Partial molal quantities—review of thermodynamics

The relation between the non-stoichiometry and the equilibrium oxygen pressure mentioned in Section 1.1 can be deduced from the phase rule. For the purpose of the derivation of the phase rule, we shall review fundamental thermodynamics. Gibbs free energy G is defined by the relation 

This equation is valid only for an ideal gas, and by introducing the function fugacity, f the equation is rewritten as 

The integration constant I is chosen so that the fugacity approaches the pressure as the pressure approaches zero. It is clear that for an ideal gas the fugacity is numerically equal to the pressure at all pressures. 

Equations (1.4), (1.5), and (1.6) can be applied only to single component gas systems. Next, we shall derive the corresponding equations for the mixed gas systems. In a phase under consideration there are many gases designated by 1, 2, 3, 4,. with n, n2, n, n, . rii. moles (the mixed gas system is thermodynamically considered to be one phase except for special cases). The partial pressure of gas i , Pi, is defined as the product of the mole fraction of that species and the total pressure (P), namely 

The relation between the partial molal free energy and the fugacity for the mixed gas system has been obtained. 

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