NOTES
2783
were measured in a Cannon-Fenske viscometer. As evident in Table I, the viscosity of the benzene mixture is lower than a value inferred from precise viscosity studies which we assume to be definitive. Viscosities were assumed to vary linearly with concentrations. Relative concentrations were estimated using a Zeiss differential refractometer.
hexane all data are consistent. For the other hydrocarbons the order of magnitude of the viscosity correction is what would be expected; the value for benzene in this work appears to be incorrect. All of the values (except the benzene value with the suspected viscosity correction) are consistent with precise binary diffusion data obtained in this laboratory. Within the experimental error, which would appear to be about 1%, the corrected quantities are independent of the concentration of the deuterated species. The invariance of Dv/voH with concentration is what would be expected in the nearly ideal case.4 Thus, if
*
Table I ma Benzene
0.5 0.399 0.253
?/?OH
1.0oj 1.003 1.002
D?/& 2 . 1 5 X 10-6 2 . 1 4 x 10-5 2 . 1 4 X 10-5
0.5 0.347 0.271 0.211
1.02 1.02 1.01 1.01
1 . 4 2 x 10-5 1 . 4 2 x 10-6 1 . 4 1 X 10-6 1 . 4 2 X 10-5
Isooctane
0,5
n-Heptane
0.318 0.19~ 0.5 0.278 0.215
1.015 1.01 1.00~ 1.03 1.02 1.01
2 . 2 6 x 10-5 2 . 3 1 X 10-5 2.27 X 10-6 3 . 0 7 x 10-6 3.09 x 3 . 1 5 x 10-5
Cyclohexane
Average Other values (x105) (~105)
+
DV/V'H = (XHDD XDDH)V/VOH 2.14 2.19f
1.42 1.42f
2.15b 2 . 2 l C 2.25d 2.1'
1.4' 1.433g
2.28
3.10
3.18
Mole fraction deuterated species assuming XD = 1 of original. K. Graupner and E. P. S. Winter, J. Chem. Soc., 1145 (1952). R. E. Rathbun and A. L. Babb, J . Phys. Chem., 65,1072 (1961). R. Mills, ibid., 67,600 (1963). e D. w. McCaU, D. c. Doughs, and E. w. Anderson, J. Chem. Phys., 31,1555 (1959). Calculated using viscosities given by J. A. Dixon and W. Schiessler, J . Phys. Chem., 58, 430 (1954). ' M. V. Kulkami, '2. F-Allen, and P. A. Lyons, ibid., 69, 2491 (1965). a
Materials. The deuterated compounds used, isooctane, benzene, cyclohexane, and n-heptane, were obtained from Merck Sharpe and Dohme, Montreal. The only recognized problem was a 0.3% low boiling component in the isooctane sample (as estimated by vapor chromatography); this was assumed to introduce no significant error. The undeuterated nheptane and isooctane were Phillips research grade; Fisher Certified reagent benzene and cyclohexane were used. All compounds were used without further purification. In Table I are listed the values for the tracer diffusion coefficients at various mean concentrations. They have been corrected for the difference in viscosity relative to pure undeuterated hydrocarbon. Representative data from other sources are included. It is interesting to note the disparity between the values for benzene. It is evident that the corrected value based on viscosity data of Dixon and Schiessler agrees very well with other measurements. For cyclo-
(where XH is the mole fraction of the normal hydrocarbon and D H is its intrinsic diffusion coefficient at that concentration with corresponding notation for the deuterated species) we may identify the limiting value of DH with the average of the values of Dq/voH assuming, in keeping with the data, the equality and constancy of DD and DH. Viewed in this way, these data illustrate striking explicit examples of ideal diffusion in binary mixtures. Given a sufficient auantitv of a deuterated comDound. better precision would be possible (to an optimum of about *0,2%j when a slight variation of D ~ / ~ o ~ with concentration might be apparent. Certainly the availability of a large amount of deuterated hydrocarbon would permit a more rational extrapolation to zero concentration of the normal hydrocarbon (lim XH+O D~/BOH is the quantity to be determined). Acknowledgment. This work was supported by Atomic Energy Commission Cont'ract AT(30-1)-1375. (4) G.S. Hartley and J. Crank, Trans. Faraday SOC.,45,801 (1949).
