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Conductivities of some tetraalkylammonium salts in acetonitrile Harkness, Alan Chisholm 1957

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CONDUCTIVITIES- OF SOME TETRAALKYLAMMONIUM SALTS IN ACETCNITRILE by ALAN CHISHOLM HARKNESS B, A., University of British Columbia, 1947 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of CHEMISTRY We accept this thesis as conforming to the required standard Members of the Department of Chemistry THE UNIVERSITY OF BRITISH COLUMBIA April, 1957 (i) ABSTRACT The conductivities of the homologous series from tetrar-methyl to tetra-n-amyl of the normal tetraalkylammonium iodides and bromides in acetonitrile at 25° C have been determined. The concen-trations studied ranged from 0.006 to 0.00003 moles per l i t r e . These salts are fairly strong electrolytes in acetonitrile. The iodides have higher conductivities and are more highly dissociated than the corresponding bromides. The conductivities decrease with increasing size of the alkyl group and the degrees of dissociation show a cor-responding increase. There i s a relatively large difference between the tetramethyl and tetraethyl ions and then smaller, fairly regular differences in going from tetraethyl to tetra-n-amyl. The limiting equivalent conductivities have been calculated by the methods of Shedlovsky and Fuoss. It is shown that the dis-sociation constants calculated by the method of Shedlovsky and those calculated by the method of Fuoss are not related in the manner pre-dicted by these authors. Ionic conductances have been calculated by assuming that Walden's rule applies to the tetrar-n-butylammonium ion. A comparison of ionic resistances in some organic solvents shows that the quaternary ammonium ions have l i t t l e tendency to interact with solvent molecules. In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements fo r an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available f o r reference and study. I further agree that permission f o r extensive copying of t h i s thesis for scholarly purposes may be granted by the Head of my Department or by h i s representative. I t i s under-stood that copying or publication of t h i s thesis f o r f i n a n c i a l gain s h a l l not be allowed without my written permission. Alan Chisholm Harkness Department of Chemistry The University of B r i t i s h Columbia, Vancouver #, Canada. Date April 1957.  ACKNOWLEDGEMENT I wish to express my appreciation to Dr. H. M. Daggett, Jr., for invaluable help and encouragement in carrying out this ; research and also to the British Columbia Sugar Refining Company Limited for the award of a scholarship. ( i i ) TABLE OF CONTENTS Page; Introduction 1 Experimental 5 (i) Materials and Apparatus 5 ( i i ) Procedure 9 (a) General 9 (b) Cell constants 9 (c) Acetonitrile solutions 10 Results 13 Discussion 24 LIST OF TABLES ( i i i ) Page I Melting Points of Tetraalkylammonium Salts 7 II Cell constants of Cells 6 and 7 11 III Cell constant of Cell 3 11 IV Cell constants of Cells 1, 2 and 4 11 V Tetramethylammonium iodide 15 VI Tetraethyl ammonium iodide 16 VII Tetra-n-propylammonium iodide 16 VIII Tetra-n-butyl ammonium iodide 17 IX Tetra-n-amylammonium iodide 17 X Tetramethylammonium bromide 18 XI Tetraethylammonium bromide 18 XII Te tra- n-propyl ammonium bromide 19 XIII Tetra-n-butylammonium bromide 19 XIV Tetra-n-amylammonium bromide 20 XV Limiting equivalent conductivities from A-^C plots; 23 XVI Experimental and Theoretical A~^C Slopes 25 XVII Values of Ao and Dissociation Constants from Fuoss and Shedlovsky Plots 27 XVIII Ion Conductances in Acetonitrile 33 XIX Resistances of Quaternary Ammonium Ions in Various Solvents 35 (iv) LIST OF FIGURES Page 1. A ~ \/C" Plots of Tetraalkylammonium Iodides 21 2. A - v/C" Plots of Tetraalkylammonium Bromides 22 3. Typical Shedlovsky Plots 28 4. Typical Fuoss Plots 29 I. INTRODUCTION The f i r s t conductivity studies of solutions were carried out by Cavendish (l) in 1776, One hundred and f i f t y years later Debye and Huckel (2) were able to place this phenomenon on a sound theoretical basis* In the intervening period the existence of ions in solution had been recognized and a great deal had been learned about their behaviour, Arrhenius had introduced his theory of incomplete ionization which appeared to be followed by weak electrolytes (although this agreement i s now known to