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Diffusion coefficients of cerate solutions McFadden, Mary Louise 1951

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If Si R 5r DIFFUSION COEFFICIENTS OF  CERATE SOLUTIONS by MARY LOUISE McFADDEN A THESIS SUBMITTED IN PARTIAL FULFIH£ENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in the department of Chemistry -We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of MASTER OF ARTS. Members of the Department, of Chemistry THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1951 ABSTRACT The apparent i n t e g r a l d i f f u s i o n c o e f f i c i e n t s of eerie sulphate solutions, 4 normal i n sulphuric acid, were measured for concentrations ranging from 0.05 normal to 0.415 normal at 25°C with the use of a pyrex sintered glass diaphragm d i f f u s i o n c e l l . A graph obtained by p l o t t i n g the calculated i n t e g r a l d i f f u s i o n c o e f f i c i e n t s versus the square root of the i n i t i a l concentration i s similar to the graphs obtained for uni-univalent s a l t s . The rate of d i f f u s i o n , however, Is.?;less by a fa c t o r of ten. The sintered glass diaphragm c e l l was calibrated with 0.1 normal potassium chloride at 25°C and the value of -2 the c e l l constant was determined to be 0.1111 ±0*0002 cm 4 ACKNOWLEDGEMENT The author would l i k e to thank Dr. L.W. Shemilt f o r his timely c r i t i c i s m s and constructive suggest-ions. His good judgment, his encouragement and his enthusiastic i n t e r e s t greatly stimulated the progress of t h i s research. The author i s also grateful to the Unive r s i t y of B r i t i s h Columbia Research Committee f o r f i n a n c i a l aid during the summer of 1950. CONTENTS DIFFUSION COEFFICIENTS OF CERATE SOLUTIONS page I Introduction 1 Diff u s i o n - History and Theory 2 Cerate Solutions 10 II Experimental Meithods and Results 14 Materials 14 Apparatus and Techniques 18 Calibra t i o n of the Diffusion C e l l 21 Determination of Integral D i f f u s i o n C o e f f i c i e n t s 24 III Discussion 27 IV Bibliography 31 Appendix I - The Determination of the Density of Hexa Nitr a t e Ammonium Cerate 33 Appendix II - The Spectrophotometrie Determination of Ceric Concentration 34 T A B L E S ^ page Table I The Results of C e l l C a l i b r a t i o n 23 Table II The Integral Diffusion Coefficients of Cerate Solutions i n 4 Normal Sulphuric Acid at 25°C 26 Table III The Composition of Cerate Solutions 27 Table IV The Apparent Integral D i f f u s i o n C o e f f i c i e n t s of Ceric Complexes i n 4 Normal Sulphuric Acid at 25°C 29 Table V The Variation of Optical Density with the Concentration of 4 Normal Sulphuric Acid Cerate Solutions at 500 rry^- 35 FIGURES following page Figure 1 The D i f f u s i o n C e l l 18 Figure 2 The Complete Thermoregulator C i r c u i t 19 Figure 3 The Integral D i f f u s i o n C o e f f i c i e n t s of Cerate Solutions i n 4 Normal Sulphuric Acid at 25°C 26 Figure 4 The Apparent Integral D i f f u s i o n C o e f f i c i e n t s of Cerate Complexes i n 4 Normal Sulphuric Acid at 25°C 29 Figure 5 The Variation o f O p t i c a l Density with Total Ceric Concentration at 500 v y - L 35 DIFFUSION COEFFICIENTS OF CERATE SOLUTIONS DIFFUSION COEFFICIENTS OF CERATE SOLUTIONS I INTRODUCTION Although much experimental work has been carried out i n the f i e l d of l i q u i d d i f f u s i o n , the results obtained have been of l i t t l e importance i n studying the theory of e l e c t r o l y t i c solutions. The majority of ex i s t i n g data has been obtained from measurements at concentrations which are not applicable to such theories as the " l i m i t i n g laws" of Nernst and 1,2 Onsager.' In order that the theory may be v e r i f i e d , data f o r very low concentrations i s required. An available 141 radioactive isotope, Ce , could be used to measure concen-t r a t i o n changes of very d i l u t e solutions d i f f u s i n g through a porous diaphragm. For this reason, eerie s a l t s were chosen 3 f o r study. Recently, however, R.H. Stokes has shown that surface transport through the diaphragm at very low concen-trations renders such c e l l s unfit, f o r d i f f u s i o n ,of solutions more d i l u t e than .05 normal. This research has been confined therefore, to a study of the d i f f u s i o n process of cerate solutions of concentrations greater than l i m i t i n g value. 2 DIFFUSION - HISTORY AND THEORY The f i r s t u seful measurements of d i f f u s i o n rates were 4 5 made i n 1850 by Graham. In 1855 Adolf Fick contributed the f i r s t t h e o r e t i c a l considerations. He stated the general law of d i f f u s i o n as follows: the quantity of a solute which d i f -fuses through a unit area i n a unit time i s proportional to the difference in concentrations of two areas i n f i n i t e l y near one another. J = - DVc (1) where J — amount of solute d i f f u s i n g D = d i f f u s i o n c o e f f i c i e n t "N7 c = concentration gradient Equation (1) , known as Fick's f i r s t law, was o r i g i n a l l y an empirical r e l a t i o n but has since been derived from osmotic theory. 