Equilibrium conditions in a multiphase, multicomponent system

Thermodynam/csandCtem/sfry, second edition, version 3 2011 by Howard DeVoe. Latest version www.chem.umd.adu/thermobook 

The system consists of areference phase, a, and other phases labeled by. Species 

This equation is like Eq. 8.1.6 on page 194 with provision for more than one species. 

In the equilibrium state of the isolated system, S has the maximum possible value, d5 is equal to zero for an infinitesimal change of any of the independent variables, and the coefficient of each term on the right side of Eq. 9.2.41 is zero. We find that in this state each phase has the same temperature and the same pressure, and for each species the chemical potential is the same in each phase. 

Suppose the system contains a species i that is effectively excluded from a particular phase, a . For instance, sucrose molecules dissolved in an aqueous phase are not accommodated in the crystal structure of an ice phase, and a nonpolar substance may be essentially insoluble in an aqueous phase. We can treat this kind of situation by setting dnf, equal to zero. Consequently there is no equilibrium condition involving the chemical potential of this species in phase a . 

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We can obtain the condition of reaction equilibrium given by Eq. 11.7.4 in a more general and rigorous way by an extension of the derivation of Sec. 9.2.7, which was for equilibrium conditions in a multiphase, multicomponent system. 

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