ELECTRICAL CONDUCTIVITY OF TETRAALKYLAMMONIUM HALIDESOLUTIONS Acknowledgment. The authors wish to thank Dr. R. L. Kay for his helpful comments and suggestions and Dr. F. Franks who made his manuscript available to us
1763
prior to publications. The authors wish to acknowledge the support of the Office of Saline Water for this study.
The Electrical Conductivity of Aqueous Tetraalkylammonium Halide Solutions under Hydrostatic Pressure by R. A. Horne and R. P. Young Arthur D . Little, Inc., Cambridge, Massachusetts OOdl4
(Received November 80, 1967)
The electrical conductivities of 0.10 aqueous solutions of the salts R4N+il-, where R is CHI, C2Hs,CaH7, n-C4H9,and n-CaHn and A- is C1-, Br-, and I-, have been measured at 4 and 25” over the pressure range 1 atm to 4000 kg/cm2. The results of these measurements support the viewpoints that (1) the hydrophobic hydration atmospheres of these ions are fundamentally different from the coulombic hydration envelopes surrounding “normal” ions such as the alkali metal cations, in particular being much more stable with respect to hydrostatic pressure, and (2) cation-cation interactions are important in solutions of the larger ions in this series.
Introduction I n order to account for cert,ain properties of liquid water and aqueous solutions, Wickel has proposed that, in addition to the “free” or monomeric water and the flickering, H-bonded Frank-Wen clusters, there exists a “third state” which he postulates consists of dimers, trimers, tetramers, etc., even though such small aggregates were specifically discounted in Nemethy and Scheraga’s2 quantitative development of the FrankWen3 theory. Similarly, in order to account for certain interface phenomena, we have been obliged to postulate a “third state”’ which we have called simply the p structure to distinguish it from the a structure of the Frank-Wen clusters and the hydration atmospheres of normal ion^.^'^ This p structure, which is largely present at interfaces, is less susceptible to destruction by the application of hydrostatic pressure than is the a structure of the Frank-Wen clusters.6 The solution properties of the tetraalkylammonium ions have long been recognized as being different from those of “normal” cations such as the alkali metal ions, and Wickel also discussed this “hydration of the second kind.” These ions are heavily hydrated and powerfully enhance the structure of the water surrounding them as reflected in their very large viscosity B coefficients, ranging from +0.10 for (CH3)4N+ to almost $0.90 for (C3H7)4N+ as compared to about +0.14 for Li+, the strongest structure maker of the alkali metal cations.e A comparison of the dependence of the B
coefficients on ionic radius of the tetraalkylammonium ions with that of the alkali metal cations (Figure 1) illustrates that the hydration of the two families of cations are profoundly different, the former exhibits hydrophobic-the latter, coulombic h y d r a t i ~ n . ~We have further proposed that the structure of the hydrophobic hydration of the tetraalkylammonium ions is the p f ~ r m . ~Inasmuch ,~ as the p form is more stable with respect to temperature than the a form, the Walden products for the tetraalkylammonium cations are notably more invariant with respect to t e m p e r a t ~ r e . ~ , ~ (1) E. Wicke, Angew. Chem., 5 , 106 (1966).
(2) G . Nemethy and H . A. Scheraga, J . Chem. Phys., 36, 3382, 3401 (1962). (3) H. S. Frank and W. Y. Wen, Discussions Faraday SOC.,24, 133 (1957). (4) R. A. Horne, “The Structural Forms of Liquid Water a t Interfaces and Near Biopolymers,” Technical Report No. 22, Arthur D. Little, Inc., May 31, 1966; Office of Naval Research Contract No. Nonr-4424(00). (5) R. A. Horne, A. F. Day, R. P. Young, and N. T. Yu, “Interfacial Water Structure: The Electrical Conductivity of Aqueous Electrolyte Permeated Particulate Solids under Hydrostatic Pressure,” Technical Report No. 23, Arthur D. Little, Inc., Sept 30, 1966; Office of Naval Research Contract No. Nonr-4424(00); Electrochim. Acta, in press. (6) R. L. Kay, T. Vituccio, C. Zawoyski, and D. F. Evans, J. Phys. Chem., 70,2336 (1966). (7) R. A. Horne, “Hydrophobic Hydration,” Technical Report No. 26, Arthur D. Little, Inc., Sept 30, 1966; Office of Naval Research Contract N o . Nonr-4424(00). (8) R. A. Robinson and R. H. Stokes, “Electrolyte Solutions,” 2nd ed, Butterworth and Co. Ltd., London, 1959. (9) R. L. Kay and D. F. Evans, J . Phys. Chern., 70,2325 (1966). Volume 7,9, Number 6 May 1968
R. A. HORNEAND R. P. YOUNG
1764 0,90 I
electrical conductivities of aqueous electrolytic solutions under pressure have been described previously. 18 The conductivity cell used was of a capillary type. In the cases of the highly hygroscopic salts, 0.10 M solutions were prepared by dilution of Volhard analyzed approximately 0.2 M solutions.