be largely fortuitous), but could not explain the be-haviour of strong electrolytes. Debye and Huckel showed that the behaviour of strong electro-lytes could be explained by assuming complete dissociation and the existence of an "ionic atmosphere11. That is, a particular ion will on the average be surrounded by more ions of opposite charge than like charge. In the phenomenon of conductivity the motion of an ion will be opposed by the ionic atmosphere in two ways. There i s a purely electro-static effect known as the relaxation effect caused by the distortion of the ionic atmosphere and an electrophoretic effect caused by the opposite motion of the ionic atmosphere and its associated solvent mole-cules. Onsager (3) refined this treatment chiefly by considering the random thermal motion of the ions. 2. The variation of conductivity of strong electrolytes with concentration follows Cnsager's equation in solvents with high dielectric constant. This equation i s of the form: A » A o - ( « Ao +£)s/C where CX and $ are constants depending only on the properties of the solvent. Strictly speaking this i s a limiting equation valid only at very low concentrations for symmetrical 1 * 1 electrolytes. Aqueous electrolyte solutions conform to the equation because water has a dielectric constant of 78.5 (at 25°)• Bjerrum (4) and Fuoss and Kraus (5) have shown that for sol-vents with a dielectric constant below about 40* ion association occurs resulting in the formation of neutral ion pairs. In solvents of very low dielectric constant higher order interactions are also possible leading to the formation of triple ions. When ion association occurs the problem arises as to what value should be assigned to the concentration term of the Onsager equation. By assuming that the mass action law holds for the equilibrium between free ions and ion pairs i t is possible, in principle, to arrive at a relation between conductivity and concentration through the use of the dissociation constant. This treatment may also be used for weak electrolytes where the equilibrium i s between free ions and undissociated covalent molecules as there i s no thermodynamic dis-tinction between the forces forming the neutral entity. If the individual ion conductances are known from measurements on completely dissociated electrolytes, then Kohlrausch's law of inde-3. pendent ionic mobilities may be applied to calculate the limiting equi-valent conductivity and dissociation constant of a weak electrolyte. This is possible in aqueous solutions as illustrated by the case of acetic acid ( 6 ) . On the other hand there are no completely dissociated electro-lytes in non-aqueous solvents and the determination of limiting equivalent conductivities and dissociation constants must be done simultaneously using conductance data for the particular system under consideration. Fuoss ( 7 , 8 ) and Shedlovsky (9) have devised methods for solving the con-ductance function for these values. In the treatment of the conductance problem the long range interactions between ions are considered by the Debye-Huckel theory ( 2 ) and the short range interactions leading to the formation of ion pairs are considered by Bjerrum (4) and Fuoss ( 7 ) . Both considerations have necessarily involved mathematical and physical approximations, tut in the limiting case of low concentration the theory i s in good agreement with experiment. In general ion-solvent interactions have been ignored although evidence i s accumulating to show that the structures of the solvent mole-cules and of the ions are important in determining conductance behaviour. Accordingly the present investigation was undertaken to determine the constitutional and structural effects on the conductance of some quaternary ammonium salts in acetonitrile. The salts chosen were the iodides and bromides of the homologous series of normal tetraalkylammonium ions from tetramethyl to tetra-n-amyl. Quaternary ammonium ions combine large size and symmetrical shape with low charge and their salts are soluble 4. in a great variety of solvents. The conductances of the homologous series of tetraalkylammonium ions from tetramethyl to tetra-n-amyl have been determined in ethylene chloride (10, 11), nitrobenzene (12), acetone (13, 14) and water (15)• In addition individual members of the series have been investigated in a large number of other solvents. Acetonitrile was chosen as solvent because i t has a fairly high dielectric constant, 36.7 at 25° (l6) and because there have been very few precise conductance measurements in acetonitrile solutions-. Work that has been done includes that of Walden (17, 18), Walden and Birr (19), Koch (20), Philip and Gourtman (21), Ralston and Eggen-berger (22), Payne (23), French and Roe (24) , Popov and Skelly (25) and Kortiim, Gokhale and Wilski (26). 