3322
R. L. KAY,D. F. EVANS, AND G. P. CUNNINGHAM
Comparison of these sums with the total rate constants for the loss of these reactant ions by cross reaction shows agreement, within experimental error, and thus provides confidence in the validity of our data and treatment.
Acknowledgments. This work was supported by Contract AT (30-1)-3570 with the U. S. Atomic Energy Commission. We also wish to thank the National Science Foundation for providing funds to assist in the original purchase of the mass spectrometer.
The Conductance of Large Hydrophobic Ions in Water, Methanol, and Acetonitrile at 25" by Robert L. Kay, D. Fennel1 Evans, and G. P. Cunningham Chemistry Department, Carneoie-Mellon University, Mellon Institute, Pittsburgh, Pennsylvania (Received March 21, 1969)
16818
The conductance of the halides of the i-AmaBuN+ and the i-AmdN+ ions were measured in water, methanol and acetonitrile at 25". The conductance of n-AmdNBr in water and i-AmaxclO4 in methanol are also included. The Walden products for these large cations were almost identical in acetonitrile and methanol but substantially lower in aqueous solution. This effectis attributed to the increased degree of hydrogen bonding in the water adjacent to the hydrocarbon side chains and is in agreement with the results found for the smaller tetraalkylammonium ions in aqueous solution. The degree of association into ion pairs in the hydroxylic solvents is shown to be substantiallygreater than that predicted by simple electrostatictheory and is attributed to a twostep process involving solvent-separated and contact ion pairs.
Introduction It has been pointed out' that the ionic mobilities of the larger symmetrical tetraalkylammonium ions in aqueous solution are significantly lower than the corresponding values for nonaqueous solvents after correction for the viscosity differences. This effect has been attributed to the enforcement of water structure around the hydrocarbon side chains' and has been shown to become effective for side chains containing more than two carbon atoms.2 This conclusion is based on a model of Frank and Wen3 and has been verified by several independent methods recently reviewed by frank^.^ Here we extend our earlier measurements to the tetra-n-amylammonium and tetraisoamylammonium ions and particularly to the unsymmetrical triisoamylbutylammonium ion. This latter ion appeared to have a much larger mobility6than would be predicted from its symmetrical analogs and a verification seemed desirable. The association behavior of these large ions is also of considerable interest since it has been shown that they are not associated in acetonitrile solutions but show a considerable degree of association in hydroxylic solvents.'j This effect can now be explained in terms of solvent-separated and contact ion pairs. Experimental Section The conductance apparatus and the improved saltThe Journal of Physical Chemistry
cup dispensing device as well as the special techniques used to handle hygroscopic salts have already been described in detail.6,' The bromides were prepared by refluxing the amines, i-AmaN or n-AmSN, and the required alkyl bromide in methanol for 12-24 hr (the straight chains react more slowIy). The mixture was dissolved in excess water and extracted with ether to remove the unreacted reagents. The salts were recrystallized four times from acetone by precipitation with ether and were dried in a vacuum oven at 70". These salts were extremely hygroscopic and were handled at all times in a drybox. The above procedure was not used for the iodides because their solubility in water was too low for an ether extraction of the reaction impurities. Instead, they were prepared by converting the corresponding bromides to the hydroxide by ion exchange and precipitatR.L. Kay and D. F. Evans, J . Phys. Chem., 70,2325 (1966). (2) D. F. Evans, G. P. Cunningham, and R . L. Kay, ibid., 70, 2974 (1966). (3) H. S. Frank and W. Y . Wen, Discussions Faraday Soc., 24, 133 (1957). (4) F. Franks in "Hydrogen-Bonded Solvent Systems," A. K. Covington and P. Jones, Ed., Taylor and Francis, Ltd., London EC4, 1968. (5) J. F. Skinner and R . M. Fuoss, J . Phys. Chem., 68, 1882 (1964). (6) R. L. Kay, C. Zawoyski, and D. F. Evans, ibid., 69, 3878, 4208 (1965). (7) R. L. Kay, B. J. Hales, and G. P. Cunningham, ibid., 71, 3925 (1967). (1)
3323
CONDUCTANCE OF'LARGEHYDROPHOBIC IONS Table I : Equivalent Conductances in Methanol, Acetonitrile, and Aqueous Solutions a t 25"
--------
CHPOH-------
10412
_-------
CHsCN
-?
