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Activity C o e f f i c i e n t s of CsH.5 and CsH72 in Aqueous NaCl Solutions
Experimental Determination and Scaled Particle Theory Calculation of the Activity Coefficients of Benzene and Cyclohexane in Aqueous Sodium Chloride Solutions' Yuh-Loo Tien Chang, Martha Y. Schrier, and Eugene E. Schrier" Department of Chemistry, State University of New York at Binghamton, Binghamton, New York 13907 (Received June 7 7, 7973) Publication costs assisted by the U.S. Public Health Service
The ratio of the solubility of the nonelectrolyte in sodium chloride solution (ws) to its solubility in water (w) has been measured over a wide range of sodium chloride molalities for the nonelectrolytes, cyclohexane and benzene. The technique of gas-liquid chromatography was utilized in the analysis. The activity coefficient ratios ( y w a / y w ) obtained for each nonelectrolyte from the solubility ratios were correlated with salt molality using an equation of the form, log (yws/yw)= A m s Bms3/2. The value of A obtained for benzene compared favorably with that from previous work. The scaled particle theory has been employed to calculate the limiting interaction parameter, A, for both benzene and cyclohexane using recently derived values of the Lennard-Jones parameters and molecular diameters for these molecules. The agreement between experimental and calculated values was poor. Use of Lennard-Jones well depths calculated from the Mavroyannis-Stephen equation gave values of the limiting interaction parameter in excellent agreement with experiment.
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Introduction
Masterton and Lee2 have shown that the scaled particle theory as extended by Shoor and Gubbins3 can be used to calculate interaction parameters for salt-nonelectrolyte interactions in aqueous solutions. Calculations were performed on a variety of nonpolar substances including the rare gases and various simple hydrocarbons for which experimental data were available in the literature. Notable in this otherwise successful application of the theory were the large discrepancies between the observed and calculated limiting interaction parameters for benzene with various electrolytes. It was concluded that either the theory is defective or aromatic molecules provide some anomalous feature in aqueous solution. Cyclohexane is similar to benzene with respect to molar volume and polarizability but exhibits differences in conformational properties and does not have T electrons. It thus provides an interesting compound with which to further test this discrepancy. Experimental Section
Materials. Cyclohexane (Matheson Coleman and Bell) was purified by the method of Morgan and Lowry.4 A small residual impurity amounting to about 2.5% of the material was resolved sufficiently from the cyclohexane peak in the glc analysis so that it could be disregarded. Benzene and sodium chloride were ACS reagent grade and were used without further purification. The sodium chloride was dried overnight a t 140" before use. Solubility Determinations. Saturated solutions of the nonelectrolytes in water or the appropriate sodium chloride solution were prepared by equilibrating the phases in 250-ml Pyrex aspirator bottles. The outlet near the bottom of these bottles was sealed with a silicone rubber seDtum. An aspirator bottle containing the sample of interest was immersed in a constant temperature water bath controlled at 25.00 f 0.05". A submersible magnetic stirrer was used to stir the sample solution until the aqueous phase was saturated with nonelectrolyte. The stirring
speed was kept as slow as possible to prevent formation of cyclohexane droplets. A time test indicated that saturation was attained after 24 hr of equilibration. Analysis of the Samples. A Beckman Model GC-4 gas chromatograph equipped with flame ionization detector was used for the analysis of the samples. In order to facilitate the analysis of nonelectrolyte in aqueous salt solution, the copper sample column was divided into three sections: (1) a section of empty column which trapped the sodium chloride after the remainder of the sample had vaporized, (2) a section containing gelatin and firebrick which selectively removed water from the sample,5 and (3) a section for partition which was packed with 25% (w/w) SE-30 gum rubber on 80/100 Mesh Chromosorb G, AW-DMCS. Samples of the aqueous solution saturated with nonelectrolyte were obtained by removing the aspirator bottle from the water bath and inserting the needle of a gastight Hamilton 10-pl syringe through the rubber septum into the aqueous phase. This sampling procedure was done a t a point in the room where the ambient temperature was 25". Five samples of water saturated with nonelectrolyte were withdrawn from the appropriate aspirator bottle and injected sequentially into the gas chromatograph. Next, five samples of NaCl solution saturated with nonelectrolyte were injected onto the column. Finally, another five samples of the nonelectrolyte saturated water were injected. This procedure allowed for compensation of any drift of the instrument during the time of analysis. The area under each peak was integrated using a disk chart integrator and average peak areas were calculated for each group of five injections. The average standard deviation of the mean for a series of five nonelectrolyte peaks was 2.5%.