5. EXPERIMENTAL Materials and Apparatus: Acetonitrile was obtained from the Carbide and Carbon Chemicals Company. The procedure finally adopted for purification was a primary distillation from AgNO^  collecting the middle two-thirds in a flask con-taining activated AL^ O^  pellets. This was allowed to stand for at least two days and then redistilled. This procedure produced solvent with a specific conductivity of 0.8 to 1 x IO"** mhos as compared to lQT^ to mhos for the material as received. The conductivity could be further reduced to 1 x 10-9 mhos by repeated distillations from AlgO^, but with a recovery of only about 15%* The final distillation was done not more than 24- hours before a run was made. The boiling point of the acetonitrile was 81,5 to 82°. The density was determined by means of a pycnometer (27) and was found to be 0.7768 g/ml at 25° compared to values of 0.77683 g/ml (28) and 0.7767 g/ml (16), The viscosity was determined by means of an Ubbelohde viscosi-meter (29) and was found to be 0.339 cp at 25° as compared to values of 0.344 cp (16) and 0.356 cp (26), Tetraalkylammonium salts were available in the laboratory. These were further purified by recrystallization until constant conduc-tivity values were obtained. Table I shows the salts, the solvent of 6. recrystallization and the melting points. The following abbreviations have been used: Me - methyl, Et - ethyl, Pr - n-propyl, Bu - n-butyl and Am - n-amyl. Only the tetra-n-amyl and tetra-n-butyl salts melted sharply. The other salts; a l l melted with some evidence of decomposition from 20 to 30 degrees below the final decomposition temperature. The decomposition point of the tetraethylammonium iodide can not be explained. It i s completely out of line with other members of the iodide series; and i s identical to the tetraethylammonium bromide. Quali-tative analysis showed that the bromide contained bromide and no iodide and that the iodide contained iodide and no bromide. Potassium chloride for determining cell constants was obtained from three different sources. Baker and Adamson KCl was precipitated three times from distilled water with ethanol and dried at 100° C in vacuo. An alar KCl was treated in the same manner, Mallinckrodt KCl was twice precipitated from distilled water by adding concentrated reagent grade HCl, recrystallized twice from distilled water and washed with ethanol. It was; dried at 200° G in vacuo. Conductivity cells were of the flask type developed by Kraus and Puoss (30) with platinized platinum electrodes. The two cells used as standards each had a large and a small electrode chamber. All other cells had one electrode chamber, A great deal of difficulty was experienced in obtaining a satisfactory electrode seal. The method finally adopted was to weld a short length of tungsten rod to the platinum rod of the electrode, 7, Table I Melting Points of Tetraalkyl ammonium Salts; Salt Recrystallization Solvent m. p. °G Me^ NI 6C# ethanol/water 375 - 380 d. Et^NI ethanol 275 - 276 d. Pr^NI ethanol 291 d. Bu^ NI ethanol ppt. with ether 145 - 146 Am.NI ethanol ppt. with ether 134 - 135 4 Me^ NBr 60$ ethanol/water 351 - 353 d. Et^NBr ethanol 276 d. Pr^NBr ethanol 26l - 262 d. Bu^NBr benzene 116 - 117 Am^ NBr benzene 99 - 101 8 . cover with a bead of Phoenix glass and seal into the Pyrex cell. A small piece of platinum wire was welded to the end of the tungsten rod to make electrical contact with the lead wire through mercury. The conductivity bridge was a high precision audiofrequency instrument designed and built by Dr. H. M. Daggett, Jr. 9. PROCEDURE General All solutions (except those used for comparing cell constants) were made up by weight directly in the cells. All weighings were cor-rected for buoyancy and concentrations were calculated from density measurements. Resistance measurements were done in an oil bath controlled at 2 5 . 0 0 0 + 0 . 