Gibbs-Diihem equation

Equation ( A2.1.39) is the generalized Gibbs-Diihem equation previously presented (equation (A2.1.27)). Note that the Gibbs free energy is just the sum over the chemical potentials. 

Using the Gibbs-Diihem equation ((A2.1.27) with dT = 0, dp = 0), one can show that the solvent must obey Raoult s law over the same concentration range where Hemy s law is valid for the solute (or solutes) ... 

Finally, a Gibbs/Diihem equation is associated with each fundamental property relation ... 

Einally, an especially useful form of the Gibbs/Diihem equation follows from Eq. (4-116) ... 

The right-hand side of this equation is exactly the quantity that Eq. (4-289), the Gibbs/Duhem equation, requires to be zero for consistent data. The residual on the left is therefore a direct measure of deviations from the Gibbs/Diihem equation. The extent to which values of this residual fail to scatter about zero measures the departure of the data from consistency with respect to this equation. 

When only one phase is under consideration, only one of the terms in Equation (30) is required, and only one of the bulk phase summations in Equation (38) survives. The result in this case is the famous Gibbs-Diihem equation ... 

By means of the Gibbs-Diihem equation, we may eliminate the terms in Equation (38) that apply to bulk phases and write... 

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