The Gibbs Energy of Fluids

In Chapter 7 we saw that the fact that minerals are to a good approximation incompressible means that the effect of pressure on the Gibbs free energy of solid phases is very easily calculated. Thus, in general 

combined with the more complex integration of dG over a temperature interval at one bar pressure, allowed us to calculate the position of phase boundaries at high pressures and temperatures. The next question is how to evaluate the pressure integral (11.1) when a fluid such as H2O or CO2 is involved, either in the pure form, mixed with other fluid components, or reacting with solid phases Obviously, assuming that the molar volume of a fluid is a constant is not even approximately true, and is unacceptable. A possible way to proceed would be to express U as a function of P in some sort of power series, just as we did for Cp as a function of T (equation 7.12). V dP could then be integrated, and we could determine the values of the power series coefficients for each gas or fluid and tabulate them as we do for the Maier-Kelley coefficients. 

Fortunately, thanks to the insight of G.N. Lewis, we can proceed in a simpler and completely different fashion. Lewis in 1901 defined a new function, the fugacity, which can be thought of as a kind of idealized or thermodynamic pressure, which expresses the value of fV dP single-handedly. To see how the inspiration for such a function might have arisen, we consider the form of the volume integral f V dP for an ideal gas. Thus, substituting RT/P for V in (11.1) we have 

If P is 1 bar and this is designated a standard or reference state denoted by a superscript then 

Thus for ideal gases RT In P all by itself gives the value of fp j dG, or in other words 

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