366
D. FENNELL EVANS AND ROBERT L. KAY
barrier decreases with pressure more slowly than the first. I n fact, since experiment only yields the sum of the effects of pressure on ionization and on mobility, we cannot, rule out the possibility that the mobility of carriers according to mechanism ( 2 ) actually decreases with pressure. This will be evident if one examines eq. 5 and notes how the pressure effect comes into AG,the free energy of ionization in carrier production, and into AG,*, the activation free energy for mobility. The coinpression data (Figure 4) indicate that a t low pressures the normal lattice undergoes compression resulting in the C1- ions being moved into more sym-
metrical positions, thus improving charge mobility. Above 25 kbars the important effect on mobility according to our model is the effect of pressure on misalignment.
Aclcnourledgment. The authors gratefully wish to acknowledge the Army Research Office (Durham) for financial support of the work under Grant No. DAARO-D-31-124-G-618. We also wish to thank contributors of compounds as listed in Table I. The valuable advice of Professors Ivan Cutler and Owen Johnson is gratefully acknowledged.
The Conductance Behavior of the Symmetrical Tetraalkylammonium Halides in Aqueous Solution at 25 and 10"
by D. Fennel1 Evans and Robert L. Kay Mellon Institute, Pittsburgh, Pennsylvania 16813 (Received June $8, 1866)
Precise conductance measurements are reported for Me4NC1, RIe4NBr, RIe4NI, EttNBr, Pr4NC1, PrtNBr, Pr4N1, Bu4NCI, Bu4NBr, and Bu4NI in aqueous solutions at 25 and 10" for the concentration range 5 X 10-4 to low2M . Salt purity was verified by the agreement obtained in the limiting ionic conductances. A Fuoss-Onsager analysis gave low ion-size parameters that increased with cation size for the chlorides, remained constant for the bromides, and decreased with increasing cation size for the iodides, indicating increasingly abnormal behavior as the anion size increased. The opposite order and much higher values have been reported for the alkali halides. This effect is attributed to increasing association as both the anion and cation size increases. Only the data for Pr4NI and Bu4NI at 25" and Bu4XI a t 10" analyzed directly for any significant amount of association.
Introduction The symmetrical tetraalkylammonium ions have long been used as good examples of spherical ions having a large variation in size. A number of recent systematic investigations of the properties of these electrolytes in aqueous solution have indicated that the interaction of water with the hydrocarbon portion of the electrolyte is of considerable importance. LindenThe Journal of Physical Chemistry
baum and Boyd2 have shown that the activity coefficients for the tetraalkylammonium chlorides increase with increasing cation size, whereas the opposite behavior is observed in the case of the bromides and (1) Presented in part at the 147th National Meeting of the American Chemical societv. Chicago. - . 111.. SeDt 1964. (2) s. Lindenbaum and G. E. Boyd, J. P h w . C h m . , 68,911 (1964). "
I
CONDUCTANCE OF SYMMETRICAL TETRAALKYLAMMONIUM HALIDES
iodides. The order in the chlorides was explained by the enforcement of water structure about the hydrocarbon portions of the cations, while the order in the bromides and iodides was attributed to “water structure-enforced ion pairing,” as first proposed by Diam ~ n d . He ~ suggested that when two large hydrophobic ions are present, the solution can best be stabilized by forming one cavity for an ion pair instead of two separate cavities, one for each ion. Such ion pairs would be stabilized primarily by water-structure considerations, rather than by the coulombic energy of electrostatic ion pairs. Hydration of the chloride ion was assumed to prohibit the formation of ion pairs in the case of the chlorides. Wen and Saito‘ have discussed the abnormal behavior of the tetraalkylammonium salts in aqueous solution and have measured the partial molar volumes in aqueous solutions of the bromides at concentrations between 0.1 and 10 m. They interpreted their results as indicating that overlapping clathrate-like cages of water formed around the hydrocarbon portions of the cations, thereby producing cavities in which both cations and anions could hide. The minima in the partial molal volumes curves were attributed to the decrease in volume due to such occluded ions. These investigations at best have involved relatively concentrated solutions where theory is least applicable. Owing to the high sensitivity of conductance measurements, we hoped to detect the effects of the interactions of water with the hydrocarbon portion of these electrolytes by noting any deviations from the behavior predicted by existing solvent-continuum theories. For this reason, we have analyzed all the available precise conductance data for the tetraalkylammonium salts in dilute aqueous solution. Kraus and coworkers6-7 have made fairly extensive measurements on many of these salts at 25’ but, in most cases, were interested in limiting conductances and, consequently, did not cover the required concentration range. Lange8 has measured the chlorides and iodides at 0’ and found, in general, that the conductance of the iodides decreased more rapidly with concentration than that of the corresponding chloride. However, his measurements do not have the required precision nor are they extensive enough for an analysis of the concentration dependence by modern theories. I n order to make a systematic study, we have made precise conductance measurements on most of the tetraalkylammonium halides at 25 and loo in the concentration range 5 X lob4 to M . These measurements for aqueous solutions supplement our previous measurements on acet~nitrile,~ methanol,l’J*and D2010bsolutions of these same salts.
