TRANSPORT PROCESSES IN HYDROGEN-BONDING SOLVENTS
3281
Transport IProcesses in Hydrogen-Bonding Solvents. I. The Conductance of Tetraalkylammonium Salts in Ethanol and Propanol at 25"
by D. Fennel1 Evans' and Philip Gardam Department of Chemistry, Case Western Reserve University, Cleveland, Ohio 44106
(Received April 8 , 1968)
Conductance measurements are reported for Me4NC1, Bu4NC1, MerNBr, EtrNBr, Pr4NBr, BurNBr, Et4N1, Pr4N1, Bu~NI,i-AmaBuNI, and HeptdNI in ethanol and propanol and Bu4NC104 in propnol at 25". Analysis of tGe data by the Fuoss-Onsager equation gave an average value of & of 4.2 0.2 A in ethanol and 5.0 i: 0.5 A in propanol, while analysis by the Fuoss-Hsia equation gave equally small, but constant, values of & !which appeared to be independent of dielectric constant. All of the salts were found to be associated, and the extent of ionic association increased with increasing size of the anion for any given cation. This unusual association pattern is discussed in terms of the normal behavior observed in acetone, a solvent which is isodielectric with propanol.
Introduction Contrary to the predictions of electrostatic theory, the association of electrolytes in solvents containing hydroxy groups appears to increase with ionic size.2 However, the data which suggest such an idea do not permit unambiguous conclusions. This is due to the presence of factors which complicate the interpretation of systems that) have been studied in detail and to the fragmentary information available in systems which lack complicating features. The two most thoroughly studied hydroxy solvents are methanol and water. Analysis of the concentration dependence of conductance in methanol solutions gives association constants for the alkali metal and tetraalkylammoniun~halides which increase as the size of the ion increasesa2 For example, constants of 0, 4, and 18 have been obtained for tetrabutylammonium chloride, bromide, and iodide, respectively. However, all of the constants in methanol are small, less than 20, and must be interpreted with reservation, since it has been shown that association constants as large as 40 may be artifacts arising from errors in the theory used to evaluate the datana The behavior of electrolytes in aqueous solution has been discussed in terms of a similar association patter11.~,5 I n this case, the extent to which the peculiar concentration dependence reflects structural effects, arising from the unique three-dimensional structure of water, and the extent to which it reflects ionic association remains ain open question. The association constants that have been recorded are small, ea. 5, as would be expected in a high dielectric medium and are often obtained only by arbitrary assumptions in the analysis of the d a h 6 When the higher alcohols are chosen as the solvent system, the pattern of ionic association of hydroxy solvents may be investigated without such complica-
tions as three-dimensional structural effects or small association constants. This homologous series also allows investigation over wide variations of dielectric constant, viscosity, and temperature. In this paper, which is the first of a series, we report the conductance behavior of the tetraalkylammonium halides and perchlorates in ethanol and propanol a t 25".
Experimental Section Materials. Conductivity grade ethanol was prepared by distilling absolute ethanol (Rossville Gold Seal) in 4-1. batches from 20 g of magnesium ethoxide and 10 g of magnesium metaL6 All distillations were carried out in a 1.3-m Stedman column under nitrogen and only the middle fraction was retained. The magnesium metal was dried a t room temperature over phosphorus pentoxide in a vacuum desiccator. Magnesium ethoxide was prepared by mixing magnesium metal with absolute ethanol, the reaction being catalyzed by a drop of bromoethane. Conductivity grade l-propanol was prepared by drying the Fisher reagent grade alcohol over calcium oxide for several days and then distilling the alcohol from a fresh batch of calcium oxide.' Tests for unsaturated impurities with bromine water were negative. The densities of these alcohols a t 25" were determined in single-neck pycnometers to be 0.78511 and 0.79960 (1) To whom all correspondence should be directed. (2) R. L. Kay, C. Zawoyski, and D. F. Evans, J . Phys. Chem., 69, 4208 (1965). (3) R. L. Kay and J. L. Dye, Proc. Nut. Acad. Sci., 49, 5 (1963). (4) R. M. Diamond, J . Phys. Chem., 67, 2513 (1963). (5) (a) B. J. Levien, Aust. J . Chem., 18, 1161 (1965); (b) H. E. Wirth, J . Phys. Chem., 71, 2922 (1967). (6) J. R. Graham, G. S. Kell, and A. R. Gordon, J . Amer. Chem. SOC.,79, 2352 (1957). (7) W. C. Vosburgh, L. C. Connel, and J. A. V. Butler, J . Chem. Soc., 933 (1933).
