Phase equilibria in terms of species

We may, with appropriate attention to the reference state, develop the relations in terms of components between the intensive variables pertinent to multiphase systems that contain species other than the components. Such relations would be rather complex, because no account would be taken of the effect of the chemical reactions that occur in the system. All deviations from ideality would appear either in the activity coefficients for substances in condensed phases or in the coefficients used in some equations of state for the gas phase. Simpler relations are obtained when the conditions of phase equilibrium are based on species rather than components, once the species have been identified. 

The fundamental condition for equilibrium between phases, the equality of the chemical potential of a component in every phase in which the component is present still applies. We then substitute for the chemical potential of a component the equivalent chemical potential of the same substance in terms of species or appropriate sums of chemical potentials of the species, as determined by the methods of Section 8.15 and used in the preceding sections. Several examples are discussed in the following paragraphs. 

Many vapors of substances, such as those of certain metals, are mixtures of monomers and dimers and, possibly, of even higher polymers. This must be taken into account when the chemical potential of the substance in a condensed phase, either pure or a solution, is determined by a study of the vapor-liquid equilibrium. We choose to consider only the components in the condensed phase, and use the molecular mass of the monomer to determine the mole numbers. We designate the component whose chemical potential is to be determined by the subscript 1. The condition of equilibrium is then 

The same conditions of equilibrium as given in Equations (11.153) and (11.155) are obtained when the vapor of the substance dissociates incompletely so that some monomeric species are present in the vapor. 

When a solute is distributed between two immiscible liquids, different species, formed from the solute, may exist in the two liquids. Thus, when an organic liquid such as benzene or carbon tetrachloride and water are used as the two liquids, a weak acid may dimerize in the organic phase and partially ionize in the aqueous phase. The condition of equilibrium is the equality of the chemical potential of the monomeric, nonionized species in the two phases. If the dimerization is complete, the condition of equilibrium involves half of the chemical potential of the dimer in the organic phase. 

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A final example concerning phase equilibria in terms of species involves the use of Equation (8.102) or similar equations. We discuss only Equation (8.102) here, which is... 

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