Partial molar equation

Partial Molar Equation-of-State Parameters The parameters in equations of state as applied to mixtures are related to composition by mixing rules. Eor the second virial coefficient... 

In Eqs. (1.3-30) aed (1.3-31), all unsubscripted quantities refer to the mixture. Quantities b, and 9, are partial molar equation-of-state pera meters, defined by... 

The partial molar equation shows a unique and important relation between the partial molar properties in a mixture. When the differential of the partial molar equation is applied to the Gibbs energy, the result is the Gibbs-Duhem equation, which we will use in Chapter 9. 

The method of tangent intercepts is shown in the main text, based on the partial molar equation, Eq. 6.5. It may also be shown purely geometrically as follows. Figure 6.13 is the same as Figure 6.6, but the point of tangency has been moved to move points b and d further apart, points c, d, and e have been added, and unnecessary text has been deleted. 

The fact that there is no volume change or heat effect on mixing for an ideal solution does not mean that there is no entropy change on mixing. Mixing is always irreversible (an increase in disorder), so ideal solutions have greater entropies than the same species would have if they existed in the pure state, unmixed. If we substitute Eq. 7.26 twice in the partial molar equation (Eq. 6.5) and simplify, we find that for an ideal solution... 

It is shown in Chapter 6 that for any partial molar property (for example, q where Q is any extensive property) of any mixture with any number of species in one phase the partial molar equation requires that... 

---