Analysis of Partial Derivatives Via Jacobian Transformations

Step 4. The Gibbs-Duhem equation is obtained by comparing total differentials in steps 1 and 3, via (29-41) and (29-44)  

Step 5. Division by the total number of moles, Motai = yields 

Step 6. At constant temperature and pressure, the Gibbs-Duhem equation relates all of the activities Uj or activity coefficients Yj in a multicomponent mixture  

It is only necessary to locate activity coefficient correlations for r — 1 components in a mixture of r components, because Yr can be obtained from, and must satisfy, the Gibbs-Duhem equation. 

Illustrative Problem. Begin with the entropy representation of the fundamental equation of thermodynamics for a multicomponent system, S(U, V, all tV,), and derive the Gibbs-Duhem equation. Does this form differ from equation (29-45) in step 4 above  

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