6 I f the d i f f u s i o n c o e f f i c i e n t i s assumed to be indepen-dent of the concentration, a second expression f o r d i f f u s i o n r e s t r i c t e d to one1 d i r e c t i o n can be obtained from equation ( 1 ) . This expression i s commonly known as Fick's seconrd law. 5 c D' ^>*~Q ( 2 ) where D^ — c o e f f i c i e n t independent of the concentration 3 1 — time increment c)x = distance increment - 3 -It i s important to r e a l i z e that these laws are l i m i t i n g laws that are v a l i d only at very low concentrations. At the time of t h e i r formulation this fact was not appreciated. In general, the d i f f u s i o n c o e f f i c i e n t i s not independent of the concentration. Therefore i t becomes necessary to d i s t i n g u i s h between d i f f e r e n t i a l (D) and i n t e g r a l (D^ d i f -fusion c o e f f i c i e n t s . The d i f f e r e n t i a l c o e f f i c i e n t , the c o e f f i c i e n t required by theory, refers to a c o e f f i c i e n t f o r one p a r t i c i i l a r concentration. The i n t e g r a l c o e f f i c i e n t , on the other hand, i s an average value of the rate of d i f f u s i o n over a concentration range. The two are related by the following i n t e g r a l . Where c 2 - c^ = the concentration range In order that Fick's laws may be applied, experimental boundary conditions must be' imposed. This gives r i s e to three types of d i f f u s i o n ; namely, free d i f f u s i o n , r e s t r i c t e d d i f f u s i o n and steady state d i f f u s i o n . In free d i f f u s i o n , which occurs from an i n i t i a l l y sharp boundary between the solution and the solvent, the concentrations at the top and the bottom of the column remain unchanged during the period of observation. In r e s t r i c t e d d i f f u s i o n , which also takes place from i n i t i a l l y sharp boundaries, the concentration at - 4 -one or both' ends of the column changes. The t h i r d type, steady state d i f f u s i o n , occurs when the concentration d i s t r i b u t i o n i n a column of solution does not change with time. Several complete reviews of the theory and experimental 6 7 8 9 methods of d i f f u s i o n have recently been published. ' ' The porous diaphragm method used i n this research i s an example of steady state d i f f u s i o n . This type i s d i f f u s i o n i n a v e r t i c a l column from one reservoir to another at a lower concentration. A steady state i s eventually attained i n which, at each height i n the column, the flow, is-constant. Thus, i f the value of J" and the concentration gradient can be determined, the d i f f e r e n t i a l d i f f u s i o n c o e f f i c i e n t can be obtained from Fick's f i r s t law, D = - J (dc/dx)" 1 (4) The experiments of Clack^ 0 which led to.the determination of the d i f f u s i o n c o e f f i c i e n t s of potassium chloride.',; sodium chloride and potassium n i t r a t e from .05 normal to high concentrations were the f i r s t of any importance i n t h i s f i e l d . In his f i r s t determinations, Clack allowed s a l t solutions to d i f f u s e upwards through a narrow tube into water. Later he modified t h i s technique by using instead of a single central tube, a group of several short tubes of small diameter. This was the f i r s t step towards the porous diaphragm method. - 5 -In 1928 Northrop and Anson published a paper describing a new type of d i f f u s i o n apparatus which appeared to be more convenient and accurate. They confined the d i f -fusion process to the pores of a sintered glass diaphragm and so were able to work with high concentration gradients. This way the time required f o r a steady state to be reached was greatly reduced. The errors caused by a g i t a t i o n and thermal disturbances were eliminated. Their apparatus con-sisted of an inverted funnel-shaped vessel with a stop cock at the top and a f l a t sintered glass diaphragm as a base. This c e l l , containing the solution, was suspended with the diaphragm just touching the solvent. The d i f f u s i o n was allowed to proceed u n t i l the solution i n the pores had reached a steady state. This preliminary d i f f u s i o n was followed by a second d i f f u s i o n into fresh outer solution. The theory of the method was also developed by Northrop 12 and Anson and l a t e r modified by McBain and L i u . The diaphragm i s assumed to be composed of a large number of p a r a l l e l pores of length "1" and e f f e c t i v e area " A ". Assumptions are made that the solution on each side of the diaphragm i s of uniform concentration and that the transfer of the solution through the sintered glass diaphragm occurs only by d i f f u s i o n . I f C f and C" are the concentrations of the two solutions, when a steady state i s reached the concen-t r a t i o n gradient across the diaphragm w i l l be ( C - C"), i f the d i f f u s i o n c o e f f i c i e n t i s independent of the concentration. This gradient w i l l be constant throughout the diaphragm. Therefore the amount of solute d i f f u s i n g i n a given time w i l l be J = - D A ( C» - C") dt (5) 1 This i s the d i f f e r e n t i a l form of F i c k ' s , f i r s t law. I f d i f -fusion i s carried out for only a short period of time, (C* -*C n) may be assumed to be constant. Now i f the two concentrations, as well as j/dt and A / l are known, the d i f f e r e n t i a l c o e f f i c i e n t may be calculated. A / l i s known as the c e l l constant and may be obtained only by allowing a d i f f u s i o n process to take place using a s a l t with an accurately known d i f f u s i o n c o e f f i c i e n t . This i s the one serious disadvantage of the diaphragm c e l l . A l l values of d i f f u s i o n c o e f f i c i e n t s are r e l a t i v e to the co e f f i c i e n t of the s a l t used i n standardization. Potassium, chloride i s usually used f o r standardization and the value of the c o e f f i c i e n t i s obtained from conductimetric methods. Because d i f f u s i o n measurements f o r longer periods of time are more p r a c t i c a l and more accurate, the. integrated form of equation (5) i s generally used. If V and 7" are the volumes of the two solutions, then where dc' and dc" are the concentration changes i n the two solutions i n a time dt. Thus i t follows that V'dc» *+• (DA/l)(C V"dc" + (DA/l)(C n C")dt = 0 )dt. « 0 (6a) (6b) - 7 T d(Ac) = - ($ D dt (7) A c where ft , the cell constant = (i/l)(l/T' + l/V") and A c = (C - C") If D is not a function of the concentration, equation (7) can be integrated between the i n i t i a l concentrations, CI and C", and the final concentrations, Cf and C£ , so. that l n A Cf =; - D± ft t . ( 8 ) AC 5, Equation ( 8 ) or some form equivalent to it is used to compute the diffusion coefficient ina