t H Q f u n c t i o n s i s b e l i e v e d t o s tem, t o a g r e a t e x t e n t , f rom d i f f e r e n c e s i n the s o l v a t i o n of these ammonium ions24>25,28^ w h i c h i s r e f l e c t e d i n the a c t i v i t y c o e f f i c i e n t term fgjj+ ° ^ ^ n e e x p r e s s i o n f B H 0 - - l o g (H+) (30) f B H + The d i f f e r e n c e s i n the s o l v a t i o n of the ammonium i o n s i s i n t u r n b e l i e v e d t o be a r e s u l t of s p e c i f i c s o l v a t i o n of these i o n s i n v o l v i n g f o r m a t i o n of s t r o n g hydrogen bonds between the hydrogen atoms on the n i t r o g e n atom of an QQ Ort ftfi amine and the oxygen atom of a water molecule » ' . The number of such i n t e r a c t i o n s and hence the s o l v a t i o n of 63 F H \ [ the ammonium i o n w i l l depend on whether the amine i s p r i m a r y , s e c o n d a r y or t e r t i a r y . Hydrogen b o n d i n g of t h i s type i n amine a n i o n s s h o u l d be of l i t t l e importance because of the n e g a t i v e charge on the n i t r o g e n atom. For these i o n s hydrogen bonds FHM—H i n v o l v i n g the e l e c t r o n p a i r s on the n i t r o g e n atom would be more i m p o r t a n t , S i n c e t h e r e are two p a i r s of u n s h a r e d e l e c t r o n s on an amine a n i o n r e g a r d l e s s of whether i t i s p r i m a r y or s e c o n d a r y i t would be e x p e c t e d ( n e g l e c t i n g s t e r i c e f f e c t s ) t h a t the s o l v a t i o n of these i o n s would be q u i t e s i m i l a r . In view of t h i s , the use of j u s t one H_ f u n c t i o n t o d e s c r i b e the i o n i z a t i o n of p r i m a r y and secondary amines i n b a s i c s o l u t i o n i s r e a s o n a b l e . 64 A t e s t of the v a l i d i t y of H _ f u n c t i o n s i s the agreement among pKjj A v a l u e s measured i n d i f f e r e n t s o l v e n t s y s t e m s . In T a b l e I i t can be seen t h a t the agreement between the pKjj A v a l u e s d e t e r m i n e d i n t h i s work and those d e t e r m i n e d i n aqueous s u l f o l a n e by L a n g f o r d and B u r w e l l 4 0 f o r 4 - n i t r o d i p h e n y l a m i n e and 4 - c h l o r o - 2 - n i t r o a n a i l i n e i s v e r y good ( d i f f e r e n c e s of .•'Ol and .05 r e s p e c t i v e l y ) . The 40 agreement w i t h the v a l u e s of Stewart and O ' D o n n e l l measured i n the same s o l v e n t i s not q u i t e as good. A l a r g e d i s c r e p a n c y e x i s t s f o r the pKjj A v a l u e of 4 - n i t r o a n i l i n e as o b s e r v e d i n t h i s work, 18 .91 , and by Stewart and O ' D o n n e l l 4 0 , 18 .37 , and by L a n g f o r d and B u r w e l l 4 0 ' 5 2 , 18 .39 . I t s h o u l d be n o t e d t h a t 4 - n i t r o a n i l i n e was not u s e d i n d e t e r m i n i n g the H _ s c a l e i n t h i s work and t h a t the s l o p e of the p l o t of l o g I v e r s u s H _ i s 0 .92 f o r t h i s compound. . 4 - N i t r o a n i l i n e was not used i n d e t e r m i n i n g the H_ s c a l e s i n c e the p l o t of l o g I v e r s u s s o l v e n t c o m p o s i t i o n f o r i t was not p a r a l l e l t o s i m i l a r p l o t s f o r the i n d i c a t o r s 4 - m e t h y l s u l f o n y l d i p h e n y l a m i n e and 2 , 3 , 5 , 6 - t e t r a c h l o r o a n i l i n e t h a t i o n i z e i n the same range of s o l v e n t c o m p o s i t i o n . Because of the b e h a v i o u r of 4 - n i t r o a n i l i n e , the a l k y l d e r  i v a t i v e s of t h i s compound were a l s o not used t o determine H _ . The s l o p e s of the p l o t s of l o g I v e r s u s H _ f o r most of these compounds (Table I I I ) l i e between 0.95 and 1.05 65 and i t appears t h a t the i o n i z a t i o n of these compounds i s governed at l e a s t a p p r o x i m a t e l y by H _ . However, f o r some o t h e r s , such as 4 - n i t r o - 2 , 3 , 5 , 6 - t e t r a m e t h y l a n i l i n e ( s l o p e = 1 . 1 8 ) , the s l o p e s of the p l o t s v a r y c o n s i d e r a b l y from u n i t y i n d i c a t i n g t h a t the i o n i z a t i o n of these compounds i s not governed by H _ . The cause of t h i s v a r i a n c e i n the b e h a v i o u r of the 4 - n i t r o a n i , l i n e d e r i v a t i v e s i s not known. The i o n i z a t i o n of one n o n - n i t r o a r o m a t i c amine, 2 , 2 ' - d i p y r i d y l a m i n e ( s l o p e = 0 . 8 5 ) , i s a l s o not governed by H _ . B . I n t e r p r e t a t i o n of S o l v e n t B a s i c i t y The a d d i t i o n of d i m e t h y l s u l f o x i d e t o aqueous s o l u t i o n s of h y d r o x i d e i o n has a g r e a t e f f e c t on the b a s i c i t y of these s o l u t i o n s . Thus the H _ of 0.011 molar tetramethylammonium h y d r o x i d e r i s e s from 12 i n water t o 26 i n 99 .5 mole % DMSO, an i n c r e a s e of 14 powers of t e n i n b a s i c i t y (as measured by i t s e f f e c t on a r y l a m i n e i o n i z a t i o n ) . In F i g u r e 1 i t can be seen t h a t the b a s i c i t y i n c r e a s e s s t e a d i l y as the s o l v e n t c o m p o s i t i o n proceeds from aqueous t o 85 mole % DMSO. In t h i s r e g i o n the p l o t of H _ v e r s u s mole % DMSO i s n e a r l y l i n e a r w i t h s l o p e , d ( H _ ) / d ( m o l e % DMSO), of about 0 . 1 0 . Above 85 mole % DMSO the s l o p e i n c r e a s e s and the b a s i c i t y r i s e s v e r y q u i c k l y as the water c o n c e n t r a t i o n approaches z e r o . From 95 t o 97 .5 mole % 6 6 DMSO, H _ i n c r e a s e s by almost one u n i t and from 97 .5 to 99 .0 mole % H _ i n c r e a s e s a g a i n by one u n i t . What are the causes f o r the g r e a t enhancement i n b a s i c i t y of h y d r o x i d e i o n i n DMSO s o l u t i o n s ? One approach t o answering t h i s q u e s t i o n i s t o c o n s i d e r the e q u i l i b r i u m between h y d r o x i d e i o n and i n d i c a t o r a c i d , HA, i n which the h y d r o x i d e i o n i s c o n s i d e r e d to be i n t i m a t e l y s o l v a t e d by a number of water m o l e c u l e s . The number n can be c o n s i d e r e d e i t h e r as the h y d r a t i o n number of the 47 h y d r o x i d e i o n o r , i f the i n d i c a t o r or i t s a n i o n are a l s o i n t i m a t e l y s o l v a t e d , as the d i f f e r e n c e i n s o l v a t i o n 42 numbers between the l e f t and r i g h t s i d e s of e q u a t i o n (31) . The e f f e c t of a d d i n g DMSO t o the system i s t o d r i v e t h i s e q u i l i b r i u m t o the r i g h t , an e f f e c t t h a t i s i n t e r p r e t e d as an i n c r e a s e i n b a s i c i t y of the h y d r o x i d e i o n . I t i s p o s s i b l e t o d e r i v e the f o l l o w i n g e x p r e s s i o n f o r H_ i n terms of the e q u i l i b r i u m i n e q u a t i o n (31) . (0H~) aq + HA A " + (n+l)H20 (31) (OH") H = l o g (n + 1) l o g (H 2 0) - l o g (32) K w 67 On t h i s b a s i s the change i n H_ w i t h i n c r e a s i n g c o n c e n t r a t i o n of DMSO can be a t t r i b u t e d to changes i n h y d r o x i d e i o n a c i t i v i t y , i n water a c t i v i t y and i n the , a c t i v i t y c o e f f i c i e n t r a t i o f A - / f H A . I t i s d i f f i c u l t t o p r e d i c t the e f f e c t upon the l a s t term i n e q u a t i o n (32) of c h a n g i n g the s o l v e n t from water t o DMSO. S i n c e such p o l a r a p r o t i c s o l v e n t s as 38 DMSO are poor a t s o l v a t i n g a n i o n s the a c t i v i t y c o e f f i c i e n t f A - of an amine a n i o n p r o b a b l y i n c r e a s e s i n the change from water t o DMSO. T h i s i n c r e a s e i s not as l a r g e as t h a t s u f f e r e d by the h y d r o x i d e i o n s i n c e a n i o n s l a r g e r than the c h l o r i d e 87 88 i o n are not c o n s i d e r e d t o be i n t i m a t e l y h y d r a t e d ' i n aqueous s o l u t i o n . At any r a t e , the term l o g f A ~ / f H A p r o b a b l y i n c r e a s e s as the amount of DMSO i n the system i n c r e a s e s and c o n s e q u e n t l y w i l l t e n d t o decrease H _ - The l a r g e i n c r e a s e s i n H _ upon the a d d i t i o n of DMSO t o the system must be due to i n c r e a s e s i n the a c t i v i t y of the h y d r o x i d e i o n and t o d e c r e a s e s i n the water a c t i v i t y . The decrease i n water a c t i v i t y i s not due j u s t t o a d i l u t i o n e f f e c t but a l s o t o the a b i l i t y of DMSO t o complex w i t h water by f o r m a t i o n of s t r o n g hydrogen b o n d s 8 9 ' 9 0 . T h i s f a c t i s a l s o e v i d e n t f rom the l a r g e h e a t s of m i x i n g of DMSO and 77 water . Data f o r the a c t i v i t y of water i n DMSO-water m i x t u r e s at 2 5 ° are not a v a i l a b l e , however data are a v a i l a b l e 68 n 91 f o r 70 . They show t h a t as the water content d e c r e a s e s and the DMSO c o n t e n t i n c r e a s e s not o n l y does the a c t i v i t y of the water decrease but a l s o the a c t i v i t y c o e f f i c i e n t , f w a t e r ' s t e a d i l y d e c r e a s e s . The i n c r e a s e i n H_ due t o decrease of the water a c t i v i t y w i l l depend on the s t a t e of h y d r a t i o n of the h y d r o x i d e i o n and t o a much l e s s e r e x t e n t on the h y d r a t i o n of the i n d i c a t o r and i t s a n i o n . As was mentioned above , l a r g e a n i o n s such as those of a n i l i n e and d i p h e n y l a m i n e are not c o n s i d e r e d t o be e x t e n s i v e l y h y d r a t e d . On the o ther hand, such s m a l l a n i o n s as the f l u o r i d e and h y d r o x i d e i o n s are 87 8R s t r o n g l y h y d r a t e d i n aqueous s o l u t i o n 5 . E s t i m a t e s of the number of water m o l e c u l e s i n the h y d r a t i o n s h e l l of ( 4 7 the h y d r o x i d e i o n have been made. Y a g i l and Anbar found t h a t the H _ v a l u e s f o r aqueous sodium and p o t a s s i u m h y d r o x i d e s c o u l d be c a l c u l a t e d assuming a h y d r a t i o n number of 3. Other e s t i m a t e s of the h y d r a t i o n number vary from 4 8 8 to 6 9 2 > 9 3 „ i f the number n i n e q u i l i b r i u m ( 3 1 ) and i n e q u a t i o n (32) i s i d e n t i f i e d w i t h the h y d r a t i o n number of the h y d r o x i d e i o n then the p o s i t i o n of the e q u i l i b r i u m and t h e r e f o r e the b a s i c i t y of the s o l u t i o n depend on at l e a s t the f o u r t h power of the water a c t i v i t y . T h i s dependence of H _ on water a c t i v i t y must account f o r a p a r t of the i n c r e a s e i n H_ w i t h i n c r e a s e i n 69 DMSO c o n t e n t e s p e c i a l l y i n the l i n e a r p o r t i o n of the curve i n F i g u r e 1. However, i t cannot account f o r a l l the i n c r e a s e i n t h i s r e g i o n . For example , i f the H_ i s assumed t o depend on the f o u r t h power of the water a c t i v i t y and 91 the a c t i v i t y data f o r DMSO-water at 7 0 ° i s assumed t o approximate t h a t at 2 5 ° then the change of H _ f o r 0,011 molar h y d r o x i d e on p a s s i n g from water t o 50 mole % DMSO s h o u l d be about 2 u n i t s . ( T h i s i s the change due to the mass a c t i o n e f f e c t and not due t o the change i n h y d r o x i d e a c t i v i t y . ) F i g u r e 1 shows t h a t the a c t u a l change i n H _ i s 5 .5 u n i t s . T h u s , the i n c r e a s e i n b a s i c i t y upon a d d i n g DMSO t o aqueous s o l u t i o n s of h y d r o x i d e i o n i s due p a r t l y to the r e d u c t i o n i n water a c t i v i t y and i t s subsequent mass a c t i o n e f f e c t on the e q u i l i b r i u m between h y d r o x i d e i o n and a c i d and p a r t l y t o the i n c r e a s e d a c t i v i t y of the h y d r o x i d e i o n . The a c t i v i t y c o e f f i c i e n t of the h y d r o x i d e must show l a r g e i n c r e a s e s even at low DMSO c o n c e n t r a t i o n s s i n c e r e a s o n a b l e assumptions about water a c t i v i t y and h y d r a t i o n numbers do not account f o r the l a r g e i n c r e a s e i n H_ i n t h i s r e g i o n of s o l v e n t c o m p o s i t i o n . I t s h o u l d be p o i n t e d out t h a t o n l y at c o m p o s i t i o n s g r e a t e r than 99 mole % DMSO does the water c o n c e n t r a t i o n become so low as to approach t h a t of the h y d r o x i d e i o n . In f a c t , i n the most, b a s i c 70 s o l u t i o n s t u d i e d , 99.59 mole % DMSO, the r a t i o of c o n c e n t r a t i o n s of water t o h y d r o x i d e i o n i s s l i g h t l y g r e a t e r than 5. An e x p l a n a t i o n of the i n c r e a s e i n h y d r o x i d e i o n a c t i v i t y at low DMSO c o n c e n t r a t i o n s may l i e i n the e f f e c t of DMSO on the s t r u c t u r e of water . L i q u i d water i s c o n s i d e r e d to r e t a i n much of the open s t r u c t u r e of i c e i n which the water m o l e c u l e s are hydrogen bonded t o f o u r o ther 94a water m o l e c u l e s i n a t e t r a h e d r a l a r r a y . S m a l l i o n s and m u l t i v a l e n t i o n s i n c r e a s e the v i s c o s i t y of water and are b e l i e v e d t o promote f o r m a t i o n of an i c e - l i k e s t r u c t u r e i n the water m o l e c u l e s beyond the n e a r e s t ne ighbour m o l e c u l e s . Such a n i o n s as F~ and O H - b e l o n g to t h i s c l a s s and are s a i d * w , . • 9 4 b t o be s t r u c t u r e - m a k i n g i o n s . L a r g e r i o n s decrease the v i s c o s i t y of water and are b e l i e v e d to break down the i c e - l i k e s t r u c t u r e of water beyond the n e a r e s t ne ighbour m o l e c u l e s . T h i s c l a s s i s s a i d t o be s t r u c t u r e - b r e a k i n g and - - 94b c o n t a i n s such a n i o n s as C l , Br , I and NOg . Some i o n s are i n t e r m e d i a t e i n c h a r a c t e r and have l i t t l e e f f e c t on the s t r u c t u r e of l i q u i d w a t e r . Q 5 F r a n k has p o i n t e d out t h a t i o n s of o p p o s i t e c h a r a c t e r i n the same s o l u t i o n b r i n g about an i n c r e a s e i n t h e i r a c t i v i t y c o e f f i c i e n t s over t h a t t o be e x p e c t e d i f they were not s t r u c t u r e - a l t e r i n g . C o n s i d e r , f o r example , a s t r u c t u r e - m a k i n g c a t i o n and a s t r u c t u r e - b r e a k i n g a n i o n . The 71 c a t i o n tends t o produce more s t r u c t u r e i n the water and c o n s e q u e n t l y c r e a t e s a h o s t i l e environment f o r the a n i o n , which i n t u r n " w a n t s " to break down the s t r u c t u r e d e n v i r o n m e n t . The r e v e r s e argument a l s o a p p l i e s . The net r e s u l t i s t h a t the i o n s t e n d to s a l t each o ther out of s o l u t i o n and thus produce an i n c r e a s e i n t h e i r a c t i v i t y c o e f f i c i e n t s . These e f f e c t s can be s u r p r i s i n g l y l a r g e . 