0,80
0.70
Results Measured values of the specific conductances of 0.10 M aqueous solutions of the tetraallcylammonium halides at 1 atm and 4 and 25" are listed in Table I. Although good data are available for very dilute solutions, for example from the study of Evans and Kay,lQsurprisingly enough there are very few data in the literature on more concentrated solutions that can be compared with the present results.
0.60
0.50
.8 U
Y
6 m
0,40
h
Y
.d
lo
Table I : Specific Conductances (ohm-1 cm-1) of 0.10 M Aqueous Solutions of the Tetraalkylammonium Halides a t 1 Atm
2
F
0.30
0.20
0.00584 0.004956 0.003377
0.10
0,005877 0,004986 0.004306 0.003873 0.003656 0.003721 0 00473 0.00402
0.00
I
-0,lO
0.0
1.0
2.0
3,o
Ionic Radius,
4,O
0 00687 I
5.0
A
Figure 1. The dependence of the water-8tructure-altering properties of cations on their radii (from ref 7 ) .
The persistence of the anomalous minimum in the isothermal compressibility of pure water to higher pressure~~ and - ~conductance ~ measurements at high pressure5J2indicate that the p structure is also much more stable with respect to the application of hydrostatic pressure than the a structure; thus the hydration of the tetraalkylammonium cations should be more stable under pressure and their electrical conductivity should exhibit a smaller pressure dependency than that of the coulombically hydrated alkali metal cations. The conductance of solutions of the latter ions, due to the reduction of their effective hydrated ionic radii by the application of hydrostatic pressure, increases more rapidly with increasing pressure than one would expect on the basis of viscosity and volume changes.13-17 The purpose of the present study was to investigate experimentally the foregoing prediction.
Experimental Section The apparatus and procedures for measuring the T h e Journal of Physical Chemistry
0.009693 0.008410 0.005856 0.009701 0,008380 0.007369 0.006621 0,006367 0.009454 0.00828
Figure 2 shows the variation of the relative specific conductance, K J K ~ atm, with pressure of a 0.10 M KC1 solution at 25.31 A 0,02" and a 0.10 M NHdC1 solution at 25.28 f 0.03". The values for the two electrolytes are very similar and in agreement with earlier published data for 0.10 M KC1 at 24.94°.20 Also shown in Figure 2 (dashed line) is the relative conductance expected on the basis of solvent viscosity and specific volume changes only, q1 ,tmoVloatm/qpOVpOin the absence of pressureinduced dehydration of the ions. (10) N. E. Dorsey, "Properties of Ordinary Water-Substance," Reinhold Publishing Corp., New York, N. Y.,1940. (11) G. 9. Kell and E. Whalley, Phil. Trans. Roy. SOC.(London), A258,565 (1965). (12) R.A. Horne and R. P. Young, J . Phys. Chem., 72,376 (1968). (13) W. A. Zisman, Phys. Rev., 39,151 (1932). (14) R.A.Horne, Nature, 200,418(1963). (15) R.A.Horne, Water Resources Res., 1, 263 (1965). (16) R. A. Horne, R. A. Courant, and D. 9. Johnson, Electrochim. Acta., 11,987 (1966). (17) R.A. Horne, Advan. High Pressure Res., in press. (18) R. A. Horne and 0. R. Frysinger, J . Geophys. Res., 68, 1967 (1963). (19) D.F.Evans and R. L. Kay, J . Phys. Chem., 70,360 (1966). (20) R.A.Home and R. A. Courant, J . Chem. Soc., 3548 (1964).