diaphragm cell measurement. In effecting the integration, it has been assumed that the cell factor remains constant throughout the experiment, i.e., it has been assumed that the solutions were constant in volume. Theoretical considerations of the cell volume, the calibration of the cell and the assumption of the steady 13 state in the diaphragm have been fully discussed by Gordon, It is important to note that the coefficient in equation ( 8 ) is an integral value. Gordon has made an important contribution in showing how differential coefficients can be evaluated from diaphragm cell measurements. SSy evaluating empirical expressions such as D/D0 = 1 -V- F(C) (9) and Dj/D0 1 -+• ( l / ^ D 0 t ) I f(C)dAC (io) - 8 -where F(C) and f(C) are functions of concentration and D 0 i s the c o e f f i c i e n t at i n f i n i t e d i l u t i o n , i f the value of the c o e f f i c i e n t D 0 i s accurately known, the values of may be converted to d i f f e r e n t i a l c o e f f i c i e n t s . In 1888 Nernst 1- formulated an expression by which DQ, the d i f f u s i o n c o e f f i c i e n t at i n f i n i t e d i l u t i o n , could be calculated from ionic m o b i l i t i e s . D o = RT ( u^.u" ) , , , x (11) ( u ++ u~) where u the mobility of the ion and v = the valence 2 Onager and Fuoss have shown that fundamentally d i f f u s i o n and conductance are cl o s e l y related. By extending the i n t e r ^ i o n i c a t t r a c t i o n theory to the d i f f u s i o n problem, they formulated a.law which may be expressed as follows: X> « "Do - S C C ± 02) c\ o c 23J±*j£L ( -~^A + 3 ^ s 9 x'° (- ) where V) 0 = v i s c o s i t y of water d i e l e c t r i c constant of water S-p = the l i m i t i n g slope >T+3 "^ ,'-) A o = equivalent io n i c and mo'lecular conductances at i n f i n i t e d i l u t i o n 9 -The Onsager- Fuoss equation, also e s s e n t i a l l y a l i m i t i n g law, because of i t s r e l a t i o n to the Debye-Hilckel concept of i n t e r - i o n i c a t t r a c t i o n , requires data at very low concentrations for t e s t i n g i t s v a l i d i t y . Recent work done by Harned and his co-workers, using a conductimetric method to measure free d i f f u s i o n , has shown that the Onsager-Fuoss l i m i t i n g law agrees very well with experimental results f o r potassium chloride Many modifications of the o r i g i n a l Northrop c e l l have been 17 made. McBain and Dawson used a glass cylinder divided into two compartments with a sintered glass diaphragm. Each compartment was f i t t e d with two stopcocks so that the c e l l could be emptied or f i l l e d without disturbing the solution i n the diaphragm. Thus new solution could be placed i n each compartment a f t e r a steady state had been reached. Mouquin 18 and Cathcart mounted a s i m i l a r c e l l on an axle. A glass bead i n each compartment s t i r r e d the solutions and kept them uniform as the c e l l turned end over end. Hartley and Runnicles-1- used a s i m i l a r modification. Recently, Stokes has developed a new method of s t i r r i n g . By placing within each compartment a short piece of iron wire enclosed i n glass tubing, he effected s t i r r i n g by means of a magnet which rotated slowly around outside the c e l l . Stokes has investigated thoroughly the e f f e c t of s t i r r i n g rate, bulk flow through the diaphragm and surface transport effects at low concentrations. Anomalous transport through the diaphragm in - 10 -very dilute solutions has a}.so been reported' by Adamson, 2o Cobble and Nielsen who obtained their results with the use of radioactive tracer techniques. CERATE SOLUTIONS The Nature of Cerate Solutions Because a stable form of Ce(S04)2,, ceric sulphate, had been isolated, i t was natural to expect that a solution of this salt would produce ceric, Ce , ions. However, the normal nitrate and chloride have not been isolated, but exist only as double salts such as (NH^)gCe(NQ3)g, hexa nitrato ammonium cerate. There is now considerable evidence of a complex formation between ceric and sulphate ions. Jones 21 and Soper have measured the transference of ceric sulphate -sulphuric acid solutions and found migration of cerium towards 22 the anode but none towards the cathode. Smith and Getz have shown from electromotive force measurements, the existence of a complex ion. "Its nature, however was not 23 determined. Very recently Hardwick and Robertson have proved the existence of three ceric sulphate complexes as well as the ceric ion. By means of optical measurements made on a Bgckmann Model D U Quartz Spectrophotometer, they were able to determine the presence of Ce + 4, CeSO^ "*" , Ce(8 0 4)2* and C e ( 8 0 4 ) 3 ions and the values for the following equilibrium constants. - 11 -This means that the exact concentration of each of the ions i n any sulphuric acid solution can be accurately calculated. The Oxidimetry of Cerate Solutions Sulphuric acid solutions of eerie sulphate have been used extensively for volumetric oxidation t i t r a t i o n s by Willard, Furman and t h e i r associates. In a series of a r t i c l e s beginning i n 1928, they describe the developement of the use of eerie sulphate solutions as oxidants. U n t i l 1931, however, there was no convenient indicator for t i t r a t i o n s involving eerie sulphate. Willard and Young had used methylene blue and diphenylamine but, because these indicators could not be added u n t i l within .4 mis of the endpoint, they were not e n t i r e l y s a t i s f a c t o r y . In 1931 - 12 -Walden, Hammett and Chapman 2 5 proposed the use of o-phenan-thr o l i n e ferrous ion which had a l l the properties of a good indicator f o r ceric-cerous systems. The oxidation of thi s complex ion, completely reversible and mobile, has a colour change from an intense red to a pale blue at a poten t i a l of 1.14 v o l t s . ( The reduction p o t e n t i a l of cerate solutions i n sulphuric acid i s 1.44 volts.) O r i g i n a l l y Furman 2^ used oxalic acid for