Volume 7B, Number 9 September 1968
3282
D. FENNELL EVANSAND PHILIP GARDAM
Table I: Equivalent Conductances in Ethanol at 25' lOC, mol/l.
A
Me4NC1 (A = 0.03) 3.304 47.093 6.595 44.898 10.076 43.077 13.775 41.532 18.281 39.986 24.437 38.385 30.602 36.911 43.106 34 790 56.299 33.085 I
104~ mol/l.
104c,
A
Et4NBr = 0.09) 3.912 48.368 7.880 46.003 12.603 43.974 17.434 42.366 21.926 41.131 27.432 39.859 33.016 38.762 37 681 39 * 399
(A
I
10v,
mol/l.
A
(A 3.844 7.969 12.206 17.003 21.901 27.571 33.711 39.957
EtdNI = 0.10) 50.976 48.124 46.010 44.135 42.578 41.092 39.741 38.569
mol/l.
A
HeaNI
(A = 0.13) 3.350 6.764 10.301 14,144 17.768 21.955 26.392 31.117
37.846 35 * 795 34.235 32.890 31.839 30.800 29.857 28.985
Bu4NC1
Pr4NBr
Pr4NI
i-AmsBuNI
(A = 0.05)
(A = 0.09)
(A = 0.11)
(A = 0.13)
2.062 4.529 7.845 11.423 15.141 23.382 28.548 34.911 42.393
39.140 37.747 36.548 35.503 34.607 33.135 32.371 31.554 30.744
MedNBr = 0.07) 5.316 47.017 11.066 43.684 16.664 41.374 22,626 39.499 28.645 37,910 35.940 36.379
(A
4.317 9.207 14.001 19.080 24.075 29.887 35.719 40.239
42.485 40.138 38.529 37.173 36.070 34.990 34.063 33.423
Bu4NBr = 0.08) 4.768 39.128 10.210 36.841 16.013 35.157 21.380 33.952 27.445 32.825 33.429 31.897 39.465 31.084 45.982 30.312
(A
g/cm3, for ethanol and propanol, respectively. These figures are slightly higher than the lowest recorded densities for these alcohols, 0.78506 for EtOHe and 0.79950 for PrOH.* The viscosities of these alcohols at 25" were determined in two Cannon Ubbelohde viscometers and found to be 0.01084 P for ethanol and 0.01952 P for propanol. The value for ethanol agrees with those previously reportedl9while that for propanol disagrees by 1%.lo Because of the large number of values reported for the dielectric constant of these solvents, this property has been redetermined using the all-glass platinum cells described by Kay and Vjdulich.11 The value of e 24.33 found for ethanol agrees best with that given by Wyman12 and that for propanol, E 20.45, agrees with that reported by Dannhauser.13 The specific conductances of these alcohols as measured in the conductance cells before beginning runs had a range of (2-10) X ohm-l ohm-' cm-l for ethanol and (2-9) X cm-l for propanol. The tetraalkylammonium salts were purified by recrystallization. For all the salts employed, except The Journal of Phisical Chemistry
4.843 10.002 15.808 22.020 28.438 34.950 41.434 48.080
44.422 41.617 39.395 37.589 36.094 34.839 33.774 32.827
4.017 8.037 12.296 16.631 21.323 26.733 32.047 37.923
40.556 38.239 36.444 35 * 000 33.717 32.480 31.453 30.470
Bu~NI
(A = 0.11) 4.601 9.303 14.751 20.074 25.533 31.306 37.366 43.718
41.492 38.956 36.869 35.296 33.991 32.829 31.769 30.829