ELECTRICAL CONDUCTIVITY OF TETRAALKYLAMMONIUM HALIDE SOLUTIONS
I
0.98
0
1
!bslin?
Pressure I
1765
1Wo
m
&
3oaJ
kglcmZ
Figure 2. Pressur'e dependence of the relative specific conductances of K@l and NH&l solutions.
I 0.94
r
I
L
0
I
1Mx)
1
am
-
I
MOO
U1
mow
Pressure kglcm2
1.16
Figure 4. Pressure dependence of the relative conductance of 0.10 A4 aqueous solutions of tetraalkylammonium bromide solutions a t 4 and 25'.
1.14
1.12 E
fl k?
1.16
8
1.12
f 1-10
e
p 1.08 E
8 -
9
1.08
.-"
I
1.m
M"
p 1.04
(Y
%
=
8
1.w
P
p
1.00
1.02
g
O.%
1. m
d
:
H
1
0.98
I
0
lm,
I
-
m
, 3mo
'\,m
Pressure kgkm2
Figure 3. Pressure dependence of the relative conductance of 0.10 M aqueous solutions of tetraalkylammonium chloride solutions a t 4 and 25".
Figures 3-5 show the pressure dependence of the relative conductance of 0.10 M aqueous solutions of the tetraalkylammonium chlorides, bromides, and iodides, respectively. For purposes of comparison, the KC1NH&1 and theoretical curves are repeated in these figures as dashed lines.
Discussion Figures 3-5, generally speaking, exhibit the predicted approach of K * / K I stm us. P of the tetraalkylammonium
0.92
0.88
0.84
I
lD00
, 2ooo Pressure kg/cm2
-
I
J
'3wo
rxNx)
Figure 5 . Pressure dependence of the relative conductance of 0.10 M aqueous solutions of tetraalkylammonium iodide solutions a t 4 and 25".
ion to the theoretical curve indicating that, as expected, the p structure or hydrophobic hydration atmosphere surrounding these ions is much more stable with respect to pressure than the a! structure or coulombic hydration atmosphere surrounding "normal" cations and that, as a consequence, there is relatively little pressure dehyVolume 79, Number 6 M a y 1968
R, A, HORNEAND R, P. YOUNG
1766
dration of these ions, especially for the larger members of the series. However, in addition to the predicted behavior, these figures show two phenomena that were quite unexpected: the series of curves are irregular in the sense of not being simply in the order of increasing size of R in R&+, and in the case of larger R + and/or the iodides, some of the observed curves actually fall below the theoretical curve; that is to say, the solutions are less conductive than they should be. These irregularities came as such as surprise that a number of the experiments were repeated, but these checks indicated that the irregularities are real. While the viscosity B coefficients form a simple series (C3H7)&+ > (CzH&N+ > (CH,)4N+ (Figure l), K J K ~ atm appears to go through a maximum for (C3H7)4N+ in the case of the bromides and for (C2H&X+in the case of the iodides. Although there is a regular sequence in the case of the chlorides, (C4H9)4X+ > (C3H7)4i\’+ > (C2HS)dNf > (CH,)J”, it is exactly the opposite of the order we might expect; that is to say, the ion with the least hydrophobic character, (CH3)4S+, does not fall furthest away from the theoretical curve nor does the ion with the most hydrophobic least coulombic character fall closest. The causes of this unexpected turn of affairs is certainly not clear at the present time. Possibly the role of the anion must be taken into consideration, inasmuch as the anion appears to be capable of changing the order. Similar reversals of order and differences between chlorides and bromides and iodides were uncovered by Lindenbaum and Bo37dZ1in their investigation of the osmotic and activity coefficients for aqueous solutions of the symmetrical tetraalkylammonium halides. They suggest that water-structure making by the cations is the dominant effect for the chlorides, but in the case of the bromides and iodides, water-structureenforced ion pairing (see below) becomes more important. Subsequently, however, the very regular behavior of the thermodynamics of solution of these salts led