104c
A
A
5.422 12.897 20.407 28.887 37.600 45.401 54.224
86.97 83.98 81.83 79.92 78.30 77.03 75.77
i-AmaBuNBr 5.565 149.82 10.951 146.40 16.337 143.82 21.501 141.79 26.397 140.11 32.008 138.40 37.360 136.94
5.925 11.723 17.030 22,292 28.638 34.924 40.718 46.726
92.50 89.62 87.61 85.93 84.21 82.72 81.50 80.35
6.568 12.114 18.301 24.026 31.300 36.629 42.505 48.878
_----
H20---------.
10v
A
36.641 46.181 55.622 63.787 74.153
90.91 90.20 89.55 89.04 88.43
11.794 18.954 25.462 33.209 40.491 47.732
92.12 91.17 90.36 89.49 87.76 88.10
7.386 15.991 24,223 32.382 39.758 45.630 52.702 59.746
93,89 92.72 91.85 91.12 90.55 90.10 89.60 89.18
-n-Am4NBr .33.074 42.192 52.307 64.174 75.493
90.57 89.81 89.03 88.25 87.54
i-AmsBuNI
_--__-
i-AmrNI--
10.244 16.513 22.791 28.536 35.587 41.631 47.460
1
89.28 86.82 84.86 83.33 81.69 80.45 79.35
-7.345 14.207 20.652 27.767 33.667 40.207 46.823 53.587
i-AmdNClO4-----6.828 15.212 23.830 31.833 38.857 45.386
97.79 93.07 89.54 86.89 84.89 83.24
ing the iodides with KI. The nonhygroscopic iodides were purified and dried in the same manner as the bromides. Conductivity water (KO = 1 X lom7ohm-' cm-l) was obtained by passing distilled water through a mixed-bed ion exchange resin. Conductivity grade anhydrous methanol and acetonitrile were prepared by standard procedures.e All solutions were prepared in closed systems under an atmosphere of argon.
Results The measured equivalent conductances are given in Table I a t various concentrations (mol lo-') for the various salts studied in methanol, acetonitrile, and aqueous solution a t 25". The solvent conductances were 2-6 X lo+, 1-5 X and 1-2 X 10-'ohm-l cm-l, respectively. The solution densities required for volume concentrations were determined by density measurements on the final solution in each case and the assumption of linearity to infinite dilution. Considerable difficulty was encountered in aqueous solutions at
151.03 147.66 144.82 142.67 140.33 138.82 137.31 135.80 --i-AmaNBr------------. 147.67 143.92 141.25 138.83 137.10 135 38 133.81 132.35 I
----
-
the dilute end. The salts tended to float owing to their low density and it was difficult to bring them into solution at concentrations less than about 2 X mol L-'. Consequently, the results quoted here for aqueous solutions do not have the usual precision. We are of the opinion that some type of dilution technique would be preferable for these salts in aqueous solutions. The data were analyzed by the Fuoss-Onsager conductance theory* in the usual form using a least-squares computer p r ~ g r a m . The ~ following dielectric constants and viscosities were used: 78.40 and 0.8903 CP for HzO;"J 32.62 and 0.5428 CPfor CH3OH;l' 35.95 and 0.3409 CP for CHsCIT." The results are given in (8) R. M. Fuoss and F. Accasoina, "Electrolytic Conductances," Interscience Publishers, New York, N. Y.,1959. Analysis with the Fuoss-Hsia equation, Proc. Nut. Acad. Sci., 57, 1550 (1967),produced no significant difference in the conductance parameters. (9) D.F. Evans and R. L. Kay, J.Phys. Chem., 70,366 (1966). (10) R. L. Kay, G. A. Vidulich, and K. 5. Pribadi, ibid., 73, 445
(1969). (11) G. P. Cunningham, G. A. Vidulich, and R. L. Kay, J . Chem. Eng. Data, 12,336 (1967).
