978
F. E. HARRIS,E. W. HAYCOCK AND B. J. ALDER
of varying cross-linking on the activity of a swelling solvent may be rather general. It remains to speculate upon the mechanism of the depression of the sorption curve for low values of 2. This, of course, represents elevation of the activity of the solvent a t comparable concentrations, or less negative deviation from Raoult's Law. It may be worthwhile to emphasize again the unusual nature of this result. Water essentially becomes a better solvent for polystyrenesulfonic acid as the degree of cross-linking is increased a t low relative humidities. This effect persists until the restraints upon the swelling become the most important factor. A possible interpretation may be found in consideration of the effect of the polar groups in this matrix. The presence of the charge on the ionized sulfonate groups attached to a benzene ring would be expected to give rise to a strong dipole.IT If the groups are relatively free to find the positions of lowest potential energy, then interactions of a polymer-polymer type will lead to more positive deviations from Raoult's Law. As the degree of cross-linking is increased, the charge density being kept approximately constant, then polymer-polymer contacts are reduced because of restrictions on (17) F. London, THISJOURNAL, 46, 305 (1942)
VOl. 57
free movements. The polymer-solvent interactions give large negative deviations from Raoult's Law and hence a crossing over on a Raoult's Law diagram can occur, as is actually observed. The heats of mixing will be less exothermic when there is polymer-polymer interaction in accord with the experimental data. Another point which seems to be corroborative is the shape of the initial part of the sorption curve of the quaternary ammonium resinates. As was indicated, lack of information about the activity coefficients of these salts precludes a definite conclusion. However, it should be noted that the quaternary ammonium cations are very large. Thus the tetramethylammonium salt of DVB 10 in the dry state has a volume of 235.7 m1.,2 corresponding t o that of the hydrogen resinate swollen with five moles of water. The large size of the tetramethyl group distends the resin so that the polymer-polymer contacts are reduced on purely mechanical grounds. Therefore, in the process of swelling with water, less polymer-polymer interactions need be overcome and the initial uptake is then larger than for a small ion in the same resin. By the same token, a t high degrees of swelling, the effect of the size of the ion is almost negligible and the latter part of the curve is shaped like those for smaller ions.
PRESSURE DEPENDENCE OF THE DIELECTRIC CONSTANT OF WATER AND THE VOLUME CONTRACTION OF WATER AND n-BUTANOL UPON ADDITION OF ELECTROLYTE BY F. E. HARRIS,^ E. W. HAYCOCK AND B. J. ALDER, Department of Chemistry and Chemical Engineering, University of California, Berkeley, Calif, Received June 8, 1068
The dielectric constant of water has been experimentally determined in the pressure range from 1 to 150 atmospheres and between 14 and 75 From these data the volume contraction of water upon addition of electrolyte has been calculated and compared with previously reported density measurements. The agreement is satisfactory at temperatures below 30" but a t temperatures above this the apparent molal volume of the salt is calculated to decrease with concentration. This decrease has not, as yet, been observed. A similar comparison has been attempted for n-butyl alcohol.
".
The variation of the dielectric constant of water with pressure has previously been reported at only one temperature2 with no estimate of the inaccuracies involved. Since the derivative of the dielectric constant with pressure and also the change of this derivative with temperature is of interest in applications of the Debye-Huckel theory, we have measured the dielectric constant of water in the pressure range from 1 to 150 atmospheres and over a temperature interval from 14 to 75". Experimental Procedure and Results.-The apparatus used for these measurements has been described previously.8 The water was urified by distillation from permangae capacitance cell was calibrated at each nate solution. temperature studied using literature values4 of the dielectric
TK
(1) Predootoral Fellow, National Science Foundation. (2) G. Falckenberg. Ann. Phvsik. 61, 145 (1920). (3) F. E. Harris, E. W. Haycock and B. J. Alder, J . Chem. P h y s . , in press. (4) J. Wymsn, Jr., and E. N. Ingalls, J . A m . Chem. Soc., 60, 1182 (1938).
constant of water a t atmospheric pressure. The experimental values of the dielectric constant, measured at various temperatures and pressures, are given in Table I. The changes in the dielectric constant are relatively small over the pressure range studied and hence there is some scatter in the results obtained. A least square line was fitted to the data a t each temperature and the resulting pressure derivative of the dielectric constant as a function of temperature is given in Table I1 and shown graphically in Fig. 1. The value of the derivative a t 25" agrees within experimental error, which is estimated to be f0.5 X 10-6 atm.-l at the lower temperatures, with the value of 4.6 X lo-' determined by Falckenberg. Experimental errors at the three highest temperatures reported may be somewhat larger than f0.5 X 10-6because of the higher conductivity of the water. It will be noted from Fig. 1 that at about 60" the derivative passes through a minimum analogous to the variation of the compressibility with temperature. Both of these minima are manifestations of the fact that around this temperature the structure of water is the most rigid. Although the change in ( b r / b P ) with ~ temperature is somewhat dependent on the change in density with temperature, it can be shown3 that it is primarily determined by the change in structure caused by the application of pressure.