LindenbaumZ2to question the relative importance of such explanations in terms of water structure, yet still later Wood, et U Z . , ~ returned ~ to structural concepts in order to account the observed heats of dilution of the tetraalkylammonium fluorides. Although, as a consequence of careful and intensive study, we now have many pieces of the puzzle, no clear picture has emerged, and the best we can do at the present time is to conclude weakly that these are very complex systems, that the water structure within them admits of alteration in at least several ways, quite probably simultaneously, and that solute-solute interactions play an important role as well. The maximum for (C3H7)4N+or (CzH5)4N+is not quite so unexplicable and is not without precedent. For example, the tetra-n-butylammonium and tetraisoamylammonium salts appear to be exceptional in that they, unlike their sister cations in the series, are The Journal of Physical Chemistry
capable of forming “higher” hydrate^,^^$^* Evidently the @-structuredhydrophobic hydration sheath is a sort of geodesic dome, possibly a multilayer one, and for a given set of bond lengths, stretchabilities, and bendabilities such a structure can enclose certain sized volumes more readily and with greater stability than others. If such is the case, a volume corresponding to (CZHJ4N+or (C3H7)4N+ is evidently particularly awkward for the encompassing water structure while a volume corresponding to (n-C4H9)4N+is particularly convenient. In the case of “normal,” i.e., coulombically hydrated, or H&O4*‘the dissociation electrolytes such as i\IgS0425 into ionic species increases with increasing pressure as a consequence of the volume decrease arising from the electrostriction of the nearby water, It should be cautioned, however, that it is specious to argue thereform that the application of hydrostatic pressure should stabilize rather than destroy ionic hydrationz7inasmuch as the electrostricted region comprises only a small part of the total hydration atmosphere i ~ n The . ~ observed volume change upon ion formation is
+
)AVH~O,BI /AVH~O,EI- IAVH~O,C/ where the subscripts B, E, and C indicate the FrankWen structure-broken region, the electrostricted region, and the local Frank-Wen cluster region, respectively, and not simply
This more detailed picture of the hydration atmosphere of cations casts considerable doubt on the meaningfulness of hydration numbers determined from compressibilities. I n sharp contrast to “normal” electrolytes, in the case of the tetraalkylammonium halides, especially for the larger cations and anions, there appear to be ion association processes which are accompanied by a volume decrease. The exact nature of these associations requires further clarification. Wen and Saito13’on t he basis of their partial molal volume studies, have proposed that there is a “structural salting in” of the larger (21) S. Lindenbaum and G. E. Boyd, J . Phys. Chem., 68, 911 (1964). (22) S. Lindenbaum, ibid.,70,814 (1966). (23) R. H. Wood, H. L. Anderson, J. D. Beck, J. R. France, W. E. deVry, andL. J. Soltzberg, ibid., 71,2149 (1967). (24) D. L. Fowler, W. V. Loebenstein, D. B. Pall, and C. A. Kraus, J. Am. Chem. Soc., 62,1140 (1940). (25) F. H. Fisher, J . Phys. Chem., 66, 1607 (1962). (26) R. A. Horne, R. A. Courant, ahd G. R. Frysinger, J . Chem. SOC., 1515 (1964). (27) Reference 9, footnote 37 (28) R. A. Horne and J . D. Birkett, Electrochim. Acta, 12, 1153 (1967). (29) R. A. Horne, “Electrostriction and the Dehydration of Ions Under Pressure,” Technical Report No. 26, Arthur D. Little, Inc., Nov 30, 1966; Office of Naval Research, Contract No. Nonr-4424(00). (30) D. S. Allam and W. H. Lee, J . Chem. SOC.,426 (1966). (31) W. Y. Wen and S. Saito, J . Phys. Chem., 68,2639 (1964).