v o h m e 78,Number 10 OctobeT 1969
R. L. KAY, D. F. EVANS, AND G. P. CUNNINGHAM ~
~~~~
tion of the B viscosity coefficients for the smaller tetraalkylammonium salts12 and the assumption that the B values were the same in acetonitrile as in methanol. The constants S and E can be calculated readily from data already publi~hed.~,e For aqueous solutions, repeated runs are reported in Table I1 but the actual data for only one run are listed in Table I for the sake of brevity. A comparison of the cation limiting conductances obtained from the bromides and iodides of the i-AmBBuN+ ion indicate an uncertainty of 0.2 unit in HzO and CH30H and the rather high value of 0.6 unit in acetonitrile. The data on the perchlorate salt were included since the limiting
Table I1 : Conductance Parameters for Aqueous Solutions at 25' Salt
A0
i-Am3BuNBr i-Am3BuNI
96.35 95.33 95.39 95.23 96.24 96.26 95.83 95.76
i-Am4NBr n-Am4NBr
J
XQ+"
114
18.13
- 109 -110
- 105 114 100 80 65
18.34 18.03 17.58
"Xo(Br-) = 87.22,Xo(I-) = 76.98; seeref 1.
Table 111: Conductance Parameters for Met'hanol and Acetonitrile Solutions a t 25' Salt
;
AO
i-AmaBuNBr i-AmaBuNI i-Am4NI i-Am4NC104
92.66 f 0.01 99.16 f 0.01 98.04 f 0.03 106.20 f 0.02
3.38 3.69 3.5 3.12
KA
CHaOH" f 0.01 f 0.06 f 0.1 f 0.07
... 14.4 f 0.4 12.8 f 0.8 32.6 f 0.6
J
XO
+
1246 1420 1360 1430
36.21 36.38 35.26 (70.94)b
1725 1692 1615
57.7 58.3 56.8
CHaCNc i-Am3BuNBr i-Am3BuNI i-Am4NBr a
x0 (Br-)
=
158.36 f 0.02 160.39 f 0.03 157.49 f 0.01
56.45, Xo (I-) = 62.78; see ref 1.
3.6 f 0 . 1 3.5 f O . 1 3.35 f 0.01
'XO ((3104-).
1.2 f0.5 1.6 f 0.7
..*
XO (Br-) = 100.7,XO (I-) = 102.1; see ref 13.
~~
Table IV : Conductance Parameters from Other Sources Salt
A0
He0 2.1
98.89 95.44 95.60
i-AmaBuNBr" i-AmaBuNIb n-Am4NBrc i-Am3BuNId i-AmaBuNPid i-Am4NPi e n-Am4NBrf n-Am4NIf
99.38 f 0.04 83.68 f 0.01 82.55 zk 0.2 91.36 f 0.01 97.42 zk 0.02
i-Am3BuNIff i-AmaBuNPi' n-Am4NBrA n-AmdNI*
160.68 135.70 156.8 f 0 . 1 158.1 f 0.04
KA
a
... ...
... ...
4.6 4.1 3.9 3.5 3.7
CHaCN
*..
.,.
20.7 18.46 17.48
19 f 3 12 40 . 5 15 f 3 3 f 0.4 16 f 1
1675 1320
36.60 36.53' 35.41i 34.91 34.64
...
1585
.
2.9 f 0.3 3.2 3~ 0.1
A0 +
96
...
CHaOH f 0.6 z t 0.1 f 0.8 f 0.06 f 0.08
J
I
.
... e..
.
- 150 ...
... .,.
*..
...
1420 1560
58.6 58.0' 56.1 56.0
Reference 15. d M. A. Coplan and R. M. Fuoss, J . Phys. Chem., 68, 1177 (1964). e E, C. Evers b Reference 14. 0 Reference 5. J . P h p Chem., 68, 1181 and A. G.Knox, J. Amer. Chem. Soc., 73, 1739 (1951). 1 Reference 6. M. A. Coplan and R. M. FUOSS, (1964). h A. C. Harkness and H. 15.Daggett, Jr., Can. J. Chem., 43, 1215 (1965). ' XO (Pi) = 47.07, see ref 6. XO (Pi) = 77.7, see ref 13.
