Fundamental residual-property relation

Fundamental Residual-Property Relation Equation (4-191) is general and may be written for the special case of an ideal gas 

Limited forms of this equation are particularly useful. Division by dP and restriction to constant T and composition lead to 

Similarly, the result of division by dT and restriction to constant P and composition is 

This equation demonstrates that In () is a partial property with respect to G /RT. The summability relation therefore applies, and 

TABLE 4-5 Relations Connecting Property Changes of Mixing and Excess Properties 

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Equation 169, the fundamental residual property relation, is so general as to be useful for practical application only in restricted forms. Division by dP and restriction to constant T and composition leads to equation 17 ... 

This is the fundamental excess property relation, analogous to the fundamental residual property relation (eq. 169). 

Whereas the fundamental residual property relation derives its usefulness from its direct relation to experimental PVT data and equations of state, the excess property formulation is useful because and are all experimentally accessible. Activity coefficients are found from vapor—Hquid... 

The fundamental excess-property relation is derived in exactly the same as the fundamental residual-property relation and leads to analogous rest Equation (13.12), written for the special case of an ideal solution, is subtra from Eq. (13.12) itself, yielding ... 

The last relation is Eq. (11.62), which demonstrates the partial property re ship that In y, bears to GE/RT. These equations are analogous to Eqs. through (13.17). Whereas the fundamental residual-property relation de usefulness from its direct relation to experimental PVT data and equati state, the excess-property formulation is useful because VE, HB, and yt experimentally accessible. Activity coefficients are found from VLE d... 

Just as the fundamental property relation of Eq. (13.12) provides complete property information from a canonical equation of state expressing G/RT as a function of T, P, and composition, so the fundamental residual-property relation, Eq. (13.13) or (13.14), provides complete residual-property information from a PVT equation of state, from PVT data, or from generalized PVT correlations. However, for complete property information, one needs in addition to PVT data the ideal-gas-state ieat capacities of the species that comprise the system. 

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