tetraheptylammonium iodide, the method of purification has been described in detail p r e v i ~ u s l y . ~ t Tetra'~ heptylammonium iodide (Eastman Kodak) was dissolved in acetone, filtered through a fritted-glass funnel, precipitated by the addition of ether, recrystallized similarly a second time, and dried in a vacuum oven overnight at 56". We would like to thank Professor J. Coetzee of the University of Pittsburgh, who provided us with a sample of the tetrabutylammonium perchlorate. Equipment and Techniques. The electrical equipment, conductance cells, and techniques were similar to those previously reported.2~14316 The measurements (8) C. B. Kretschmer, J . Phys. Colloid Chem., 55, 1351 (1951). (9) 0. L. Hughes and H. Hartley, Phil. Mag., 15, 610 (1933). (10) T. A. Gover and P. G. Sears, J . Phys. Chem., 60, 330 (1956). (11) G . A. Vidulich and R. L. Kay, Rev. Sci. Instrum., 37, 1662 (1966). (12) J. Wymrtn, J . Amer. Chem. Soc., 53, 3292 (1931). (13) W. Dannhauser and L. W. Bahe, J . Chem. Phys., 40, 3068 (1964). (14) D. F. Evans, C. Zawoyski, andR. L. Kay, J . Phys. Chem., 69, 3878 (1965).
TRANSPORT PROCESSES IN HYDROGEN-BONDING SOLVENTS
3283
Table 11: Equivalent Conductances in Propanol a t 25" 104~
104~7, mol/l.
A
Me4NC1 = 0.02) 5.811 19 * 483 10.703 17.542 15.736 16.181 21.720 15.011 27.704 14.126 33.629 13.425 43.393 12.528
(A
Bu4NC1 = 0.05) 2.338 19.167 7.141 17.433 12.025 16.334 16.953 15.526 22.932 14.772 31.391 13.944 40.306 13.275 44.879 12.991
(A
mol/l.
A
E4NI
he4ni ( A = 0.10)
4.301 8.630 13.780 18.027 23.136 29.151 34.013 39.952
22.604 20.537 18.925 17.950 17.023 16.166 15 594 14.999 I
PraNBr = 0.05) 5.844 19.976 12.246 17.926 17.928 16.738 24.713 15.696 31.259 14.921 37.775 14.297 45.381 13.692 54.150 13.119
3.305 7.370 11.092 15.863 21.403 26.591 33.062 39.672
(A
BQNBr 4.253 9.014 13.910 18.885 23.939 29.506 34.926 41.946
24.477 21.935 20.431 19.034 17.834 16.961 16.083 15.366
19.406 17.652 16.463 15.565 14.846 14.203 13.680 13.113
Results The measured equivalent conductances and the corresponding electrolyte concentrations in moles per liter are shown in Table I for ethanol and Table I1 for 1propanol. Also given is A , the density increment used t o calculate the volume concentration. These increments were obtained by density measurements on the most concentrated solutions used in the conductance measurements and were assumed to follow the relationship d = do A&, where & represents the moles of salt per kilogram of solution.
2.819 5.760 9.655 13,372 17.440 22.102 27.009 31.983
18 909 17.276 15,860 14,886 14.064 13.316 12.679 12.142 I
Pr4NI
i-AmsBuNI
( A = 0.09)
( A = 0.10)
5.259 10.255 17.035 24.587 30 529 36.624 43.462 50.529
21.004 18.914 17.139 15.803 15.012 14 350 13.734 13.199
I
I
Bu~NI
were carried out in Kraus type conductance cells16and the precision, speed, and convenience of the measurements were all enhanced by the use of the Hawes-Kay cup-dropping device.17 The use of this device generally allows several complete conductance runs to be carried out in 1 day by one worker. The cells, which had cell constants of approximately 0.8, were calibrated with reagent grade potassium chloride. 18g18 The usual small frequency correction was applied to a resistance measurement. The temperature of the conductance bath was controlled to d=0.005" and was set at 25" with a calibrated platinum resistance thermometer.
+
A
( A = 0.09)
( A = 0.07)
23.295 20.755 19.312 18.189 17.218 16.134 15.311 14.500
1040, mol/l.