Table I1 for aqueous solutions and in Table I11 for methanol and acetonitrile solutions and typical results are plotted in Figure 1 where A' is given by A'
E
A
- Ao + SC"' - EC log C = (J - B&)C
(I)
The necessary values of B were obtained by extrapolaThe Journal of Physical Chemistry
conductance of that ion was not known and because its large association in methanol demonstrated the effect of hydroxylic solvents on the association behavior of large ions. (12) R. L.Kay, T.Vituccio, C. Zawoyski,and D. F. Evans, J.Phys.
men.,70,2336 (1966).
3325
CONDUCTANCE OF LARGE HYDROPHOBIC IONS Table V : Limiting Conductances and Walden Products for Large Ions at 25' ,
H --L -,I Xo
Ion
Xo +?
+
18.3 18.0 17.5
i-AmlBuN -I. i-Am4N + n-Am4N +
0.163 0.160 0.156
4
7.0k 0
-1
.o
i-Am3BuNBr
1
1
A
A 20 30 40 50 10
104c
Figure 1. A plot of eq 1 for the bromides (circles) and iodides (squares) of the i-A.m3BuN+ion in acetonitrile (filled symbols), methanol (half-filled symbols), and water (open symbols). The triangles indicate the data from ref 14 for i-AmaBuNI.
The recent precise transference data for Me4NC104 were used to obtain the ionic conductances in acetonitrile.I3
Discussion Limiting Conductances. All known precise data from other sources on the i-Am,BuN+, the i-Am4N+,and the n-AmdN+ ions in water, methanol, and acetonitrile have been compiled in Table IV after recalculation to bring them into comformity with the Fuoss-Onsager equation and, in some cases, after giving very little weight to points at the ext)remely dilute end. Although the precision in Xo+ for these large ions is understandably lower than that obtained with smaller ions that are more readily purified and easier to handle, there does seem to be a definite trend in that ho+from the bromides are always significantly lower than that from the iodides in our results. Moreover, our data tend to Be somewhat lower than the corresponding literature values for all the solvents.
CHsOH----? Xo +
36.4 35.3 34.8
c-----CHaCN Xo +?
0.197 0.191 0.189
Xo
7 +
58.1 56.8 56.0
Xo +q
0.198 0.194 0,191
One point seems quite clear. Our value for the i-AmsBuNr+ ion in HzO is in good agreement with that reported by Quintin and J u ~ t i c e 'and ~ gives a Walden product that conforms to the behavior of the other large tetraalkylammonium ions as shown in Figure 2. On the other hand, the Skinner and Fuoss5 value appears too high and not in line with the other large ions. Thus, it appears that the asymmetry of the ion does not produce any unique behavior as far as conductance is concerned. Our value of 17.6 is in good agreement with the value 17.5 obtained by Kraus, et a1.,I6 for the n-Am*N+ ion. It should be noted, however, that this ion is often mistakenly quoted6J4 as the i-Am4N+ion and some confusion has resulted. In Table V are listed the most probable values of the limiting conductances and Walden products for the three cations in the three solvents at 25" based on all the available data. The branched-chain cation can be seen to be faster than the normal-chain cation in methanol and acetonitrile by 1.4% and by twice that percentage in water. The viscosity-conductance products plotted in Figure 2 show that these large ions in aqueous solutions show the same hydrophobic effect characteristic of the BudN+ and Pr&+ ions.' They appear to have a mobility deficiency relative to the corresponding values in the nonaqueous solvents owing presumably to an increased degree of hydrogen bonding around their hydrocarbon chains.' In both acetonitrile and methanol the Walden product is almost the same and only diverges as the ion size decreases sufficiently so that the specific ionic properties attributable to the dipole moment and/or base strength can become important.' The lack of complete agreement in the Walden product for the three large ions in the two organic solvents could be attributed to errors in the conductances or in the viscosities or possibly to the inadequacy of the model on which Stokes' law is based. Concentration Dependence. The effect of a concentration change on A for the i-Am,BuN halides can be inferred from the plot of eq 1 shown in Figure 1. These (13) C. H. Springer, J. F. Coetzee, and R. L. Kay, ibid., 73, 471 (1969). (14) M. Quintin and M. C. Justice, Compt. Rend., 261, 1287 (1965). (15) H. M. Daggett, Jr., E. J. Bair, and C. A. Kraus, J. Amer. Chem. Soc., 73,799 (1951).