367
Experimental Section The electrical equipment, conductance cells, and general techniques were the same as previously described.+” The measurements were carried out with the highest possible precision, using conductance cells of the erlenmeyer type, as described by Daggett, Bair, and Kraus16which contained 500 ml of solution and had cell constants of about 1.3 cm-l. The cell was fitted with the Hawes-Kay salt-cup dispensing device which permitted the successive addition of salt samples, contained in 11-mm Pyrex cups, to the continuously stirred solution without exposing the cell contents to the atmosphere. Both the cell and the dispensing device contained stopcocks which permitted the cells to be thoroughly swept with argon before addition of solvent, during the addition of solvent, and when the dispensing device containing the salt cups was placed on the cell. Conductivity water was added to the cell directly from an all-glass closed system, and solvents of specific conductance 1-3 X lo-’ ohm-’ cm-I were obtained. The solvent underwent almost no detectable conductance change once temperature equilibrium had been attained. Temperature equilibrium was hastened and maintained during a measurement and electrode contamination was minimized by rapid magnetic stirring of the solution using a seamless Teflon-coated magnet. The room temperature was maintained above that of the bath to avoid condensation of the solvent in the saltcup dispensing device. The cell constants obtained from a calibration with aqueous KC1’2 were constant over the whole range of resistances encountered in this research. The usual small frequency correction was made on all the resistance measurements. Conductivity water was prepared by passing distilled water through a 1.2-m column of mixed-bed ion-exchange resin that was thoroughly rinsed before each use. The preparation, (3) R. M. Diamond, J . Phys. Chem., 67, 2513 (1963). (4) W. Y.Wen and S. Saito, ibid., 68, 2639 (1964). (5) H. M.Daggett, E. J. Bair, and C. A. Kraus, J . Am. Chem. Soc., 73, 799 (1951). (6) E. L. Swarts and C. A. Kraus, Proc. NatE. Acad. Sci., 40, 382 (1954).
R.W. Martel and C. A. Kraus, ibid., 41,9 (1955). (8) J. Lange, Z. Physik. Chem., A168, 147 (1934). (9) D. F. Evans, C. Zawoyski, and R. L. Kay, J . Phvs. Chem., 69, (7)
3878 (1965). (IO) (a) R. L. Kay, C. Zawoyski, and D. F. Evans, ibid., 69, 4208 (1965); (b) R. L. Kay and D. F. Evans, ibid., 69, 4216 (1965). (11) J. L.Hawes and R. L. Kay, ibid., 69, 2420 (1965). (12) J. E. Lind, Jr., J. J. Zwolenik, and R. M. Fuoss, J . Am. Chem. Soc., 81, 1557 (1959).
Volume 70, Number 3 February 1966
D. FENNELL EVANS AND ROBERT L. KAY
368
purification, and drying of all the tetraalkylammonium salts has been described el~ewhere.~J~
Table I: Density Increments A and Viscosity B Coefficients for Aqueous Solutions at 25 and 10’ -CI-----. A
10 25 Et4N+ IO 25 Pr4N+ 10 25 B u ~ N + IO 25
Me,N+
B
0.022 0.022
0.09 0.11
0.018
1.01
0.015 0.015
1.49 1.27
-----Br-A
0.045 0.044 0.042 0.041 0.038 0.036 0.032 0.031
--I--B
0.06 0.08 0.38 0.34 0.98 0.81 1.46 1.24
A
B
0.078 0.078
0.03 0.05
0.067 0.065 0.060 0.060
0.93 0.71 1.41 1.19
They were obtained by density measurements on the most concentrated solution used in the conductance measurements and were assumed to follow the relationship d = do A*, where do = 0.99707 at 25’ and 0.9997313 g ml-l at 10’ and where m is the concentration in moles per kilogram of solution. The data for the bromides and iodides at 25’ were measured directly, whereas the values for the chlorides a t 25’ were estimated and those for all the salts at 10’ were estimated from direct measurements on Me4NBr and Bu4NI and the corresponding values a t 25’. At worst, the uncertainty in A is estimated to be no more