Diffusion in the System Cyclohexane-Benzene
by L. Rodwin, J. A. Harpst, and P. A. Lyons Department of Chemistry, Yale University, New Haven, Connecticut (Received March 31, 1966)
For binary nonaqueous solutions showing only a slight deviation from ideality, it has been proposed that diffusion data may be described by the HartleyCrank relation1 (1) G. 5. Hartley and J. Crank, Trans. Faraday Soc., 45,801 (1949).
Volume 60,Number 8 August 1966
NOTES
2784
D=--RT d ln.flx,[xl Nq d In
XI
+
3
a2
if the frictional coefficients, ui, for each component at given mole fractions, xi, are evaluated from a straight line joining the measured values at xi = 0 and xi =
efficient is very small and can be obtained from the linear approximation rule. Thus in dilute solutions the deviation of the solute frictional coefficient from the linear approximation can be determined. Calling 33 I
1.2
At xi = 0, ui may be obtained from the limiting value of the binary diffusion coefficient as xi + 0. At xi = 1, oi may be obtained from a self-diffusion experiment. This procedure fits the carbon tetrachloridecyclohexane system very well. Whereas a linear approximation for the ui terms may be the normal first-order approximation, deviations from this simple rule are to be expected for systems showing larger deviations from ideality. In particular, in systems with large positive deviations from ideality, diffusive mobilities relative to viscosity may be expected to be high with correspondingly abnormally low frictional coefficients.4 Data for the system cyclohexane-benzene support this thesis. They are listed in Table I together with auxiliary data of interest in predicting the results.
0.0
0.5
1.0
Zc6Elf
Figure 1. Frictional coefficients ( U) us. mole fraction: upper curve, u06H12;lower curve, U O ~ H ~ .
Table I -Auxiliary ---Diffusion ZCeHi2
0.0100 0.0501 0,0911 0.1101 0.2000 0.3017 0.3658 0.3961 0.5205 0.6418 0.7795 0.9299 0.9800
data-
D X lo6
ZCeHtz
2.090 2.044 1.999 1.978 1.903 1.845 1.822 1.815 1.796 1.799 1.829 1.866 1.876
0.0407 0.0977 0,1489 0.1991 0.3011 0.3991 0.4987 0.6017 0.6986 0.8006 0.8959 0.9313 0.9638 0,9864
data Density, Viscosity, g./ml. CP.
0.86765 0.85963 0.85291 0.84648 0.83424 0.82282 0.81322 0.80344 0.79503 0.78688 0.77992 0.77757 0.77530 0,77398
0.5938 0.5871 0.5839 0.5810 0.5852 0.5953 0.6127 0.6403 0.6783 0.7301 0.7929 0.8219 0.8484 0,8732 0
Diffusion measurements were made using the Gouy t e ~ h n i q u e . ~A~ ~twin-armed pycnometer was used to measure densities. Viscosities were obtained with a Cannon-Fenske viscometer. The self-diffusion coefficients quoted derive from Rayleigh measurements on the interdiffusion of the deuterated and ordinary hydrocarbons. In very dilute solutions, u for the solute can be calculated precisely from measured binary diffusion coefficients since the term involving the solvent coThe Journal of Physical Chemistry
1.0
Figure 2. Diffusion curves; circles are measured values ( =tO.Zo/,); broken curve represents values calculated from u values in Table 11. (2) J. A. Harpst, Thesis, Yale University, 1962. (3) M. V. Kulkami, G. F. Allen, and P. A. Lyons, J . Phys. Chem., 69,2491 (1965). (4) L. Onsager, Ann. N. Y . A d . Sci., 46, 241 (1946). (5) L. G. Longsworth, J. Am. Chem. Soc., 69, 2510 (1947). (6) G. Kegeles and L. J. Gosting, &id., 69, 2516 (1947). (7) J. D.Birkett and P. A. Lyons, J . Phys. Chem., 69, 2782 (1965).