95 F r a n k has i n t e r p r e t e d some e . m . f . measurements as i n d i c a t i n g t h a t the a c t i v i t y c o e f f i c i e n t of the i o d i d e i o n i n 0 .03 molar te t rabutylammonium i o d i d e i s 8.65 t imes as l a r g e as the a c t i v i t y c o e f f i c i e n t of the i o d i d e i o n i n 0.03 molar p o t a s s i u m i o d i d e . The i o d i d e i o n i s s t r u c t u r e - b r e a k i n g , the te t rabutylammonium i o n i s s t r o n g l y s t r u c t u r e - making and the p o t a s s i u m i o n i s weakly s t r u c t u r e a l t e r i n g . The i n c r e a s e d a c t i v i t y of the i o d i d e i o n i n the f i r s t s o l u t i o n i s a r e s u l t of the s t r o n g l y opposed c h a r a c t e r s of the te"trabutylammonium and i o d i d e i o n s . As was mentioned above, the h y d r o x i d e i o n i s a s t r u c t u r e - m a k i n g i o n . C o n s e q u e n t l y , a n y t h i n g t h a t breaks down the s t r u c t u r e of water w i l l i n c r e a s e the a c t i v i t y c o e f f i c i e n t of the h y d r o x i d e i o n and, t h e r e f o r e , the b a s i c i t y of the s o l u t i o n . The a d d i t i o n of DMSO t o the s o l u t i o n may have t h i s e f f e c t . The a b i l i t y of DMSO to form s t r o n g 89 90 hydrogen bonds w i t h water m o l e c u l e s ' may p e r m i t i t t o break down the p a r t i a l i c e s t r u c t u r e of w a t e r . T h i s i s 72 s u p p o r t e d by the f a c t t h a t the d e n s i t y of DMSO-water 77 m i x t u r e s i s g r e a t e r than t h a t e x p e c t e d from a d d i t i v i t y T h i s would not be e x p e c t e d i f the open, i c e - l i k e s t r u c t u r e of water p e r s i s t e d . F u r t h e r , the a d d i t i o n of DMSO t o water causes the water p r o t o n magnetic resonance 96 s i g n a l t o s h i f t t o h i g h e r magnet ic f i e l d , an e f f e c t t h a t 97 i s g e n e r a l l y i n t e r p r e t e d as a r e d u c t i o n i n hydrogen b o n d i n g , T h i s i s a l s o c o n s i s t e n t w i t h a break-down of the water s t r u c t u r e . A l l the e v i d e n c e , however, i s not c o n s i s t e n t w i t h t h i s p i c t u r e . The v i s c o s i t y of DMSO-water m i x t u r e s i s g r e a t e r than would be e x p e c t e d from a d d i t i v i t y whereas break-down of the hydrogen-bonded i c e - l i k e s t r u c t u r e of water s h o u l d be accompanied by an i n c r e a s e d f l u i d i t y 9 4 * 3 . I t i s p o s s i b l e , t h e n , t h a t the b a s i c i t y of h y d r o x i d e i o n s o l u t i o n s i s i n c r e a s e d at low DMSO c o n c e n t r a t i o n s due to b r e a k i n g down of the water s t r u c t u r e . T h i s argument, however, has n e g l e c t e d the e f f e c t s of these changes on the a c t i v i t i e s of the i n d i c a t o r and i t s a n i o n . I t i s p o s s i b l e t h a t the e f f e c t s would be s i m i l a r f o r b o t h s p e c i e s because of the r e l a t i v e l y s m a l l s t r u c t u r a l changes of the amines on i o n i z a t i o n and the charge d i s p e r s a l over one or two a r o m a t i c r i n g s i n the a n i o n . In t h i s case the e f f e c t s on the e q u i l i b r i u m i n e q u a t i o n (31) would c a n c e l . 73 The cause of the r a p i d u p - s w i n g i n H_ as the s o l v e n t changes from 80 t o 100 mole % DMSO i s most p r o b a b l y the break-down of the h y d r a t i o n s h e l l of the h y d r o x i d e i o n brought about by the e f f i c i e n c y w i t h which the DMSO competes w i t h the h y d r o x i d e i o n f o r the water m o l e c u l e s . A decrease i n the number of water m o l e c u l e s s o l v a t i n g the h y d r o x i d e i o n b r i n g s about a g r e a t i n c r e a s e i n i t s a c t i v i t y and t h e r e f o r e i n the b a s i c i t y of the s o l u t i o n . T h i s i s s u p p o r t e d by the v e r y low s o l u b i l i t y of sodium h y d r o x i d e i n DMSO (upper l i m i t of 7.6 x 1 0 " 4 m o l a r ) 9 8 . I t might be p o i n t e d out t h a t DMSO p o s s e s s e s the a b i l i t y not o n l y t o produce l a r g e changes i n e q u i l i b r i u m p r o c e s s e s , as o b s e r v e d i n t h i s work, but a l s o i n k i n e t i c p r o c e s s e s . The base c a t a l y z e d r a c e m i z a t i o n of c e r t a i n h y d r o c a r b o n s 7 0 , the s a p o n i f i c a t i o n of e s t e r s 9 0 ' 9 9 and n u c l e o p h i l i c a r o m a t i c s u b s t i t u t i o n 1 0 0 a l l show d r a m a t i c i n c r e a s e s i n r a t e when the s o l v e n t i s changed from water or a l c o h o l to DMSO or m i x t u r e s of these s o l v e n t s w i t h DMSO. C . V a l i d i t y of the H 0 F u n c t i o n The H Q s c a l e i n e t h a n o l - a q u e o u s s u l f u r i c a c i d has been d e t e r m i n e d u s i n g i n d i c a t o r s of one s t r u c t u r a l t y p e , s u b s t i t u t e d d i p h e n y l a m i n e s . T h i s i s an i m p o r t a n t p o i n t , c o n s i d e r i n g the s e n s i t i v i t y of H Q f u n c t i o n s t o the 74 s t r u c t u r e of the b a s i c c e n t e r . U n f o r t u n a t e l y , the measure ments c o u l d not be made i n c o m p l e t e l y aqueous s u l f u r i c a c i d because of i n s u f f i c i e n t s o l u b i l i t y of the d i p h e n y l a m i n e s . The i n t r o d u c t i o n of e t h a n o l i n t o the s o l v e n t p r e c l u d e s any d i r e c t comparison of the r e s u l t s o b t a i n e d i n t h i s work 0*3 04 w i t h the r e s u l t s o b t a i n e d u s i n g p r i m a r y and t e r t i a r y a r o m a t i c amines . The i n t r o d u c t i o n of e t h a n o l i n t o the s o l v e n t a l s o makes i t p a r t i c u l a r l y i m p o r t a n t t h a t i n d i c a t o r s of one type be u s e d . T h i s can be i l l u s t r a t e d by a r e s u l t o b t a i n e d w i t h 4 - n i t r o a n i l i n e and d i p h e n y l a m i n e . F i r s t , e q u a t i o n (29) may be r e a r r a n g e d as f o l l o w s : l o g I A - l o g I D = P K B H + - P K B H g - l o g VBH'/ D \ -B (33) where " A " and " D " r e f e r t o 4 - n i t r o a n i l i n e and d i p h e n y l a m i n e , r e s p e c t i v e l y , and I ' r e f e r s t o the r a t i o of the c o n c e n t r a t i o n s of ammonium i o n t o amine. I t w i l l be r e c a l l e d t h a t the q u a n t i t y on the l e f t s i d e of e q u a t i o n (33) i s e q u a l t o 0.22 and the l a s t term i s z e r o i n aqueous s o l u t i o n s of h y d r o c h l o r i c a c i d . In s o l u t i o n s of s u l f u r i c a c i d of 0 .03 t o 0 .9 molar i n 20 volume % e t h a n o l - w a t e r the q u a n t i t y on the l e f t s i d e of e q u a t i o n (33) i s 0.07 - . 01 . S i n c e the d i f f e r e n c e between 75 the PKgjj+ v a l u e s f o r the two amines i s 0.22 the l a s t term i n the e q u a t i o n cannot be z e r o , t h a t i s , the Hammett a c t i v i t y c o e f f i c i e n t p o s t u l a t e 1 0 i s not obeyed. C o n s e q u e n t l y , 4 - n i t r o a n i l i n e cannot be used t o anchor an H Q s c a l e f o r s e c o n d a r y amines i n 20 volume % e t h a n o l - w a t e r . The Hammett p o s t u l a t e appears t o be obeyed i n t h i s s o l v e n t when amines of the same type are u s e d . From p r e l i m i n a r y measurements i n aqueous d i l u t e s u l f u r i c a c i d the d i f f e r e n c e i n the pKgjj+ v a l u e s f o r 4 -methoxydiphenylamine and d i p h e n y l a m i n e was found to be 0 .59 . In 20 volume % e t h a n o l the d i f f e r e n c e was found t o be 0.58 (Table I V ) . The f a c t t h a t the Hammett p o s t u l a t e i s not obeyed when comparing the p r o t o n a t i o n of a p r i m a r y w i t h a secondary amine i n 20 volume % ethanol-water i s p r o b a b l y a r e s u l t of the importance of hydrogen b o n d i n g i n the s o l v a t i o n of t h e i r 26 28 86 ammonium i o n s 5 5 and the s e n s i t i v i t y of the s o l v a t i o n t o s o l v e n t changes In T a b l e V , i t can be seen t h a t the agreement among the H Q v a l u e s c a l c u l a t e d f o r a g i v e n s o l u t i o n u s i n g d i f f e r e n t , i n d i c a t o r s i s g e n e r a l l y v e r y good. F i g u r e V shows t h a t f o r the most p a r t c l o s e l y spaced i n d i c a t o r s w i t h a c c u r a t e l y p a r a l l e l i o n i z a t i o n s l o p e s have been u s e d . 76 The pKBjj+ v a l u e s f o r almost a l l the d i p h e n y l a m i n e s used i n t h i s work have not been h i t h e r t o d e t e r m i n e d . Hammett g and Deyrup , i n t h e i r o r i g i n a l work i n s u l f u r i c a c i d , o b t a i n e d a v a l u e of -2 .50 f o r the pKgjj+ of 4 - n i t r o d i p h e n y l - amine. T h i s had been d e t e r m i n e d w i t h r e f e r e n c e t o an H Q 28 s c a l e c o n s t r u c t e d u s i n g a n i l i n e i n d i c a t o r s . T a f t has shown t h a t the i o n i z a t i o n b e h a v i o u r of t h i s compound i n s u l f u r i c a c i d i s anomalous when compared to the b e h a v i o u r of the p r i m a r y amines used by Hammett and D e y r u p . The H Q v a l u e of 5 .5 molar s u l f u r i c a c i d i s 12 -2 .50 d e t e r m i n e d u s i n g p r i m a r y amines , and 4 - n i t r o d i p h e n y l - amine i s h a l f i o n i z e d i n t h i s s o l u t i o n . U s i n g the t e r t i a r y 24 amine s c a l e , the H Q of 5 .5 molar s u l f u r i c a c i d i s - 3 . 5 8 . C o n s e q u e n t l y , i f the " p K B H + " va lue f o r t h i s compound had been d e t e r m i n e d w i t h r e f e r e n c e t o the second H Q s c a l e a v a l u e of - 3 . 5 8 would have been o b t a i n e d . Of c o u r s e , the t r u e pKgjj+ v a l u e f o r 4 - n i t r o d i p h e n y l a m i n e cannot, be o b t a i n e d from e i t h e r of these s c a l e s but must be determined w i t h r e f e r e n c e t o an H Q f u n c t i o n f o r secondary amines . There i s no reason t o b e l i e v e t h a t the H Q of 5.5 molar s u l f u r i c a c i d f o r secondary amines would not l i e between the v a l u e s f o r p r i m a r y (-2.50) and t e r t i a r y (-3.58) amines . T h i s a l s o means t h a t the p K Rti+ v a l u e f o r 4 - n i t r o d i p h e n y l a m i n e 77 s h o u l d a l s o l i e between the same l i m i t s . The pKgjj+ found i n t h i s work i s - 3 . 1 3 and l i e s near the middle of these e x t r e m e s . D . Comparison of the H Q F u n c t i o n f o r D i p h e n y l a m i n e s w i t h  Other H 0 F u n c t i o n s As was mentioned b e f o r e , the H Q s c a l e o b t a i n e d i n t h i s work i s not d i r e c t l y comparable w i t h those d e t e r m i n e d f o r p r i m a r y and t e r t i a r y amines because of the use of e t h a n o l i n the s o l v e n t . J a f f e and c o - w o r k e r s ' 0 ' ' ° have d e t e r m i n e d an H 0 s c a l e f o r the p r o t o n a t i o n of azobenzenes (XI) i n the same s o l v e n t system t h a t has been used i n t h i s work. F i g u r e 6 i s a p l o t of H Q v e r s u s m o l a r i t y of s u l f u r i c a c i d f o r : ( i ) azobenzenes i n 20 volume % e t h a n o l - a q u e o u s s u l f u r i c 78 79 a c i d ' , ( i i ) d i p h e n y l a m i n e s i n 20 volume % e t h a n o l - aqueous s u l f u r i c a c i d , ( i i i ) a n i l i n e s i n aqueous s u l f u r i c 12 a c i d , and ( i v ) t e r t i a r y a r o m a t i c amines i n aqueous s u l f u r i c . ,24 a c i d X I FIGURE 6 Ho ACIDITY FUNCTIONS IN SULFURIC ACID MEDIA DIPHENYLAMINES) IN 20 VOL % ETHANOL-AQUEOUS • • AZOBENZENES J SULFURIC ACID PRIMARY AROMATIC AMINES 1 IN AQUEOUS TERTIARY AROMATIC AMINESJ SULFURIC ACID CONCENTRATION OF H2S04 (MOLARITY) -si oo 79 su a For purposes of d i s c u s s i o n the s c a l e f o r p r i m a r y amines i n aqueous s u l f u r i c a c i d w i l l be c a l l e d H Q ' , the s c a l e f o r d i p h e n y l a m i n e s i n 20 volume % e t h a n o l - a q u e o u s l f u r i c a c i d w i l l be c a l l e d H Q ' ' , the s c a l e f o r t e r t i a r y r o m a t i c amines i n aqueous s u l f u r i c a c i d w i l l be c a l l e d H 0 ' ' ' , and the s c a l e f o r azobenzenes i n 20 volume % e t h a n o l - aqueous s u l f u r i c a c i d w i l l be c a l l e d H Q ^ = ^ . F i r s t , i t s h o u l d be p o i n t e d out t h a t i t i s p o s s i b l e t h a t the H 0 N = N s c a l e of Yeh and J a f f £ 7 9 s h o u l d be s h i f t e d to more n e g a t i v e H Q v a l u e s . T h i s a r i s e s because of the manner i n which t h e i r s c a l e was anchored to the r e g i o n of d i l u t e a c i d . Azobenzenes of s u f f i c i e n t b a s i c i t y t o p r o t o n a t e i n t h i s r e g i o n were not a v a i l a b l e and so 4- and 2 - n i t r o a n i l i n e were used as i n d i c a t o r s . I t has j u s t been shown t h a t the Hammett p o s t u l a t e i s not obeyed i n 20 volume % e t h a n o l - water when comparing the p r o t o n a t i o n of a p r i m a r y and secondary amine. There i s no reason to b e l i e v e t h a t i t would be obeyed on comparing the p r o t o n a t i o n of a p r i m a r y amine and an azobenzene. Azobenzene b e a r s c l o s e s t resemblance t o a t e r t i a r y amine because of the l a c k . o f hydrogens a t t a c h e d to the n i t r o g e n atoms. T h i s would cause the d i s c r e p a n c y i n the apparent pK v a l u e s o b t a i n e d i n the comparison of an azobenzene w i t h an a n i l i n e t o be g r e a t e r than t h a t o b s e r v e d i n the case of 4 - n i t r o a n i I i n e and d i p h e n y l a m i n e . The N=N d i r e c t i o n of t h i s d i s c r e p a n c y i s such t h a t the H Q s c a l e 80 would be s h i f t e d t o more n e g a t i v e v a l u e s had i t been based i n the d i l u t e a c i d r e g i o n on the i o n i z a t i o n of an azobenzene w i t h known pKgjj+. I t i s not p o s s i b l e t o e s t i m a t e the magnitude of t h i s s h i f t . F i g u r e 6 shows t h a t at c o n c e n t r a t i o n s of a c i d l e s s than 4 molar the H Q N = N s c a l e i s s l i g h t l y more p o s i t i v e than the H Q ' ' s c a l e but at g r e a t e r c o n c e n t r a t i o n s the H 0 ^ = ^ s c a l e becomes p r o g r e s s i v e l y more n e g a t i v e than the H 0 ' ' s c a l e . C o n s i d e r i n g the d i s c u s s i o n above, the r e l a t i v e p o s i t i o n s of the two s c a l e s might a c t u a l l y be r e v e r s e d i n the low c o n c e n t r a t i o n r a n g e . A t any r a t e , the d i v e r g e n c e of the two s c a l e s at h i g h a c i d c o n c e n t r a t i o n i s not unexpected , I t can be seen t h a t the H Q ' and H Q ' ' ' s c a l e s d i v e r g e as the a c i d c o n c e n t r a t i o n i n c r e a s e s . I f the cause of t h i s d i v e r g e n c e i s the s p e c i f i c i n t e r a c t i o n of the ammonium i o n s 25 28 of the p r i m a r y and t e r t i a r y amines w i t h s o l v e n t m o l e c u l e s ' then a d i v e r g e n c e would a l s o be e x p e c t e d f o r the H 0 ' ' and N=N H Q s c a l e s . Azobenzenes resemble t e r t i a r y amines and c o n s e q u e n t l y a d i f f e r e n c e i n the H 0 s c a l e s f o r azobenzenes and f o r d i p h e n y l a m i n e s (secondary amines) would be e x p e c t e d . At a c i d c o n c e n t r a t i o n s of l e s s than 3 molar both the H Q ' and H Q ' ' ' s c a l e s i n aqueous a c i d are more n e g a t i v e than the H 0 ' 1 s c a l e i n 20 volume % e t h a n o l - a q u e o u s a c i d . At h i g h e r c o n c e n t r a t i o n s of a c i d , however, the s c a l e i n 20 81 volume % e t h a n o l d e c r e a s e s at a g r e a t e r r a t e than e i t h e r of the aqueous s c a l e s . The f i r s t o b s e r v a t i o n i s c o n s i s t e n t w i t h the f a c t t h a t the a d d i t i o n of e t h a n o l t o aqueous s o l u t i o n s tends to i n c r e a s e the p H 7 9 ' 1 0 1 . A l s o Braude and S t e r n 1 0 2 have shown t h a t H Q i n 0 .1 molar h y d r o c h l o r i c a c i d i n c r e a s e s on p r o c e e d i n g from aqueous t o 55 mole % e t h a n o l - w a t e r s o l u t i o n s and then d e c r e a s e s u n t i l i n e t h a n o l H Q i s l e s s (more a c i d i c ) than i n w a t e r . The second o b s e r v a t i o n , t h a t the H Q ' ' f u n c t i o n i n the e t h a n o l - a q u e o u s s u l f u r i c a c i d m i x t u r e s d e c r e a s e s (becomes more a c i d i c ) at a g r e a t e r r a t e than e i t h e r the H 0 * or H 0 ' ' ' f u n c t i o n s i n aqueous a c i d at the h i g h e r a c i d c o n c e n t r a t i o n s , can be e x p l a i n e d , as p o i n t e d out by Yeh and J a f f e , on the b a s i s of two e f f e c t s . The f i r s t i s t h a t at a c o n s t a n t m o l a r i t y of a c i d the mole f r a c t i o n of H2SO4 i n 20 volume % e t h a n o l - a q u e o u s a c i d i s g r e a t e r than i t i s i n aqueous s o l u t i o n due t o the g r e a t e r m o l e c u l a r weight and molar volume of the e t h a n o l as compared t o the w a t e r . At h i g h a c i d c o n c e n t r a t i o n s t h i s becomes i m p o r t a n t s i n c e there