~
~
ELECTRICAL CONDUCTIVITY O F TETRAALKYLAMMONIUM HALIDESOLUTIONS
1767
Table I1 : Arrhenius Activation Energies of Electrical Conductance (in kcal/mole) at 13"
-Pressure
--
-
_ ~ I -
------
1 atm
500
1000
1500
2000
3.76 4.01 4.13 4.30 3.92 4.04 4.20 4.18 4.33 3.92 4.40 4.19
3.59 3.77 3.90 4.03 3.65 3.79 3.90 3.95 4.10 3.60 4.16 3.95
3.43 3.60 3.76 3.83 3.51 3.62 3.75 3.73 3.95 3.33 3.96 3.81
3.40 3.51 3.63 3.71 3.43 3.54 3.67 3.65 3.87 3.13 3.85 3.71
3.29 3.45 3.57 3.63 3.39 3.49 3.61 3.59 3.83 2.97 3.79 3.66
tetraalkylammonium cations. Wood, et al., 32 have similarly found evidence for cation-cation interactions in their heats of dilution data, and Frank33has represented the processes as a sort of merger of the hydration cages of two cations to form a combined species accompanied by an over-all volume decrease. Our own and equivalent view of the interaction is that it represents an example of hydrophobic bonding, that, in order to minimize the perturbation of water structure caused by the weakly coulombic, strongly hydrophobic solutes, the water minimizes their volume by forcing them into one another's a.rms. The effect is the more pronounced the greater the hydrophobic character of the solute and is affected also by the water-structure-altering properties of the anion present. Inasmuch as the interaction gives rise to an over-all volume decrease, the application of hydrostatic pressure favors the ion-association process even though pressure is, in general, a waterstructure-breaking variable, both locally and in bulk. Thus the observed tendency of K = / K ~ atm us. P to fall below the theoretical curve, especially in the case of the iodides of the higher tetraalkylammonium cations, can be interpreted as further evidence supporting the theory of cation-cation interactions in these systems. I n our earlier studies we have found the Arrhenius activation energy, E,, t o be a useful property in investigating the mechanism of solvent and solute transport processes in aqueous solution.16 Values of E , (calculated from the 4 arid 25" conductances to give an average value at, 13", remembering that in aqueous solutions E , is not independent of temperature) are listed in Table I1 and plotted as a function of pressure in Figure 6. Generally speaking, E , increases with the increasing size of the cation, although (n-C3H7)&+may be an exception to the rule. No clear trend on the dependence on anion size is evident. The values of E , are reliable to within about 5%. Earlier we reported that E , of electrical conductance us. P goes through a minimum for aqueous solutions of strong 1:1 salts such as KCla4335 and the same phenomenon in the case of the tetraalkyl-
kg/cmL-----2500
3.23 3.43 3.53 3.58 3.39 3.46 3.57 I
.
3500
4000
4500
3.24 3.41 3.53
3.27 3.35 3.55
3.30 3.48 3.60
...
...
3.28 3.43 3.59
3.42 3.44 3.52
3.45 3.46 3.49
3.49 3.49 3.49
3.54 3.52 3.55
3.83 2.72 3.76 3.65
3.86 2.64 3.77 3.68
3.43 2.56 3.81 3.71
4.02 2.51 3.87 3.74
.
.
3.80 2.84 3.76 3.65
*'
4.2
7
3000
#
.
...
...
*..
...
R
4.1 =:
4.0 L+
3.9
E .cJ
._ B
.-26
3.8
3.7
E 3.6
2
3.5
3.4 0
lm,
am 3wo 4mo 5 Pressure kglcm2
-
x)
Figure 6. The pressure dependence of the Arrhenius activation energy of electrical conductance.
ammonium salts is exemplified in Figure 6. To repeat, the structure of the coulombic hydration of K + is presumably quite different from the structure of the hydrophobic-hydration envelope of RdN+; therefore, the similarity of the curves for K + and R4N+ in Figure 6 implies that the minima arise from structural changes in the bulk water rather than in the local water structure near the ions. However, if such is the case, then it is surprising that these minima do not tend t o flatten out as the ratio of bulk to local water is decreased by increasing the electrolyte concentration or as the structure of the bulk water is loosened by increasing the temperatures. 35
Acknowledgment. This work was supported by the Office of Naval Research. (32) R. H.Wood, H. L. Anderson, J. D. Beck, J. R. France, W. E. deVry, andL. J. Soltzberg, J . Phys. Chem., 71,2149 (1967). (33) H.S . Frank, 2.Physik. Chem., 228,367 (1965). (34) R.A. Horne, B. R. Myers, and G. R. Frysinger, J . Chem. Phys., 39,2666 (1963). (35) R.A. Horne and R. P. Young, J . Phus. Chem., 71,3824 (1967). Volume '78, Number 6 M a y 1988