than 0.004 or 0.004% in the density. The viscosity B BC1’aJ coefficients, defined by ( q - qo)/qoC1/’ = are included in Table I and were obtained directly in an independent set of measurements“ of the viscosity of concentral ed solutions of the iodides and bromides at 25 and 10’. The B values for the chlorides were obtained by adding the constant difference of 0.03 to the value for the corresponding bromide.15 The measured equivalent conductances and the corresponding concentrations in moles per liter are given in Table I1 for 25’ and in Table I11 for 10’. The data were analyzed by the Fuoss-Onsager conductance theory16in the form
+
+
A -- bo -
sc”’ + EC log c + ( J - e)c
(I)
and, in the few cases where association was detected, by A = bo - S(C7)”’
+ ECr log Cy + ( J - e m - KACYAP
(2)
The AA in Tables I1 and 111 are the differences beThe Journal nf PhVsical Chemistry
tween the measured A and that calculated by eq 1 or by eq 2 in the case of those salts marked with a super-
where. l l l’~ These computations used unweighted values of A since the measurements were carried out a t approximately equal increments in C. The coefficient e in eq 1 and 2 was set equal to B h . The recently determined values18 of 78.38 and 83.96 were used for the dielectric constant of water at 25 and lo’, respectively. The values of 0.8903 and 1.306 cp were used for the viscosity of water at 25 and lo’, r e s p e c t i ~ e l y . ’ ~ ~ ~ ~ Included in Tables IV and V are the standard deviations in each parameter and the standard deviations of the individual points CTA. For convenience of calculation, the values of J have also been included. Runs were repeated if the precision obtained from a single run was felt to be inadequate, but the results for all runs are recorded here. Only the results marked with a superscript a were analyzed by eq 2 since it was found that, if the other salts were treated as associated electrolytes, negative association constants were obtained or the standard deviation in KA was larger than KA. In either case, the result is meaningless. The constants CY, 0, El, and E2 have the values 0.2296, 60.62, 0.5307, and 20.52 a t 25’ and 0.2238, 40.97, 0.5041, and 13.52 at lo’, respectively, where, in eq 1 and 2, S = CY&/3 and E = El& - Ez.
+
Discussion Limiting conductances for the tetraalkylammonium ions a t 25’, obtained from the average values of bo in Table IV after weighting by their standard deviation, are given in Table VI. These values are the result of subtracting the limiting conductance for the corresponding halide ion as obtained from the self-consistent values for the transference numbersz1 and the A0 obtained by a FuossI o n Conductances.
(13) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworth and Co. Ltd., London, 1959,p 457. (14) R. L. Kay, D. F. Evans, and T. Vituccio, to be published. (15) H. S. Harned and B. B. Owen. “The Phvsical Chemistry of Electrolytic Solutions,” 3rd ed, Reinhold Pubiishing Corp., New York, N. Y., 1958,p 241. (16) R. M. Fuoss and F. Accascina, “Electrolytic Conductance,” Interscience Publishers, Inc., New York, N. Y., 1959. (17) R. L. Kay, J. Am. Chem. Soc., 8 2 , 2099 (1960). (18) G. A. Vidulich and R. L. Kay, J . Phya. Chem., 66, 383 (1962). (19) J. F.Swindells, J. R. Coe, Jr., and T. B. Godfrey, J. Res. Natl. Bur. Std., 48, 1 (1952). (20) J. R. Coe, Jr., and T. B. Godfrey, J . Appl. Phys., 15, 625 (1944). (21) See ref 15,p 234.
CONDUCTANCE OF SYMMETRICAL TETRAALKYLAMMONIUM HALIDES
369
Table 11: Equivalent Conductances in Aqueous Solutions a t 25' 104c
AA
A
104c
117.55 116.020 115.049 113.951 113.261 112.618 111.934 111.455
116.087 114.156 113.003 111.351 110.232 109.247 108.312 107.395
104c
0.14 -0.133 -0.032 -0.005 0.007 0.013 0.007 0.006