In the development of the experimental method, it was assumed that the ratio of the peak heights for a nonelectrolyte in water (w) and in salt solution (ws) was equal to The Journal of Physical Chemistry, Voi. 78, No. 2, 1974
Y.-L. Tien Chang, M. Y. Schrier, and E. E. Schrier
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TABLE I: Coefficients for Representation of Log
ywS/yw
by Eq 2 Coefficient
Nonelectrolyte
A , kg/rnol
Benzene Cyclohexane
0.1999 f 0.0096 0.2713 f 0.0064
% standard deviation of fit
B , (kg/rn01)~/~
2.2 5.4
-0.0143 f. 0.0074 -0.0160 zk 0.0044 0.800
0.350
0.300
0.60C
0.250
-
I
B
I
h 0.200
h
;g
$h -0" 0.150
-
I
0.400
0
0
0.200 0.100
0.050 0.000
ooOO".o
015
110
115
2L
I
I
I
3
1.0 2.0 SALT MOLALITY
30
Figure 2. The logarithms of the activity coefficient rates for cyclohexane plotted as a function of NaCl molality, m, at 25". The size of the points indicates the range of the experimental values at a given salt molality. The line shown was calculated from eq 2 using the coefficients given in Table I . TABLE 11: Comparison of Calculated and Experimental Values of the Limiting Interaction Parameter, A , for Benzene and Cyclohexane in Sodium Chloride Solutions
Nonelectrolyte
Benzene Cyclohexane
" Reference 13.
u (nonelectrolyte) X 108 crn
5.26~ 5.268 5.630 5.63a
a/k
531" 214b 573a 183b
Arralod
Aexptl
0.102 0,205 ,0.101 0.245
0.200 0.200 0.271 0.271
Calculated from eq 3; we text.
Discussion Theoretical calculation of the limiting interaction parameter, A in eq 2, is readily accomplished using the extended scaled particle formulation.2*3 We have used eq 11, 19, and 32 in the paper of Masterton and Lee2 for these calculations. The polarizabilities for N a f , C1-, and4 benzene are those employed by Masterton and Lee. The polarizability for cyclohexane was calculated from the bond refractions for the C-H and C-C bonds given in the compilation of Price.9 The diameters for sodium ion and chloride ion were those derived by Waddingtonlo in accordance with the recent findings of Masterton, Bolacofsky, and Lee11 regarding the best set of ionic diameters to be used in calculations involving the scaled particle theory. The hard sphere diameter for water is taken2 to be 2.75 X 10-8 cm. The depth of the potential well, c / k , for each of the ions was given by the Mavroyannis-Stephen equation2.12.