EtaNBr
MeaPIJBr
I
A
( A = 0.07)
( A = 0.05) 1.991 5 003 7.637 10.382 13,422 17.774 22,015 27.390
1040, mol/l.
( A = 0.09) 4.550 9.492 14.109 18.790 24.055 29.984 36.303 43.119
2.907 6.442 9.724 14.616 19,499 24.836 30.197 35.516
20.402 18,368 17.120 15.788 14.812 13.982 13,313 12.763
BQNClOa = 0.07) 3.848 21.151 8.979 18.028 14.748 16.034 20.649 14.665 26.794 13.618 33.609 12.737 40.770 12.003 50.361 11.227
(A
20.028 17.894 16 596 15.619 14.762 13.998 13.337 12.750 I
The data were analyzed with the Fuoss-Onsager equation in the forml9 A = ho -
cy)"^
+
cy In (cy) + (J - BA0)cy - KBf'cyh
(1) The value of B , which corrects for the effect of the added electrolyte on the viscosity of the solvent, was set equal to zero. The value of B does not affect the limiting conductance or the association constant. I n all nonaqueous solvents, where the B correction has been determined, the value of d was increased by the constant amount of 0.2 angstroms for all of the tetraalkylammonium halides. Shown in Table I11 are the parameters obtained from the Fuoss-Onsager equation by a least-squares computer program. Included are the standard deviations (15) C. G. Swain and D. F. Evans, J. Amer. Chem. SOC.,88, 383
(1966). (16) H. M. Daggett, E. J. Blair, and C. A. Kraus, ibid., 73, 799 (1951). (17) J. L. Hawes and R. L. Kay, J . Phys. Chem., 69, 2420 (1965). (18) J. E. Lind, J. J. Zwolenik, and R. M. Fuoss, J . Amer. Chem. SOC.,81, 1557 (1959). (19) R. M. Fuoss and F. Accaacina, "Electrolytic Conductance,'' Interscience Publishers, New York, N. Y.,1959. Volume 73, Number 9 September 196'8
3 284
D. FENNELL EVANSAND PHILIP GARDAM
Ethanol and Propanol at 25’ Salt
Ao
d,
A
UA
MeaNCl BuaNCl
EtOH 51.67f0.07 4 . 2 f 0 . 2 41.54f0.05 4 . 4 5 0 . 3
122 f 4 39 f 5
0.05 0.04
MerNBr Et4NBr PrrNBr Bu4NBr
53.56f0.09 53.15 f 0 . 0 3 46.86f0.03 43.5110.05
4.1f0.3 4.550.1 4.3f0.1 4.3f0.2
146 f 6 99 f 2 78 f 3 75 f 4
0.03 0.02 0.02 0.03
EbNI Pr4NI BunNI i-Am3BuNI He4NI
56.34f0.03 49.94f0.04 46.6510.04 45.31 f 0 . 0 2 41.93 f 0 . 0 2
4.6f0.1 4.1fO.l 4.010.1 4.050.1 4.3 f O . l
133 f 2 120 12 123 f 3 130 f 2 139 f 3
0.02 0.02 0.02 0.01 0.01
Me4NCl BuaNCl
PrOH 25.0510.02 4.2 f O . l 21.16f0.03 4 . 4 f 0 . 1
456 f 3 149 f 5
0.01 0.02
MeaR’Br EtaNBr PraNBr BurNBr
26.91 f 0.02 27.19 f 0.02 24.42f0.05 22.9210.03
6 . 4 10 . 2 5.0 f 0.1 4.4f0.1 4.6 f O . l
638 f 5 373 f 4 270 f 7 266 f 6
0.01 0.01 0.02 0.01
EtdNI Pr4NI Bu~NI i-AmsBuNI He4NI
29.01 f 0 . 0 5 26.08f0.05 24.60f0.04 24.0210.03 22.1810.03
5.5f0.2 4.5 5 0 . 1 4.7 f O . l 4.9 f 0 . 2 4.8f0.2
466 f 8 391 f 7 415 f 6 462 f 6 442 f 6
0.02 0.02 0.01 0.01 0.01
BuaNClO4
27.13 f 0 . 0 3
4.210.1
769 A= 6
0.01 --
in each parameter and the standard deviation, uA, of the individual points.