2.911 9.203 17.586 25.399 34.359 43.317 55.717 68.510
121.10 119.95 118.877 118.127 117.382 116.725 115.938 115.214
-0.04 0.02 0.001 0.016 0.011 -0.002 -0.003 -0.009
3.783 10.347 19.543 30.306 41.452 52.749 64.481 76.564
108.29 106.559 105.034 104.033 103.152 102.278 101.550
95.80 94.74 93.642 92.650 91.779 91.018 90.272 89.581 1 0 7 ~= ~
1 0 7 ~= 1.6
6.083 19.250 36.992 51.933 67.215 84.336 100.263
AA
104c
0.01 -0.002 -0.011 -0.006 -0.001 0.001 0.007
4.291 10.049 21.207 33.005 45.436 57.811 68.174 81.356
-0.04 0.03 0.010 0.011 0.004 0.014 -0.007 -0.014
4.600 13.479 22.676 31.193 42.969 56.439 71.480 85.132
2.1
95.77 94.80 93.484 92.426 91.485 90.668 90.043 89.321
A
AA
Pr4NIa 107K0 = 1.9
1 0 7 ~=~
Et4NBr -0.001 -0.002 0.004 -0.002
A
BaNBr 2.1
1 0 7 ~=~
1 0 7 ~=~1.3
25.268 53.329 75.887 116.233 148.901 180.540 216.083 245.093
AA
Me'NBr 1.7
Me4NC1 1.5
1 0 7 ~=
11.274 23.127 36.821 54.988 68.468 82.475 98.785 111.407
A
98.35 96.89 95.786 94.953 93.944 92.943 91.948 91.116 1 0 7 ~=
0.00 0.01 -0.002 -0.004 -0.009 -0.005 -0.003 0.012
4.457 12.209 21.523 30.397 41.049 11.200 65.489 75.579
0.00 0.01 -0.007 0.000 -0.003 0.001 0.005 -0.003
1.4
98.33 97.05 95.905 95.022 94.093 93.308 92.590 91.672
-0.01 0.02 0.002 0.002 -0.007 -0.007 0.004 0.002
Pr4NBr 1O7hO = 1 . 8
Bu~NCI 1 0 7 ~=~
9.893 18.834 25.586 35,423 44.128 52.540 60.919 69.094
1.0
93.01 91.931 91.294 90.546 89.970 89.484 89.001 88.630
0.06 -0.009 -0,037 -0.029 -0.021 0.004 -0.012 0.044
2.980 8.268 14.492 20.930 30.801 40.251 51.679 63.232 75.992 88.346 105.234
99.91 98.94 98.086 97.387 96.508 95.772 95.022 94.370 93.648 93.015 92.215 1 0 7 ~=
3.261 10.033 17.615 26.233 35.473 45.520 58.799 67.132 a
-0.01 0.03 0.004 - 0.008 -0.010 -0.028 -0.011 0.031 0.010 0.002 -0.009
Bu~NI~ 2.4
Me4NI 1.9
1 0 7 ~=
1 0 7 ~=
5.835 14.116 20.704 30.057 42.376 55.055 84.156
119.16 118.00 117.276 116.421 115.470 114.619 113.029
-0.05 0.01 0.023 0.022 0.011 -0.010 -0.012
3.791 9.454 19.654 29.893 40.160 52.717 63.272 76.501 86.121 98.506
2.0
99.85 98.70 97.756 96.919 96.099 95.399 94.550 94.071
94.50 93.46 92,062 90.942 89.927 88.896 88.119 87.233 86.597 85.841
-0.04 0.03 0.031 0.024 -0.032 -0.025 -0.010 0.020 0.002 0.001
1 0 ' ~= 3 . 1 -0.03 0.03 0.013 0.017 -0.038 - 0.008 0.000 0.011
6.175 13.602 24.765 34.897 48,503 59.808 71.519 82.875
94.03 92.85 91.493 90.479 89.288 88.408 87.570 86.817
-0.01 0.01 0.004 0.003 -0.004 -0.005 -0.002 0.005
Analyzed as an associated electrolyte using eq 2.
Onsager analysis of existing conductance data.'? The actual values used here are XO (Cl-) = 76.39, io (Br-) = 78.22, and Xo (I-) = 76.98. As can be seen, there is excellent agreement in our cation conductances from the bromide and iodide salts but somewhat poorer agreement for the hygroscopic The agreement with the data of Kraus and COw0rkers,5-~ Kortum and co-workerslZ2and LeVien,"
after recalculation on the basis of t,he Fuoss-Onsager equation, is entirely satisfactory. The excellent agreement here for the limiting ionic conductances from different salts with a common cation gives us consider(22) G. Kortum, 5. D. Gokhale, and H. Wilski, 2. Physik. Chem. (Frankfurt), 4, 286 (1955). (23) B. J. Levien, Australian J. C h m . , 18, 1161 (1965)~
Volume 70, Number 8
February 1966
370
D. FENNELL EVANS AND ROBERT L. KAY
Table III: Equivalent Conductances in Aqueous Solutions a t 10' 104c
A
AA
10'C
Me4NCl 0 7 ~= 0.95
1
82.50 81.419 80.688 80.124 79.651 79.218 78.869 78.598
17.247 35.830 52.337 67.557 81.748 96.200 108.801 119.986
A
1
0.00 0.002 0.002 0.004 -0.001 -0.004 -0.008 0.009
11.379 18.773 32.540 46.633 61.223 77.464 93.102 110.141
AA
104c
A
Me4NBr 0 7 ~= 1 . 4 85.00 84.400 83.524 82.839 82.205 81.591 81.071 80.540
1
-0.01 0.004 -0.009 0.012 0.003 -0.003 0.003 -0.005
