63
THERMODYNAMIC FUNCTIONS OF SOMEBINARYNONELECTROLYTE MIXTURES 3
vE =
XlZZ~C,(Xl 0
- XZ),
The coefficients C , were calculated as in the treatment of calorimetric data and were collected in Table 111. The excess volumes of this system are positive and large; the vE vs. curve is quite asymmetric with the maximum occurring at $1 = 0.53 toward the nonpolar
end of the scale. The equimolar value of vE is 0.59 ml mole-' at 40".
Acknowledgment. This work was supported by the C.S.I.R. India and forms part of a program of the C.S.I.R. Research Unit. Thanks are due to Professor S. R. Palit, Head of the Physical Chemistry Department, I.A.C.S., Calcutta, India.
Excess Thermodynamic Functions of Some Binary Nonelectrolyte Mixtures.
11. Analyses of gE,hE, and v E
Data in Terms of a Generalized Quasi-Lattice Theory by S . N. Bhattacharyya, R. C. Mitra, and A. Mukherjee Indian Association for the Cultivation of Science, Jadavpur, Calcutta, India (Received March 88, 1967)
The experimental data on molar excess enthalpies, Gibbs free energies, and volumes of the systems toluene-fluorobenzene and methylcyclohexane-fluorobenzene presented in part I of this series have been examined from the point of view of a generalized quasi-lattice treatment. Although this approach cannot provide an independent estimate of excess enthalpy and free energy, it is nonetheless possible to predict the excess functions in terms of various molecular interaction pairs once these are obtained uniquely from the analysis of data of other carefully chosen allied binary mixtures.
I. Introduction The results of measurements of the molar excess enthalpy, hE, Gibbs free energy, gE, and volume, vE, at different temperatures for the systems toluenefluorobenzene and methylcyclohexane-fluorobenzene were reported in part 1' of this series. The present paper describes an attempt to interpret the data based on the generalized quasi-lattice theory as developed by Barker2 in a very systematic way. This theory was originally formulated to take into account the molecular interactions which are strongly directional, as in hydrogen-bonded systems, and also the effects arising out of the large difference in molecular size of the parent molecules constituting the mixture. The theory could be extended to the general case of mixtures of nonelectrolytes where the strong angle-dependent forces would be replaced by comparatively much weaker ones or even may be completely absent, while the molecules constituting the mixture may continue to be very different in size,. The systems to be analyzed here obviously come under this category. Systematic works
already attempted in this direction are very f e ~ ,and ~ , ~ practically no work has been done to interpret both excess free energies and enthalpies of such nonelectrolyte mixtures.
11. Quasi-Lattice Theory In his generalized rigid-lattice model, Barker assumes that in the solution a molecule of type i occupying ri sites in a x co-ordinated lattice has ( q i x ) contact points. These contact points are divided into various classes, p, Y , . , ,, the number in the pth class being Qri. The thermodynamics can then be expressed in terms of interaction energies for all possible combinations of these contact points. The final expressions for (1) S. N. Bhattacharyya and A. Mukherjee, J . Phys. Chem., 72, 56 (1968). (2) J. Barker, J . Chem. Phys., 20, 1526 (1952). (3) J. B. Ott, J. R. Goates, and R. L. Snow, J . Phys. Chem., 67, 515 (1963).
(4) I. A. MoLure, J. E. Bennet, A. E. P. Watson, and G. C . Benson, ibid., 69, 2759 (1965).
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S. N. BHATTACHARYYA, R. C. MITRA,AND A. MUKHERJEE
64 the molar excess enthalpy and free energy, according to him, are
lies in the arbitrary way the number of sites could be assigned to different molecules. The assumption that a carbon atom occupies one site of a fourfold cohE = - 2 R T [ C C ( X , i X U ' ordinated lattice ( i e . , x = 4) would no doubt allow as1 ,vu signment of the contact surfaces of a molecule in terms of its molecular structure, but it would not necessarily ensure equal volume per segment in different molecules. gE = CXi/.tiE i The latter is important from the point of view of the theory of r-mer solutions and is one of the factors gov/.tiE = RT Qai In (X,'/~iX,il) erning the shapes of the plots of the excess functions against mole fraction, particularly when the interaction is weak (Uij