PRESSURE DEPENDENCE OF THE DIELECTRIC CONSTANT OF WATER
Dee., 1953
979
TABLEI PRESSURE DEPENDENCE OF THE DIELECTRIC CONSTANT OF WATER 14.5’
25.6’ e
Patm
1.0 73.5 120.4 144.2
82.39 82.73 82.89 83.00
Temp., ‘C. T
x
106
K (eq. 2) K (eq. 1)‘ K (eq. 1) See ref. 8.
74.50
e
Patm
a
Patm
4
Patm
e
Patm
e
1.0 77.2 127.2
78.31 78.63 78.75
1.0 44.2 84.0 107.1
74.68 74.79 74.85 74.93
1.0 50.7 99.7 146.9 188.1
70.92 70.95 71.01 71.05 71.08
1.0 94.9 135.7 174.7
66.99 67.05 67.05 67.05
37.1 72.5 107.5 139.1
63.37 63.33 63.60 63.60
TABLEI1 EVALUATION OF THE VOLUME CONTRACTION OF WATER
A(”> e ap
60.7’
47.50
35.90
Patm
14.5
25.6
5.11 1.92 2.1 1.9’
4.53 3.00 1.73 0.92 1.7 1.86c
See ref. 6.
35.9
47.5
60.7
74.5
1.26 -0.14 1.5
0.54 -0.66
4.47 2.15
I
I
I
I
I
I
I
i-
See ref. 7. I
Discussion
K = d+/dcVt
I
I-
By use of the pressure derivative of the dielectric constant in conjunction with the Debye-Hiickel theory, it is possible to evaluate the volume contraction a t infinite dilution when an electrolyte is added to water? These contractions can then be compared with those determined by direct experiment. The volume contraction is expressed in terms of K,defined by (1)
where 6 is the apparent molal volume in cc. and c is the concentration in moles/liter. The DebyeHiickel theory yields for a 1-1 electrolyte K =R [;(a)T 1 ae - 8/31 (2)
(a)’’’
where R is the gas constant, e the electronic charge) k the Boltzmann constant, N the Avogadro number9 8 the compressibility, and E the dielectric constant. Values of K calculated using equation 2 are compared with the experimentally determined onesEJ in Table 11. I n view of the experimental uncer) ~ in the density measuretainties in ( b ~ / d Pand ments required for the determination of volume contraction, satisfactory agreement is obtained at the lower temperatures. At 47.5”, however, the value of K calculated from equation 2 is negative corresponding to an apparent molal volume contraction with concentration. This is in contradiction to the only reported result of direct density determination.B The authors have previously determined the pressure dependence of the dielectric constant of n-butyl alcoh01.~ Since volume contraction measurements for this substance have also been reportedJg a similar comparison to that made for water is possible for this system. Equation 2 yields a value of K of 38 a t 25”, while the data of Vosburgh, et al., give a value of 9. These latter data gave a good straight line when 4 was plotted against cl/z in a range of c from 0.13 to 1.0 molar, as predicted by equation 1. This, however, is no ( 5 ) 0. Redlich, 2. physik. Chem., 6166, 65 (1931). (6) T. Batuecas, ibid., A182, 167 (1938).
(7) 0.Redlich and J. Bigeleisen, Chem Reus., 80, 174 (1942). (8) G. P. Baxter and C. C. Wallace, J . Am. Chena. Soc., 88, 70 (1916). (9) W. C.Vosburgh, L. C. Connell and J. A. V. Butler, J . Chem. Soc., 933 (1933).
1
1
I
1
f
I
Vol. 57
980
ADDITIONS AND CORRECTIONS M. H. Polley, W..D. SchaefCer and W.R. Smith. Development of Stepwise Isotherms an Carbon Black Surfaces. D.F. P e pard, J. P. Paris, P. R.Gray and G. W.Mason. Page 470. In Table I, note a, line 1to read “B” and line 3 Studies of tie Solvent Extraction Behawor of the Transition to read “are not linear for samples heated at 1500’ and Elements. I. Order and Degree of Fractionation of the higher.’’-MmTLE H. PamnY. Trivahat Rare Earths. Roger L. Jany and Wallace Davis, Jr. The Vapor Pressure, Association, and Heat of Vaporization of Hydrogen %ge 298. In 2, line 33, for 6e500 ml.,, read G‘450 Fluoride. ml. Page 600. To footnote (1)(b) add the Document No. Page 299. In Table VII, note a, for “ R = 4.00” read “4069”,,and the cost of photostats and microfilm both a8 “ R = 0.24.”-D. F. PEPPARD. “$1.25.
Vol. 57, 1953
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