5.556 12.691 24.133 32.339 42.150 54.104 64.582 74.761
AA
10'C
Pr4NBr 0 7 ~=~ 1.4 70.08 69.36 68.538 67.981 67.471 66.961 66.442 66.040
A
pr4ni 1 0 7 ~=
-0.02 0.00 0.034 -0.025 -0.010 0.048 -0.019 -0.012
5.607 12.866 21.214 29.337 37.373 47.800 57.987 69.866
1
67.93 67.165 66.463 66.048 65.665 65.330 64.996 Ci4.705
7.590 17.305 28.611 36.771 44.565 53.031 62.101 70.548
1
-0.02 0.026 0.011 0,009 -0.021 -0,008 0.000 -0.006
5.928 13.813 22.401 33.023 42.940 50.573 61.521 73.172
Et4NBr 0 7 ~= 1 . 2 76.53 75.81 75.129 74.492 73.984 73.628 73.167 72.688
1
-0.03 0.04 -0.004 -0.001 0.002 0.002 0.009 -0.013
4.521 12.097 22,057 32.396 42.583 53.070 63.936 76.624
BurNBr 0 7 ~= 1 . 2 67.51 66.61 65.846 65.178 64.611 64.084 63.595 63.054
0.03 -0.03
0.OOo -0.005 -0.005 -0.005 0.006 0.006
10K ' Q = 2.2 1
9.832 20.223 30,873 41.091 52.221 62.109 71.671 80.384
a
Bu4NC1 0 7 ~=~ 1 . 0 65.16 64.397 63.783 63.256 62.770 62.378 62.025 61.739
-0.02 0.010 0.021 0.000 -0.001 -0.004 -0.009 0.003
7.550 15.022 23.375 31.946 41.408 51.865 61.695 72.372
76.40 75.69 75.103 74.568 74.074 73.587 73.161 72.735
0.00 -0.01 0,009 -0.006 0.000 0.005 0.000 -0.003
Me4NI 1 0 7 ~= 1 . 6 6.407 15.999 25.978 36.343 48.656 60.640 74.537 84.394
84.71 83.81 83.083 82.475 81.848 81.305 80.751 80.389
-0.02 0.02 0.004 0.005 0.000 -0.007 -0.002 0.002
4.653 11.367 17.414 25.024 34.078 42.393 52.163 60.370
1.6
69.24 68.47 67.762 67.143 66.619 66.023 65.514 64.913 1 0 7 ~=
Pr4NCl 0 7 ~=~ 1.0
AA
-0.02 0.03 0.023 -0.014 -0.025 -0.016 0.018 0.006
1.5
69.38 68.63 68.056 67.479 66.877 66.371 65.849 65.430
-0.02 0.03 -0.002 0. OOO -0.001 -0.011 0.003 0.003
BuaNI" 1 0 7 ~= 1 . 5
8.570 19.166 28.316 38.098 47.619 61.300 71.086 76.660
66.13 65.032 64.340 63.600 63.040 62.347 61.847 61.489
0.01 -0.014 0.025 -0.044 -0.017 0.050 0.044 -0.055
107~o= 1 . 6 5.594 12.414 18.947 25.174 30.015 37.904 46.439 61.928
66.43 65.63 65.033 64.514 64.155 63.600 63.081 62.217
-0.01 0.00 0.016 0.002 0.002 -0.017 -0.004 0.007
Equation 2.
able confidence in the purity of our bromides and iodides, and we feel this is as good a criterion of purity as chemical analysis. Included in Table VI are cation conductances obtained from the picrates by Swarts and Krause using XO (Pic-) = 30.6 as obtained from sodium rather than potassium picrate. This value for the picrate conductance gives cation conductances in much bett,er agreement with our data than those which result from using the conductances of the potassium salt. By combining Xo (K+) = 73.55 with XO (KN03) = 145.12 f 0.01'' to give Xo (NO3-) = 71.57, a value The Journal of PhysieQl Chemistry
of Xo (Me4N+) = 44.38 results from the A. (Me4N03) = 115.95 f 0.00 of Swarts and Krausa and the agreement with our average value of 44.43 is good. The numbers in the last column of Table VI are our estimates of the best values for the cation-limiting conductances as obtained from the bromide and iodide results. The limiting conductances for the chloride, bromide, and iodide ions at 10' were obtained from those for 25' by means of the temperature-dependence equation quoted by Harned and Owenz4which is based on precise
CONDUCTANCE OF SYMMETRICAL TETRAALKYLAMMONIUM HALIDES
37 1
Table IV : Conductance Parameters at 25" Salt
Me4NCl BuaNCl Me4NBr Et4NBr PrrNBr Bu4NBr MelNI PrtNI
Bu~NI
0
2.4 1 0 . 1 2.37 f 0.01 3.6 1 0 . 1 1.77 f 0.05 1.72 f 0.02 1 . 8 6 f 0.03 1 . 6 1 f 0.08 2.21 f 0.07 2.04 f 0.02 1.41 f 0.06 0.28 f 0.02 2.7 f 0 . 4 5 0.28 f 0.01 1.1 f 0 . 5 " 0.11 f 0.02 3 15 0.09 f 0.01 1.7 1 0 . 4 "
UA
0.08
J
2 . 0 1 0.35
0.04 0.02 0.008 0.02 0.02 0.02 0.008 0.03 0.03 0.007 0.01 0.009 0.05 0.03 0.02 0.007
129.3 124.9 165.9 92.5 84.5 94.1 80.7 103.3 95.0 65.9 -20.4 130.4 -21.2 46.5 -47.3 154.0 -52.8 79.7
KA
OA
J
0.004
2.1 f 0 . 3 1 . 0 f 0.45 3 . 1 f 0.g5
Equation 2.