0 0 2 ° and were determined at two or three different frequencies to eliminate polarization effects. Cell Constants The constants of the large electrode chambers of the two double cells, Nos. 6 and 7, were determined directly by making up KC1 solutions in the cells and measuring the resistance. The specific conductivities; of the solutions were calculated from the concentrations by means of the empirical Shedlovsky equation (31) corrected to the Jones and Bradshaw (32) standard. A correction was made for the conductivity of the water used. Solutions of tri-n-butylammonium picrate in ethanol were used in comparing the cell constants of the different cells. The constants of the small electrode chambers were determined in terms of the large 10. electrode chambers. Another cell, No. 3> was used as a secondary standard. All other cell constants were then determined in terms of Cell 3. The results of the cell constant determinations are shown in Tables II, III and IV. Acetonitrile Solutions; A salt sample in a weighing piggy was dried overnight in vacuo. The piggy was weighed, the salt transferred to a clean dry cell and the piggy was reweighed. The cell containing the salt was then weighed. Sol-vent was transferred to the cell from the storage flask under nitrogen pressure and the cell was again weighed. The cell was shaken to insure mixing and placed in the o i l bath. After temperature equilibrium had been reached the resistance of the solution was measured. The cell was then removed from the bath, thoroughly shaken, replaced in the bath and the resistance again determined. This procedure was repeated until a constant resistance was attained. In most cases this occurred after the second mixing. The cell was removed from the bath and weighed after f i r s t cleaning off the o i l with.benzene. This weighing was done to allow for differences in the surface condition of the cell. Some solution was removed by nitrogen pressure, the amount being determined by reweighing the cell. More solvent was added, the cell reweighed, shaken and the resistance determined as before. The procedure was repeated so that from four to six different concentrations were Table II Gell constants of large electrode chambers of Cells 6 and 7 11, Cell 6-L Cell 7-L KCl J KCl J B&A. 8.452 B&A 7.402 BM 8.447 Analar 7.404 Ahalar 8.441 Analar 7.406 Malinckrodt 7.386 Malinokrodt 7.392 Average 8.447 7.398 Table III Cell constant of Cell 3 Cell 6 Ratio L/S 26.36 Ratio S/3 1.305 Cell 3 . 0.2455 Average 0.2454 Table IV Cell constants based on Cell 3 Cell RatiotCell 3 J 1 0.7829 0.1921 2 1.032 0.2533 4 0.8133 0.1996 Cell 7 23.33 1.293 0.2453 12. obtained from the original salt sample. In general there was a very slight decrease (less than 0.1$) of resistance with time, but the original value could be reproduced by agitating the cell in the bath. This effect has been noticed by other investigators(33)• The solutions were very stable, the resistances being essentially constant for periods up to two days, A density value was; determined for one solution of each salt in acetonitrile. Interpolated values were then used in the calculation of concentrations. The maximum density used was only 0.1% greater than that of the pure solvent. The viscosity of one solution of each of the iodide salts was determined and found to be the same as that of the solvent. The values of constants used in the calculations were density of pure solvent 0.7768 g/ml, viscosity 0,00344 poise and dielectric constant 36,7, 13. RESULTS In general, the conductance of a particular salt was deter-mined with samples that had been recrystallized three times and five times. If a check was not obtained the salt was again recrystallized and another run was done. Altogether 27 runs were made on the 10 salts investigated. Only those runs which checked are reported (one exception is noted later). Details of the others are recorded in the research note books. Tables V to XIV show the results obtained together with the cell constants; used. In a l l runs except for run 6, the conductivity of the solvent was 1 x 1CT0 mhos. In run 6 i t was 4 x 10 mhos. Cor-rections were made for the solvent conductance. The results were plotted on a A~\/cT graph and were treated by the method of least squares. Only those points which showed a straight line relationship between A and v/CT were used in the least square treatment. The results are shown in Figures 1 and 2. The lines drawn on the graphs and the intercepts are calculated values. In Table XV are shown the limiting equivalent conductance A o , the average