the standard-i z a t i o n of cerate solutions. Because of a slow reverse reaction necessitating that the oxalic acid solution be t i t r a t e d into a hot c e r i c solution, this was not p r a c t i c a l . Willard and ?7 Young, using iodine monochloride as a catalyst, were able to carry out the same reaction at room temperature. An advance 28 was made when Swift and Gregory introduced a method of .standardization using arsenious oxide as a primary standard. They employed iodine monochloride as both a catalyst and an ind i c a t o r . In 1931 Willard and Young 2 9 further improved the technique of standardization. T i t r a t i o n of ceric solution against either arsenious oxide or sodium oxalate was carried out i n hydrochloric acid solution at a temperature of 50°C. using iodine monochloride as a catalyst and o-phenanthroline 30 ferrous sulphate as an indicator. That same ;year, Gleu discovered the use of osmium tetroxide as a catalyst f o r this reaction. Today, the use of arsenious oxide i s the accepted method of standardization. "Osmic a c i d " (.1 normal sulphuric acid 13 solution of osmium tetroxide) i s used as a catalyst and " f e r r o i n " (1.485 grams of o-phenanthroline monohydrate dissolved i n 100 m i l l i l i t e r s of .025 molar ferrous sulphate solution) -as an indicator. Publications by the G. Frederick 31 32 33 Smith Chemical Company ' ' thoroughly review the sub-ject of cerate oxidimetry* - 14 II EXPERIMENTAL METHODS AND RESULTS MATERIALS  Water Water with a s p e c i f i c conductance of 3 x 10 ohms - 1 cm" was used i n preparing a l l solutions. D i s t i l l e d water was used in a l l t i t r a t i o n s . Salts Standard of reference purity hexa n i t r a t o ammonium cerate prepared by the G Frederick Smith Chemical Company was used in the preparation of a l l cerate solution f o r d i f f u s i o n . Merck reagent grade potassium chloride, used f o r c a l i b r a t i o n of the d i f f u s i o n c e l l , was r e c r y s t a l l i z e d three times from conductivity water. A l l the other chemicals used were either chemically pure (CP.) or reagent grade. No further p u r i -f i c a t i o n s were attempted. Solutions Approximately 4 normal sulphuric acid solution was made by adding the required amount of 36 normal Nichols reagent sulphuric acid, s p e c i f i c gravity 1.84, to two l i t e r s of water. The presence of appreciable amounts of SO would cause considerable interference by reducing the cerate ion. However, the concentration of S0£ i n the f i n a l solution has been estimated ( from manufacturer's analysis ) to be less than — 6 3 x 10 percent. This 4 normal acid was then used i n the - - 15 -preparation of the cerate solutions to be used f o r d i f f u s i o n . This acid was also used as the solvent i n the c e l l so that the acid concentration of the solution and the solvent was always the same. Thus there was no concentration gradient of solvent through the diaphragm. The sulphuric acid was standardized against Thorn Smith Company standard sodium carbonate]'previously dried f o r two hours at 110°C i n an e l e c t r i c oven kept esp e c i a l l y f o r the purpose of drying s a l t s . Modified methyl orange and bromophenol blue were used as ind-i c a t o r s . The water used f o r d i s s o l v i n g the s a l t was previous-l y boiled in order to remove the dissolved gases. Cerate solutions to be used i n the d i f f u s i o n c e l l were 34 prepared according to the method of Smith and F l y > Ceric hydroxide was precipitated from a water solution of hexa n i t r a t o ammonium cerate with a one hundred percent excess of 1 normal ammonium hydroxide. The 1 normal solution was prepared from Nichols 14'normal ammonium hydroxide, ( s p e c i f i c gravity 0.90). Complete oxidation to the ceric state was achieved by heating the r e s u l t i n g mixture with d i l u t e hydrogen peroxide/ The excess peroxide was e a s i l y decomposed by b o i l i n g the solution. The res u l t i n g yellow ceric hydroxide was f i l t e r e d through a large clean pyrex sintered glass f i l t e r and washed thoroughly with s i x l i t e r s of water i n 100 m i l l i -l i t e r portions. Because the concentration of ammonium ions was much greater than that of the n i t r a t e , a negative test for ammonium ions i n the wash water was considered s u f f i c i e n t evidence f o r the complete removal of both types of ions. - 16 -The test f o r ammonium ion was carried out i n the following way. A f t e r the precipitate had been washed with f i v e l i t e r s of conductivity water, f i v e hundred m i l l i l i t e r s of wash water were then collected i n a f l a s k . To t h i s , one m i l l i l i t e r of saturated sodium carbonate solution was added and the solution was d i s -t i l l e d u n t i l f i f t y m i l l i l i t e r s of d i s t i l l a t e were coll e c t e d . ( A l l the d i s t i l l i n g apparatus was e s p e c i a l l y cleaned by b o i l i n g i t with sodium carbonate solution u n t i l one m i l l i l i t e r of added Nessler's reagent produced no yellow t u r b i d i t y . ) I f upon the addition of one m i l l i l i t e r of Nessler's reagent to the d i s t i l l a t e no yellow t u r b i d i t y was evident, ammonium ions were s u f f i c i e n t l y removed'. (About 10"" ^  grams per l i t e r or more produce a yellow coloration.) This test was compared with a blank test on the conductivity water by means of a K l e t t Summerson colorimeter. Having removed the n i t r a t e and ammonium ions i n t h i s manner, the ceric hydroxide was e a s i l y soluble i n warm 4 normal sulphuric a c i d . Cerate solutions to be used f o r t i t r a t i o n s only were prepared by d i s s o l v i n g c e r i c sulphate or c e r i c ammonium sulphate i n d i l u t e sulphuric acid. The concentration of these solutions and the solutions for d i f f u s i o n was determined by t i t r a t i n g a known weight of arsenious oxide, dissolved i n NaOHt with the