Table V:
Conductance Parameters at 10"
Sslt
A0
d
Me4NCl PraNCl BuaNC1 Me4NBr EtaNBr
85.02 f 0 . 0 0 4 69.53f0.01 66.99f0.01 87.09f0.005 78.03f0.01 78.06 f 0.004 71.50f0.02 68.74f0.01 86.31f0.008 70.70f0.009 70.70f0.02 67.87f0.01 67.91 f 0 . 0 2 " 67.91f0.04 68.01f0.084
2.12 f O . 0 1 3.2 f O . l 3.66 f O . 0 7 1.40 1 0 . 0 2 1.29 1 0 . 0 8 1.21 1 0 . 0 2 1.6 f O . l 1.56 1 0 . 0 7 0.86 1 0 . 0 3 0.16 1 0 . 0 2 0.12 f 0 . 0 2 0.023f0.004 1.9 f 1 . 6 5 0.04 f 0 . 0 2 5.7 1 5 . 7 "
Pr4NBr BudNBr Me4NI Pr4NI Bu~NI
5
120.39f0.06 120.52f0.004 95.59 f 0.03 122.67f0.01 110.44 f 0.006 101.40 1 0 . 0 1 101.43f0.02 97.50f0.01 97.54f0.006 121.39f0.02 100.20f0.02 100.26 f 0,0085 100.19 f 0.008 100.21f0.015 96.19f0.03 96.28 f 0.035 96.23f0.02 96.29 f 0.008°
KA
d
ila
2 . 5 1 1.1" 5 . 0 f 3.45
0.006 0.02 0.01 0.007 0.02 0.006 0.03 0.02 0.01 0.01 0.02 0.02 0.01 0.05 0.05
74.0 104.0 114.0 46.2 39.4 35.9 48.7 47.0 19.0 -35.4 -27~4 -61.8 179.9 -61.8 59.9
Equation 2.
transference data. The actual values used for 10' are ho (Cl-) = 54.33, XO (Br-) = 56.15, XO (I-) = 55.39. The resulting equivalent conductances for the tetraalkylammonium ions in aqueous solution a t 10' are given in Table VII. The best values, given in the last column, were obtained by averaging the results from the bromides and iodides and ignoring the results from the hygroscopic chlorides. The most interesting feature of the ionic conductances for these large cat.ions is that their variation with size and temperature indicates a very definite dependence
on the three-dimensional structure that is known to be present in liquid water and in aqueous solutions of hydrocarbon^.^^ A comparison of the conductanceviscosity products for the tetraalkylammonium ions in HzO at 25' with those for 10' and those for the same ions in nonaqueous solvents indicates that this product (24) See ref 15, p 233. (25) G. N h e t h y and H. A. Scheraga, J . Chem. Phys., 39, 3401 (1962). The subject of water structure haa been reviewed in detail recently by J. C. Kavanau, "Water and Solute-Water Interactions," Holden-Day, Inc., San Francisco, Calif., 1964.
Volume 70,Number 2 February 1966
D. FENNELL EVANS AND ROBERT L. KAY
372
Table VI: Limiting Cation Conductances at 25' Best Me4N+
44.13 44. 23a
Et4N + 32.62d Pr4N+ Bu4N+
a
19.20
See ref 6.
* See ref
I-
Br-
c1-
Pia-
44.45 44.41 44.41' 44.40' 44.30" 44.49a 32.22 32.26* 32. Ogd 31. 9Za 32.19" 23.19 23.26 23.19" 23. 2gb 19.31 19.31 1 9 . 3 l C 19.30" 5.
See ref 7.
value
44.42 44.5a 32.22 23.22 19.31
See ref 22.
e
See ref
23.