deviation and the maximum deviation for each set of figures used in constructing the graphs. The deviations are calculated on the basis of the difference between the value obtained for A o and that which would have resulted i f the line had passed through the individual points with the same slope. Those points which l i e above the straight lines at higher concentrations 14. have not been included as i t i s f e l t that these are real deviations. The lowest point on the graph for Et.NI has not been included i n the 4 calculations, but i s included i n the deviations. The average deviation i s i n the neighbourhood of 0.1$, but this may be misleading. Attention i s drawn to the results for Me^NI. Here the average deviation i s 0.06$ with a maximum deviation of 0.10$ based on the results of runs 4 and 22. However, the value for /\o calculated from run 2 i s 196.4. The value calculated from run 4 i s 198.8. These values were obtained from the same sample of salt i n the same c e l l (no. l ) . In view of the close agreement between runs 4 and 22, run 2 i s probably i n error. In the absence of definite evidence to the contrary (and lack of agreement of one sample from two others i s not s t a t i s t i c a l evidence) sample 4 should be included i n any calculations. However, i t i s the usual practice i n conductivity measurements to dis-card such results and this has been done. 15. Table V M B . N I Run 2 J = 0.1921 A Run 4 J = 0.1921 A C X IO 4 R C X IO 4 R 46.20 254.2 163.6 30.73 368.2 169.8 27.80 404.4 170.9 10.53 1003.1 181.9 9.679 1092.8 181.6 2.788 3623 190.5 4.150 2483 186.4 0.8960 11049 194.0 0.3051 32110 195.7 Run 22 J = 0.2454 A C X 104 R 15.99 860.9 178.2 8.060 1652.7 184.2 2.936 4401.1 189.9 1.569 8135 192.2 Units* C = moles/litre R Z ohms A a em^ /ohm .16. Table 71 Et.NI Run 3 J * 0.1996 A Run 5 J = 0.2533 A C X 10 4 R C X 10 4 R 43.62 285.0 160.6 54.91 292.4 157.8 16.16 724.0 170.6 21.36 704.9 168.2 5.348 2100 177.7 6.232 2297.6 176.8 1.540 7118 182.0 1.434 9675 182.5 0.5824 18630 183.7 0.1364 78870 184.8 Table VII Pr.NI Run 6 J = 0.1996 A Run 7 J - 0.1921 A C X10 4 R C X 10 4 R 41.21 324.6 149.2 36.76 . 347.1 150.5 18.57 686.0 156.7 8.478 1398.2 162.1 7.738 1586.5 162.4 2.614 4398.4 167.0 2.845 4201.6 166.4 0.8579 13162 170.1 1.267 9305 169.0 0.3625 30865 171.3 Table VIII 17. Btt.NI Run 8 J = 0„2533! Run 9 J = 0.1921 cr x i o 4 R A 0 X IO 4 R A 25.12 690.5 146.0 31.68 421.9 143.7 14.58 1156.6 150.2 17.42 740.9 148.9 7.936 2073.1 154.0 5.925 2086.4 155.4 3.179 5046.0 157.9 1.380 8677 160.4 1.293 12214 160.3 0.3763 31299 162.9 Table IX Am^ NI Run 10 J = 0.1996 Run 11 J = 0.1921 C X IO 4 R A C X 104 R A 15.68 884.9 143.9 28.28 487.3 139.4 8.199 1647.7 147.7 10.10 1295.4 146.8 3.274 4021.4 151.6 4.419 2879.1 151.0 1.556 8345 153.7 1.412 8801 154.5 0.7247 17742 155.1 Run 23 J " 0.2533 Run 25 J * 0.1996 C X 104 R A C X 10^ R A 12.86 1354.1 145.5 8.777 1544.0 147.3 3.800 3475.6 151.1 1.929 6745.7 153.3 0.7102 18065 155.4 18. Table X Me.NBr Run 12 J - 0.2533 Run 13 J = 0.1921 C X 10 4 R A C X 10 4 R A 61.97 273.0 147.0 42.07 292.6 156.0 35.89 445.3 158.5 12.84 857.3 174,5 12.17 1191.2 174.7 3.157 3269*0 186.1 5.129 2700.7 182.8 1.558 6501.7 189.6 1.986 6781.5 188.0 Table XI Et,NBr Run 15 J = 0.2533 Run 24 J z 0.2454 C X 10 4 R A C X 1 0 4 R A 53.52 304.3 155.5 37.35 410.1 160.2 17.80 848.8 167.6 16.07 905.3 168.7 5.076 2832.5 176.2 5.356 2606.2 175.8 2.189 6444.9 179.5 2.684 5115.5 178.7 0.7965 1746.3 181.9 1.053 12853 181.2 19. Table XII Pr^NBr Ron 17 J s 0.1921 Run 26 J : 0.2454 c n o * R A C X IO 4 R A 27.03 472.2 150.5 33.87 489.2 148.1 8.462 1426.3 159.2 14.89 1060.8 155.3 2.958 3954.4 164.2 6.722 2276.6 160.4 1.156 9936 167.1 1.838 8066 165.5 0.6710 21665 168.7 Table XIII Bu.NBr Run 18 J « 0.2533 Run 27 J = 0.2454 C X IO 4 R A C X IO 4 R A 32.90 542.5 141.9 12.78 1285.8 149.4 13.54 1254.6 149.1 4.409 3594.7 154.8 5.247 3128.6 154.3 1.600 9703 158.0 2.104 7640.8 157.5 0.7908 19421 159.7 1.054 15093 159.1 20. Table XIV Am.NBr Run 20 J = 0.1921 Run 21 J » 0.2533 C X 10 4 R A C X IO 4 R A 19.88 637.0 140.6 18.23 983.0 141.4 6.628 1968.3 147.2 7.292 2368.4 146.6 2.212 5738.3 151.3 3.586 4721.4 149.6 0.7845 15932 153.6 1.566 10647 151.9 0.2791 44271 155.1 F i g u r t I 200 r Conductivities of Tetro alky IQ mmonium Iodides in Acetonitrile Figure 2 22. 