i s l e s s h y d r o x y l i c s o l v e n t p r e s e n t t o s o l v a t e the p r o t o n s i n the e t h a n o l i c s o l u t i o n s than there i s i n the aqueous s o l u t i o n s . The second e f f e c t stems from the f a c t t h a t e t h a n o l i s a weaker 102 base than water . T h i s means t h a t E t O H * i s a s t r o n g e r a c i d than H 3 0 + . As the m o l a r i t y of s u l f u r i c a c i d i n c r e a s e s , the c o n c e n t r a t i o n of water d e c r e a s e s w h i l e the c o n c e n t r a t i o n 82 of e t h a n o l remains c o n s t a n t i n the e t h a n o l - w a t e r - s u l f u r i c a c i d s y s t e m . T h i s l e a d s t o an i n c r e a s i n g amount of EtOHg as compared t o the amount of I ^ O * and c o n s e q u e n t l y t o a g r e a t e r a c i d i t y f o r the s o l u t i o n because of the g r e a t e r i n h e r e n t a c i d i t y of EtOHrj. E . C o r r e l a t i o n of S t r u c t u r e w i t h A c i d i t y One of the i m p o r t a n t consequences of the g r e a t b a s i c i t y of s o l u t i o n s of h y d r o x i d e i o n i n DMSO-water m i x t u r e s i s t h a t i t has a l l o w e d the pKjj A v a l u e s of a r o m a t i c amines t h a t do not p o s s e s s the n i t r o group as a s u b s t i t u e n t t o be d e t e r m i n e d . Hammett a c i d i t y s c a l e s , i n both s t r o n g a c i d and base m e d i a , u s i n g amine i n d i c a t o r s , have a l l made e x c l u s i v e use of n i t r o - s u b s t i t u t e d a r o m a t i c amines . T h i s has r e s u l t e d from n e c e s s i t y r a t h e r than c h o i c e . However, the e x t e n s i o n of the H_ s c a l e t o v a l u e s beyond 19 has a l l o w e d the s t u d y of the a c i d i t y of a s e r i e s of d i p h e n y l a m i n e s w i t h a wide v a r i e t y of s u b s t i t u e n t s whose e f f e c t s on the a c i d i t y of d i p h e n y l a m i n e are not dominated by the presence of a n i t r o s u b s t i t u e n t . I n s p e c t i o n of T a b l e I w i l l show t h a t the pKjj A of d i p h e n y l a m i n e i s v e r y s e n s i t i v e t o s u b s t i t u e n t e f f e c t s . The pKjj A v a l u e s of a l l the m o n o s u b s t i t u t e d d i p h e n y l a m i n e s do not c o r r e l a t e w i t h the Hammett CP v a l u e s nor w i t h any one m o d i f i c a t i o n of them. However, i f o n l y d i p h e n y l a m i n e s w i t h 83 w e l l - b e h a v e d s u b s t i t u e n t s are c o n s i d e r e d , a good c o r r e l a t i o n i s o b t a i n e d between p K H A and CT . From a p l o t of l o g K H A v e r s u s , j - l 0 3 a ^ Q J , ^ e u n s u b s t i t u t e d , 4 - m e t h y l , 3-methoxy, 4 - c h l o r o , 3 - c h l o r o , and 3 - n i t r o d i p h e n y l a m i n e s a p v a l u e 104 of 4 .07 i s f o u n d * . The c o r r e l a t i o n c o e f f i c i e n t , r , f o r t h i s p l o t i s 0 .991 . The p l o t i s shown i n F i g u r e 7. The magnitude of the p v a l u e i s a measure of the s e n s i t i v i t y of the a c i d s t r e n g t h of d i p h e n y l a m i n e t o s u b s t i t u e n t s . I t s h o u l d be compared t o p v a l u e s of 1.00 f o r b e n z o i c a c i d s 1 0 4 , 2 .23 f o r p h e n o l s 1 0 5 , and 2.89 f o r a n i l i n i u m i o n s 1 0 5 f o r aqueous systems at 2 5 ° . Thus the a c i d i t y of d i p h e n y l a m i n e i s more s e n s i t i v e t o s u b s t i t u e n t e f f e c t s than are the a c i d i t i e s of b e n z o i c a c i d , phenol or the a n i l i n i u m i o n . The pKjj A v a l u e s f o r 3 , 4 ' d i c h l o r o and 3 - t r i f l u o r o - m e t h y l d i p h e n y l a m i n e were not u s e d i n the c o r r e l a t i o n i n F i g u r e 7; the f i r s t because the compound has two s u b s t i t u e n t s i n d i f f e r e n t r i n g s and the second because the <j~ v a l u e of the s u b s t i t u e n t i s not w e l l e s t a b l i s h e d . I f , however, the * In t h i s and subsequent c o r r e l a t i o n s the method of l e a s t mean squares has been used t o c a l c u l a t e the best, s t r a i g h t l i n e . The e q u a t i o n s g i v e n by J a f f e ^ ° 4 have been u s e d f o r t h i s p u r p o s e . 8 4 FIGURE 7 HAMMETT CORRELATION OF THE ACIDITY OF GUSBSTITUTED DIPHENYLAMINES a 4-NH 2 \ f J 4- O C H 3 - 2 3 o\4-- C H 3 - 2 2 \ G 3-OCH3 \ \ r=.99i ON4-CI - 21 © \ 3 - C I \)< 3-CF3 - 2 0 X 3 (4 ' -diCI P K H A 3 - N O 2 - 19 \ . A 4-S0 2CH 3 - 13 \ . - 17 ° - - cr VALUES U^ED IN CORRELATION \/ /\ --cr VALUES 'NOT USED IN CORRELATION •- S° VALUES - 1 6 A- --6~ VALUES 4-N02 L SIGMA .3 -.2 -.1 l 1 i 0 .1 .2 .3 .4 .5 .6 .7 .8 .9 10 II 1.2 1 1 i 1 1 > 1 1 1 1 1 1 1 85 sum of the CH v a l u e s f o r the two c h l o r o groups and the 1 Ofi v a l u e of 0 .49 f o r the 3 - t r i f l u o r o m e t h y l g r o u p , o b t a i n e d from the i o n i z a t i o n of a n i l i n i u m i o n s , are used then the p o i n t s f o r these two compounds f a l l near the l i n e . There are f o u r compounds, 4 - a m i n o - , 4-methoxy, 4 - m e t h y l s u l f o n y l , and 4 - n i t r o d i p h e n y l a m i n e , f o r which the P K HA v a l u e s d o n ° t c o r r e l a t e w i t h 0~. T h i s i s not a l t o g e t h e r s u r p r i s i n g s i n c e the s u b s t i t u e n t s i n these compounds d i s p l a y v a r i a b l e resonance e f f e c t s depending on the na ture of the r e a c t i o n s i t e 1 ' 3 ' 1 0 4 , The a c i d i c s i t e i n d i p h e n y l  amines i s a t t a c h e d d i r e c t l y to the a r o m a t i c r i n g w h i l e i t i s not i n b e n z o i c a c i d s (whose i o n i z a t i o n s are used to determine c r v a l u e s 1 ^ 3 ) . . I t might be e x p e c t e d , t h e n , t h a t the f o u r s u b s t i t u e n t s mentioned above would behave d i f f e r e n t l y i n the i o n i z a t i o n of d i p h e n y l a m i n e s . Thus f o r the 4-amino and 4-methoxy groups resonance i n t e r a c t i o n of the t y p e , ( X I I ) , t h a t i s v e r y p r o b a b l y of some importance i n the b e n z o i c a c i d s 1 ' 3 i s of l i t t l e importance i n the d i p h e n y l a m i n e s . T h i s i s s u p p o r t e d by the f a c t t h a t HpN- X I I 86 the p K H A v a l u e s f o r these two compounds are f a i r l y w e l l c o r r e l a t e d ( f i g u r e 7) w i t h CT° v a l u e s (determined from r e a c t i o n s i n which resonance e f f e c t s are minimal 1 0 *^* 3 ) . On the o ther hand, resonance i n t e r a c t i o n of the f o l l o w i n g type i s of g r e a t e r importance f o r the a n i o n of OpN- XIII d i p h e n y l a m i n e than f o r the a n i o n of b e n z o i c a c i d . The 0~"value f o r the 4 - n i t r o group i s 0 .778 i n the i o n i z a t i o n of b e n z o i c a c i d s 1 0 ^ 3 , 1.27 i n the i o n i z a t i o n of p h e n o l s and a n i l i n i u m i o n s 1 0 3 c and must be a s s i g n e d a v a l u e of 1.65 i n the i o n i z a t i o n of d i p h e n y l a m i n e s . Comparison of s u b s t i t u e n t e f f e c t s on the a c i d i t y of p h e n o l s and d i p h e n y l a m i n e s s h o u l d be i n t e r e s t i n g s i n c e these compounds are q u i t e s i m i l a r . ( A n i l i n e s would be b e t t e r n i t r o g e n a n a l o g s of p h e n o l s than are d i p h e n y l a m i n e s , however t h e r e i s i n s u f f i c i e n t data f o r a good c o m p a r i s o n . ) The p v a l u e f o r i o n i z a t i o n of d i p h e n y l a m i n e s i s 1.8 t imes as l a r g e as the p f o r i o n i z a t i o n of p h e n o l s ; t h a t i s , the e f f e c t s of s u b s t i t u e n t s on the a c i d i t y of d i p h e n y l a m i n e are 1.8 t imes as g r e a t as they are on the a c i d i t y of p h e n o l . T h i s i s 87 p r o b a b l y a r e s u l t of the g r e a t e r importance of charge d e l o c a l i z a t i o n i n the a r o m a t i c r i n g i n the a n i o n of d i p h e n y l a m i n e than of p h e n o l . In terms of the resonance v i e w p o i n t , s t r u c t u r e s such as (XIV) and (XV) s h o u l d c o n t r i b u t e more t o the fi < — > < > w X I V x v • f i resonance h y b r i d of the d i p h e n y l a m i n e a n i o n than the c o r r e s p o n d i n g s t r u c t u r e s , (XVI) and ( X V I I ) , t o the C r <- >=0 X V I X V I I resonance h y b r i d of the phenoxide i o n . T h i s i s because of the s m a l l e r d i f f e r e n c e i n e l e c t r o n e g a t i v i t y between carbon (2.5) and n i t r o g e n (3.0) than between carbon and oxygen ( 3.5) l c' 1 0 7 . S u b s t i t u e n t s on the r i n g s h o u l d p e r t u r b the charge d e l o c a l i z a t i o n . T h i s p e r t u r b a t i o n w i l l t h e r e f o r e be g r e a t e r f o r the a n i o n of d i p h e n y l a m i n e than the phenoxide i o n . T h i s i n ' t u r n s u g g e s t s t h a t the a c i d i t y 8 8 of d i p h e n y l a m i n e s h o u l d be a l t e r e d more by s u b s t i t u e n t s i n the a r o m a t i c r i n g than the a c i d i t y of p h e n o l . From these same arguments i t would be e x p e c t e d t h a t the a c i d i t y of t o l u e n e i s even more s e n s i t i v e t o s u b s t i t u e n t e f f e c t s than the a c i d i t y of d i p h e n y l a m i n e or p h e n o l . A l t h o u g h the e q u i l i b r i u m a c i d i t i e s of s u b s t i t u t e d (34) t o l u e n e s have not been d e t e r m i n e d , t h e r e i s i n d i r e c t e v i d e n c e t h a t the a c i d i t y of t o l u e n e i s a f f e c t e d t o a g r e a t e r e x t e n t by s u b s t i t u e n t s . S t r e i t w i e s e r and K o c h ^ 0 8 have measured the r e l a t i v e r a t e s of d e u t e r i u m exchange of a s e r i e s of s u b s t i t u t e d t o l u e n e s i n c y c l o h e x y l a m i n e w i t h l i t h i u m and cesium c y c l o h e x y l a m i d e as c a t a l y s t s . A p l o t of l o g ( r e l a t i v e exchange r a t e ) v e r s u s Hammett CT v a l u e s y i e l d s a l i n e w i t h p ( s l o p e ) of 4 . I f the r e l a t i o n s h i p between the r e l a t i v e r a t e of h y d r o g e n - d e u t e r i u m exchange and the e q u i l i b r i u m a c i d i t i e s of s u b s t i t u t e d t o l u e n e s were known then the p value f o r i o n i z a t i o n of t o l u e n e s c o u l d be c a l c u l a t e d . T h i s r e l a t i o n s h i p i s not known; however, i t i s known f o r another s e r i e s of carbon a c i d s . 89 A n d r e a d e s ® 4 has d e t e r m i n e d the r e l a t i v e r a t e s of t r i t i u m exchange f o r a s e r i e s of carbon a c i d s w i t h the f l u o r e n e s t r u c t u r e (XVIII) i n sodium m e t h o x i d e - m e t h a n o l . S t r e i t w i e s e r and c o - w o r k e r s have d e t e r m i n e d the e q u i l i b r i u m a c i d i t i e s f o r these same a c i d s i n the c y c l o - hexylamine s y s t e m . A p l o t of l o g ( r e l a t i v e exchange r a t e ) v e r s u s pK f o r t h i s s e r i e s of a c i d s g i v e s a f a i r l y good ' 60 p l o t w i t h s l o p e of - 0 . 4 . I f a s i m i l a r r e l a t i o n s h i p were to h o l d f o r the t o l u e n e s e r i e s then the p v a l u e f o r t o l u e n e i o n i z a t i o n would be a p p r o x i m a t e l y 10. There i s a g r e a t d e a l of u n c e r t a i n t y in^ such an e s t i m a t i o n ; X V I I I however, i t does i n d i c a t e t h a t the p> f o r i o n i z a t i o n of t o l u e n e s i s g r e a t e r than f o r the i o n i z a t i o n of phenol or d i p h e n y l a m i n e . T h i s i s i n agreement w i t h the p r e d i c t i o n t h a t the magnitude of s u b s t i t u e n t e f f e c t s on a c i d i t i e s s h o u l d i n c r e a s e i n the s e r i e s p h e n o l , d i p h e n y l a m i n e ( a n i l i n e ) , t o l u e n e . 90 The data on the i o n i z a t i o n of a n i l i n e s i s i n s u f f i c i e n t t o attempt a Hammett p l o t or even t o make a d i r e c t comparison w i t h the data f o r d i p h e n y l a m i n e s . However, i t i s p o s s i b l e t o make a comparison of the a c i d i t i e s of a n i l i n e s and d i p h e n y l a m i n e s i n d i r e c t l y by comparing them both t o a common q u a n t i t y , the a c i d i t y of p h e n o l s . T h u s , F i g u r e 8 c o n t a i n s a p l o t of the pKjj A v a l u e s of a n i l i n e s and d i p h e n y l a m i n e s v e r s u s those of p h e n o l s . The pKjj A v a l u e s of the m o n o s u b s t i t u t e d p h e n o l s are f rom the data of B i g g s and R o b i n s o n 1 0 ^ and those f o r the d i c h l o r o - 109 p h e n o l s are from the data of Robinson The b e s t s t r a i g h t l i n e t h r o u g h the p o i n t s f o r the d i p h e n y l a m i n e s i s drawn. I t was c a l c u l a t e d o m i t t i n g the p o i n t s f o r the 4 - n i t r o and 4 - m e t h y l - s u l f o n y l s u b s t i t u e n t s and has s l o p e 1.95 - .13 and c o r r e l a t i o n c o e f f i c i e n t , r , of 0 .988 . T h i s s l o p e i s s l i g h t l y h i g h e r than the p v a l u e s f o r the i o n i z a t i o n of d i p h e n y l a m i n e s and p h e n o l s would l e a d one t o e x p e c t . A l i n e w i t h the same s l o p e i s drawn through the p o i n t s f o r the a n i l i n e s . I t can be seen t o accomodate most of the p o i n t s , s u g g e s t i n g t h a t s u b s t i t u e n t e f f e c t s i n , t h e i o n i z a t i o n of a n i l i n e s are the same as i n d i p h e n y l a m i n e s . The d i f f e r e n c e a l o n g the o r d i n a t e between the two l i n e s , 4 .9 pK u n i t s , r e p r e s e n t s the d i f f e r e n c e i n pKjj A v a l u e s 91 FIGURE 8 PLOT OF P K H A OF ANILINES AND DIPHENYL- 70 Q 75 8.0 8.5 9.0 9.5 10.0 92 caused by r e p l a c i n g an amino hydrogen of a n i l i n e w i t h a p h e n y l g r o u p . T h i s can be used t o c a l c u l a t e a pKjj^ v a l u e of 27.3 f o r a n i l i n e from the v a l u e 22.44 of d i p h e n y l a m i n e . T h i s i s i n e x c e l l e n t agreement w i t h the PKJJA v a l u e of 27 59 o b t a i n e d by McEwen t h i r t y y e a r s ago. The agreement, however, must be c o n s i d e r e d l a r g e l y f o r t u i t o u s s i n c e h i s v a l u e s were based on s e m i - q u a n t i t a t i v e measurements i n a s o l v e n t of low d i e l e c t r i c and on an a r b i t r a r y v a l u e of 16 f o r the pKjj^ of m e t h a n o l . I t might be noted i n F i g u r e 8 t h a t the p o i n t s f o r the 4 - n i t r o s u b s t i t u e n t f o r both the a n i l i n e and the d i p h e n y l a m i n e f a l l w e l l below the l i n e s t h a t c o r r e l a t e most of the d a t a . T h i s s u b s t i t u e n t , t h e n , has a much g r e a t e r e f f e c t on the a c i d i t y of a r o m a t i c amines than would be e x p e c t e d from i t s e f f e c t on the a c i d i t y of p h e n o l . T h i s was mentioned e a r l i e r i n a d i f f e r e n t way when i t was s t a t e d t h a t the 4 - n i t r o s u b s t i t u e n t has an apparent sigma v a l u e of 1.65 i n the i o n i z a t i o n of d i p h e n y l a m i n e s as compared t o 1.27 i n the i o n i z a t i o n of p h e n o l . On the o ther hand, the 3 - n i t r o s u b s t i t u e n t behaves as would be e x p e c t e d s i n c e the p o i n t f o r i t l i e s on the l i n e c o r r e l a t i n g the P K HA v a l u e s o f p h e n o l s and d i p h e n y l a m i n e s . The d i f f e r e n c e i n b e h a v i o u r of the n i t r o group at the 3 (meta) and 4 (para) p o s i t i o n s i s no doubt due to 9 3 the l a r g e c o n t r i b u t i o n made i n the l a t t e r case by the s t r u c t u r e (XIX) t o the resonance h y b r i d of the a n i o n of 4 - n i t r o a n i l i n e and of 4 - n i t r o d i p h e n y l a m i n e . 