(3)
Activity Coefficients of C6H6and
in Aqueous NaCl Solutions
where L Y ~ is the polarizability of the ion, Zi is the total number of electrons in the ion, and Ui is its diameter. The value of the apparent molal volume of sodium chloride a t infinite dilution, &O, is taken as 16.62 ml/mol. The choice of the molecular parameters, u and c/k for benzene and cyclohexane, is particularly important in the situation under consideration. Wilhelm and Battinol3 (WB) recently calculated the Lennard-Jones parameters for a number of different solvents from gas solubility data using the scaled particle theory to calculate the work of cavity formation. Their values of U, the hard-sphere diameter, and c / k for benzene and cyclohexane are in good agreement with the same parameters calculated previously from liquid-state properties. The agreement is not as good with parameters calculated from transport properties of the gas-phase molecules. The values of u tend to be smaller in the WB calculation and the values of elk are larger than those derived from gas-phase properties of these molecules. In any case, it seemed to us that the parameters derived from interactions in the liquid phase would be better suited for use in further calculations involving species in solution. We have, therefore, adopted the WB values. In addition to these values of u and c/k, an alternative value of r/k was made available by using the WB value of u for each nonelectrolyte in conjunction with eq 3 as suggested previously.2 The results of the calculation are given in Table 11. Equation 9 of the paper by Masterton, e t ul.,11 has been used to bring the calculated values of the limiting interaction parameter into the molality scale, The experimental limiting interaction parameters are not in agreement with those calculated on the basis of the WB values of u and elk. Indeed, no set of Lennard-Jones parameters obtained from the literature gave calculated results in agreement with experiment for both nonelectrolytes. On the other hand, the limiting interaction parameters calculated using t/k derived from eq 3 are in excellent agreement with the experimental values. It is noteworthy that the values of r/k derived from eq 3 for the nonelectrolytes are very much smaller than those obtained from the literature. Clearly, the anomaly in the scaled particle theory representation of ion-nonelectrolyte interactions in aqueous solution is not restricted to aromatic nonelectrolytes as had been suggested previously.11 This problem most likely arises from one of two causes. First, the assumption of a spherical symmetry in the theoretical treatment may break down for these disk-shaped molecules.1* Indeed, the assumption of a random distribution of water and ions
167
around even a spherical nonelectrolyte could stand refinement. Second, the effective ion-nonelectrolyte interaction potential may be smaller than that given by the geometric mean of c/k values for the ion and the nonelectrolyte because of the considerable disparity in size between the two particles, More work, both experimental and theoretical, is required to distinguish the precise cause of this interesting discrepancy. In addition, the utility of the Mavroyannis-Stephen equation in the prediction of molecular properties in condensed phases is worthy of further investigation. If we take into account the increase of the apparent molal volume of the salt, @v, with increasing salt concentration, it is also possible to estimate a value for the B coefficient of eq 2 from the theoretical treatment.15 The calculation can be carried out by using values of 4v calculated from the equation,l6 $v = 16.62 1.868~~'~ 0.02cs, a t various salt concentrations in the equations of Masterton and Lee.2 After bringing the resulting data onto the molal scale,ll calculated values of log (yws//yw)/ ms were plotted as a function of the square root of the salt molality. The slope of this plot is equal to B. The calculated values of B, -0.025 (kg/mo1)3j2 for cyclohexane and -0.021 (kg/mol)3/2 for benzene, compare favorably with the experimental values given in Table I of -0.016 0.004 (kg/mo1)3'2 for cyclohexane and -0.014 f 0.007 (kg/mo1)3/2 for benzene. Since 4v comes into the scaled particle equations in several places, the ability of the theory to account for a coefficient such as B which is important only a t finite salt molalities is pleasing.
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*
References and Notes This work was supported in part by Public Health Service Grant No GM11762 from the Institute of General Medical Sciences. W. L. Masterton and T. P. Lee, J. Phys. Chern.. 74, 1776 (1970) S. K . Shoor and K. E. Gubbins, J. Phys. Chern.. 73,498 (1969). S.0. Morgan and H. H. Lowry, J. Phys. Chem., 34,2385 (1930). H. A. Syzmanski and T. Amabile, J. Chromatogr. Sci., 7, 575 (1969). W. McDevit and F. A. Long, J. Arner. Chern. SOC., 74,1773 (1952). Complete tables of experimental data are given in the M.S. Thesis of Y. L. Tien, State University of New York, Binghamton, 1971. M. Y. Spink and E. E. Schrier, J. Chem. Thermodyn., 2, 821 (1970). A. H. Price in "Dielectric Properties and Behavior," N. E. Hill, Ed.. Van Nostrand-Reinhold, London, 1969, p 238. T. C. Waddington. Trans. Faraday Soc., 62, 1482 (1966). W. L. Masterdon, D. Bolacofsky, and T. P. Lee, J. Phys. Chern., 75,2809 (1971). C. Mavroyannis and M. J. Stephen, Mol. Phys., 5,629 (1962). E. Wilhelm and R . Battino, J. Chern. Phys., 55,4012 (1971) M. A. Cotter and F. H. Stillinger, J. Chern. Phys.. 57,3356 (1972). We are grateful to a referee for pointing out this possibility. F. J. Miller0 in "Water and Aqueous Solutions," R . A Horne, Ed., Wiley-lnterscience, New York, N. Y., 1972, p 519.
The Journal of Physical Chemistry, Vol. 78, No. 2, 1974