cerate solution to be standardized. Osmium tetroxide solution was used as a catalyst and o-phenanthrfoline ferrous ion (Ferroin) as an indicator. It has been shown that such cerate solutions are stable i f kept at room temperature and away from strong sunlight. The solutions show no reduction f o r several months. - 17 -The f e r r o l n indicator solution was prepared by dissolve ;ing,1.485yg©ams of o-phenanthroline monohydrate ( G.Frederick Smith Chemical Company) i n one hundred m i l l i l i t e r s of .025 normal ferrous sulphate solution.' One- drop of thi s solution was s u f f i c i e n t f o r each t i t r a t i o n and no indicator blank was necessary. The catalyst was made by dis s o l v i n g 0.25 grams of osmium tetroxide i n 100 m i l l i l i t e r s of .1 normal sulphuric acid solution. Three to f i v e drops of t h i s solution were required to catalyzq. the reaction. Ferrous solutions were prepared by di s s o l v i n g Mallinckrodt a n a l y t i c a l reagent ferrous ammonium sulphate i n one normal sulphuric acid. The normality of the ferrous solutions was determined by t i t r a t i o n with a standardized cerate solution. No catalyst i s needed fo r this reaction. Potassium chloride solutions were made up gravimetrically using r e c r y s t a l l i z e d potassium chloride dried at 500 °C f o r one hour. The weights used i n these and other weighings were calibrated to four one-hundredths of a milligram. A l l weighings were corrected to vacuum. - 18 APPARATUS AND TECHNIQUES Diff u s i o n C e l l The pyrex d i f f u s i o n c e l l , with a sintered pyrex glass diaphragm ( fine ), has an o v e r a l l length of t h i r t e e n and one-h a l f inches. The other dimensions are s p e c i f i e d i n fig u r e 1. The volumes of the compartments are 51.68ft and 51.69: m i l l i -12 l i t e r s . The usual method of determining the c e l l volume i s to weigh the c e l l ( the diaphragm f i l l e d and the remaining c e l l dry); f i l l one compartment with a l i q u i d of known density ( water was used i n t h i s case) and again weigh the c e l l ; and f i n a l l y , completely f i l l the c e l l and reweigh i t . This method although apparently very crude gives re s u l t s with an accuracy of about 0.2 percent. In each compartment the hollow glass sphere kept the solution uniform by moving up and down as the c e l l was rotated end over end. In order that a l l a i r i s removed from the pores of the diaphragm and to insure that the solution completely f i l l e d the pores, the c e l l was f i l l e d i n the following manner. The solvent was drawn through the diaphragm,which was clamped i n a horizontal position, from the upper compartment to the lower by means of ,a reduced pressure i n the lower compartment. The l e v e l of the solvent i n the upper compartment was maintained at least one-half inch above the surface of the diaphragm so that no a i r could possibly be sucked into the pores. When the a i r was completely removed and the diaphragm was f i l l e d with solvent, s:d:i]it:$oh was drawn through i n this manner u n t i l to follow page 18 FIGURE 1 THE DIFFUSION CELL - 19 -u n t i l the pores were f i l l e d with undiluted solution* The upper compartment was then f i l l e d with solution* No a i r bubbles must be trapped i n the compartment. The c e l l was then inverted and the other compartment c a r e f u l l y rinsed with solvent. The removal and addition of solvent was accomplished with a pipette so that the solution i n the diaphragm was not disturbed* When thoroughly rinsed, t h i s compartment was f i l l e d with the pure solvent. Both the solvent and the solution were previously degassed by the application of a reduced pressure ( about ten millimeters of mercury f o r t h i r t y minutes ) and placed i n a water bath at 25°C±.005°C' f o r ten to twelve hours u n t i l thermal equilibrium was reached. This method of f i l l i n g completely eliminated the formation of bubbles during the' d i f f u s i o n and avoided the chance of grease contamination of the diaphragm. The d i f f u s i o n c e l l was cleaned i n fuming: m i t r i c acid and rinsed ten or twelve times with conductivity water. The c e l l was then completely f i l l e d with water and allowed to stand f o r two.or more days. During this time the water was frequently i changed. The n i t r i c acid was removed from the pores of the diaphragm by drawing through by suction several l i t e r s of water, f i r s t i n one d i r e c t i o n and then i n the other. Before use the c e l l was again thoroughly rinsed. A l l other glass ware was cleaned i n chromic acid f o r twenty four hours and then very thoroughly rinsed with and then stored f i l l e d with d i s t i l l e d water. Before use the glassware was rinsed again with conduc-t i v i t y water. to follow page 19 FIGURE 2 THE COMPLETE THERMOREGUIATOR CIRCUIT - 20 -Constant Temperature Bath The bath consisted of an asbestos insulated tank, 2 f t . x 1.5 f t . x 1.5 f t . Thorough s t i r r i n g was maintained by a three propeller shaft driven by a 0.1 H.P. motor. This s t i r r e r , placed at the center,of one side of the bath, was reinforced by an a u x i l i a r y s t i r r e r i n each corner of the other side. Heat was supplied by three knife heaters. ( 500, 250, 125 watts ) A i r running through a single copper c o i l on the f l o o r of the vessel served to cool the bath. The temperature was maintained at 25 o C i r.005°C by means of an adjustable Nurnberg mercury thermo-s t a t . This thermostat was set with a Beckmann thermometer calibrated against a platinum resistance thermometer ( with a N.B.S. c e r t i f i c a t e ) to 25°C ±.002°C. The complete thermoregu-l a t o r c i r c u i t , including an e l e c t r o n i c a l l y operated relay, i s shown i n figure 2. By means of a set of pulleys, a clamp which f i r m l y held the c e l l was rotated i n the water bath at a rate of 10 rpm. The s t i r r i n g motors and the device for turning the c e l l were fir m l y attached to a r i g i d frame so that v i b r a t i o n was minimized* 21 CALIBRATION OF THE DIFFUSION CELL 13 The c e l l was calibrated according to the method of Gordon* Use was made of the standard equation f o r steady state d i f f u s i o n ( equation 8 ). The i n t e g r a l c o e f f i c i e n t may then be written as follows: 1 A C f 1 ft t A °i If C! = the concentration of the i n i t i a l solution l C" = 0 i — C' and C M - the f i n a l concentrations of the solutions i n f f each compartment i t can be assumed, i f both compartments are of equal volume, that A C f = C»_.