0 2 N - H <—> ~ 0 p K t = < ) - = N H X I X The s t u d y of a s e r i e s of a l k y l - s u b s t i t u t e d 4 - n i t r o a n i l i n e s p r o d u c e d some i n t e r e s t i n g r e s u l t s . The e f f e c t of a l k y l s u b s t i t u e n t s o r t h o t o the amino group i s t o i n c r e a s e the a c i d s t r e n g t h (decrease the pKjjA) of 4 - n i t r o a n i l i n e . Thus one o r t h o methyl group d e c r e a s e s the pK|jA o f 4 - n i t r o a n i l i n e by 0 .08 u n i t s , two o r t h o methyl groups by 0.20 u n i t s and two t - b u t y l groups by more than 1.0 u n i t s . The e f f e c t of these groups i s i n the o p p o s i t e d i r e c t i o n to t h a t which would be e x p e c t e d on the b a s i s of s i m p l e i n d u c t i v e e f f e c t s . I t i s e n c o u r a g i n g , a t l e a s t w i t h r e g a r d to the v a l i d i t y of the r e s u l t s , t h a t s i m i l a r t r e n d s are o b s e r v e d i n the a c i d i t i e s of o r t h o - a l k y l - 4 - n i t r o - p h e n o l s . The p K ^ v a l u e s of these compounds have been measured i n aqueous s o l u t i o n where i t i s not n e c e s s a r y t o r e s o r t t o the Hammett 94 t e c h n i q u e t o determine a c i d d i s s o c i a t i o n c o n s t a n t s . The pKjj^ v a l u e s f o r these a n i l i n e s and p h e n o l s are l i s t e d i n T a b l e V I . The e f f e c t of a l k y l s u b s t i t u e n t s i s b e t t e r i l l u s t r a t e d by the data i n T a b l e VI f o r p h e n o l s s i n c e they are more complete than f o r a n i l i n e s . The p K ^ of 2 , 6 - d i m e t h y l p h e n o l i s a p p r o x i m a t e l y 0.6 u n i t s g r e a t e r than the pKjj^ of p h e n o l ; t h a t i s , phenol i s the s t r o n g e r a c i d . I t might be e x p e c t e d then t h a t 4 - n i t r o p h e n o l would be about 0.6 pK u n i t s s t r o n g e r as an a c i d than 2 , 6 - d i m e t h y l - 4 - n i t r o p h e n o l . In f a c t i t i s n o t ; the pKjj^ v a l u e s of the two compounds are r o u g h l y the same. With b u l k i e r o r t h o groups the e f f e c t i s even g r e a t e r s i n c e 2 , 6 - d i - t - b u t y l - 4 - n i t r o p h e n o l i s 0 .5 pK u n i t s s t r o n g e r as an a c i d than 4- n i t r o p h e n o l r a t h e r than b e i n g an e x p e c t e d 1.7 u n i t s weaker . The data f o r 4 - n i t r o a n i l i n e s , though l i m i t e d , i s s i m i l a r i n t r e n d . The e x p l a n a t i o n f o r the a c i d s t r e n g t h e n i n g e f f e c t s of o r t h o a l k y l groups on the a c i d i t y of 4 - n i t r o  a n i l i n e and 4 - n i t r o p h e n o l i s not at a l l o b v i o u s . S t e r i c i n h i b i t i o n to s o l v a t i o n of the a n i o n s would be e x p e c t e d t o b r i n g about the o p p o s i t e e f f e c t . That s o l v a t i o n i s p r o b a b l y r e s t r i c t e d f o r the a n i o n s w i t h b u l k y o r t h o groups i s e v i d e n c e d by the f a c t t h a t 2 , 6 - d i - t - b u t y l p h e n o l i s too i n s o l u b l e i n 95 TABLE VI The P K J J A V a l u e s of some A l k y l - S u b s t i t u t e d A n i l i n e s and P h e n o l s S u b s t i t u e n t s P^HA v a ^ u e ° f p K H A v a l u e o f L i t s u b s t i t u t e d s u b s t i t u t e d r e f a n i l i n e phenol none 10.00 105 2 - m e t h y l 10.29 113 4 - m e t h y l 10.26 113 4 - t - b u t y l 10.23 110 2 , 6 - d i m e t h y l 10. 59 114 3 , 5 - d i m e t h y l 10.14 114 2 , 6 - d i - t - b u t y l 11.70b 110 4 - n i t r o 18.91 7.15 105 2 - m e t h y l - 4 - n i t r o 18.83 2 , 6 - d i m e t h y l - 4 - n i t r o 18.71 7.19 114 2 , 6 - d i - t - b u t y l ~ 4 - n i t r o 17 . 4 a 6.65 110 3 , 5 - d i m e t h y l - 4 - n i t r o 21.16 8.25 114 2 , 3 , 5 , 6 - t e t r a m e t h y l - 4 - n i t r o 22.66 a approximate v a l u e e s t i m a t e d from a Hammett p l o t f o r 4 - s u b s t i t u t e d - 2 , 6 - d i - t - b u t y l p h e n o l s 96 water at h i g h pH t o a l l o w s p e c t r a l measurements t o be made on i t s i o n i z a t i o n 1 1 0 . In f a c t i t has been r e p o r t e d t h a t 2,6 - d i - t - b u t y l —4 - m e t h y i p h e n o l i s i n s o l u b l e i n aqueous a l k a l i of any s t r e n g t h 1 1 1 . A p o s s i b l e e x p l a n a t i o n of these phenomena might l i e i n s o l v a t i o n e f f e c t s on both the i o n i z e d and u n i o n i z e d s p e c i e s . In the a n i o n of phenol the n e g a t i v e charge must r e s i d e p r i m a r i l y on the oxygen atom where i t can be s t a b i l i z e d by s o l v a t i o n . The i n t r o d u c t i o n of b u l k y a l k y l groups o r t h o to the oxygen h i n d e r s s o l v a t i o n and c o n s e q u e n t l y i n c r e a s e s the energy of the a n i o n . However, i f a s u b s t i t u e n t such as the n i t r o group i s p l a c e d at the 4 - p o s i t i o n of p h e n o l a l a r g e p o r t i o n of the i o n s n e g a t i v e charge w i l l r e s i d e on t h i s s u b s t i t u e n t . which has no h i n d r a n c e t o s o l v a t i o n . T h u s , the e f f e c t of s u b s t i t u e n t s i n the para p o s i t i o n capable of s u p p o r t i n g p a r t of the n e g a t i v e charge i n the phenoxide i o n (or a n i l i n e anion) i s t o l e s s e n the a c i d weakening e f f e c t of o r t h o a l k y l g r o u p s . The f i n d i n g s of Cohen and J o n e s 1 1 0 s u p p o r t such and e x p l a n a t i o n . They measured the pKjj A v a l u e s of two s e r i e s of p h e n o l s of the type (XX) and (XXI) and found t h a t the d i f f e r e n c e between the pK v a l u e s f o r members of the 97 F W / V - O H = t-BUTYL X X X X I two s e r i e s w i t h a g i v e n s u b s t i t u e n t R d e c r e a s e s as the s u b s t i t u e n t becomes more e l e c t r o n w i t h d r a w i n g (as measured by the Hammett0 p a r a m e t e r ) . T h i s e x p l a n a t i o n can account f o r a l e s s e n i n g of the a c i d weakening e f f e c t of o r t h o a l k y l g r o u p s ; however i t cannot account f o r the apparent a c i d s t r e n g t h e n i n g e f f e c t of these groups i n 2 , 6 - d i - t - b u t y l - 4 - n i t r o a n i l i n e and the c o r r e s p o n d i n g p h e n o l . A f u r t h e r p r o c e s s i s r e q u i r e d t o e x p l a i n t h i s and i t i s p o s s i b l e t h a t i t i n v o l v e s s o l v a t i o n of the amino and h y d r o x y l f u n c t i o n s of the u n i o n i z e d a n i l i n e s and p h e n o l s . In a r e c e n t attempt t o e x p l a i n the b a s i c i t i e s of a l i p h a t i c amines and of N - a l k y l a n i l i n e s i n terms of the h y d r a t i o n of the n e u t r a l amines and t h e i r ammonium i o n s , 26 86 Condon ' was drawn t o the c o n c l u s i o n t h a t h y d r a t i o n of the f r e e a n i l i n e or N - a l k y l a n i l i n e i s base weakening by 1.6 pK u n i t s as compared t o a l i p h a t i c amines . T h i s i n c r e a s e d 98 importance of h y d r a t i o n i n the a n i l i n e bases as compared t o the a l i p h a t i c amines was a t t r i b u t e d t o the g r e a t e r importance of hydrogen b o n d i n g of the type (XXII) i n a n i l i n e than i n a l i p h a t i c amines ( X X I I I ) . T h i s i s r e a s o n a b l e s i n c e X X I I X X I I I the n i t r o g e n atom i s at the p o s i t i v e end of the d i p o l e i n X 07 to a n i l i n e whereas i t i s p r o b a b l y at the n e g a t i v e end i n a l i p h a t i c a m i n e s ^ . Hydrogen b o n d i n g s h o u l d be of s i m i l a r 112 or g r e a t e r importance i n p h e n o l s The presence of l a r g e groups o r t h o t o the h y d r o x y l or amino f u n c t i o n may weaken or e l i m i n a t e hydrogen bond s o l v a t i o n and c o n s e q u e n t l y r a i s e the energy of the phenol or a n i l i n e . T h i s would be an a c i d s t r e n g t h e n i n g e f f e c t which i n c o n j u n c t i o n w i t h the f i r s t e x p l a n a t i o n might r e s u l t i n 2 , 6 - d i - t - b u t y l - 4 - n i t r o p h e n o l b e i n g a s t r o n g e r a c i d than 4 - n i t r o phenol and 2 , 6 - d i - t - b u t y l - 4 - n i t r o a n i l i n e b e i n g a s t r o n g e r a c i d than 4 - n i t r o a n i l i n e . 9 9 The importance of the n i t r o group i n d e l o c a l i z i n g the charge on the a n i o n s of 4 - n i t r o p h e n o l and 4 - n i t r o a n i l i n e can be seen from the e f f e c t of p u t t i n g a l k y l groups o r t h o t o the n i t r o g r o u p . Two methyl groups o r t h o t o the n i t r o group t w i s t i t out of p l a n a r i t y w i t h the r i n g , r e d u c i n g the resonance i n t e r a c t i o n w i t h the r i n g 1 1 ^ . The r e s u l t i s a decrease of 1.1 pK u n i t s i n the a c i d i t y of 4 - n i t r o p h e n o l and 2.2 pK u n i t s i n the a c i d i t y of 4 - n i t r o a n i l i n e . With methyl groups o r t h o t o both the n i t r o and amino f u n c t i o n s the pKjj A o f 4 - n i t r o a n i l i n e i n c r e a s e s by 3.7 u n i t s ; t h a t i s , i t becomes a c o n s i d e r a b l y weaker a c i d . The pKjj^ v a l u e s of some 4 - n i t r o a n i l i n e s w i t h a l k y l s u b s t i t u e n t s on the n i t r o g e n , as w i t h the o ther a l k y l s u b s t i t u t e d 4 - n i t r o a n i l i n e s , showed some unexpected e f f e c t s . The data are l i s t e d i n T a b l e I I I . The s t r i k i n g f e a t u r e i s t h a t the pKjj A v a l u e s of N - m e t h y l , N - e t h y l , and N - i s o p r o p y l - 4 - n i t r o a n i l i n e are l e s s than t h a t of 4 - n i t r o a n i l i n e i t s e l f . As b e f o r e , i t would be e x p e c t e d on the b a s i s of the u s u a l i n d u c t i v e e f f e c t s t h a t the s u b s t i t u t i o n of methyl f o r the hydrogen of the amino group would i n c r e a s e the P K HA O J " 4 - n i t r o a n i l i n e . The a c i d i t i e s of the N - a l k y l - 4 - n i t r o a n i l i n e s do f a l l i n the o r d e r e x p e c t e d from t h e i r i n d u c t i v e e f f e c t s as measured by T a f t ' s C P * p a r a m e t e r s 1 0 3 ^ ; however, they do not show a l i n e a r c o r r e l a t i o n . 100 An e x p l a n a t i o n f o r the f a c t t h a t N - m e t h y l - 4 - n i t r o a n i l i n e i s a s t r o n g e r a c i d than 4 - n i t r o a n i l i n e might l i e i n the s o l v a t i o n of the u n i o n i z e d amines . I f , as 26 s u g g e s t e d by Condon , these amines are s o l v a t e d by f o r m a t i o n of hydrogen bonds as shown, (XXIV) and (XXV), the s u b s t i t u t i o n of methyl f o r one of the hydrogen atoms on the n i t r o g e n d e s t r o y s the s i t e of one of the hydrogen bonds . S i n c e the measurements were made i n DMSO-water m i x t u r e s i t i s p o s s i b l e t h a t DMSO r e p l a c e s water i n t h i s type of hydrogen b o n d i n g , p a r t i c u l a r l y s i n c e DMSO forms s t r o n g hydrogen bonds QQ I "I C w i t h p r o t o n donors ' . The l o s s of s o l v a t i o n d e s t a b i l i z e s N - m e t h y l - 4 - n i t r o a n i l i n e w i t h r e s p e c t t o 4 - n i t r o a n i l i n e . I t might be p o s s i b l e t h a t t h i s decrease i n s o l v a t i o n energy i s l a r g e enough t o overcome the i n d u c t i v e e f f e c t of the methyl group c a u s i n g N - m e t h y l - 4 - n i t r o a n i l i n e to be a s t r o n g e r a c i d than 4 - n i t r o a n i l i n e . 101 The e f f e c t of s u b s t i t u e n t s on the a c i d i t y of the diphenylammonium i o n (the b a s i c i t y of d i p h e n y l a m i n e ) i s s i m i l a r i n t r e n d to t h e i r e f f e c t on the a c i d i t y of d i p h e n y l a m i n e A g a i n , no one s e t of Hammett s u b s t i t u e n t c o n s t a n t s c o r r e l a t e s the a c i d i t i e s of a l l the ammonium* i o n s . F i g u r e 9 c o n t a i n s a p l o t of pKgH+ v e r s u s C~^^^a f o r the f o l l o w i n g d i p h e n y l a m i n e s : 3-methoxy, 4 - c h l o r o , 3 - c h l o r o and 3 - n i t r o d i p h e n y l a m i n e and d i p h e n y l a m i n e i t s e l f . The r e a c t i o n c o n s t a n t p i s 3.36 - .04 w i t h c o r r e l a t i o n c o e f f i c i e n t r of 0 .999 . The p o i n t s f o r 3 - t r i f l u o r o m e t h y l d i p h e n y l a m i n e ( 0 ~ •» .49 ) and f o r 3 , 4 ' - d i c h l o r o d i p h e n y l a m i n e ( ^ O - = .600) f a l l v e r y c l o s e t o the l i n e . As b e f o r e , the pK B I j+ v a l u e s f o r the compounds w i t h the 4-methoxy, 4 - m e t h y l , 4 - m e t h y l s u l f o n y l , and 4 - n i t r o w s u b s t i t u e n t s do not c o r r e l a t e w i t h o~. The p o i n t s f o r the e l e c t r o n - r e l e a s i n g s u b s t i t u e n t s , 4-methoxy and 4 - m e t h y l , can be brought near the l i n e by u s i n g CT0^^ i n s t e a d of <J~. F o r the s t r o n g l y e l e c t r o n w i t h d r a w i n g s u b s t i t u e n t s , 4 - m e t h y l s u l f o n y l and 4 — n i t r o , the use of 0 1 0 3 c r a t h e r than G - b r i n g s the p o i n t s c l o s e r to the l i n e . There i s c o n s i d e r a b l y more data on the b a s i c i t i e s of a n i l i n e s than of d i p h e n y l a m i n e s s i n c e the p r o t o n a t i o n of the m o n o s u b s t i t u t e d a n i l i n e s t a k e s p l a c e w i t h i n the pH 105 r a n g e . B i g g s and R o b i n s o n found t h a t f o r twelve a n i l i n e s w i t h s u b s t i t u e n t s r a n g i n g from 4 - m e t h y l «T" = - . 170 1 0 3 a ) t o 1 0 2 4 - 0 C H \ • FIGURE 9 HAMMETT CORRELATION OF THE BASICITY OF SUBSTITUTED DIPHENYLAMINES - 1.0 6) H - 0 . 5 CD 3 - 0 C H 3 - 0 . 0 \ ) 4-CI p = 3-36 \ r = . 9 9 9 - - 0 . 5 \ > 3—Cl \ x 3 - C F 3 - - 1 . 0 P^BH V 3,4-diCI + \ - - 1 . 5 C3 3 - N 0 2 0 — 0 " VALUES USED IN CORRELATION \ - - 2 . 0 X - - - 0 " VALUES NOT USED IN CORRELATION \ 0 ~ ° VALUES \ A--CT" VALUES \ - - 2 . 5 \ A 4 - S O 2 C H 3 - - 3 . 0 - . 2 i SIGMA V-NO 2 0 0 . 2 . 4 . 6 , 8 1 . 0 \ l . 2 A 1 1 1 J 1 ^ " 1 103 3 - n i t r o (CT" •= .710 1 0 3 a ) t h e r e i s a good c o r r e l a t i o n of p K B H + w i t h 0~. The r e a c t i o n c o n s t a n t p i s 2 . 89 , a l t h o u g h a v a l u e of 3.00 i s o b t a i n e d f o r p u s i n g the pKgjj* v a l u e s f o r the f i v e a n i l i n e s c o r r e s p o n d i n g t o the f i v e d i p h e n y l  amines used above i n c a l c u l a t i n g p f o r the p r o t o n a t i o n of 117 d i p h e n y l a m i n e s . F i c k l i n g and c o - w o r k e r s have f o u n d t h a t the r e a c t i o n c o n s t a n t p f o r the p r o t o n a t i o n of s u b s t i t u t e d N , N - d i m e t h y l a n i l i n e s i s 3 . 4 3 . On t h i s b a s i s , s u b s t i t u e n t e f f e c t s on the b a s i c i t y of s e c o n d a r y and t e r t i a r y a r o m a t i c amines are s l i g h t l y l a r g e r i n magnitude than on p r i m a r y a r o m a t i c amines . A p l o t of the p K B H + v a l u e s of d i p h e n y l a m i n e s v e r s u s the pKg H + v a l u e s of the c o r r e s p o n d i n g a n i l i n e s , u s i n g a wider v a r i e t y of s u b s t i t u e n t s than those u s e d t o c a l c u l a t e p , g i v e s a f a i r l y good s t r a i g h t l i n e w i t h s l o p e near u n i t y . F o r e l e v e n compounds whose b a s i c i t i e s range over 5 pK u n i t s , the e q u a t i o n r e l a t i n g the pKgH+ of a d i p h e n y l a m i n e (DPA) to the pKgH+ of the c o r r e s p o n d i n g a n i l i n e (An) i s <? K BH + ) DPA = "3 .98 + 1 .01 ( p K g H + ) A n (35) F i g u r e 10 i s a p l o t of the data f o r t h i s l i n e which has c o r r e l a t i o n c o e f f i c i e n t , r , of 0 .998 . The pKgH+ v a l u e s of 1 O S the a n i l i n e s are taken from the data of B i g g s and Robinson 104 F IGURE 10 PLOT O F P K B H + O F ANIL INES V E R S U S P K B H + O F D I P H E N Y L A M I N E S P I W (ANILINE) 0 1 2 3 4 5 6 105 except f o r the v a l u e s f o r 3 - t r i f l u o r o m e t h y l a n i l i n e , g i v e n by 106 Shephard , and 4 - m e t h y l s u l . f o n y l a n i l ine , f rom the 118 c o m p i l a t i o n of P e r r i n . On the b a s i s of the r e l a t i o n s h i p e x p r e s s e d i n e q u a t i o n (35) the magnitude of s u b s t i t u e n t e f f e c t s on the b a s i c i t i e s of a n i l i n e and d i p h e n y l a m i n e a r e , on the a v e r a g e , the same. For the h y p o t h e t i c a l a n i l i n e w i t h pKgjj+ of z e r o the pKgy+ of the c o r r e s p o n d i n g d i p h e n y l a m i n e i s - 4 . 