Table VII: Limiting Cation Conductances at 10' Best Me4N EtrN + Pr4N+ Bu4N +
+
c1-
Br-
I-
value
30.69
30.94 21.90 15.35 12.59
30.92
30.93 21.90 15.33 12.56
15.20 12.66
15.31 12.52
is too high for the hIe4N+ ion and decreases to much too low a value for the Bu4N+ ion. This behavior can best be explained by assuming that, as the hydrocarbon portion of the electrolyte increases in length, water structure enforcement about these chains decreases the ionic mobility. Since the question of ionic effects on solvent structure in both H20 and DzO will be the subject of a forthcoming paper, this topic will not be developed in greater detail here. Concentration Dependence. Although it can be demonstrated that solvent structure plays a large role in determining the magnitude of the limiting conductance, it is not clear that it has much of an effect on the concentration dependence of conductance in the dilute concentration range where present theories are most applicable. I n Figure 1 are plotted the ion-size parameters it obtained from J in eq 1 for the tetraalkvlammonium halides. Included with our results are it values for (h4e3Pr)NBr28and(i-AmsBu)NBr.27 I n contrast to the resillts obtained for nonaqueous solvents, a is not constant and equal to about 3.7,9J0 but is much smaller in magnitude and, with increasing cation size at both temperatures, increases for the chlorides, remains about constant for the bromides, and decreases almost to zero for the iodides. This variation in the iOn-SiZe parameter is analogous, posThe Journal of Physical Chemistry
Figure 1. A plot of the ion-size parameters obtained from eq 1 (see Table I V ) against the sum of the crystallographic radii for the halides of: 1, M e a + ; 2, Et4N +; 3, Pr4N+; 4, BubN+; 5, i-AmlBuN+ (ref 27); 6, MelPrNf (ref 26).
sibly, to the order found by Lindenbaum and Boyd2 for the activity coefficientsof these same salts in aqueous solution at 25'. The obvious explanation for this type of behavior is some type of ion-pair association, which reduces the number of charged species as the anion and cation size increases. It should be noted that this is exactly the association pattern found for the same salts in alcohol solutions.'" As has been pointed out already, negative association constants or association constants smaller than the standard deviation were obtained if the data were processed by eq 2 with the exception of Pr4NI, Bu4NI at 2 5 O , and Bu4NI at 10'. These salts analyzed for an exceedingly small but definite amount of association, as can be seen in Tables IV and V.28 The question must now be asked whether these association constants are real or whether they are artifacts resulting from experimental error or incomplete theory. One simple test that can be applied is to see if eq 2, with its parameters, fits the data better than eq 1. An inspection of uA in Tables IV and V shows that, in general, this is the case for the salts mentioned above. A further test of association lies in plotting A', given by A'
= A - ho + sc'" - EC log c
=
(J - e)c (3)
where 0 = B b . If association is significant in magnitude, A' should not be linear in C but, rather, should (26) H. 0. Spivy and F. M. Snell, J. Phys. C h a . , 68, 2126 (1964). (27) J. F. Skinner and R. hf. Fuoss, ibid., 68, 1882 (1964). (28) LevienZS obtained KA (MerNBr) = 1.4 and K A (MedNI) = 1.8 by setting ii in eq 2 equal to the crystallographic radii. We have resisted this approach because it gives too strict a physical significance t o &. Such an interpretation of d has not been verified by experiment and could result in association constants that are meaningless. Levien's data when analyzed by eq 1 give d = 1.79 f 0.05 and 1.33 0.04 for the bromide and iodide, respectively, in good agreement with our results in Table I\'.
*
CONDUCTANCE OF SYMMETRICAL TETRAALKYLAMMONIUM HALIDES
1’
I
I
I
I
I
I
I
/
373
I
I
I
I
I
I
CHLORIDES BROMIDES
I .s
I
.o
r
0
I
10
20
!
30
,
,
40
50
1
I
60
70
80
,
90
IO‘C
h’
Figure 3. A plot of eq 3 and 4 for BudNI in aqueous solutions a t 25 and 10”. The data of Martel and Kraus7 are included.
os
0.0
- 0.5 I
I
20
40
I
I
60
80
100
IO‘C
Figure 2. Plot of A’ (eq 3) showing the opposite dependence on anion size for the quaternary halides as compared to the potassium halides: Me,PrNBr, Mea(C3H6NO)NCl,and Me3(EtOH)NCl, see ref 26; i-Am3BuNBr, see ref 27; Me,(EtOH)NI and MeZ(EtOH)*NI, J. Varimbe and R. AI, Fuoss, J. Phys. Chem., 64, 1337 (1960).
be curved. Furthermore, the leading term in an expansion of the last term in eq 2 is K A ~ Cwith , the next largest but substantially smaller term being a C”/” term. Consequently, since this is a negative term, a small amount of curvature in A’ requires A’ to be substantially lower than usual if the curvature is to be attributed to association. I n Figure 2, A‘ for the data in Table I1 at 25’ are plotted, along with all the pertinent data that could be found in the literature. The data at 10’ were not plotted since they showed the same behavior as the data for 25’. For the sake of clarity only the best straight line through the experimental points is shown in the plot. The most significant feature to be seen in this plot is the fact that A’ for the quaternary ammonium iodides are much lower than for the other salts and decrease with increasing cation size. The bromides and chlorides are bunched more closely together, but with the chlorides definitely the highest. In contrast, the completely dis~ociated’~ potassium halides show just the opposite and theoretically correct order in A’.