-. CJ and &C± = C» + CJ . ACj, was obtained from the two f i n a l concentrations because. d i l u t i o n of the o r i g i n a l solution may have occurred during the f i l l i n g process. The ,2 percent difference i n the volumes of the two compartments of the c e l l has been neglected because the standard potassium chloride solution was placed i n one compartment during some c a l i b r a t i o n runs and i n the other for the remaining c a l i b r a t i o n s . The average deviation i n the calculated c e l l 13 constants was only .1 percent, , Gordon who has investigated the question of c e l l volume very thoroughly has found that the uncertainty i n the measured d i f f u s i o n c o e f f i c i e n t due to error i n volume c a l i b r a t i o n i s e n t i r e l y n e g l i g i b l e . According to Gordon, f o r 0,1 normal potassium chloride d i f f u s i n g into' water at 25°C, Di= 1.830 x 10" 5 cm2/sec when - 22 - .. . A C f / A C i ^ O . S and 1.838 x io~ 5_cm 2/sec when ACf/ASi^ i s very close to unity. Although Stokes has recently suggested a change inithe c a l i b r a t i o n values, the values suggested by Gordon have been used i n t h i s research. The c e l l was f i l l e d a's previously described with 0.1 normal potassium chloride solution. The solution was allowed, to d i f f u s e f o r s i x to twelve hours u n t i l a steady state had been reached. A rough rule f o r estimating the time necessary 2 for the attainment of a steady state i s to set Dt/.5 =* 1.2. This i s a purely empirical rule where t i s the time necessary, D i s the d i f f u s i o n c o e f f i c i e n t and .5 i s 160 percent of the 0 apparent thickness of the diaphragm. After t h i s time fresh s o l u t i o n and solvent were placed i n the c e l l and d i f f u s i o n was allowed to proceed f o r about eighty f i v e hours. Times were recorded to the nearest minute using the U n i v e r s i t y clock as a standard. At the end of a p a r t i c u l a r run the c e l l was removed and twenty m i l l i l i t e r s of solution from each compart-ment were transferred with a calibrated pipette to weighing bottles of known weight. The open bottles were placed under a raised beaker to prevent contamination with dust and evapor-ated slowly with an i n f r a red heat lamp. In t h i s way no loss of the s a l t due to splashing occurred. In addition, the s a l t was further dried at 110°C f o r several hours i n a clean e l e c t r i c oven. After cooling i n an empty, dry, a i r - t i g h t desiccator, the bottles were weighed and the concentrations of the two f i n a l solutions were calculated. The c e l l was calibrated i n t h i s way several times during the year,, but l i t t l e or no change i n the c e l l constant was found. 23 -The values calculated for the c e l l constant are given i n Table I. Table I - The Results of C e l l C a l i b r a t i o n . Run l n M l t i n sec ft X ± c e l l f a c t o r A .09784 .05488 .5783 2.838 x 105; .1113 cm2 D .09629 .05208 .6149 3.024 .1111 E .09919 .05233 . 5828 2.886 .1103 I .11140 .06010 ,6168 3.042 .1108 J .11120 .06327 2.776 .1112 BT .09991 .05173 .6591 3.242 .1111 The average value of the c e l l constant i s .1111 cm"? The maximum.deviation i s 0.3 percent; the average deviation i s 0.1 percent. 24 -DETERMINATION OF INTEGRAL DIFFUSION COEFFICIENTS Measurement of Concentration Changes The d i f f u s i o n c e l l was f i l l e d with 4 normal sulphuric acid and the cerate solution to be measured ( 4 normal i n acid concentration) i n the manner previously described. Afte r a preliminary d i f f u s i o n had proceeded f o r over f i f t e e n hours, the c e l l was r e f i l l e d with fresh solvent and solution and allowed to diffuse f o r about one hundred hours. ( In r e f i l l -ing, the solvent compartment was c a r e f u l l y rinsed i n order that CJ was always equal to zero.) After d i f f u s i o n , the solution i n each compartment was removed to a previously cleaned and dried f l a s k . (The rubber stoppers used i n these flasks were cleaned by b o i l i n g them i n d i s t i l l e d water f o r two hours, scrubbing them and then r e b o i l i n g them i n conductivity water for three hours. The stoppers were dried in a vacuum dessicator overnight.) The concentrations of the solutions were determined as follows. Solutions of Concentration 0.07N or Greater. Ten m i l l i l i t e r portions of the solution, measured with a calibrated pipette, were t i t r a t e d with standard ferrous ammon-ium sulphate solution using o-phenanthroline as an ind i c a t o r . A few t i t r a t i o n s were made using xylene cyanol FF as the indicator. It was found, however, that the endpoint was very hard to di s t i n g u i s h i n a r t i f i c i a l l i g h t . Therefore the use of t h i s indicator was abandoned. Solutions of Concentrations less than 0.07N. The concentrations were determined by adding twenty - 25 -m i l l i l i t e r s of an unknown cerate solution with a calibrated pipette to an accurately known volume of standard ferrous ammonium sulphate solution. The excess ferrous ion was then t i t r a t e d with a standard cerate solution* From t h i s the concentration of the unknown cerate solution was deter-, mined. Solutions of Very Low Concentrations. Very d i l u t e solutions were analyzed c o l o r i m e t r i c a l l y by the o-phenanthroline