0 ; t h a t i s , the replacement of a p r o t o n of the amino group of the a n i l i n e by a p h e n y l group d e c r e a s e s the b a s i c i t y by 4.0 u n i t s . I t w i l l be r e c a l l e d t h a t the same replacement i n c r e a s e s the a c i d i t y of a n i l i n e by 4 .9 pK u n i t s . The d i f f e r e n c e i n the b a s i c i t i e s of an a n i l i n e and the c o r r e s p o n d i n g d i p h e n y l a m i n e i s due not o n l y to the d i f f e r e n t e l e c t r o n i c e f f e c t s of p h e n y l as compared t o hydrogen but a l s o t o d i f f e r e n c e s i n the s o l v a t i o n e n e r g i e s of the p r i m a r y and secondary amines and t h e i r conjugate J 26,86 a c i d s F . A c i d and Base S t r e n g t h s of N i t r o - s u b s t i t u t e d A r o m a t i c  Amines I t was mentioned i n the I n t r o d u c t i o n t h a t there i s a body of e v i d e n c e t o suggest t h a t the n i t r o group t a k e s p a r t i n some s p e c i f i c i n t e r a c t i o n w i t h a component of c o n c e n t r a t e d a c i d s o l u t i o n s . The e x a c t na ture of t h i s 106 i n t e r a c t i o n i s not known. H o g f e l d t and L e i f e r 1 1 9 have i n t e r p r e t e d the s o l u b i l i t y d a t a 3 3 f o r n i t r o b e n z e n e i n aqueous s u l f u r i c a c i d i n terms of complex f o r m a t i o n between the n i t r o group and mono- and t r i h y d r a t e d p r o t o n s . Deno and 27 P e r r i z z o l o have s u g g e s t e d the e x i s t e n c e of a hydrogen bonded complex between a molecule of n i t r o b e n z e n e and another of s u l f u r i c a c i d . The q u e s t i o n then a r i s e s of how the b a s i c i t i e s of n i t r o - s u b s t i t u t e d a r o m a t i c amines are a f f e c t e d i n s o l u t i o n s of h i g h a c i d c o n c e n t r a t i o n . I t 37 has been s u g g e s t e d t h a t n i t r o a n i l i n e s are weak bases p a r t l y because of such i n t e r a c t i o n s between the n i t r o group and the a c i d i c m e d i a . I t was f e l t tha t some i n f o r m a t i o n might be g a i n e d about the e f f e c t of s t r o n g l y a c i d i c media on the b a s i c i t y of n i t r o a r o m a t i c amines from measurement of the b a s i c i t i e s of a s e r i e s of s u b s t i t u t e d d i p h e n y l a m i n e s . Any p e c u l i a r i t y of the n i t r o s u b s t i t u e n t might show up i n a Hammett 0~jO p l o t or i n a c o r r e l a t i o n of the b a s i c i t i e s of s u b s t i t u t e d a n i l i n e s w i t h the c o r r e s p o n d i n g d i p h e n y l a m i n e s . The p r o t o n a t i o n of 4 - n i t r o a n i l i n e o c c u r s i n r e l a t i v e l y d i l u t e a c i d ( a p p r o x i m a t e l y 0 .1 N HC1) i n which the n i t r o group s h o u l d not be a f f e c t e d by the a c i d . On the o ther hand, 4 - n i t r o d i p h e n y l a m i n e and 2 - n i t r o d i p h e n y l a m i n e are h a l f i o n i z e d i n 5.9 and 7 .3 molar a q u e o u s - e t h a n o l i c s u l f u r i c a c i d r e s p e c t i v e l y . 1 0 7 I t i s o b v i o u s from F i g u r e s 9 and 1 0 t h a t the b e h a v i o u r of the n i t r o group as a s u b s t i t u e n t i n s u l f u r i c a c i d i s v e r y s i m i l a r to i t s b e h a v i o u r i n aqueous s o l u t i o n s w i t h i n the pH r a n g e . In terms of the Hammett s u b s t i t u e n t c o n s t a n t , the 4 - n i t r o group has sigma v a l u e of 1 . 1 6 i n the p r o t o n a t i o n of d i p h e n y l a m i n e s as compared to 1 . 2 7 f o r the p r o t o n a t i o n of a n i l i n e s 1 0 ^ 0 . In view of the l i m i t e d data (5 pKgjj+ v a l u e s ) u s e d t o c a l c u l a t e p f o r the p r o t o n a t i o n of d i p h e n y l a m i n e s and the change i n s t r u c t u r e between d i p h e n y l a m i n e and a n i l i n e , the d i s c r e p a n c y i n the signma v a l u e s f o r the 4 - n i t r o s u b s t i t u e n t i s not s i g n i f i c a n t . In the c o r r e l a t i o n of the P K B H + v a l u e s of a n i l i n e s w i t h those of the d i p h e n y l a m i n e s ( F i g u r e 1 0 ) the f i t of the p o i n t s f o r the 2 - and 4 - n i t r o s u b s t i t u e n t s i s as good as f o r the o ther s u b s t i t u e n t s . The b a s i c i t i e s of the f o l l o w i n g two s e r i e s of d i p h e n y l a m i n e s a l s o c o r r e l a t e q u i t e w e l l w i t h one a n o t h e r . X X V I X X V I I F i g u r e 1 1 i s a p l o t of the P K B H + v a l u e s of the mono- s u b s t i t u t e d d i p h e n y l a m i n e s (XXVI) v e r s u s the PK R TT+ v a l u e s 108 FIGURE II CORRELATION OF THE BASICITY OF SUBSTITUTED DIPHENYLAMINES AND 4'-NITR0DIPHENYLAMINES h "7 0 -I -2 -3 -4 J I I I L 109 of the c o r r e s p o n d i n g l y s u b s t i t u t e d 4 - n i t r o d i p h e n y l a m i n e s ( X X V I I ) . The s l o p e of the l i n e i s 0.86 i n d i c a t i n g t h a t the e f f e c t of s u b s t i t u e n t s on b a s i c i t y i s s m a l l e r i n the second s e r i e s than i n the f i r s t . T h i s i s p r o b a b l y a r e s u l t of the i n t e r a c t i o n of the amino group w i t h the n i t r o group i n one r i n g c a u s i n g a decrease i n i t s i n t e r  a c t i o n w i t h s u b s t i t u e n t s i n the o ther r i n g . The p o i n t f o r Z e q u a l to 3 - n i t r o f a l l s on the p l o t w i t h three n o n - n i t r o s u b s t i t u e n t s w h i l e the p o i n t f o r Z e q u a l t o 4 - n i t r o f a l l s a l i t t l e below the l i n e . I t can be seen t h a t the e f f e c t of the n i t r o group on the b a s i c i t y of d i p h e n y l a m i n e s does not e x h i b i t any o b s e r v a b l e change on p r o c e e d i n g from d i l u t e to c o n c e n t r a t e d a c i d . T h i s i s not to say t h a t the n i t r o group does not form a complex w i t h some component of s t r o n g l y a c i d i c media s i n c e i t may do so at h i g h e r a c i d c o n c e n t r a t i o n s than were u s e d here ( a p p r o x i m a t e l y 11 molar s u l f u r i c a c i d ) or i t may be t h a t the presence of such an i n t e r a c t i o n i s not o b s e r v a b l e i n such an i n d i r e c t , f a s h i o n as t h i s . 1 1 0 I t i s i n t e r e s t i n g t o c o n s i d e r the e f f e c t of the n i t r o group on the a c i d i t y of a r o m a t i c amines . The 4 - n i t r o s u b s t i t u e n t i n c r e a s e s the a c i d i t y of a n i l i n e and d i p h e n y l a m i n e by a p p r o x i m a t e l y 8 . 4 and 6 . 8 pK u n i t s r e s p e c t i v e l y . On the o ther hand the 3 - n i t r o s u b s t i t u e n t i n c r e a s e s the a c i d i t y of d i p h e n y l a m i n e by o n l y 2 . 9 pK u n i t s . The e x a l t e d a c i d i t y of 4 - n i t r o a n i l i n e and 4 - n i t r o d i p h e n y l a m i n e , i n which the s u b s t i t u e n t i s c o n j u g a t e d w i t h the amino g r o u p , must s u r e l y be a r e s u l t of the e x t e n s i v e d e l o c a l i z a t i o n of the charge i n the a n i o n s of these a c i d s . The e f f e c t of two n i t r o groups on the a c i d i t y of an a r o m a t i c amine i s not a d d i t i v e ; the second n i t r o group causes a s m a l l e r i n c r e a s e than e x p e c t e d . T h i s i s i l l u s t r a t e d i n T a b l e V I I f o r d i p h e n y l a m i n e s where the c a l c u l a t e d p K H A v a l u e s r e f e r t o the v a l u e s e x p e c t e d from a d d i t i o n of the i n c r e m e n t s f o r the i n d i v i d u a l s u b s t i t u e n t s . I t i s o b v i o u s t h a t the s u b s t i t u e n t e f f e c t s are not a d d i t i v e . In the case of p h e n o l s , the d e v i a t i o n from a d d i t i v i t y i s i n the o p p o s i t e d i r e c t i o n . T h u s , 2 , 4 , 6 - t r i n i t r o p h e n o l i s a s t r o n g e r a c i d ( P K H A of 0 . 2 2 ) by more than 1 pK u n i t than would be e x p e c t e d from the p K H A v a l u e s of phenol ( 1 0 . 0 0 ) , 2 - n i t r o - phenol ( 7 . 2 1 ) and 4 - n i t r o p h e n o l ( 7 . 1 5 ) 1 0 5 . In T a b l e V I I the l a r g e s t d e v i a t i o n s from a d d i t i v i t y occur i n the compounds w i t h n i t r o groups i n both r i n g s , as I l l TABLE V I I The pKjj^ V a l u e s of Some N i t r o - s u b s t i t u t e d D i p h e n y l a m i n e s S u b s t i t u e n t s O b s e r v e d p K ^ C a l c u l a t e d p K H ^ none 22.44 2- n i t r o 17.91 3- n i t r o 19.53 4- n i t r o 15.67 2 , 4 - d i n i t r o 13.84 11.14 3 , 4 ' - d i n i t r o 14.66 12.76 4 , 4 ' - d i n i t r o 1 4 . 0 8 a 8 .90 2 , 4 , 6 - t r i n i t r o 1 0 . 3 8 a 6 .61 2 , 4 , 4 ' - t r i n i t r o 1 2 . 3 5 a 4 .37 a r e f . 40 a r e s u l t , no d o u b t , of the i n a b i l i t y of b o t h r i n g s t o a t t a i n , s i m u l t a n e o u s l y , maximum o v e r l a p w i t h the n i t r o g e n atom. Not o n l y does the n i t r o s u b s t i t u e n t produce l a r g e i n c r e a s e s i n the a c i d i t y of a r o m a t i c amines but i t a l s o produces l a r g e r a t e a c c e l e r a t i o n s i n the a t t a c k of n u c l e o p h i l e s 1 on 121 on a r o m a t i c s u b s t r a t e s . F a r r , B a r d and Wheland have o b s e r v e d t h a t the d i s s o l u t i o n of m - d i n i t r o b e n z e n e (XXVIII) i n l i q u i d ammonia y i e l d s a p u r p l e s o l u t i o n capable of c o n d u c t i n g an e l e c t r i c a l c u r r e n t p r o b a b l y due to the f o r m a t i o n of the i o n (XXIX) . S i m i l a r l y , B o l t o n , M i l l e r and P a r k e r 1 2 2 found t h a t 4 - n i t r o f l u o r o b e n z e n e (XXX) r e a c t s i n d i m e t h y l - formamide w i t h a z i d e i o n w i t h o u t l i b e r a t i o n of f l u o r i d e i o n 112 + 2NH3 NHl- N02 XXVIII 0; H2NH N02 X X I X t o g i v e a c o l o r e d s o l u t i o n b e l i e v e d t o be a r e s u l t of the f o r m a t i o n of the i o n (XXXI) . X X X X X X I Such a d d i t i o n r e a c t i o n s are a l s o p o s s i b l e w i t h h y d r o x i d e or a l k o x i d e i o n s . T h i s means t h a t a d d i t i o n of these i o n s t o n i t r o a r o m a t i c amines may be a competing p r o c e s s w i t h i o n i z a t i o n by p r o t o n l o s s , p a r t i c u l a r l y i n the case of amines w i t h more than two n i t r o s u b s t i t u e n t s i n 123 one r i n g . T h u s , Crampton and G o l d have shown, u s i n g n u c l e a r magnetic resonance s p e c t r o s c o p y , t h a t 2 , 4 , 6 - t r i n i t r o a n i l i n e (XXXII) i n DMSO r e a c t s w i t h sodium methoxide p r e d o m i n a n t l y by methoxide i o n a d d i t i o n r a t h e r than by p r o t o n d i s s o c i a t i o n . 113 On the o ther hand, 2 , 4 - d i n i t r o a n i l i n e (XXXIII) and 2 , 4 - d i n i t r o d i p h e n y l a m i n e i o n i z e by p r o t o n l o s s . X X X I I I H y d r o x i d e i o n a d d i t i o n can compete w i t h d i s s o c i a t i o n even i n m o n o - n i t r o a n i l i n e s . The n i t r o group i s most e f f e c t i v e at i n c r e a s i n g a c i d s t r e n g t h when s i t u a t e d at the 2 or 4 p o s i t i o n of a n i l i n e . S i m i l a r l y the n i t r o group f a c i l i t a t e s a d d i t i o n t o a r o m a t i c compounds i n the o r t h o and para p o s i t i o n s . 114 In 4 - n i t r o a n i l i n e (XXXIV) the n i t r o group e x h i b i t s a g r e a t a c i d s t r e n g t h e n i n g e f f e c t so t h a t t h i s compound r e a c t s w i t h h y d r o x i d e i o n by p r o t o n l o s s r a t h e r than h y d r o x i d e a d d i t i o n . NH 2 OH" N 0 2 X X X I V H 2 0 NH NO; In 3 - n i t r o a n i l i n e (XXXV) the n i t r o group d i s p l a y s i t s weakest a c i d s t r e n g t h e n i n g e f f e c t whereas the compound i s s t i l l s u s c e p t i b l e t o h y d r o x i d e i o n a d d i t i o n at a p o s i t i o n o r t h o or para t o the n i t r o g r o u p . X X X V T h u s , i n 97 mole % DMSO c o n t a i n i n g 0.011 molar h y d r o x i d e i o n 3 - n i t r o a n i l i n e does not u n d e r g o , as does 115 4 - n i t r o a n i l i n e , a r a p i d s p e c t r a l change c h a r a c t e r i s t i c of i o n i z a t i o n by p r o t o n l o s s but r a t h e r produces a b r o a d a b s o r p t i o n i n the r e g i o n from 300 to 550 mjj t h a t i n c r e a s e s i n i n t e n s i t y w i t h t i m e . In the same s o l u t i o n a s i m i l a r s p e c t r a l change o c c u r s w i t h n i t r o b e n z e n e f o r which p r o t o n 124 a b s t r a c t i o n from the a r o m a t i c r i n g i s improbable . I t appears then t h a t these two compounds r e a c t by h y d r o x i d e i o n a d d i t i o n i n s t r o n g l y b a s i c s o l u t i o n s . I t i s i n t e r e s t i n g t h a t 3 - n i t r o d i p h e n y l a m i n e (XXXVI) r e a c t s by d i s s o c i a t i o n X X X V I r a t h e r than a d d i t i o n . T h i s i s due t o the f a c t t h a t the a d d i t i o n of the p h e n y l group t o the amino group of 3- n i t r o a n i l i n e i n c r e a s e s the a c i d i t y of the amino hydrogen by n e a r l y 5 pK u n i t s whereas i t produces o n l y a secondary e f f e c t on the s u s c e p t i b i l i t y of the a r o m a t i c r i n g t o h y d r o x i d e i o n a d d i t i o n . 125 R o c h e s t e r , f rom a s t u d y of the u l t r a v i o l e t a b s o r p t i o n spectrum of 4 - n i t r o a n i l i n e i n aqueous sodium h y d r o x i d e (0 t o 17 molar) has c o n c l u d e d t h a t 4 - n i t r o a n i l i n e t a k e s p a r t i n two e q u i l i b r i a depending on the c o n c e n t r a t i o n 116 of the b a s e . The f i r s t e q u i l i b r i u m predominates i n the r e g i o n from 0 t o 8 molar sodium h y d r o x i d e , and i s c h a r a c  t e r i z e d by a s h i f t i n the l o n g wavelength a b s o r p t i o n maximum from 381 t o 400 mju ; the second e q u i l i b r i u m predominates from 8 t o 17 molar base and i s c h a r a c t e r i z e d by a f u r t h e r s h i f t of the a b s o r p t i o n maximum t o 433 mjj, . R o c h e s t e r has s u g g e s t e d t h a t the f i r s t e q u i l i b r i u m i s h y d r o x i d e i o n a d d i t i o n t o the 4 - n i t r o a n i l i n e and the second i s p r o t o n a b s t r a c t i o n from t h i s complex. O t h e r s 4 ^ ' ^ who have u s e d 4 - n i t r o a n i l i n e as an i n d i c a t o r i n aqueous s u l f o l a n e w i t h added base have not r e p o r t e d t h a t i t i o n i z e s by o ther than s i m p l e p r o t o n l o s s . S i m i l a r l y , the s p e c t r a l changes o b s e r v e d i n t h i s work suggest o n l y one e q u i l i b r i u m . I t seems q u i t e p o s s i b l e t h a t the s h i f t of a b s o r p t i o n maximum o b s e r v e d by R o c h e s t e r i n 0 to 8 molar base i s not the r e s u l t of h y d r o x i d e i o n a d d i t i o n t o 4 - n i t r o a n i l i n e but r a t h e r i s a r e s u l t of a change i n the c h a r a c t e r of the medium. There must be a c o n s i d e r a b l e change i n the nature of the s o l v e n t i n g o i n g from water t o 8 molar sodium h y d r o x i d e s i n c e the c o n c e n t r a t i o n of f r e e water (water not bound t o the h y d r o x i d e i o n ) i n 8 molar sodium h y d r o x i d e i s r e d u c e d t o one h a l f of i t s v a l u e 47 i n water . The e f f e c t s of change i n s o l v e n t on the p o s i t i o n of the l o n g wavelength a b s o r p t i o n maximum of 4 - n i t r o a n i l i n e 117 are l a r g e . P e a r s o n 1 2 6 h a s o b s e r v e d s h i f t s from 320 mjj i n n-hexane t o 380 mjj i n d i m e t h y l f ormamide . The p o s s i b i l i t y of the spectrum change b e i n g the r e s u l t of a medium e f f e c t was t e s t e d by measur ing the a b s o r p t i o n spectrum of 4 - n i t r o a n i l i n e i n a p p r o x i m a t e l y 7 molar p o t a s s i u m f l u o r i d e s o l u t i o n . T h i s showed t h a t the l o n g wavelength a b s o r p t i o n maximum i s s h i f t e d 8 t o 10 mp. t o the r e d w i t h an i n c r e a s e of about 10 % i n the molar a b s o r p t i v i t y , £ , as compared t o i n water . A s m a l l e r s h i f t of 4 to 6 mjj^ was o b s e r v e d i n 8 molar sodium p e r c h l o r a t e . Roches ter o b s e r v e d a s h i f t of about 19 mjj i n 8 molar sodium h y d r o x i d e w i t h a s m a l l i n c r e a s e i n molar a b s o r p t i v i t y (the a c t u a l i n c r e a s e i s not r e p o r t e d ) 1 2 5 o I t seems q u i t e r e a s o n a b l e , t h e n , to conc lude t h a t the a b s o r p t i o n maximum of 4 - n i t r o a n i l i n e i s s h i f t e d to the r e d on p a s s i n g from water to 8 molar sodium h y d r o x i d e due t o a change i n the s o l v e n t and i t s i n t e r a c t i o n w i t h the 4 - n i t r o a n i l i n e . The s i z e of the s h i f t depends on the added s a l t - p r o b a b l y on i t s a b i l i t y t o complex the w a t e r . T h i s means t h a t 4 - n i t r o a n i l i n e does not r e a c t by h y d r o x i d e i o n a d d i t i o n i n 0 t o 8 molar sodium h y d r o x i d e as s u g g e s t e d 125 by R o c h e s t e r 118 G . Comparison of the A c i d i t y and B a s i c i t y of A n i l i n e s  and D i p h e n y l a m i n e s 69 Stewart and O ' D o n n e l l have found t h a t a p l o t of p K H A (as o r d i n a t e ) v e r s u s pKB Jj+ (as a b s c i s s a ) f o r a s e r i e s of a n i l i n e s and d i p h e n y l a m i n e s w i t h n i t r o group s u b s t i t u e n t s y i e l d s a l i n e w i t h s l o p e of 0 . 