2 0 0 X I O 3 C o n d u c t i v i t i e s of T etraalkylammoni um Bromides in A c e t o n i t r i l e 23. Table XV Limiting equivalent conductivities from plots Salt Runs Ao Max. Dev. % Ave. Dev. % Me^ NI 4, 22 198.8 0.10 0.06 Et.NI 4 3, 5 187.1 0.43 0.15 Pr^NI 6, 7 173.5 0.17 0.08 Bu^ NI 3, 9 164,8 0.24 0.11 Am^ NI 10, 11, 23, 25 158.4 0.25 0.11 Me^ NBr 12, 13 197.3 0.20 0.12 Et^NBr 15, 24 185.7 0.05 0.03 Pr^NBr 17, 26 171.8 0.23 0.12 Bu^ NBr 18, 27 163.0 0.06 0.06 Am^ NBr 20, 21 156.7 0.19 0.11 24. DISCUSSION In Tables XVI the slopes of the A ~ p l o t s of the various salts are shown together with the theoretical Onsager slopes and the ratio of the experimental to the theoretical slopes. I t i s seen that the tetramethyl salts show the largest deviation from the theoretical and that from tetraethyl on there i s a gradual approach to the theoretical slope. Ah examination of these plots shows that there i s an upward deviation from the straight l i n e as the concentration i s increased. The tetramethyl salts do not show this deviation, but with the others the concentration at which i t appears f a l l s with increasing ion size. The two main causes for deviation from the Onsager equation are ion association which causes a negative deviation and the neglect of the size of the ions i n the derivation of the equation. As has been shown by Robinson and Stokes (34) neglecting the f i n i t e size of the ions accounts for positive deviations from the Onsager equation. Thus the slope of the plotsmay be interpreted by ion association which decreases with increasing ion size according to Bjerrum's (4) theory. The positive deviations from l i n e a r i t y at increased concentrations are also attributable to increasing size of the ions. The dissociation constants and limiting equivalent conduc-t i v i t i e s for the various salts have been calculated by the methods of 25. Table XVI Experimental and Theoretical A~N/C Slopes Salt —BxPk Slope -Th. Slope Exp./Th. Me^ NI 520 371 1.40 Et^NI 409 363 1.13 Pr^NI 393 354 1.11 Bu^ NI 378 347 1.09 Am^ NI 366 343 1.06 Me^ NBr 641 369 1.74 Et^NBr 426 362 1.18 Pr^NBr 433 352 1.23 Bu^NBr 385 346 1.11 Am^ NBr 364 342 1.06 26, Fuoss: (7, 8) and Shedlovsky (9) using Daggett's (35) table for the latter method. Both methods give the same values for /\o » but result in differing dissociation constants. The results are shown in Table XVII. The column headed Kp contains values of the Fuoss dissociation constants, Kj?, calculated from Shedlovsky1 s constants, Kg. It should be noted that the value of /\o for Me^ NBr calculated by Fuoss' method is 194.7. Typical Shedlovsky and Fuoss plots are shown in Figures 3 and 4. The dissociation constants confirm the results of the plots. The tetraalkylammonium iodides and bromides are quite strong electrolytes in acetonitrile. The bromides are somewhat weaker (more strongly associated) than the iodides and the tetramethyl compounds are relatively much weaker than the higher members of the series. Tetra-n-propylammonium bromide falls out of line with the other members of the series. This might possibly have beenecaused by impurities which were not removed by the recrystalllzations. At any rate this is probably an experimental rather than a real phenomenon. The question of two widely differing dissociation constants is rather bothersome. Fuoss based his method of calculation on the assumption that i f the electrolyte were completely dissociated i t would obey Onsager's equation. That is,an incompletely dissociated electrolyte obeys the equation A s y(A>-cxv€7) where Y * s *be degree of dissociation and <X i s the Onsager slope. Table XVII Values of A o and Dissociation Constants from Fuoss and Shedlovsky Plots Salt Ao K s % Me^ NI 197.6 0.034 0.043 Et^NI 186.8 0.075 0.13 Pr^NI 173.2 0.076 0.14 Bu^ NI 164.5 0.082 0.20 Am^ NI 158.2 0.094 0.20 Me^ NBr Et^NBr Pr^NBr Bu^ NBr Am.NBr 195.0 185.2 171.1 162.8 156.5 0.019 0.061 0.047 0.061 0.09J 0.023 0.087 0.064 0.104 0.27 2 8 . Shtdlovtky Plots 29. F u o t t P l o t s 30. This was combined with the mass action law where f i s the mean activity coefficient assuming that the activity coefficients: of the two ions are equal and that of the neutral molecule or ion pair i s one. The combination of the two equations was brought about by a function F such that Y - A A.F The resulting equation F . _ ! _ + CAf* A Ao K FA: F i s that of a straight line with intercept — j r — and slope ^ z . In the Shedlovsky treatment instead of the Onsager equation the empirical equation is used. This