method. To an excess of ferrous ammonium sulphate solution, .2 m i l l i l i t e r s of the d i l u t e cerate solution was added by means of a calibrated 200 pipette. To t h i s , a saturated solution of o-phenanthroline and a 2N solution of sodium acetate buffer were added. Conductivity water was added to make up the solution to a known volume. The concentration of unoxidized ferrous ion was measured as the i n t e n s i t y of the red colour of the o-phenanthroline ferrous complex produced on a K l e t t Summerson photoelectric colorimeter. ( A green f i l t e r was • used ) Knowing the amount of cerate solution added and the amount and the concentration of the ferrous ion, the concen-. t r a t i o n of the cerate solution was e a s i l y determined. Results of Diffusion Measurements The i n t e g r a l d i f f u s i o n c o e f f i c i e n t s were calculated from y • - . . . . . . . equation (16). This may be written in,the. following way. (17) -26-Integral c o e f f i c i e n t s were calculated for solutions of concentrations ranging from 0.05 normal (Stokes* minimum) to 0.415 normal ( the l i m i t of s o l u b i l i t y of ceric sulphate i n 4 normal sulphuric acid). The results obtained are l i s t e d i n Table II and i l l u s t r a t e d graphically i n Figure 3. TABLE II Integral D i f f u s i o n C o e f f i c i e n t s of Cerate Solutions, i n 4 Normal Sulphuric Acid, at 25° C. (C i n moles per l i t e r ; D 1 2 i n cm sec ; t i n sees.) Run A C± A c f l n A C ? t 1 1 8 "5 D x 10 I A .09698 .08398 . 1432 3,748 .3441 .3114 B .09779 .08815 .1035 2.706 .3450 .3126 C .09768 .08596 .1267 3. 321 .3434 ,3119 II A .04887 .04209 .1493 3.862 .3480 .2210 B .04849 .04171 .1518 3.862 . .3541 .2202 •'• C .04803 .04093 .1579 3.996 .3556 .2191 III A .07345 .06239 .1630 4.302 .3410 .2710 B .\07185 .06115 .1613 4.285 .3390 .2680 cc; .07413, .06421 .1432 3.768 .3401 .2722 .07360 .06530 .1195 3.342 .3412 .2712 ' 17 A .41495 .3508 . 1680 3.463 .4367 ,6438 B .4106 .3476 .1664 3.425 .4372 • 6408 V A .2456 .2118 .1475 3.422 .3880 .4956 B .2467 .2132 • 1459 3.374 .3890 ,4967 VI A .1606 .1398 . 1396 3.473 .3618 .4008 B .1611 ..1423 .1239 3.032 .3621 .4014 VII A .09272 .08256 .1161 3.048 .3427 .3045 to follow page 26 ,30 .35 .40 .46 .50 .55 .60 ( FIGURE 3 THE INTEGRAL DIFFUSION COEFFICIENTS OF CERATE SOLUTIONS IN 4 NORMAL SULPHURIC ACID AT 25°C . - 27 -II I DISCUSSION The d i f f u s i o n c o e f f i c i e n t s calculated and l i s t e d i n Table II are not the true i n t e g r a l c o e f f i c i e n t s of a simgle s a l t , but rather they represent the apparent rate of d i f f u s i o n of the. t o t a l amount of cerium, Ce 1^, i n i t s various forms. By making use of the d i s s o c i a t i o n constants determined by 23 ' Hardwick ( equations 13, 14, 15 ), the exact concentrations of the ions, Ce*"4, CeSO^T Ce(804)3, a n d C e( s04.)2t c a n be determined using a method of successive approximations. In a l l the concentrations of C e I V considered i n this research, + 4 0.05 normal to 0.4 normal, the concentration of the Ce ion -8 i s 10 moles per l i t e r or less and can therefore be assumed to be n e g l i g i b l e . The concentrations of the remaining three ions at 0.1, .048, and .489 moles per l i t e r are l i s t e d i n Table III so that the variations i n proportion with respect to the concentration of the t o t a l amount of C e 1 7 c a n b e s e e n » TABIE III Composition of Cerate Solutions- 4 normal i n Sulphuric Acid* ( C e 1 7 = t o t a l c e r i c concentration, C]_ = CeSO^concentration, Cg-CefSO^g concentration, C3--Ce(S04,)3 < concentration i n moles per l i t e r . C e ^ 0l • >2 C3/C2 0,100 •3,17 x 10**5 .00547 .0945 17.3 0.0480 1.28 x 10" 5 .00238 .0465 19,2 0.489 3.33 x l O - 4 .0387 .450 11.6 In an attempt to analyze the r e s u l t s of Table I I , the apparent d i f f u s i o n c o e f f i c i e n t s of CefSO^g and of the Ce(S0!4)3 ion have been calculated by determining t h e i r respective concentrations i n the i n i t i a l s olution and i n the two f i n a l solutions* These concentrations and the calcu-lated apparent i n t e g r a l d i f f u s i o n c o e f f i c i e n t s are l i s t e d i n Table IV and i l l u s t r a t e d graphically i n Figure 4. The curve representing the apparent d i f f u s i o n of the predom^ inant ion, Ce(SO^g , does not vary greatly from the t o t a l ceric d i f f u s i o n curve. Possibly the values of the calculated c o e f f i c i e n t s do not vary greatly from the true i n t e g r a l values. However, i n the case of CefSO^Jg, a true i n t e g r a l d i f f u s i o n curve at such low concentrations would not be expected to have a minimum. The values calculated f o r the i n t e g r a l d i f f u s i o n c o e f f i c i e n t s of Ce(S0 4)g have, therefore, no physical meaning. It i s extremely doubtful that the true rate of d i f f u s i o n of ions i n an equilibrium mixture could be measured because a l l the ions of a p a r t i c u l a r species w i l l not t r a v e l the f u l l length of the d i f f u s i o n path. At the f i r s t change i n concentration of any one of the components, the e q u i l i -brium would be disturbed. Because of the complexity of t h i s problem, i t would seem p r o f i t a b l e , i f d i f f u s i o n of ions i n equilibrium mixtures i s to be understood, to f i r s t study an equilibrium of fewer components. Acetic acid solutions represent a possible a l t e r n a t i v e , - 29 -Table IV Apparent Integral D i f f u s i o n Coefficients of Cerate Complexes i n 4 Normal Sulphuric Acid at 25 and C 3 = concentrations i n moles per l i t e r of C e ( S 0 4 ) 2 and Ce(S04).g respectively; t i s i n seconds; Di i s i n cm sec A) Run A C 3 i A C 3 f , Ac< In ^ sc*. -5 t x 10 5 D^x 10 VII A .08767 .07808 .