6 . U s i n g some of the data o b t a i n e d i n t h i s work, a s i m i l a r p l o t f o r a s e r i e s of seven m o n o s u b s t i t u t e d d i p h e n y l a m i n e s , a d i c h l o r o - d i p h e n y l a m i n e and d i p h e n y l a m i n e i t s e l f a l s o g i v e s a s t r a i g h t l i n e but w i t h s l o p e 1.30 - .05 and w i t h c o r r e l a t i o n c o e f f i c i e n t r of 0 .995 . The p l o t i s shown i n F i g u r e 12. The p o i n t s f o r t h r e e m o n o - s u b s t i t u t e d d e r i v a t i v e s - 4 - m e t h y l s u l f o n y l , 2 - n i t r o , and 4 - n i t r o d i p h e n y l a m i n e - do not f a l l on t h i s l i n e . The v a l u e of 0.6 f o r the s l o p e found by Stewart 69 and O ' D o n n e l l i n d i c a t e s t h a t s u b s t i t u e n t s have a g r e a t e r e f f e c t on b a s i c i t y than on a c i d i t y f o r n i t r a t e d a n i l i n e s and d i p h e n y l a m i n e s whereas the s l o p e of 1.30 f o r the compounds i n F i g u r e 12 i n d i c a t e s t h a t the o p p o s i t e i s t r u e f o r d i p h e n y l  amines w i t h most o ther s u b s t i t u e n t s , i n c l u d i n g the n i t r o group i n the meta p o s i t i o n . F i g u r e 13 i s a p l o t s i m i l a r t o F i g u r e 12 w i t h most of the data at p r e s e n t a v a i l a b l e f o r a n i l i n e s and d i p h e n y l a m i n e s . T h i s i n c l u d e s the data i n F i g u r e 12 and 119 - 2 4 F IGURE 12 PLOT O F P K H A V E R S U S PKBH+ F O R D I P H E N Y L A M I N E S 7 p 4 - 0 C H 3 - 23 / 4 - C H 3 p H - 2 2 © / 3 - 0 C H 3 SLOPE =1.30 / r= -995 / 4-c| - 2 1 A 3-CI P K HA / 3 _ C F 3 - 20 / © 3y4-"-diCI © / 3 - N 0 2 - 19 \ * s \ / 4 - S 0 2 C H 3 ~ 18 X 2 -N02 P KHA=2I .44-HI .30PKBH+ - 1 7 / - 1 6 / 4 - N 0 2 PKBH+ - 15 - 4 - 3 1 1 - 2 - 1 0 1 2 1 1 1 1 1 120 FIGURE 13 h 26 2 4 22 P^HA h 20 - 16 r 14 PLOT OF pKH A VERSUS P K B H + FOR ANILINES AND DIPHENYLAMINES <•>,• ANILINES B,X DIPHENYLAMINES A' ^ > / ^ o a n d p-NITRO AMINES 2 -10 __L_ -8 -6 -4 P ^ B H f -2 0 4 121 a l s o t h a t of Stewart and 0 ' D o n n e l l D y except t h a t d i s s o c i a t i o n c o n s t a n t s d e t e r m i n e d i n t h i s work were used where a p p l i c a b l e . The p K B H + and p K f l A v a l u e s are l i s t e d i n T a b l e V I I I . S t a t i s t i c a l c o r r e c t i o n s f o r the number of i o n i z a b l e 86 127 p r o t o n s ' were a p p l i e d to the pK v a l u e s i n T a b l e V I I I b e f o r e p l o t t i n g them i n F i g u r e 13. The c o r r e c t i o n s a r e : f o r the pKgjj+ of a n i l i n i u m i o n s , add l o g 3; f o r the pKjj^ of a n i l i n e s and the pKgjj+ of diphenylammonium i o n s , add l o g 2; f o r the p K H A of d i p h e n y l a m i n e s , no c o r r e c t i o n . . In F i g u r e 13 i t can be seen t h a t the amines appear t o f a l l i n t o two c l a s s e s . The a n i l i n e s and d i p h e n y l a m i n e s w i t h o u t n i t r o groups form one c l a s s . The p o i n t s f o r the a n i l i n e s i n t h i s group f a l l s l i g h t l y below the p r o j e c t i o n of the l i n e f o r the d i p h e n y l a m i n e s but show a s i m i l a r t r e n d . The o t h e r c l a s s of amines i s c o m p r i s e d of those a n i l i n e s and d i p h e n y l a m i n e s c o n t a i n i n g at l e a s t one n i t r o group o r t h o or para t o the a c i d i c amino g r o u p . These amines f a l l on a s l i g h t l y c u r v e d l i n e of s m a l l e r s l o p e . The d i f f e r e n t b e h a v i o u r of the n i t r a t e d a n i l i n e s and d i p h e n y l a m i n e s as compared t o the o t h e r s u b s t i t u t e d amines must be a r e s u l t of the p e c u l i a r e f f e c t t h a t the n i t r o group has on the a c i d i t y of a r o m a t i c amines . The e f f e c t of the n i t r o group on the b a s i c i t y of a n i l i n e i s q u i t e 122 TABLE V I I I V a l u e s of p K g ^ and p K H A f o r A n i l i n e s and D i p h e n y l a m i n e s S u b s t i t u e n t s P K B H + L i t . P ^ A L i t . r e f . a R e f . A n i l i n e s 3 - c h l o r o 3.52 105 25.63 3 - t r i f l u o r o m e t h y l 3.20 106 25.40 3 -cyano 2.75 105 24.64 4 -cyano 1.74 118 22.68 3 , 4 - d i c h l o r o 2.97 109 24.60 3 , 5 - d i c h l o r o 2 .38 109 23.59 2 , 3 - d i c h l o r o 1.76 109 23.14 2 , 4 - d i c h l o r o 2.02 109 23.46 2 , 5 - d i c h l o r o 1 .53 109 22.71 2 , 6 - d i c h l o r o 0.42 109 22.40 4 - n i t r o 1.00 105 18.91 2 - n i t r o - 0.26 105 17.88 40 2 - n i t r o - 4 - c h l o r o - 1.07 128 17.08 4 - n i t r o - 2 , 5 - d i c h l o r o - 1 .78 23 16.05 40 4 - n i t r o - 2 , 6 - d i c h l o r o - 3.27 23 15.55 40 2 , 4 - d i n i t r o - 4 .26 128 15.00 40 2 , 4 - d i n i t r o - 6 - b r o m o - 6 .68 23 13.63 40 2 , 4 , 6 - t r i n i t r o -10 .10 23 12.20 40 D i p h e n y l a m i n e s 4-methoxy 1.36 23.22 4-methyl 1.20 22.95 none 0 .78 22.44 3-methoxy 0.40 22.22 4 - c h l o r o 0.01 21 .33 3 - c h l o r o - 0 .45 20.73 3 - t r i f l u o r o m e t h y l - 0 .78 20.48 3 , 4 ' - d i c h l o r o - 1.19 19.73 3 - n i t r o - 1.61 19.53 4 - m e t h y l s u l f o n y l - 2.54 18.80 C o n t i n u e d . 123 T a b l e V I I I - C o n t i n u e d . . S u b s t i t u e n t s P K B H + L i t . P K HA L i t . R e f . a R e f . a D i p h e n y l a m i n e s 2 - n i t r o - 4 .12 17.91 4 - n i t r o - 3.13 15.67 4 - n i t r o - 3 ' - t r i f l u o r o m e t h y l - 4 ,47 14.96 3 , 4 ' - d i n i t r o - 5.19 14.66 4 , 4 ' - d i n i t r o - 6.21 14.08 40 a v a l u e s w i t h o u t r e f e r e n c e were d e t e r m i n e d i n t h i s work 125 r e g u l a r . The pKgjj+ of 2 , 4 , 6 - t r i n i t r o a n i 1 ine would be e x p e c t e d t o be -9 .72 based on the p K _ „ + v a l u e s of a n i l i n e bn ( 4 . 6 0 ) , 2 - n i t r o a n i l i n e ( - 0 . 2 6 ) , and 4 - n i t r o a n i l i n e ( 1 . 0 0 ) 1 0 5 . 23 I t has been d e t e r m i n e d t o be - 1 0 . 1 0 . On the o t h e r hand, the e f f e c t of the n i t r o group on the a c i d i t y of a n i l i n e i s q u i t e i r r e g u l a r . The p K H A v a l u e of 2 , 4 , 6 - t r i n i t r o a n i l i n e would be e x p e c t e d to be 0 .1 based on the p K y A of a n i l i n e ( e s t i m a t e d t o be 2 7 . 3 ) , 2 - n i t r o a n i l i n e ( 1 7 . 8 8 ) 4 0 , and 4- n i t r o a n i l i n e ( 1 8 . 9 1 ) . I t has been f o u n d 4 0 t o be 12 .20 . Thus the f i r s t n i t r o group i n the o r t h o or para p o s i t i o n of a n i l i n e produces a g r e a t enhancement i n a c i d i t y , however the e f f e c t on a c i d i t y of the second and subsequent s u b s t i t u e n t s i s dampened. On the o ther hand the b a s i c i t i e s of a n i l i n e s v a r y r e g u l a r l y w i t h m u l t i p l e s u b s t i t u t i o n . The e q u a t i o n f o r the l i n e i n F i g u r e 12 r e l a t i n g the a c i d i t i e s t o the b a s i c i t i e s of d i p h e n y l a m i n e s i s P K HA = 21.44 + 1 .30 (pK B R +) (36) I t i s i n t e r e s t i n g t o use t h i s e q u a t i o n t o e s t i m a t e a v a l u e f o r the p K H A of ammonia from i t s pKg H + . The P K B H + ° f ammonia 67 i s 9 .25 but s i n c e t h e r e are f o u r i o n i z a b l e p r o t o n s on the ammonium i o n as compared t o two on the diphenylammonium ion the f a c t o r l o g 2 must be added t o the pKg H + . U s i n g the value 9 .55 f o r the PKgjj+ ° f ammonia a v a l u e of 33.8 i s 126 o b t a i n e d f o r the p K R A f rom e q u a t i o n (36) . T h i s i n t u r n must be c o r r e c t e d f o r the f a c t t h a t ammonia has t h r e e i o n i z a b l e p r o t o n s whereas d i p h e n y l a m i n e has one so t h a t the d i s s o c i a t i o n c o n s t a n t f o r the former compound s h o u l d be three t imes as l a r g e as t h a t g i v e n i n e q u a t i o n (36) . Thus the f a c t o r l o g 3 must be s u b t r a c t e d from 33.8 t o g i v e 6 8 a v a l u e of 33.3 f o r the p K j ^ of ammonia. B e l l has e s t i m a t e d t h a t the p K „ . of ammonia i s 35. 127 SUGGESTIONS FOR FURTHER WORK One of the p o t e n t i a l a p p l i c a t i o n s of Hammett a c i d i t y f u n c t i o n s i s the e l u c i d a t i o n of r e a c t i o n mechanisms t h r o u g h the q u a n t i t a t i v e t reatment of a c i d and base c a t a l y s i s . P r o c e d u r e s have been o u t l i n e d f o r use of 31 32 129 c o r r e l a t i o n s of r e a c t i o n r a t e s w i t h H Q ' or H_ as a c r i t e r i o n of mechanism. Most c o r r e l a t i o n s t h a t have been made i n v o l v e d r e a c t i o n s of a c i d s or bases of s t r u c t u r a l t y p e s d i f f e r e n t f rom those of the i n d i c a t o r s t h a t were used t o determine H_ or H Q . In o r d e r to draw v a l i d c o n c l u s i o n s about the r e a c t i o n mechanism i t i s n e c e s s a r y that the i o n i z a t i o n of the s u b s t r a t e i n v o l v e d i n the r e a c t i o n be governed by the a c i d i t y f u n c t i o n used i n the c o r r e l a t i o n . T h i s has p r o b a b l y not been so i n many c a s e s . S i n c e a r o m a t i c amines were u s e d t o e s t a b l i s h the H _ s c a l e i n DMSO-water i t would be p r e f e r a b l e , i n any i n v e s t i g a t i o n of c o r r e l a t i o n s of r a t e w i t h H_ i n t h i s sys tem, t o s t u d y the r e a c t i o n of an a r o m a t i c amine s u b s t r a t e One such r e a c t i o n i s the f o l l o w i n g base c a t a l y z e d i n t r a - 130 131 m o l e c u l a r c o n d e n s a t i o n of 2 - a m i n o - 2 ' - n i t r o b i p h e n y l ' 128 T h i s r e a c t i o n proceeds almost q u a n t i t a t i v e l y i n r e f l u x i n g 131 methanol c o n t a i n i n g sodium h y d r o x i d e , p r o b a b l y by an a l d o l - t y p e mechanism i n v o l v i n g i o n i z a t i o n of the amino group f o l l o w e d by a t t a c k of the a n i o n on the n i t r o g e n atom of the n i t r o g r o u p 1 3 2 . The i o n i z a t i o n of the amino group s h o u l d be governed by the H _ s c a l e e s t a b l i s h e d i n t h i s work f o r DMSO-water m i x t u r e s . I t s h o u l d be p o s s i b l e t o m o d i f y the r a t e of the r e a c t i o n by p l a c i n g s u b s t i t u e n t s i n e i t h e r r i n g . The k i n e t i c s c o u l d be f o l l o w e d c o n v e n i e n t l y by measur ing the i n c r e a s e i n l i g h t a b s o r p t i o n due t o the azoxy chromophore of the p r o d u c t . An i n t e r e s t i n g companion s t u d y would be the r e a c t i o n 1 3 0 ' 1 3 1 i n which the n u c l e o p h i l i c atom i s carbon r a t h e r than n i t r o g e n . 129 I t would be interesting t o s t u d y the b a s i c i t y i n p o l a r a p r o t i c s o l v e n t s of such weak bases as p h e n o x i d e , b e n z o a t e j a c e t a t e , and f l u o r i d e i o n s s i n c e i t i s q u i t e p o s s i b l e t h a t some of these i o n s , when s t r i p p e d of t h e i r s o l v a t i n g water m o l e c u l e s , would become q u i t e b a s i c . For example, the f l u o r i d e i o n appears to be a s t r o n g base i n a p r o t i c s o l v e n t s s i n c e te t raethylammonium f l u o r i d e when warmed i n these s o l v e n t s y i e l d s e t h y l e n e and t r i e t h y l a m m o n i u m f l u o r i d e 1 ^ ^ Such a s tudy s h o u l d p r o v i d e i n f o r m a t i o n about the s o l v a t i o n of these i o n s i n aqueous s o l u t i o n . C C H 3 C H 2 - ) 4 N + F " — ^ — * CCH 3CH 2 - ) 3NHF +• CH 2 =CH 2 134 A solvent , t h a t has proven t o be u s e f u l i n c a r r y i n g out a g r e a t number of o r g a n i c r e a c t i o n s i n v o l v i n g a n i o n s i s hexamethylphosphoramide (XXXVII ) . 130 [(CH 3)2N-] 3P=0 X X X V I I I t has a wide l i q u i d range ( 4 - 2 3 2 ° ) and a f a i r l y l a r g e 135 d i e l e c t r i c c o n s t a n t (D = 30 at 2 5 ° ) . Because of the 135 e x t r e m e l y weak a c i d i t y of i t s hydrogen atoms h e x a m e t h y l - phosphoramide does not r e a c t w i t h such s t r o n g bases as the a n i o n of c y c l o h e x y l a m i n e , u n l i k e DMSO. S i n c e p o t a s s i u m h y d r o x i d e and t - b u t o x i d e appear t o be v e r y s t r o n g bases i n h e x a m e t h y l p h o s p h o r a m i d e 1 3 5 i t might be p o s s i b l e t o e x t e n d the H _ s c a l e i n t h i s s o l v e n t . R e c e n t l y , Gordon has made s t u d i e s i n molten q u a t e r n a r y ammonium s a l t s and h i s r e s u l t s s h o u l d s t i m u l a t e i n t e r e s t i n t h i s f i e l d . The r e l a t i v e l y low m e l t i n g p o i n t s of some of these s a l t s s h o u l d a l l o w them t o be s t u d i e d 136a u s i n g s t a n d a r d i n s t r u m e n t a t i o n . Gordon s u g g e s t s t h a t the n u c l e o p h i l i c r e a c t i v i t y of a n i o n s i s enhanced as the medium p r o g r e s s e s from p r o t i c s o l v e n t t o p o l a r a p r o t i c s o l v e n t t o f u s e d s a l t . The b a s i c i t y of a n i o n s s h o u l d a l s o be enhanced i n f u s e d s a l t s and d e s e r v e s some s t u d y . S o l u b i l i t y s h o u l d be no problem s i n c e n e a r l y a l l t y p e s of o r g a n i c compounds, w i t h the e x c e p t i o n of s a t u r a t e d h y d r o c a r b o n s , 131 are m i s c i b l e w i t h the f u s e d s a l t s near t h e i r m e l t i n g . 136c p o i n t s 132 APPENDIX A : P r e p a r a t i o n and P u r i f i c a t i o n of I n d i c a t o r s 4 - M e t h o x y d i p h e n y l a m i n e : p r e p a r e d by r e a c t i o n of 4 - h y d r o x y - d i p h e n y l a m i n e (Eastman O r g a n i c C h e m i c a l s ) w i t h d i  m e t h y l s u l f ate i n b a s i c s o l u t i o n . The p r o d u c t m e l t e d at 104.5 - 1 0 5 ° a f t e r r e c r y s t a l l i z a t i o n t h r e e t imes from aqueous e t h a n o l and once from p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) f o l l o w e d by s u b l i m a t i o n . L i t . m . p . 1 0 5 ° . 