The exponent n in the relation E= -A/Vn is shown to be of great significance in the behavior of liquid solutions. The modified version of Flory's theory presented here indicates that the enthalpy of mixing of binary solutions can be calculated from density measurements, if the value of n for the system is known. The method is applied to binary solutions of aliphatic hydrocarbons of various chain lengths and it is found that the value n=1.29±0.03 gives good agreement between measured and calculated values of HEfor this group of solutions. Good agreement is also observed for systems containing spherical molecules and for mixtures composed of aromatic hydrocarbons. The advantage of using n coupled with X12 rather than the
It has been shown recently6"83 that the excess enthalpy of binary solutions can be predicted with high accuracy if the behavior of the pure constituents and the density-concentration dependence of the mixture itself are known. The difficulty in deriving an accurate expression for the combinatorial partition function seems to be the main reason for the poor results found for second-law functions. Recent calculations in our laboratory indicate some progress in predicting secondlaw functions, although satisfactory solution will require more intensive research.In this relatively short article we suggest combining our statistical method of obtaining^E from^E data6"8) with a semiempirical approach that makes possible the evaluation of the excess Gibbs free energy, &E9 or excess entropy, T<9*E9 from^E data4'5). The results obtained by this combined procedure seem to be of better quality, at least for the systems investigated here, than those obtained by applying the van der Waals m= l approach1"^.
A statistical theory of fluid mixtures is derived which is able to predict the excess enthalpy of binary liquid mixtures accurately from volumetric data. The treatment is a modification of the methodology developed by Flory and coworkers, in which the van der Waals energy-volume relationship is replaced by the more general expression, E= -a\Vm. The exponent m is postulated to be a fundamental property of each liquid component and the value of m for a binary mixture is assumed to be a volume fraction averaged function of the values of m for the individual components. The mixture is treated as being composed of two pseudocomponents whose potential energies and properties are not quite the same as those of the pure componentsfrom whichthey are derived. The theory permits the interaction energy between two like molecules in a mixture to vary with concentration.
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