}.1161 3.046 0.3429 .2968 III A .06958 .05909 .1630 4.302 0.3410 .2637 II C .04600 .03960 .1506 3.862 0.3509 .2144 .3822 .3240 .1647 3.425 0.4328 .6182 V A .2291 .1976 .1475 3.422 0.3880 .4786 VI A .1517 .1321 .1388 3.473 0.3597 .3894 Run A c 2 1 AC2f AG In ^ c <•' «»5 I t x 10 T)± x 10 5 VII A .005030 .004476 .1169 3.048 0.3452 .0709 III A .003869 .003295 .1605 4.302 0.3357 .0622 II'" C .002468 .002118 .1535 3.862 0.3579 • 0497 IV B .02835 .02362 .1823 3.425 0.4791 .1682 V A .01646 .01417 .1493 3.422 0.3928 .1283 VI A •008881 .007698 . 1484 3.473 0.3690 .0942 to follow page 29. FIGURE 4 THE APPARENT INTEGRAL DIFFUSION COEFFICIENTS OF CERATE COMPLEXES IN 4 NORMAL SULPHURIC ACID AT 25°C . - 30 -If the study of the d i f f u s i o n of cerium s a l t s i s to be continued, i t i s suggested that one of the many water soluble cerous s a l t s be chosen • The theory of d i f f u s i o n of electro-i lytes has not been f u l l y developed for other than uni-univalent strong e l e c t r o l y t e s . Therefore, i t would seem that d i f f u s i o n studies of the t r i - u n i v a l e n t cerous s a l t s would lead to results of more t h e o r e t i c a l significance than can be concluded from t h i s research and therefore, possibly aid the further development of the e l e c t r o l y t i c theory of d i f f u s i o n . 31 -TV BIBLIOGRAPHY 1. W. Nernst,, Z e l t , Phys. Chem., 2, 613, (1888). 2. L. Onsager and R.Fuoss, J". Chem. Phys., 36, 2689,(1932). 3. R.H. Stokes, J.A.C.S., 72, 763, (1950). 4. T. Graham, Lieb. Ann., 77, 56, 129, (1851). 5. A. Fick, Pogg. Ann.,94, 59, (1855). 6. J.W. Williams, L.C.Cady,-Chem, Rev,, 14, 174, (1934). 7. H.S, Harned, i b i d , , 40, 461, (1947). 8.- S,G. Longsworth, Ann. N.Y, Acad. S c i . , 46, 211, (1945). 9. L. Onsager, i b i d . , 46, 241, (1945). 10. B. Clack, Proc. Phys. Soc. Lo#d,, 21, 374, (1908). , 11. J . Northrop, M. Anson, J . Gen. Physiol., 12, 543, (1923). 12. J . McBain, T. Liu, J.A.C.S., 53, §9, (1931), 13* A.R. Gordon, Ann. N.Y, Acad. S c i . , 46, 285, (1945). 14. H.S. Harned, D.M. French, i b i d . , 46, 267, (1945). 15. H.S. Harned, B.L. N u t t a l l , J.A.C.S., 69, 737, (1947). i b i d . , 71» W O » (1949). 16. H.S. Harned, R.L. N u t t a l l , Ann. N.Y. Acad. S c i . , 51, 781, (1949). 17. J . McBain, C.R. Dawson, Proc. Roy. Soc. A148; 32,(1935),; 18i H. Mouquin, W. Cathcart, J.A.C.S., 57,- 1791, (1935). ,19. G. Hartley, D. Runnicles, Proc. Roy. Soc. A168, 401,' (1938/. 20. A.W. Adamson, J.W, Cobble, J.M. Nielsen, J . Chem. Phys,, 17, 740, (1949). 21. E.G. Soper, E.G. Jones, J . Chem, S o c , 802, (1935), - 32 -22. F.J. Smith, C.A. Getz, INd. Eng. Chem., 10, 191, 304, (1938) 23. T.J. Hardwick, E. Robertson, private communication. 24. ' H. Willard, P.,-Young, J.A.C.S., 50y 1322,. (1928) . . 25. < G.H. Walden, L.P. Hammett, R.P. Chapman, J.A.C.S. 55; 3908, (1931). 26. N.H. Furman, J.A.C.S., 50, 755, (1928). 27. H. Willard, P. Young, i b i d . , '.' so_, /J7£, (1928). 28. E. Swift, C. Gregory, i b i d , 52, 901, (1930). 29. H. Willard, P Young, i b i d . , 55, 3260, (1931). 30. K. Gleu, Zeit.Anal. Chem., 45, 305, (1933). 31. G.F. Smith, "Cerate Oxidimetry", G. F. Smith Chem. Co. 1942 32. G.F. Smith, "Ceric Sulphate", G. F. Smith Chem. Co. 1940 33. G.F. Smith, " O r t h o Phenanthroline", G.F. Smith Chem. Co. 34. G.F. Smith, W.Fly, Anal. Chem. 21, 1233, (1949),. 33 -APPENDIX I THE DETERMINATION OF THE DENSITY  OF HEXA NITRATO AMMONIUM CERATE The density.of hexa n i t r a t o ammonium cerate, (NH4) 2Ce(N03)g $ was needed when an accurate weight i n vacuo of the s a l t was required* Because an extensive l i t e r a t u r e search did not reveal the density of the s a l t , i t was determined i n the following manner'.' A twenty f i v e m i l l i l t e r s p e c i f i c g r a v i t y b o t t l e was thoroughly cleaned and i t s weight and volume were deter-mined. Conductivity water at 25°C was used f o r the volume determination* 0,6787 grams of the s a l t were introduced into the clean dry bottle which was then f i l l e d with x y l o l , ( s p e c i f i c gravity.at 25°C was determined to be ,8601 grams per m i l l i l t e r ) and placed i n a thermostat at 25°C for t h i r t y minutes* After weighing the b o t t l e and determining the weight and volume of x y l o l , the volume of the s a l t was found to be ,2175 ccs. Thus the density of hexa n i t r a t o ammonium cerate was determined to be 3.120 grams per cc* A l l weighings were corrected to vacuum* - 34 -APPENDIX II THE SPECTROPHOTOMETRIC DETERMINATION  OF CERIC CONCENTRATION The concentration of t o t a l cerium, Ce-^, i n solution, and consequently the concentrations of the constituent ions, can be determined spectrophotometrically. Although, t h i s method of concentration determination was not used i n th i s research, i t was investigated and found to have d e f i n i t e advantages over the t i t r a t i o n method. Primarily, the method i s convenient and short* After a c a l i b r a t i o n curve of o p t i c a l density, O, D,, versus concentration has been determined at a p a r t i c u l a r wavelength with the use of standard ceric solutions, the unknown concentrations can be quickly and e a s i l y dtermined. The small amount of solution required i n the spectrophotometer c e l l s i s also an advantage. The v a r i a t i o n of o p t i c a l density with concentration at 500*y*is shown i n Figure 5 and the res u l t s are l i s t e d i n Table V. The deviation from the straight l i n e at higher concentrations may be due to either a deviation from Beer's Law or to the fact that the s e n s i t i v i t y of the instrument decreases at high o p t i c a l density. A l l measurements were made on a Beckmann Model D U .Spectrophotometer, 35 *» TABLE V The Vari a t i o n of Optical Density with the Concentration of, 4 Normal Sulphuric Acid Cerate Solutions at 500*Y>U. . Qohcentratioh moles / l i t e r O p t i c a l •01123 .102 .0188 .166 .0315 .268 .07913 .725 .0910 .805 .09322 .810 .1483 1.29 .1500 1.31 .1829 1.58 .2269 1.80 .2279 1.85 .2296 1.90 to follow page 35 FIGURE 5 THE VARIATION OF OPTICAL DENSITY WITH TOTAL CERIC CONCENTRATION AT 500 mu. 

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