The Fugacity of Pure Substances

If we now take the total differential of Eq. 7.5 and substitute the total differential of the Gibbs energy of a pure substance (Eq. 4.30) we find 

This constant is not defined so far, and we could really make many choices of its value. However, the most sensible choice is zero, so that for ideal gases we have 

For any real gas, as P approaches zero the behavior of real gases approaches ideal gas behavior, so we can say that for any material in the gas state 

Equation 7.6 shows the most useful derivative of the fugacity. The other one regularly seen is (dlnf/dT)p. In principle, we could begin with Eq. C.l and divide by dT, holding P constant, but that approach leads to a mathematical mess because the derivative of g° appears. Therefore, the 

Physical and Chemical Equilibrium for Chemical Engineers, Second Edition. Noel de Nevers. 2012 John Wiley Sons, Inc. Published 2012 by John Wiley Sons, Inc. 

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Appendix C shows the mathematics of the fugacity of pure substances and of mixrnres. We may summarize the findings... 

Equations 7.5 to 7.9 are the whole story on the fugacity of pure substances. They are derived here and copied into the main text. 

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