Distribution coefficient thermodynamic treatment

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

For multicomponent mixtures, graphical representations of properties, as presented in Chapter 3, cannot be used to determine equilibrium-stage requirements. Analytical computational procedures must be applied with thermodynamic properties represented preferably by algebraic equations. Because mixture properties depend on temperature, pressure, and phase composition(s), these equations tend to be complex. Nevertheless the equations presented in this chapter are widely used for computing phase equilibrium ratios (K-values and distribution coefficients), enthalpies, and densities of mixtures over wide ranges of conditions. These equations require various pure species constants. These are tabulated for 176 compounds in Appendix I. By necessity, the thermodynamic treatment presented here is condensed. The reader can refer to Perry and Chilton as well as to other indicated sources for fundamental classical thermodynamic background not included here. 

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