NOTES
2785
UA,, the value predicted by the linear rule and Au the deviation from the predicted value, the relative deviation ACT/CTA,,in dilute solutions is proportional to the corresponding quantity Aq/TApp. (In the system C6H~-CeH12 the volume change on mixing is positive; the frictional coefficients are lower than the linear first-order approximation.) If the dilute solution behavior, Au/uA,, = kAq/qapp, is assumed to hold at all concentrations, values of ui for each component can be predicted at all concentrations; they are displayed in Figure 1 and listed in Table 11. These u terms may be used in the Hartley-Crank equation to compute binary diffusion coefficients over the entire range of concentrations. The comparison with measured values is in Table 11. The agreement, apparent in Figure 2, is very good, approaching the experimental accuracy of the thermodynamic term and optical self-diffusion data.
Table I1 $0
Qa
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
1.000 0.896 0.828 0.780 0.758 0.758 0.780 0.816 0.864 0.924 1.000
a
Q
=
[1
Uc
0.601 0.587 0.581 0.585 0.595 0.614 0.640 0.679 0.730 0.797 0.888
x lo*
32.54 31.70 31.10 30.71 30.46 30.40 30.43 30.67 31.09 31.71 32.63
ag
x
lo8
31.26 30.42 29.63 28.90 28.20 27.53 26.88 26.27 25.70 25.15 24.65
Dcalod
Dobad
10'
10'
x
2.104 1.989 1.905 1.821 1.777 1.759 1.779 1.802 1.829 1.857 1.880
x
2.104 1.988 1.903 1.846 1.813 1.798 1.796 1.810 1.834 .1.859 1.880
+ ( b I n f d b In sdl.
The success of the second-order approximation for eva.luating u values is probably not as impressive as it appears at first glance. This empirical device only demonstrates the internal consistency of the diffusion data. It may be observed that the linear approximation predicts results fairly well, with a maximum discrepancy of about 6% ; this second approximation cuts the discrepancy by a factor of three. Finally, despite the satisfactory numerical agreement there is a discernible trend in the data; calculated diffusion coefficients are slightly lower than measurements. It will, nonetheless, be a matter of some interest to discover the limit of the range of applicability of this simple rule. Acknowledgment. This work was supported in part by Atomic Energy Commission Contract AT(30-1)1375.
On the Compressibility of Molten Alkali Halides
by E. L. Heric Department of Chemistry, University of Georgia, Athens, Georgia (Received February 10, 1966)
Among similar compounds the isothermal compressibility, p = - (l/V)(hV/hP)?.,may vary considerably. Thus, among the alkali halides experimental values' range at 800" from 28.6 to 82.7 X cm.2 dyne-' for lithium chloride and cesium bromide, respectively. The work from which these values were obtained is unusually comprehensive. A number of the alkali halides were omitted, however, and the estimation of p for several of these from p us. ion size plots is not feasible. There is, in general, a paucity of p data for molten salts, and a simple correlation between the values in a series of related compounds is desirable. Such a relationship is reported here for the alkali halides, being the ratio of p to the molal volume, V . Thus, the quantity is the compressibility per unit volume. Table I lists the p/V ratios a t 200" intervals for 12 alkali halides. Ten of these represent experimentally measured' values of p. RbCl and RbBr p values were obtained by the present author through interpolation from well-defined, isothermal plots of p us. cation radius for alkali chlorides and bromides.' V values were obtained from the data of Jaeger,2 except for LiBr from the data of Yaffe and Van Art~dalen.~The temperatures included in Table I for the alkali halides cover the range of their fusion temperatures. Thus, many of the p/V values correspond to a supercooled liquid state. Those p values were obtained by interpolation of plots of compressibility vs. temperature. For this purpose the data of Bockris and Richards were combined with those of Bridgman4at or near room temperature. The latter data are actually adiabatic compressibilities rather than isothermal, but at those low temperatures the difference between the two comparatively small values is not significant to the present conclusions. It is evident from Table I that at a given temperature p/V is constant within an average deviation of (1) J. O'M. Bockris and N. E. Richards, Proc. Roy. SOC.(London), A241, 44 (1957). (2) F. M. Jaeger, 2. anorg. allgem. Chem., 101, 1 (1917). (3) I. S.-Yaffe and E. R. Van Artsdalen, J. Phys. Chem., 60, 1128 (1956). (4) P. W. Bridgman, PTOC. Am. Acad. Arts Sci., 67, 345 (1932).
'Volume 69, Number 8 August 1966