Discussion Limiting Ionic Conductance. Some indication of the internal consistency of the data (Table 111) can be ob-
tained from the values of Ao(R4XI) - Ao(R4NBr)and Ao(R4YBr) - Ao(R4NC1)for the Me4N+, EtdN+, Pr4N+, and Bu4N+salts. The iodide-bromide differences are 3.14 f 0.04 and 1.70 f 0.06 in ethanol and propanol, respectively, while the analogous bromide-chloride differences are 2.01 f 0.03 and 1.81 f 0.05. Meaningful comparison of our results with those of other workers can be made only where the data in the literature are of a high enough precision and over a wide enough concentration range to be analyzed by modern theories. Such data have been analyzed by eq 1 and the resulting conductance parameters published elsewhere.*O Hartley, et al., investigated the tetramethylammonium and tetraethylammonium halides in ethanol and from their data the following values of limiting conductances in ethanol have been calculated: Ao(hle41L’C1) = 51.87 f 0.04, Ao(Me4NBr) = 54.03 f 0.02, Ao(Et4NBr) 53.54 & 0.03, and Ao(Et4NI)= 56.5 0.6. A similar analysis of the Whorton and Amis data from their studies of the corresponding picThe Journal of Physical Chemistry
rates furnished the following values for A,: Ao(hle4NPi) = 55.03 0.05 and Ao(Et4NPi) = 54.2 f 0.1. The single-ion conductances, Xo, in ethanol given in Table IV were obtained from the A. values in Table I11 and Gordon’s limiting chloride conductance, Xo(C1-) = 21.87, by use of the following procedure. From Ao(Me4NC1) and Ao(Bu4NC1) the values of Ao(Me4N+) and Ao(Bu4Nf) were obtained; these latter results together with Ao(Bu4NBr) and Ao(Me4NBr) gave an average value of Xo(Br-) = 23.88 f 0.03, which, when combined with Ao(Et4NBr) and Ao(Pr4NBr), gave values for Xo(Et4N+) and Xo(Pr4N+). Having io(EtdN+), Xo(Pr4N+),and Xo(BudN+), an average value of Xo(I-) = 27.00 A 0.04 was obtained by subtraction from the A. values for the corresponding iodides in Table 111. It should be noted that the ethanol values given in Table IV differ from the previously tabulated valuesz1by as much as 3% in extreme cases. However, owing t o the internal consistency of our data and the absence of such consistency in the previously published data, our results should be given considerably more weight.
*
Table 111: Conductance Parameters in
Table IV : Values for Limiting Single-Ion Conductances 7 -
Ion
Me4N+ Et4N + Pr4N+ Bu~N + i-AmaBuN Hept4N+
+
c1Br-
Ic104-
. - -X
In EtOH
I n PrOH
29.65 29.27 22.98 19.67 18.31 14.93
14.40 15.05 12.19 10.71 10.17 8.29
(21.87) 23.88 27.00
10.45 12.22 13.81 16.42
Gover and Sears studied the tetramethylammonium and tetrapropylammonium halides in l-propanol. The A0 values obtained from a recalculation by the FuossOnsager equation agree with those given in Table I11 in the case of the bromides, but there is a discrepancy of 1 to 2y0 for the iodides. Because of the high density of the propanol used by Gover and Sears, p = 0.8008 as compared with a density of p = 0.7996 reported here, and because of the internal consistency of our data, we believe that our values are t o be preferred. The A0 values in propanol given in Table I11 cannot be unambiguously split into single-ion conductances because of the lack of the necessary transference numbers. As a tentative approach to this problem, the (20) See ref 2 for conductance parameters recalculated by the Fuoss-Onsager equation from data of Hartley, et al., Whorton and ~ ~and G~~~~ i and ~ sears. , (21) R. I,. Kay and D. F. Evans, J . P ~ Y SChem., . 70, 2325 (1966).