4 - M e t h y l d i p h e n y l a m i n e : p r e p a r e d from p - t o l u i d i n e and bromo- benzene by the same method u s e d by S c a r d i g l i a and R o b e r t s 1 3 8 t o prepare 3 - m e t h y l d i p h e n y l a m i n e . A f t e r s e v e r a l r e c r y s t a l l i z a t i o n s from p e t r o l e u m e t h e r (65 - 1 1 0 ° ) f o l l o w e d by s u b l i m a t i o n the p r o d u c t m e l t e d at 87.5 - 8 8 ° . L i t . m . p . 8 9 ° 1 3 7 . D i p h e n y l a m i n e : o b t a i n e d from Eastman O r g a n i c C h e m i c a l s was r e c r y s t a l l i z e d from p e t r o l e u m e t h e r ( 3 0 - 6 0 ° ) and o 0 137 s u b l i m e d , m . p . 53-53 .5 . L i t . m . p . 54 3-Met .hoxydiphenyl amine : 3 - h y d r o x y d i p h e n y l amine p r e p a r e d from 139 a n i l i n e and r e s o r c i n o l by the method of Calm was m e t h y l a t e d i n b a s i c s o l u t i o n w i t h d i m e t h y l s u l f a t e . A f t e r s u b l i m a t i o n f o l l o w e d by two r e c r y s t a l l i z a t i o n s from p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) the p r o d u c t m e l t e d at 6 8 . 5 - 6 9 ° . L i t . m . p . 7 2 ° 1 4 ° . 133 3- C h l o r o d i p h e n y l a m i n e : p r e p a r e d from 3 - c h l o r o a c e t a n i l i d e 141 and iodobenzene by G o l d b e r g ' s method of p r e p a r i n g 20 d i p h e n y l a m i n e s , b . p . 3 3 5 ° / 7 3 9 mm, n ^ 1 .6507. L i t . b . p . 3 4 0 ° / 7 6 6 mm 1 4 2 . 4- C h l o r o d i p h e n y l a m i n e : p r e p a r e d by the g e n e r a l method of 143 144 Chapman ' . N - P h e n y l b e n z i m i n o - 4 - c h l o r o p h e n y l e t h e r ( X X X V I I I ) , p r e p a r e d from 4 - c h l o r o p h e n o l and i 43a b e n z a n i l i d e by the same method u s e d by Chapman f o r the p r e p a r a t i o n of N - p h e n y l b e n z i m i n o - 3 - h y d r o x y - p h e n y l e t h e r , was hea ted f o r two hours at 2 8 0 - 3 0 0 ° i n a Woods' metal bath to y i e l d a d a r k , v i s c o u s m a t e r i a l t h a t was h y d r o l y z e d and the r e s u l t i n g 4 - c h l o r o d i p h e n y l a m i n e (XXXIX) i s o l a t e d a c c o r d i n g t o the method of C h a p m a n 1 ^ ^ . A f t e r s e v e r a l r e c r y s t a i l i z a t i o n s from p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) f o l l o w e d by s u b l i m a t i o n , the p r o d u c t m e l t e d at 6 8 . 5 - 6 9 ° . L i t . m . p . 7 0 . 6 ° 1 4 5 . 134 3 , 4 ' - D i c h l o r o d i p h e n y l a m i n e : p r e p a r e d by the same method u s e d i n the p r e p a r a t i o n of 4 - c h l o r o d i p h e n y l a m i n e . N - 3 - 143a C h l o r o p h e n y l b e n z i m i n o - 4 - c h l o r o - p h e n y l e t h e r , p r e p a r e d from 4 - c h l o r o p h e n o l and b e n z - 3 - c h l o r o a n i l i d e , was heated f o r two hours at 2 9 0 - 3 0 0 ° and the r e s u l t i n g m a t e r i a l r e f l u x e d i n a l c o h o l i c p o t a s s i u m h y d r o x i d e f o r two h o u r s 1 4 3 < * . A f t e r s e v e r a l r e c r y s t a l l i z a t i o n s from p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) f o l l o w e d by s u b l i m a t i o n the p r o d u c t , 3 , 4 ' - d i c h l o r o d i p h e n y l a m i n e , m e l t e d at 6 1 - 6 2 ° . L i t . m . p . 6 3 - 6 4 ° 1 4 6 . 3 - T r i f l u o r o m e t h y l d i p h e n y l a m i n e : o b t a i n e d from A l d r i c h C h e m i c a l C o . was d i s t i l l e d under r e d u c e d p r e s s u r e , the m i d d l e cut d i s s o l v e d i n d r y e t h e r and hydrogen c h l o r i d e gas b u b b l e d t h r o u g h the s o l u t i o n . The p r e c i p i t a t e was f i l t e r e d o f f , washed w i t h e t h e r and r e c r y s t a l l i z e d from d r y benzene . I t was then d i s s o l v e d i n aqueous sodium c a r b o n a t e , e x t r a c t e d w i t h e t h e r , the e t h e r s o l u t i o n d r i e d , the e t h e r removed and the amine d i s t i l l e d a g a i n , n 2 0 1 .5675. L i t . n 2 5 1.5655 1 4 7 . 3 - N i t r o d i p h e n y l a m i n e : p r e p a r e d from 3 -ni t robromobenzene and 1 48 a c e t a n i l i d e by the method u s e d by Hodgson and Dodgson f o r the p r e p a r a t i o n of 3 , 3 ' - d i n i t r o d i p h e n y l a m i n e . A f t e r t h r e e r e c r y s t a l l i z a t i o n s from aqueous e t h a n o l , s u b l i m a t i o n and another r e c r y s t a l l i z a t i o n from aqueous 135 e t h a n o l the p r o d u c t m e l t e d at 1 1 0 - 1 1 1 ° . L i t . m . p . o 137 1 1 2 ° 4 - M e t h y l s u l f o n y l d i p h e n y l a m i n e : p r e p a r e d from 4 - b r o m o p h e n y l - 149 m e t h y l s u l f o n e and a c e t a n i l i d e by the method used by N o d i f f and c o - w o r k e r s f o r the p r e p a r a t i o n of 3 - m e t h y l s u l f o n y l d i p h e n y l a m i n e . The p r o d u c t was r e  c r y s t a l l i z e d from benzene , e t h a n o l and e t h y l a c e t a t e , s u b l i m e d , p a s s e d down an alumina column w i t h b e n z e n e - acetone (3:1) mix ture and f i n a l l y r e c r y s t a l l i z e d from b e n z e n e - p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) , m . p . 1 6 8 - 1 6 8 . 5 ° . A n a l y s i s ; C H N S c a l c . 63.13% 5.30% 5.66% 12.96% f o u n d 63.20% 5.80% 5.45% 12.80% 4 - N i t r o d i p h e n y l a m i n e : had been p r e p a r e d and p u r i f i e d p r e v i o u s l y 7 6 d i n t h i s l a b o r a t o r y , m . p . 131-133 . L i t . m . p . 1 3 3 ° 1 4 1 . 2- N i t r o d i p h e n y l a m i n e : o b t a i n e d from Eastman O r g a n i c C h e m i c a l s was r e c r y s t a l l i z e d twice from a c e t i c a c i d , m . p . 7 3 - 7 4 ° . L i t . m . p . 7 5 ° 1 4 1 . 3- 4 ' - D i n i t r o d i p h e n y l a m i n e : p r e p a r e d from the sodium s a l t of 2 - c h l o r o - 5 - n i t r o b e n z e n e s u l f o n i c a c i d (Eastman O r g a n i c C h e m i c a l s ) and 3 - n i t r o a n i l i n e by the g e n e r a l method 1 51 of Ul lmann and Dahmen . The p r o d u c t was r e c r y s t a l l i z e d from aqueous a c e t i c a c i d , p a s s e d down an alumina column 136 w i t h benzene-ace tone (1:1) mixture and r e c r y s t a l l i z e d from b e n z e n e - p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) p a i r , m . p . 215- 2 1 6 ° . L i t . m . p . 2 1 7 ° 1 5 2 . 4 - N i t r o - 3 ' - m e t h y l d i p h e n y l a m i n e : p r e p a r e d and p u r i f i e d by D r . A . B u c k l e y i n t h i s l a b o r a t o r y , m . p . 1 2 7 - 1 2 8 ° . 4 - N i t r o - 3 ' - c h l o r o d i p h e n y l a m i n e : p r e p a r e d and p u r i f i e d by Dr A . B u c k l e y i n t h i s l a b o r a t o r y , m . p . 1 2 9 - 1 3 0 ° . L i t . m . p . 1 2 9 ° 1 5 3 . 4 - N i t r o - 3 ' - t r i f l u o r o m e t h y l d i p h e n y l a m i n e : p r e p a r e d and p u r i f i e d by D r . A . B u c k l e y i n t h i s l a b o r a t o r y , m . p . 1 3 7 . 5 - 1 3 8 . 5 ° . 2 , 4 - D i n i t r o d i p h e n y l a m i n e : had been p r e p a r e d and p u r i f i e d p r e v i o u s l y 7 ^ i n t h i s l a b o r a t o r y m . p . 1 5 5 - 1 5 6 ° . T . 1 c c o 154 L i t . m . p . 155 4 , 4 ' - D i n i t r o d i p h e n y l a m i n e : had been p r e p a r e d and p u r i f i e d 76 o p r e v i o u s l y i n t h i s l a b o r a t o r y , m . p . 213-216 . L i t . m . p . 2 1 6 ° 1 5 5 . 3 - C h l o r o a n i l i n e : o b t a i n e d from Eastman O r g a n i c C h e m i c a l s was d i s t i l l e d from z i n c dust and r e d i s t i l l e d b e f o r e u s e , n 2 0 1 .5933. L i t . n 2 ° 1.5931 1 5 3 . 3 - T r i f l u o r o m e t h y l a n i l i n e : o b t a i n e d from Matheson, Coleman and B e l l was d i s t i l l e d t w i c e , n ^ ° 1 .4795. L i t . n 2 5 137 1.4775 1 5 6 3- C y a n o a n i l i n e : p r e p a r e d from 3 - b r o m o a n i l i n e and cuprous c y a n i d e by the g e n e r a l method of Fr iedman and S c h e c t e r 157 The p r o d u c t was s u b l i m e d , r e c r y s t a l l i z e d from c h l o r o f o r m - p e t r o l e u m e t h e r ( 3 0 - 6 0 ° ) p a i r , s u b l i m e d , r e c r y s t a l l i z e d from c y c l o h e x a n e - c h l o r o f o r m p a i r , and 1 I n s u b l i m e d a g a i n , m . p . 52-53 . L i t . m . p . 5 2 ° 4- C y a n o a n i l i n e : o b t a i n e d from Eastman O r g a n i c C h e m i c a l s was s u b l i m e d , r e c r y s t a l l i z e d t h r e e t imes from aqueous e t h a n o l , s u b l i m e d , r e c r y s t a l l i z e d from c y c l o h e x a n e - c h l o r o f orm p a i r and s u b l i m e d a g a i n , m . p . 8 5 - 8 6 ° . o 117 L i t . m . p . 86 2 . 3 - D i c h l o r o a n i l i n e : o b t a i n e d from A l d r i c h C h e m i c a l C o . was d i s t i l l e d and r e c r y s t a l l i z e d once from cyc lohexane and twice from hexane, m . p . 26 - 2 6 . 5 ° . L i t . m . p . 23 .5 - 2 4 ° 1 0 9 . 2 . 4 - D i c h l o r o a n i l i n e : o b t a i n e d from Eastman O r g a n i c C h e m i c a l s was r e c r y s t a l l i z e d twice from methanol and s u b l i m e d , m . p . 61 .5 - 6 2 . 5 ° . L i t . m . p . 6 3 ° 1 0 9 . 2 . 5 - D i c h l o r o a n i l i n e : o b t a i n e d from A l d r i c h C h e m i c a l C o . was r e c r y s t a l l i z e d twice from cyc lohexane and s u b l i m e d m . p . 49 - 5 0 ° . L i t . m . p . 50 - 5 0 . 5 ° 1 0 9 . 138 2 , 6 - D i c h l o r o a n i l i n e : o b t a i n e d from A l d r i c h C h e m i c a l C o . was r e c r y s t a l l i z e d from c y c l o h e x a n e , d i s t i l l e d , and r e c r y  s t a l l i z e d from hexane, m . p . 3 7 . 5 - 3 8 ° . L i t . m . p . 3 8 . 5 - 39 o 109 3 , 4 - D i c h l o r o a n i l i n e : p r e p a r e d by the r e d u c t i o n of 3 , 4 - d i c h l o r o n i t r o b e n z e n e (Columbia O r g a n i c C h e m i c a l s C o . ) w i t h s tannous c h l o r i d e by the method of F e r r y and c o - w o r k e r s 1 5 8 used f o r the r e d u c t i o n of 4 - n i t r o - 4 ' - a c e t y l a m i n o d i p h e n y l s u l f o n e . A f t e r s u b l i m a t i o n and two r e c r y s t a l l i z a t i o n s from cyc lohexane the p r o d u c t m e l t e d at 7 1 - 7 2 ° . L i t . m . p . 7 2 ° 1 0 9 . 3 , 5 - D i c h l o r o a n i l i n e : p r e p a r e d by f i r s t d e a m i n a t i n g 2 , 6 - d i c h l o r o - 4 - n i t r o a n i l i n e (Eastman O r g a n i c C h e m i c a l s ) 159a u s i n g the procedure of V o g e l f o r the d e a m i n a t i o n of 2 , 4 , 6 - t r i b r o m o a n i l i n e and then r e d u c i n g the r e s u l t i n g 3 , 5 - d i c h l o r o n i t r o b e n z e n e i n the same manner 158 u s e d f o r 3 , 4 - d i c h l o r o n i t r o b e n z e n e . A f t e r s u b l i m a t i o n two r e c r y s t a l l i z a t i o n s from c y c l o h e x a n e , and s u b l i m a t i o n a g a i n the p r o d u c t m e l t e d at 49 .5 - 5 1 ° . L i t , m . p . 50 - 5 0 . 5 ° 1 0 9 . 3 , 4 , 5 - T r i c h l o r o a n i l i n e : p r e p a r e d by the r e d u c t i o n of 3 , 4 , 5 - t r i c h l o r o n i t r o b e n z e n e (Columbia O r g a n i c C h e m i c a l s C o . ) w i t h s tannous c h l o r i d e by the same m e t h o d 1 5 8 used i n the r e d u c t i o n of 3 , 4 - d i c h l o r o n i t r o b e n z e n e . A f t e r 1 3 9 r e c r y s t a l l i z a t i o n from e t h a n o l and cyc lohexane f o l l o w e d by s u b l i m a t i o n the p r o d u c t m e l t e d at 9 7 - 9 7 . 5 ° . L i t . m . p . 8 9 ° 1 6 0 ; 9 4 - 9 5 ° 1 6 1 ; 1 0 0 ° 1 6 2 ; 1 0 1 ° 1 6 3 . 2 , 3 , 5 , 6 - T e t r a c h l o r o a n i l i n e : p r e p a r e d by r e d u c t i o n of the c o r r e s p o n d i n g n i t r o compound. 2 , 3 , 5 , 6 - T e t r a c h l o r o n i t r o - benzene (Columbia O r g a n i c C h e m i c a l s C o . ) ( 0 . 0 5 m o l e ) , 5 0 gram of z i n c amalgam I ^ J J D a n c j 59 m\ Q± c o n c e n t r a t e d h y d r o c h l o r i c a c i d were r e f l u x e d i n 1 5 0 ml of e t h a n o l f o r t h r e e h o u r s . On c o o l i n g the r e a c t i o n mix ture the p r o d u c t c r y s t a l l i z e d out and was c o l l e c t e d . A f t e r r e c r y s t a l l i z a t i o n twice from p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) , once from e t h a n o l , and twice from aqueous a c e t i c a c i d f o l l o w e d by s u b l i m a t i o n the p r o d u c t m e l t e d at 1 0 6 . 5 - 1 0 7 . 5 ° . L i t . m . p . 1 0 7 - 1 0 8 ° 1 6 4 . 4 - N i t r o a n i l i n e : o b t a i n e d from Eastman O r g a n i c C h e m i c a l s was r e c r y s t a l l i z e d twice from aqueous e t h a n o l , m . p . 1 4 7 - 1 4 8 ° . L i t . m . p . 1 4 8 . 5 - 1 4 9 . 5 ° 1 6 5 . 2 - M e t h y i - 4 - n i t r o a n i l i n e : p r e p a r e d by the method of Page 1 6 6 and Heasman . A f t e r two r e c r y s t a i l i z a t i o n s from methanol the p r o d u c t m e l t e d at 1 2 9 . 5 - 1 3 0 . 5 ° . L i t . o 1 6 6 n 1 6 7 m . p . 1 3 4 - 1 3 4 . 5 ° ; 1 3 1 . 5 - 1 3 2 . 5 ° . 140 2 , 6 - D i m e t h y l - 4 - n i t r o a n i l i n e : p r e p a r e d by the method of • I C Q Wepster . A f t e r two r e c r y s t a l l i z a t i o n s from aqueous e t h a n o l the p r o d u c t m e l t e d at 1 6 1 - 1 6 2 ° . L i t . m . p . 163.5 - 1 6 4 . 5 ° 1 6 8 . 2 , 6 - D i - t - b u t y l - 4 - n i t r o a n i l i n e : 1 , 3 , 5 - t r i - t - b u t y l b e n z e n e was p r e p a r e d from 1 , 4 - d i - t - b u t y l b e n z e n e (Eastman O r g a n i c C h e m i c a l s ) and t - b u t y l c h i o r i d e by the method of Ross and c o - w o r k e r s 1 * * 9 . T h i s compound was then n i t r a t e d and the n i t r o group r e d u c e d t o y i e l d 2 , 4 , 6 - t r i - t - 170 b u t y l a n i l i n e by the method of B u r g e r s and c o - w o r k e r s The l a t t e r compound was n i t r a t e d by the method of 171 B u r g e r s and c o - w o r k e r s t o g i v e the d e s i r e d 2 , 6 - d i - t - b u t y l - 4 - n i t r o a n i l i n e , w h i c h , a f t e r r e c r y s t a l l i z a t i o n once from aqueous e t h a n o l and twice from e t h y l a c e t a t e - p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) p a i r , m e l t e d at 2 5 9 - 2 6 0 ° . L i t . m . p . 2 5 7 - 2 5 8 ° 1 7 1 . 3 , 5 - D i m e t h y l - 4 - n i t r o a n i l i n e : p r e p a r e d by the method of 172 Wepster and Verkade . A f t e r two r e c r y s t a l l i z a t i o n s from e t h a n o l f o l l o w e d by s u b l i m a t i o n the compound m e l t e d at 130.5 - 1 3 1 ° . L i t . m . p . 1 3 1 - 1 3 2 ° 1 7 2 . 2 , 3 , 5 , 6 - T e t r a m e t h y l - 4 - n i t r o a n i l i n e : 1 , 2 , 4 , 5 - t e t r a m e t h y l - benzene (Eastman O r g a n i c C h e m i c a l s ) was n i t r a t e d t o g i v e the d i n i t r o d e r i v a t i v e by the method of Smith and D o b r o v o l n y 1 7 3 w h i c h , i n t u r n , was p a r t i a l l y r e d u c e d . 141 by the method of Hampson and c o - w o r k e r s 5 to g i v e the d e s i r e d p r o d u c t . A f t e r two s u b l i m a t i o n s and t h r e e r e c r y s t a i l i z a t i o n s from e t h a n o l the compound m e l t e d at 160.5 - 1 6 1 ° . L i t . m . p . 1 6 1 - 1 6 2 ° 1 7 5 . N - M e t h y l - 4 - n i t r o a n i l i n e : p r e p a r e d from 4 - n i t r o a c e t a n i l i d e and methyl i o d i d e by the method of P a c h t e r and K l o e t z e l 176 A f t e r two r e c r y s t a i l i z a t i o n s from e t h a n o l f o l l o w e d by s u b l i m a t i o n the p r o d u c t m e l t e d at 150.5 - 1 5 1 . 5 ° . L i t . m . p . 1 5 3 - 1 5 4 ° 1 7 6 . N - E t h y l - 4 - n i t r o a n i l i n e : p r e p a r e d from 4 - n i t r o a c e t a n i l i d e -1 rvsy and e t h y l i o d i d e by the same method used f o r the N-methyl compound. A f t e r two r e c r y s t a i l i z a t i o n s from e t h a n o l f o l l o w e d by s u b l i m a t i o n the p r o d u c t m e l t e d at 9 4 . 5 - 9 5 . 5 ° . L i t . m . p . 9 5 ° N , 2 - D i m e t h y l - 4 - m i t r o a n i l i n e : p r e p a r e d from 2 - m e t h y l - 4 - n i t r o - a n i l i n e and methyl i o d i d e by the same procedure u s e d i n the p r e p a r a t i o n of N - m e t h y l - 4 - n i t r o a n i l i n e . A f t e r r e c r y s t a l l i z a t i o n from aqueous e t h a n o l , s u b l i m a t i o n and two more r e c r y s t a i l i z a t i o n s from aqueous e t h a n o l the p r o d u c t m e l t e d at 135.5 - 1 3 6 . 