equation better describes the behaviour of strong electro-lytes to higher concentrations in aqueous solution than does the Onsager equation. The correction term —^—may in effect be allowing for the / N o size of the ions. This equation leads to the following one for incom-pletely dissociated electrolytes* where Q i s now the degree of dissociation. Combination with the mass 31. action law by means of the function S such that leads to the equation ' - _ J _ , CASi* AS ' Ao HSA0Z which i s analogous to that of Fuoss but results in a different slope. Fuoss and Shedlovsky (36) have agreed that the Shedlovsky extrapolation function i s the better one to use. They have also shown that the two dissociation constants are related by the expression This i s the expression that has been used to calculate the values of Kp in Table XVII. These values do not agree with those for Kp, the discrepancies being more pronounced at higher values of the dissociation oonstants. Popov and Skelly (25) report Fuoss and Shedlovsky dissociation constants for tetramethylammonium chloride, bromide and iodide in acetonitrile. Evers and Knox (37) report both for several salts including some tetraalkylammonium picrates in methanol. In neither case has one constant been calculated in terms of the other, although Evers and Knox did comment on the apparent impossibility of experimentally determining which method i s the better. Calculations of KF from the Kg values of Popov and Skelly and of Evers and Knox indicate that for K<, less than about 0.025 the relation-32. ship between Kg and Kp i s given by the above expression. However, as Kg increases above 0.025 this relationship f a i l s . This casts serious doubts as to the reliability of dissociation constants obtained by either method for relatively strong, but somewhat associated electrolytes. When an ion moves through a solution i t meets with a resis-tance due to the viscosity of the solution. In the limiting case when electrophoretic and relaxation effects vanish the mobility of the ion is determined only by the viscosity of the solvent and by interaction with the solvent molecules. It is of interest then to examine the variation of ionic conductances from solvent to solvent as this may give some indication of whether ion solvent interactions occur. To evaluate ion conductances i t i s necessary to know their transport numbers. Unfortunately very few such data are available for non-aqueous solvents. There is, however, an empirical method which yields results consistent within 5%, Fowler and Kraus (38) have assumed that the conductances of the tetra-n-butylammonium ion and the triphenyl-borofluoride are the same. Pickering and Kraus (39) have suggested that Walden's rule holds for the tetra-n-butylammonium ion. Therefore, assuming that the conductance viscosity product of this ion in acetonitrile is the same as in other solvents (water is an apparent exception) the value of 0»208 has been averaged from solvents in which the ion conduc-tance has been obtained by Fowler's method. The values of ion conductances in acetonitrile are shown in Table XVIII on the basis of /C0 for Bu^ N* being equal to 60,. 5. It i s Table XVIII Ion Conductances in Acetonitrile Salt Ao At Me4NI 197.6 93.6 EfyNI 186.8 82.8 Pr4NI 173.2 69.2 Bu^NI 164.5 60.5 Jto4NI 158.2 54.2 Me^ NBr 195.0 92.7 Et^NBr 185.2 82.9 Px^NBr 171.1 68.8 Bu4NBr 162.8 60.5 Am4NBr 156.5 54.2 34. seen that the results are quite consistent within themselves except for the Me^ N* ion which differs in the two salts by about 1%, In comparing ion conductances i t i s convenient to compare the reciprocals of the conductance viscosity product. This i s actually the resistance of the ion corrected for the viscosity of the solvent and allows comparison between solvents. The averaged values are shown in Table XIX together with similar values for water (15), nitrobenzene (12), acetone (13, 14) and ethylene chloride (10, 11). It is apparent that in the non-aqueous solvents the viscosity of the solvent i s the controlling factor in the conductances of the tetraalkylammonium ions. If ion-solvent interactions are present in these solvents they must a l l be of the same order. With regard to the effect of the ionic structures on their conductance not very much can be said. It would appear that the size of the ion i s the moat important factor. There i s a relatively large change in dissociation and in conductance in