TRANSPORT PROCESSES IN HYDROGEN-BONDING SOLVENTS limiting ionic conductances for the ions i-AmsBUN+ and Hept4N+ in ethanol were calculated from the corresponding values in methanolzz using the appropriate Walden product ratio. The resulting ethanol figures agreed with those given in Table IV to within 0.5-1.5%. This suggested that the same procedure could be used to obtain values for the limiting ionic conductances in! propanol. The propanol values given in Table IV were calculated from the ratio of the viscosities in ethanol and propanol and the limiting ionic conductances for i-AmBBuN+ and HeptdN+ ions in ethanol (see Table IV). An average value for Xo(I-) of 13.87 f 0.08 in propanol was obtained and used to calculate the other limiting ionic conductances in propanol shown in Table IV. A further discussion of the variation of the limiting ionic conductance-viscosity product with solvent will not be presented here, because similar data from butanol and pentanol will permit a more detailed discussion. Ion-Size Parameter. The Fuoss-Onsager ion-size parameter d was found to be constant for all of the salts investigated and equal to 4.2 f 0.2 b for ethanol and 5.0 f 0.5 for propanol. A slightly smaller but constant value of d = 3.5 k 0.2 ,k has been obtained for the same salts in methanol, acetonitrile, and nitromethane,2~*4~z3 suggesting a small but real dependence of d on dielectric constant. The data shown in Tables I and I1 were also analyzed by the Fuoss-Hsia equation.24 I n this equation, the terms in c*' have been explicitly integrated and retained. This results in a complex expression which is most conveniently evaluated with the aid of a computer. The following examples are typical of the parameters resulting from this analysis : for RSerNBr in propanol, A. = 26.90 f 0.01, d = 4.4 f 0.1 b, and K , = 626 f 4; for Bu4NI in propanol, ho = 24.67 f 0.02, d = 3.7 f 0.1 b and K , = 423 i 4. Comparison of all the results obtained from the Fuoss-Hsia equation with those in Table 111 showed that the two sets of parameters were almost identical within the leastsquares-determined precision of the parameters. The one exception was the d arameter, which was found to be equal to 3.9 f 0.3 in both solvents. This result confirms the observation by Fuoss and Hsia that this new equation gives d parameters which are more independent of dielectric constants. However, the fact remains that the value of d obtained in the alcohols from either analysis is unrealistically small and does not follow the trend in ionic crystallographic sizes. Ionic Association. Inspection of Table I11 shows that the pattern of ionic association in ethanol and propanol solutions does not exhibit the simple dependence upon ionilc size predicted by electrostatic theory. This can be seen more clearly in Figure 1, where log K A for salts in propanol is plotted against the reciprocal of the sum of the estimated crystallographic radii. The discussion given below is equally applicable to ethanol;
1
3285
'\. c 104I
I
1
I
I
I 0.15
1
I
I
I
I
I 0.17
I 0.18
I 0.19
-
2.8
I
log 26-
KA
2.2 2.4
1 1
0.12
I
0.13
0.14
0.16
I
I/r,
Figure 1. Association constants for the tetraalkylammonium halides and perchlorates as a function of ionic size in propanol: 0 , Me4N+; 0, Et4N; A, Pr4N; 0,Bu4N; V, i-AmaBuN +; 0, n-Hept4N +.
1
I
I
I
I/rx
Figure 2. Association constants for tetrabutylammonium salts in the isodielectric solvents acetone and propanol: 0, C1; A, Br; 0 , I ; 0, Clod.
however, the values of K Aare smaller and hence subject to more uncertainty.* Each solid line in Figure 1 connects the points of salts of a common anion. The association constants for the chlorides and bromides change in the manner predicted by the relative size of the cations, while K A for the iodides appears to be almost constant. The most interesting feature is the fact that the association constant increases with increasing size of the anion. This is illustrated most vividly in Figure 1, where the points for K A for the tetrabutylammonium salts in propanol are connected by the dashed curve. The association constant for the (22) The conductance parameters for ( ~ - C I H ~ ~in ) ~MeOH N I at 26O are A8 = 92.08 f 0.08, a = 4.1 =t0.6 %, and K A = 20 f 3. (23) R. L. Kay, 8.L. Blum, and H. I. Schiff,J. Phys. Chem., 67,1222
(1963).