104c
Figure 4. A plot of eq 3 for BurNBr in aqueous solutions at 25 and 10’.
The curvature in the A’ plot for B u 4 M a t 25 and 10’ can be seen in Figure 3. In contrast, A’ for Bu4NBr gives a very good straight line with a positive slope as can be seen in Figure 4. The curvature in A’ is Bu4NI is verified by the data of Martel and Kraus,’ which are included in Figure 3.29 The excellent straight line and large increase in A’ which results from taking association into account is shown in the top curves in Figure 3. Here, A’ is given by A’EA
- A0 4-i3(Cr)”*
-
ECr log C r 4- BC
+ KACrAf’
=
JCr
(4)
and is plotted us. C r in Figure 3. There are a t least three other means of introducing dependence into eq 1 without assuming assome C”/’ sociation. The very low ci values obtained here mean that the electrophoretic effect used in the calculation was too large, since an of 5 or 6 would probably be more correct. I n the test of this possibility, we re(29) The points do not approach zero as the concentration approaches zero, due to the fact that the least-squares computation tends to reduce the curvature in A’ by splitting the error equally between do and J in eq 1.
Volume 70, Number 8 February 1966
374
calculated A‘ using 6 from 0.5 to 6.5 to evaluate the electrophoretic effect, but found that the curvature in A‘ was affected to an insignificant degree. The second method of producing some C”’ dependence rests in the function used for 0 in eq l. There is no doubt that a viscosity correction must be made since the presence of these large cations affects the solution viscosity to a significant extent. If the correct viscosity correction amounts to multiplying the measured A by the ratio of the solution to the solvent viscosity, 11/11,,, then 0 can be shown to be equal to BA in place of the Bh, as first proposed by F ~ o s s . In ~~ this calculation, we assume that the small term resulting from long-range electrostatic interaction between the ions can be neglected. The result of setting 0 equal to B A instead of BAo is shown in Figures 3 and 4. The curvature is not affected significantly, and the only result is a lower A’. If the same substitution is made in eq 2, the only effect is to decrease 6 by about 0.7 and K Aby 0.4 in the case of Bu4NI at 25’. The third method of introducing some C*/’ dependence into eq l would be to include the -J2C”/’ term contained in the original Fuoss-Onsager equation3‘ or by using the Pitts equati0n,~2which also contains a -J2Ca’/’ term. Both of these terms are negative and increase in magnitude with increasing ion size for the systems under investigation here. This is in the correct direction to explain the decreased conductance of the tetradkylammonium iodides over that of the bromides. This term would be significantly smaller for the much smaller K I and KBr and the reversed order would be found in the conductance of these salts due to the higher J term for the larger KI. However, there is considerable doubt as to the authenticity of this term in the Fuoss-Onsager equation, both on experimental and theoretical grounds. In any case, the magnitude of Jz required to explain the effect is many times greater than any realistic value of J 2 based on ion sizes. There are indications that the Pitts equation fits conductance data for aqueous solutions better
The Journal of P h y s k d Chemistry
D. FENNELL EVANSAND ROBERT L. KAY
than the Fu~ss-Onsager.~~ However, in order to explain the decrease in the conductance of the iodides over that of the bromides, i t would be necessary to attribute a differencein a between the iodides and bromides of over 8 A; that is, the J 2 coefficient in the Pitts equation would have to be unrealistically large. It should also be pointed out that attributing greater association to the iodide over the bromide due to the greater polarizability of the iodide ion will explain the results for B h N I and BhNBr but will not explain the higher conductance of K I compared to KBr. Owing to the excellent agreement in Xo (Bu4N+)obtained from both the iodides and the bromides, we feel that the curvature found in the A‘ plots cannot be attributed to salt impurities which are present in Bu4NI but which are absent in Bu4NBr. Since the same association pattern was found for these salts in the alcohols a t low dielectric constant where association can be detected with some confidence, we feel that a t least Bu4NI is exhibiting some ion-pair association in aqueous solution at both 25 and 10’. Whether this is purely electrostatic ion pairing or association that is stabilized by solvent-structural considerations, as used by Wen and Saito4 to explain the partial molar volumes of these salts in concentrated solution or by Lindenbaum and Boyd2 to explain their activity coefficients, cannot be said with certainty at this point. However, the lack of a significantly greater amount of association a t 10’ over that at 25’ would seem to argue that solvent-structural features are not involved.
Acknowledgment. This work was supported by Contract No. 14-01-0001-359 with the Office of Saline Water, U. S. Department of the Interior. (30) R. (31) R. (32) E. (33) R. from J.
M. FUOSS, J . ~ mcam. . SOC., 79,3301 (1957). M. Fuoss and L. Onsager, J . Phys. Chen., 61, 668 (1957). Pitta, Proc. Roy. SOC.(London), A217, 43 (1953). Fernhdez-Prine and J. E. Pme, private communication E. P.