going from tetramethyl to tetraethyl and smaller fairly regular changes in proceeding to tetra-n-emyl. It now remains to compare the results of the present investi-gation with those reported in the literature. For Et^NI the values of 186.8 for A 0 and °«13 f o r % are ^ S o o d agreement with those of Kortiim, Gokhale and Wilski (26) who found 187.0 and 0.12. In the only other recent work Popov and Skelly (25) report Ao values for Me^ NI and Me^ NBr of 195.3 and 192.7 res-pectively. Table XIX Resistances of Quaternary Ammonium Ions in Various Solvents Corrected for Viscosity Ion CH?CN C6H5NQ2 (CH3)2C0 C2H4CI2 H20 Me^ N* 3.12 3.19 3.36 2.99 2.49 E t / 3.51 3.37 3,61 3.33 3.42 P r / 4.21 4.09 4.20 4.04 4.77 B u / 4.81 4.64 4.90 4.86 5.84 Am/ 5.36 5.11 5.62 5.47 6.52 36.. These contrast with 197.6 and 195.0 for the same salts in this investi-gation. Their values of Kg are 0.036 and 0.024 as opposed to the present values of 0.034 and 0.023. It is impossible to resolve these differences in / \ 0 without further work, but i t may be pointed out that in both cases the values for Me^ NI are 2.6 units higher than for Me^ NBr. This suggests a constant error which i s unlikely in the present case in view of the close agreement with Kortum1s value for Et^NI. With regard to earlier work (17, 19, 21) there i s substan-ti a l disagreement with the exception of one value for Et^NI and this agreement is probably fortuitous. 37. REFERENCES 1. McKenna, N. A. Theoretical electrochemistry, Macmillan and Co. Ltd., London, 1939, p. 1. 2. Debye, P. and Huckel, E. The collected papers of Peter J., W. Debye, Interscience Publishers Inc., New York, 1954. pp. 217-310. 3. Onsager, L. Trans.. Faraday Soc. 23_, 341 (1927). 4. Bjerrum, N, Niels Bjerrum selected papers, Einar Munksgaard, Copenhagen, 1949. pp. 108-119. 5. Fuoss, R, M. and Kraus, C. A. J. Am. Chem., Soc. Jj4>. 1429, (1933). 6. Maclnnes, D. A. and Shedlovsky, T. J. Am. Chem. Soc. j>4j 1429, (1932). 7. Fuoss, R. M. and Kraus, C. A. J. Am. Chem. Soc. $1, 476, (1933). 8. Fuoss, R. M. J. Am. Chem. Soc. £2, 488 (1935). 9. Shedlovsky, T. J. Franklin Inst. 225. 739 (1938). 10. Tucker, L. M. and Kraus, C. A. J. Am. Chem. Soc. 6j£, 454, (1947). 11. Mead, D. J., Fuoss, R. M, and Kraus, C. A. Trans. Faraday Soc. 3J2, 594 (1936). 12. Taylor, E. G. and Kraus, C. A. J. Am. Chem. Soc. 62,_ 1731, (1947). 13. Reynolds, M.. B. and Kraus, C. A. J. Am. Chem. Soc. 70, 1709, (1948). 14. McDowell, M. J. and Kraus, C. A. J. Am. Chem. Soc. 22, 3293> (1951). 15. Daggett, H. M., Bair, E. J., and Kraus, C. A. J. Am., Chem. Sbc. 22,. 799, (1951). 16. Robinson, R. A. and Stokes, R. H. Electrolyte solutions, Butter-worths Scientific Publications, London, 1955. p. 448. 17. Walden, P. Z. physik. Chem., 5 4 , 184 (1905). 18. Walden, P. Z. physik. Chem. ^ 8, 505 (1905). 38. 19. Walden, P. and Birr, E. J. Z. physik. Chem. 144. 269 (1929). 20. Koch, F. K. V. J. Chem. Soc. 647 (1927). 21. Philip, J. C. and Courtman, J. R. J. Chem. Soc, 1270 (1910). 22. Ralston, A. W. and Eggenberger, D. N. J. Phys. & Colloid Chem. 22, 1499 (1948). 23. Payne, D. S. J. Chem. Soc., 1052 (1953). 24. French, C. M. and Roe, I. G. Trans. Faraday Soc. L&,_ 314 (1953). 25. Popov, A. I. and Skelly, N. E. J. Am. Chem. Soc. 7^ ,. 5309 (1954). 26. Kortum, G,, Gokhale, S. D. and Wilski, H. Z. physik. Chem. 4» 286 (1955). 27. American Society for Testing Materials, Standard method for measure-ment of density of hydrocarbon liquids by the pycnometer, D 941 — 49, (1949). 28., Weissberger, A., Proskaner, E., Riddick, J. A. and Toop, E. E. Organic solvents, 2nd ed. Interscience Publishers, Inc., New York, 1955, p. 224, 29. American Society for Testing Materials, Tentative method of test for kinematic viscosity, D 445 - 46 T (1946). 30. Kraus, C. A. and Fuoss, E. M. J. Am. Chem. Soc. 21 (1933). 31. Shedlovsky, T. J. Am. Chem. Soc. 2k» 1411 (1932). 32. Jones, G. and Bradshaw, B. C. J. Am. Chem. Soc. 5^ , 1780 (1933). 33. Cox, N. L., Kraus, C. A. and Fuoss, R. M. Trans. Faraday Soc. J i , 749 (1935). 34. Reference 16. Chap. 7. 35. Daggett, H. M. J. Am. Chem. Soc. 21» 4977 (1951). 36. Fuoss, R. M. and Shedlovsky, T. J. Am. Chem. Soc. 2Lt 1496 (1949). 37. Evers, E. C. and Knox, A. G. J. Am. Chem. Soc. 22t 1>739 (1951). 38. Fowler, D. L. and Kraus, C. A. J. Am. Chem. Soc. Gg, 2237 (1940). 39. Pickering, H. L. and Kraus, C. A. J. Am. Chem. Soc. JX» 3288 (1949). 

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