Volume 73, Number 10 October 1969
3326
R. L. KAY,D. F. EVANS, AND G. P. CUNNINGHAM 0.26
P
either solvent and if anything, solvation of the halides would stabilize free ions more readily in methanol than in acetonitrile. The coulombic contribution to the association constant in these solvents can be calculated from the Fuoss equation”
K A = 2.524 X 10-3Zaeb
0.19
0.21
0.20
0.22
II r ;
Figure 2. The limiting conductance-viscosity product as a function of reciprocal radius for several hydrophobic cations in methanol, acetonitrile, and water a t 25”.
lines should be linear with slope J - Bho. B is of the order 1.6 in HzO and 0.9 in the nonaqueous solvents, whereas J is about an order of magnitude larger in the latter. Consequently, Bh, has almost a controlling effect on the slope of these A’ plots in aqueous solutions. The ion size parameters, 8 which vary almost linearly with J in the pertinent region are not included in Table I1 for the salts in aqueous solutions since, as was the case with the smaller tetraalkylammonium salts, they were abnormally low and bore no relationship to the real ionic size. For example, the values for the bromides were about 2 but less than 0.1 for the iodides. The most obvious explanation for this behavior is that the iodides exhibit a significant amount of ion pairing in aqueous solution but the bromides very little. A calculation shows that to explain the difference in the slopes for the iodides and bromides in Figure 1 on this basis, the iodide would have an association constant K A = 2.3. This increased association of large ions in hydroxylic solvents has already been discussed jn some and has been shown to be quite general. In acetonitrile, the degree of association decreases with increasing ionic size in a manner predicted by the electrostatic theory, whereas in the alcohols and in waterg association appears to increase with increasing ionic size. The same behavior can be seen here by examining in the data in Table I11 and IV and in plots in Figure 1. In methanol, the iodides and the perchlorate are significantly associated but not the bromide, whereas in acetonitrile the degree of association of the halides is negligible as was the case with Bu4NC104.16 An appeal to solvation to explain this effect is not possible. These larger cations should not be solvated in
The Journal of Physical Chemistry
(2) where b = e2/aekT. Any reasonable estimate of the values in eq 2 predicts KA values no larger than 10-15 for methanol solutions. This could account for the iodides but not the perchlorate. The most likely explanation for this effect is that advanced by Evans and Gardam118who studied the association behavior of large ions in the higher alcohols where the degree of association was considerably larger, thereby decreasing the uncertainty in the association constants attributable to possible deficiencies in conductance theory. They assumed that a two-step mechanism involving solvent-separated and contact ion pairs was in operation in hydroxylic solvents. Since both types of ion pairs are nonconducting, it is easy to show that
KA = Ki(1
+ K2)
(3) where K1 and Kz are the equilibrium constants for each association step. Applying this equation to i-Am4NC104 in methanol with KI = 10 as calculated from eq 2, a value of K? = 2.3 is obtained. This is in line with the K 2 values obtained by Evans and GardamI8 for large ions in the higher alcohols. If eq 2 is applied to aqueous solution, it predicts an increasing K , for 6 values greater than approximately 3. As a first approximation, this has been used to explain what appears to be increased ion pairing in aqueous solution as the size of the ions become very large. However, as pointed out above, K A for the iodides in aqueous solution must be at least 2.3 larger than that for the bromides but eq 2 only predicts a negligibly small difference based on the difference in ionic size between a bromide and iodide ion. Consequently, solvent-separated ion pairs appear to be the most realistic model on which to base an explanation for the conductance behavior of large ions in dilute aqueous solutions as well as dilute solutions of such ions in nonaqueous hydrogen-bonded solvents.
Acknowledgment. The work was supported by Contract No, 14-01-0001-1729 with the Office of Saline Water, U. S. Department of the Interior. (16) J. F. Coetzee and G. P. Cunningham, J . Amer. Chem. Soc., 87, 2529 (1965). (17) R.M.Fuoss, {bid., 80,5059 (1958). (18) D.F.Evans and P. Gardam, J . Phys. Chem., 73,158 (1969).