5 ° . L i t . m . p . 1 3 7 ° 1 7 8 . N - I s o p r o p y l - 4 - n i t r o a n i l i n e : 4 - n i t r o a n i l i n e (2 gm) was d i s s o l v e d i n 10 ml of DMSO and 1 gm of powdered p o t a s s i u m h y d r o x i d e added c a u s i n g the s o l u t i o n t o t u r n h i g h l y c o l o u r e d . 2-Bromopropane (2 gm) was added, the mix ture 142 s t i r r e d f o r ten m i n u t e s , and then heated on a steam bath f o r an h o u r , a f t e r which i t was poured on t o i c e . A y e l l o w s o l i d m a t e r i a l was s u b l i m e d from the r e s u l t i n g dark t a r r y p r o d u c t and on r e c r y s t a l l i z a t i o n from benzene- p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) p a i r y i e l d e d a h i g h m e l t i n g p r o d u c t - p r o b a b l y u n r e a c t e d 4 - n i t r o a n i l i n e . E v a p o r a t i o n of the mother l i q u o r gave about 0 .5 gm of another y e l l o w s o l i d m a t e r i a l t h a t was p a s s e d down a s i l i c a g e l column w i t h b e n z e n e - e t h y l a c e t a t e (5 :1) m i x t u r e . The f i r s t band o f f the column was c o l l e c t e d and r e c r y s t a l l i z e d from p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) , m . p . 8 3 - 8 4 ° . A n a l y s i s : C H N C a l c . 59.99% 6.71% 15.55% Found 59.85% 6.41% 15.59% The NMR spectrum of the compound i n carbon t e t r a c h l o r i d e w i t h i n t e r n a l TMS s t a n d a r d c o n t a i n s : a d o u b l e t c e n t e r e d at 2 .03 X and another at 3.55 TJ" both w i t h r e l a t i v e area of two and s p l i t t i n g of about 9 .3 c . p . s . ; a broad a b s o r p t i o n at about 5.19 X w i t h r e l a t i v e area of one; a h i g h l y s t r u c t u r e d a b s o r p t i o n at about 6 .35 TT w i t h r e l a t i v e area of one; and a d o u b l e t c e n t e r e d at 8.79 X w i t h r e l a t i v e area of s i x and s p l i t t i n g of about 6 .5 c . p . s . 143 N - t - B u t y l - 4 - n i t r o a n i l i n e : p r e p a r e d from the r e a c t i o n of 4 - n i t r o a n i l i n e and t - b u t y l a l c o h o l i n p h o s p h o r i c 179 a c i d by the method of G l e i m . The p r o d u c t was p a s s e d down a s i l i c a g e l column with b e n z e n e - e t h y l a c e t a t e (10:1) m i x t u r e and the f i r s t band o f f the column was c o l l e c t e d . T h i s m a t e r i a l was s u b l i m e d and r e c r y s t a l l i z e d from e t h y l a c e t a t e - p e t r o l e u m e t h e r 1 1 0 ° ) o 180 ( 6 5 - p a i r , m . p . 68 .5 - 6 9 . 5 ° . L i t . m . p . 68- 69 .5 A n a l y s i s : C H N c a l c . 61.84% 7.27% 14.42% found 61.95% 7.36% 14.42% N - T r i p h e n y l m e t h y l - 4 - n i t r o a n i l i n e : p r e p a r e d from t r i p h e n y l m e t h y l c h l o r i d e and 4 - n i t r o a n i l i n e b y the method of Verkade 1 81 and c o - w o r k e r s . A f t e r t h r e e r e c r y s t a l l i z a t i o n s from e t h a n o l - c h l o r o f o r m p a i r the compound m e l t e d at 2 2 3 - 2 2 5 ° . L i t . m . p . 2 2 3 - 2 2 4 ° 1 8 1 . 2 , 2 s - D i p y r i d y l a m i n e : o b t a i n e d from Columbia O r g a n i c C h e m i c a l s C o . was r e c r y s t a l l i z e d twice from aqueous e t h a n o l 182 and s u b l i m e d , m . p . 9 3 - 9 4 . L i t . m . p . 94-95 4 - A m i n o d i p h e n y l a m i n e : o b t a i n e d from Matheson, Coleman and B e l l was d i s t i l l e d , d i s s o l v e d i n a s m a l l amount of benzene and p r e c i p i t a t e d w i t h p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) , r e c r y s t a l l i z e d from b e n z e n e - p e t r o l e u m e t h e r ( 6 5 - 1 1 0 ° ) 144 p a i r and then d i s t i l l e d a g a i n . The d i s t i l l a t e was a p a l e y e l l o w c o l o u r and s o l i d i f i e d t o g i v e c r y s t a l s m e l t i n g at 72 .5 - 7 4 . 5 ° . L i t . m . p . 7 5 ° 1 5 3 . 145 APPENDIX B : S p e c t r a l Data f o r the I n d i c a t o r s TABLE IX A b s o r p t i o n Maxima and Molar A b s o r p t i v i t i e s of the I n d i c a t o r s i n 95.6% E t h a n o l Observed V a l u e s Repor S u b s t i t u e n t \ <• max. max. d i p h e n y l a m i n e s 4-methoxy 284 19,000 4-methyl 286 21,400 none 285 21,300 285 3-methoxy 283 18,500 4 - c h l o r o 289 24,000 3 - c h l o r o 286 21,300 3 - t r i f l u o r o m e t h y l 286 21,600 285 3 , 4 ' - d i c h l o r o 290 25,300 3 - n i t r o 27 5 22,300 399 1,180 4 - m e t h y l s u l f o n y l 309 26,300 4 - n i t r o 392 21,700 390 2 - n i t r o 426 6 ,710 422 423 4 - n i t . r o - 3 ' -methyl 394 22,300 4 - n i t r o - 3 ' - c h l o r o 385 22,700 4 - n i t r o - 3 ' - t r i f l u o r o  methyl 381 19,200 3 , 4 ' - d i n i t r o 375 23,200 4,4* - d i n i t . r o 403 34,100 402 2 , 4 - d i n i t r o 352 17 ,700 350 351 a n i l i n e s 3 - c h l o r o 242 8,650 293 1 ,970 3 - t r i f l u o r o m e t h y l 242 9,450 298 2,190 3-cyano 251 7 ,320 320 4,040 r e f 2 0 , 2 5 0 a 183 11.200 184 2 1 , 2 0 0 a 183 6 , 6 0 0 d 183 37,600 183 17 ,000 a 183 146 TABLE IX (Cont inued) O b s e r v e d V a l u e s R e p o r t e d V a l u e s S u b s t i t u e n t ") \ (mu) max. / € A (mu) max. ' £ r e f a n i l i n e s (Cont inued) 4 - cyano 275 23,600 2 , 3 - d i c h l o r o 243 6,670 297 2,830 2 , 4 - d i c h l o r o 245 11,500 306 2,510 2 , 5 - d i c h l o r o 244 8,520 300 3,260 2 , 6 - d i c h l o r o 239 6,780 296 3,490 3 , 4 - d i c h l o r o 248 l l , 6 0 0 305 2,040 3 , 5 - d i c h l o r o 249 9,360 300 2,320 3 , 4 , 5 - t r i c h l o r o 249 12,200 311 2,430 2 , 3 , 5 , 6 - t e t r a c h l o r o 309 4,070 4 - n i t r o 373 16 ,300 370 16,200 185 4 - n i t r o - 2 - m e t h y l 375 14,900 379 17,400 185 4 - n i t r o - 2 , 6 - d i m e t h y l 377 14,600 374 14,200 185 4 - n i t r o - 2 , 6 - d i - t . - b u t y l 379 14,400 4 - n i t r o - 3 , 5 - d i m e t h y l 382 4,970 386 5,000 185 4 - n i t r o - 2 , 3 , 5 , 6 - t e t r a m e t h y l 394 1,590 391 1,500 185 4 - n i t r o - N - m e t h y l 386 18,400 391 18,400 185 4 - n i t r o - N - e t h y l 388 19,800 386 1 8 , 9 0 0 a 183 4 - n i t r o - N - i s o p r o p y l 389 20,800 4 - n i t r o - N - t - b u t y l 389 20,100 4 - n i t r o - N - t r i p h e n y l - methyl 376 19,000 4 - n i t r o - N , 2 - d i m e t h y l 388 17,900 383 15,300 185 2 , 2 f - d i p y r i dylamine 264 22,200 312 14,700 a i n a b s o l u t e e t h a n o l 147 TABLE X A b s o r p t i o n Maxima and Molar A b s o r p t i v i t i e s of D i p h e n y l a m i n e s i n 20% E t h a n o l S u b s t i t u e n t s ' \ max. (ray.) £ 4-methoxy 280 14,500 4 -methyl 282 15,900 none 282 16,400 3-methoxy 282 14,800 4 - c h l o r o 286 18,600 3 - c h l o r o 284 16,900 3 - t r i f l u o r o m e t h y l 284 17,300 3 , 4 ' - d i c h l o r o 288 20,700 3 - n i t r o 280 22,000 4 - m e t h y l s u l f o n y l 309 25,200 4 - n i t r o 409- 410 20,500 2 - n i t r o 444 6,550 4 - n i t r o - 3 ' - m e t h y l 411 20,500 4 - n i t r o - 3 ' - c h l o r o 403 20,600 4 - n i t r o - 3 ' - t r i f l u o r o  m e t h y l 3 400 17,400 3 , 4 ' - d i n i t r o 3 396 20,200 4 , 4 ' - d i n i t r o b 422 32,300 3 20% e t h a n o l c o n t a i n i n g 2.25 molar s u l f u r i c a c i d b 20% e t h a n o l c o n t a i n i n g 2.50 molar s u l f u r i c a c i d 148 TABLE XI A b s o r p t i o n Maxima and Molar A b s o r p t i v i t i e s of I n d i c a t o r A n i o n s i n DMSO-Water S u b s t i t u e n t max O b s e r v e d V a l u e s (ny) £ Mole c, DMSO 3 d i p h e n y l a m i n e s 4-methoxy 370 28,100 99. 8 4 - m e t h y l 375 29,700 99. 5 4-amino 372 23,900 99. 8 none 376 28,500 99. 5 3-methoxy 380 25,800 99. 0 4 - c h l o r o 374 30,200 97. 1 3 - c h l o r o 370 26,900 97. 1 3 - t r i f l u o r o m e t h y l 368 28,800 97. 1 3 - n i t r o 375 14,800 99. 5 3 , 4 ' - d i c h l o r o 376 30,600 97. 1 4 - m e t h y l s u l f o n y l 383 29,400 83. 1 2 - n i t r o 548 9,220 83. 1 2 , 4 - d i n i t r o 434 19,000 46. 5 a n i l i n e s 3 - c h l o r o 386 2,710 l o o p 3 - t r i f l u o r o m e t h y l .404 2,500 100 c i 3-cyano 447 2,530 100 b i 4-cyano 337 37,100 99. 5 2 , 3 - d i c h l o r o 381 3,550 99. 8 2 , 4 - d i c h l o r o 399 3,030 99. 8 2 , 5 - d i c h l o r o 385 3,640 99. 5 2 , 6 - d i c h l o r o 380 4,500 98. 7 3 , 4 - d i c h l o r o 400 2,450 99. 8 3 , 5 - d i c h l o r o 386 2,820 99. 8 3 , 4 , 5 - t r i c h l o r o 397 2,610 99. 5 2 , 3 , 5 , 6 - t e t r a c h l o r o 380 4,480 92. 5 4 - n i t r o 467 30,800 87. 8 4 - n i t r o - 2 - m e t h y l 471 31,900 92. 3 4 - n i t r o - 2 , 6 - d i m e t h y l 474 33,300 92. 3 4 - n i t r o - 2 , 6 - d i - t - b u t y l 470 29,300 95. 3 4 - n i t r o - 3 , 5 - d i m e t h y l 466 23,600 97. 1 R e p o r t e d V a l u e s 545 432 9 , 1 7 0 c 76 2 1 , 8 0 0 d 76 467 3 2 , 3 0 0 ° 76 149 TABLE XI (Cont inued) S u b s t i t u e n t O b s e r v e d V a l u e s R e p o r t e d V a l u e s ^ a x . ^ G M o l e * l a x . ^ C r e f a n i l i n e s DMSO a 4 - n i t r o - 2 , 3 , 5 , 6 - t e t r a m e t h y l 507 17,000 99. 5 4 - n i t r o - N - m e t h y l 483 31,200 97. 1 4 - n i t r o - N - e t h y l 482 31,300 97. 1 4 - n i t r o - N i s o p r o p y l 480 32,000 97. 1 4 - n i t r o - N - t - b u t y l 480 32,000 97. 1 4 - n i t r o - N - t r i p h e n y l - methyl 490 38,600 92. 5 4 - n i t r o - N , 2 - d i m e t h y l 485 31,500 97. 1 2 - n i t r o - 4 - c h l o r o 495 8,440 78. 4 520 8,440 78. 4 2 , 2 ' - d i p y r i d y l a m i n e 370 16,200 92. 5 516 6 , 9 0 0 c 76 a DMSO-water m i x t u r e s c o n t a i n i n g 0.011 molar t e t r a m e t h y l  ammonium h y d r o x i d e b DMSO c o n t a i n i n g p o t a s s i u m t - b u t o x i d e as base c 95 mole % s u l f o l a n e - w a t e r - 0 . 0 1 1 molar tetramethylammonium h y d r o x i d e d p y r i d i n e c o n t a i n i n g 0.011 molar tetramethylammonium h y d r o x i d e 150 APPENDIX C : I o n i z a t i o n R a t i o Data TABLE XII E x p e r i m e n t a l V a l u e s of Log [A~] / [HA] f o r the I n d i c a t o r s Used t o Determine the H _ V a l u e s i n DMSO-Water- Tetramethylammonium H y d r o x i d e (0.011 M.) < a < < H < Q 0 Q CO •p Q CM < r-i ra CM /•> o CM u o ^ \ CM 1 o Q •H CM o - < !Z5 < CM 1 T3 o CO ft 1 o CD C w 1 Q CM Q xn •* M I CM CM 1 CM CO i n 1 - o O rH O K Mole % S5 o S5 CO 1 1 1 I 1 •» DMSO CM CO CM CM 10.32 - .674 15.20 .009 -.741 -1.012 20.18 .683 -.185 - .483 23. 57 1.067 .195 - .117 -.788 26.95 .571 .252 -.452 30.11 .891 .585 -.135 33.42 .933 .183 36.79 .503 -.913 39.86 .757 -.597 43.27 -.253 46.54 .068 -.808 49.59 .356 -.489 52.55 .639 -.170 55.95 .962 .179 -.700 58.56 .447 -.444 59.38 -.8 62.27 .833 -.071 151 TABLE XII (Cont inued) fl < 0 /-s P* -P < r-i a a o< cj CN •H CM I < r-l <! ft C CO - Q ^ Q P< ft O IH CO lO CM I CO Q Q CO K O - fer-itHK O C O S s ^ O O O O I I I I I I T f t C N C O C O C O C O < t f C O Mole ' DMSO 64.20 - . 3 1 9 - . 6 0 9 - . 8 0 5 65 .48 .247 68.51 .558 69.09 .182 - . 1 1 7 - . 314 71 .12 .833 71.35 .442 .128 - . 0 8 3 - . 8 3 8 73.69 .730 .354 .167 - . 594 76.12 .609 .428 - . 330 78.01 - . 3 9 7 78.36 .827 .653 - . 062 - . 918 80.78 .176 - . 660 82.75 .207 83.14 .489 - .361 85.17 .496 85.46 .789 - . 021 87.51 . .810 - . 644 87.79 .294 89.92 - . 2 6 9 90.07 .658 92.29 .172 152 TABLE X I I (Cont inued) O CO fi c ca o O <5 ft < CM CM <M •w CL Q r - l rH •3 c i a o o o q e < in n co ^ ^ <§ Mole % 3 4 < C O ~ T J < 4 M " " DMSO i' 87.79 - .836 90.07 - . 4 6 5 - . 7 0 3 - . 882 90.56 - . 8 6 0 91.48 - . 6 9 3 - . 9 4 5 92.47 .012 - . 2 2 9 - . 4 3 4 92.52 - . 463 - . 741 93.47 - .261 - . 524 94.34 - . 0 5 8 - . 330 94 .74 .562 .310 .156 - .577 95.04 .133 - . 133 95.55 .311 .009 95.77 .874 .644 .479 - . 280 96.21 .799 .644 - . 103 96.64 .650 .407 97 13 .274 - . 6 8 8 - . 740 97.31 .358 97 89 .653 - . 3 4 5 - .396 153 TABLE XII (Cont inued) O +•' o C a < < ^ > ^ T3 rH _ DMSO c 10 J< S * H o cj o Mole % ~ - i t " C O CO CO CO 98.29 .935 - .111 _ . i 4 0 - . 906 ll'il " 2 4 4 - 2 0 3 - ' 5 5 8 ~-777 - 7 3 0 -640 - . 1 0 5 - .336 a y ' D a .837 .510 NOTE DPA i s d i p h e n y l a m i n e An i s a n i l i n e 154 TABLE X I I I E x p e r i m e n t a l V a l u e s of Log [ A - ] / [ H A ] f o r V a r i o u s I n d i c a t o r s i n DMSO-Water-Tetramethylammonium H y d r o x i d e (0.011 M) a < C M r H > » < r H c < • P 3 a < c >> a C M S H Xi r H C O < 0 C O O 1 >> c a i H X a + J P P < o >> a u < a s - ' • H C O X ! 0 C O o 1 rH x 1 P CO 1 X • r l C O P u C M CD • H C D o T 3 1 1 1 i *** 1 C C N r 5 r S Jz; C M C M c r - l 1 1 1 1 I 1 1 1 C M C M C M C M C M C M C M C M C M O O o o o O O O o r 3 r 5 r 3 Mole % 1 1 i 1 i 1 1 "<# 1 <f* 1 DMSO 40.03 -.849 44.97 -.370 -.973 49.82 .069 -.495 -.922 53.96 -.750 -.870 54.63 .461 -.038 -.502 -.588 -.570 -.634 -.849 58.78 -.314 -.434 59.38 .767 .439 -.057 -.145 -.140 -.209 -.437 63.57 .101 .010 64.20 .974 .878 .389 .317 .326 .237 .004 68.41 .534 .430 69.09 .903 . 816 .785 .714 .458 71.35 .940 .704 73.69 .989 155 TABLE X I I I (Cont inued) c < cu /-> c c CM G •H < O < s CM 55 i—i CQ >> r H CO 1 H •H >> W CD 0 3 13 u -H XI •rH a in c c c C8 1 rH 1 < •• < < < o •P >> m CM CO CM CM CM • r l 1 a /~\ / - \ /-> n 55 • 1 •H CO r H CM r - l r H r H a X5 1 CJ 1 u CJ l-H CM 1 CM CM V O - O 1 O 1 1 1 55 1 CM 55 | CO 55 1 m CO Mole % 1 TH CM CM CM CM CM DMSO 64 .20 - . 714 - . 802 69 .09 - . 240 - . 4 1 9 71.35 .006 - . 2 2 8 73.69 .248 - . 0 3 0 76.12 .519 .188 78.36 .788 .402 - .801 80.78 .652 - . 5 2 9 83.14 .907 - . 2 1 8 85.46 .104 87.79 .481 90.07 .913 - . 4 2 5 - . 8 0 7 - . 721 92.47 - .276 - . 282 94.74 .629 .417 .299 - . 1 2 2 - . 445 95.34 .822 .506 .083 - . 264 95.77 .930 .775 .635 - . 135 96.21 .969 .798 .323 .012 96 .66 .966 .499 .178 NOTE An i s a n i l i n e t r i t y l i s t r i p h e n y l m e t h y l 156 TABLE XIV E x p e r i m e n t a l V a l u e s of Log [ B H + ] / [ B ] f o r the S u b s t i t u t e d D i p h e n y l a m i n e s Used t o Determine the H 0 V a l u e s i n 20 Volume P e r c e n t E t h a n o l - A q u e o u s S u l f u r i c A c i d -p c CD 3 -P •H -P CO £2 3 CO M o l a r i t y H 2 S 0 4 i O CO O I TT I CO K CJ I TP CD C O a i o CO K CJ I CO CJ I TP rH CJ I CO i CO CJ I co CM <<"-\ r-l CJ I TP CO .0163 - . 4 8 7 - . 6 6 5 .0339 - . 2 0 2 - . 350 - . 792 .0567 .017 - .141 - . 5 5 5 .0808 .175 .011 - . 409 .163 .490 .330 - . 0 9 8 .245 .682 .531 .102 .406 .955 .788 .365 .611 .602 .763 .741 .914 . 869 1.26 1.47 1.72 1.98 2.25 2.49 2.73 .937 .778 .467 - . 8 6 3 .286 - . 642 .023 - . 3 9 7 - . 8 5 5 . 227 - . 151 - . 5 9 9 . 359 - . 0 2 8 - . 473 - .806 .494 .105 - . 3 4 4 - .676 .741 .356 - . 1 1 5 - .436 - . 855 .890 .492 .020 - .296 - . 715 .658 .175 - . 1 5 5 - . 572 .797 .337 .005 - . 400 .932 .470 .152 - .261 .615 .293 - . 120 .753 .420 .009 157 TABLE XIV (Cont inued) •+-> c CD 3 + 5 CC 3 CO M o l a r i t y H 2S0 4 i co U i CO CM rH o I CO I CM o 55 I CO I CM O CO CO tc o I I CO B c j I CO I CM o 55 I I CM O 55 I I CM o 55 I CM CJ I CO I CM § I 1.98 .005 - . 400 - . 818 2.25 .152 - .261 - . 693 2.49 .293 - . 120 - . 540 2.73 .420 .009 - . 385 3.07 .637 .212 3.29 .771 .348 - . 0 7 2 3.58 .928 .516 .080 3.76 .632 .192 4 .14 .863 .432 4 .38 .555 4 .62 .722 4.90 .900 5.15 5.41 5.66 5.95 6.47 - . 850 - . 7 3 5 - . 500 - . 9 0 7 - . 3 5 7 - . 780 - . 954 - . 2 2 0 - .626 - . 789 - . 023 - . 4 3 5 - . 633 .114 - . 280 - . 465 .268 - . 1 2 2 - . 324 .429 .036 - . 165 .638 .245 .048 - . 957 - . 914 .964 .585 .381 - .621 - . 602 158 TABLE XIV (Cont inued) co -p c <D 3 P •H P CC 43 3 W M o l a r i t y H 2 S 0 4 i co X CJ l CO I CM o 55 I I CN o 55 I TT I CM o 55 I CM CJ I CO I CM O 55 I TP I CO CJ i CO CM O 55 I I CM <»-\ CM O 55 I IN CO CM /—\ CM O 55 I OS TP 6.47 .585 .381 - .621 - . 602 - . 8 8 8 6.81 .825 .612 - . 385 - . 3 8 5 - . 6 8 8 7.16 . 858 - . 1 2 8 - . 144 - . 455 7.64 .204 .160 - .156 8.14 .601 . 523 .207 8.44 . 840 .766 .420 8.86 .780 9. 9, 9, 10 59 95 10.40 10.96 - .857 - .516 - .306 .012 .357 .735 -1.026 • .662 - .298 • .017 .320 .762 159 BIBLIOGRAPHY 1. 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