R. M. Fuosa and K.-L. Hsia, Proc. Nat. Acad. Eci., 57, 1660 (1967). We would like t o thank Professor Fuoss for a copy of the (24)
computer program.
Volume 7% Number 9 September 1968
ALLENR. OVERMAN
3286 perchlorate is greater than that for the chloride by a factor of 5. This is the type of behavior that would be predicted if solvation were the predominant factor in controlling the extent of ion pairing. The observed peculiarities can be accounted for by the assumption that solvation of the anion increases in the order C1 > Br > I > Clod and that solvation of the cations is relatively independent of size. It should be noted that in the cases where solvation is the predominant factor the extent of ion pairing will always be diminished. The value of K A obtained in such a situation will be less than that which would be obtained in the absence of solvation. Shown in Figure 2 are the association constants for tetrabutylammonium salts in propanol as compared with those in acetone.25 The dielectric constant for acetone is 20.47 at 25". Thus acetone and propanol are isodielectric.2e I n contrast to propanol, acetone is a normal solvent, in the sense that the association constants for electrolytes increase with decreasing ionic size. As the size of cation and anion increases, it is reasonable to anticipate that specific interaction with the solvent will become less important and that the ionic association should be only a function of the dielectric constant. Therefore, as 1/1; approaches zero, the association constants for salts in isodielectric solvents
should approach one another asymptotically. As can be seen in Figure 2, the lines diverge as l/rx becomes small, so that the association constant for the Bu4C104 in propanol is greater than that in acetone by one order of magnitude. This would seem to rule out simple solvation as the major factor controlling ionic association in propanol. The alcohols appear to constitute a separate class of solvents, distinct in behavior from many other nonaqueous solvents but similar in some respects to water. The implications of this will be discussed in forthcoming papers. Acknowledgment. This work was supported by Contract No. 14-01-0001-1281 with the Office of Saline Water, U. S. Department of the Interior. (25) M. B. Reynolds and C. A. Kraus, J . Amer. Chem. Hoc., 70, 1709 (1948); M. J. McDowell and C. A. Kraus, ibid., 73, 3293
(1951). (26) In their study of isodielectric solvents, J. T. Denison and J. B. Ramsey, J . Amer. Chem. SOC.,77, 2615 (1955),found that K A was smaller by a factor of 7-10 for a number of electrolytes in ethylene chloride ((25 10.23) than in ethylidene chloride (€25 10.00). They attributed this decrease in K A to preferential solvation of the ions by the more polar gauche form of ethylene chloride and were able to
obtain agreement between the experimental and calculated values of K A by assuming an effective dielectric constant of 11.8. Although this points out the shortcomings of using a bulk property of a liquid in interpreting short-range interactions, it should be noted that no such adjustment of e will account for the opposite trends in K A in propanol and acetone.
Transient Convective Diffusion in Capillaries
by Allen R. Overman Agronomy Department, University of Illinois, Urbana,Illinois (Received April 8, 2968)
A transient solution has been obtained of the one-dimensional continuity equation for convective diffusion in a capillary. The resulting equation has been compared with data in the literature for the system D20-H20,and an agreement of 2% was found in the transient domain for a Peclet number of 3.88. A simple physical concept of solute transport in this system accrues from the analysis.
I n a recent paper a simplified treatment of convective diffusion in capillaries was presented.' An expression for solute distribution within the capillary was obtained as a function of the Peclet number and the boundary conditions for the steady state. The expression for the average solute concentration was used to test the theory for the system D20-H20 at a Peclet number of 3.88 and an agreement of 2% was found. This paper presents an extension of the analysis to the transient state. The Journal of Physical Chemistry
Theory First consider the continuity equation for convective diffusion (cf. Taylora)
V0[l
,I,
-
r2
BC
- ac at = 0
(1)
where C is the solute concentration; r, X , and t are the
