Partial property excess

This definition is analogous to the definition of a residual property as given by Eq. (4-67). However, excess properties have no meaning for pure species, whereas residual properties exist for pure species as well as for mixtures. In addition, analogous to Eq. (4-99) is the partial-property relation,... 

All three quantities are for the same T, P, and physical state. Eq. (4-126) defines a partial molar property change of mixing, and Eq. (4-125) is the summability relation for these properties. Each of Eqs. (4-93) through (4-96) is an expression for an ideal solution property, and each may be combined with the defining equation for an excess property (Eq. [4-99]), 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... 

Example 1.14 Estimation of partial excess properties The heat of mixing (excess enthalpy) for a binary mixture is... 

Molar or specific value, extensive tlrenrrodyiramic property Partial property, species i in solution Excess property == M — M "... 

It is convenient to think of the excess property as a mathematical operator that removes the ideal-solution part from a thermodynamic property. It is a linear operator and can be combined with other operators, such as the partial molar differentiation. Expressions that can be written between regular properties may be written for the excess and for the partial molar excess properties. For example, starting with the fundamental relationship... 

Excess partial molar properties are obtained by applying the partial molar operator on an excess property. Recall that the definition of the partial molar operator is... 

Partial molar excess properties can be defined analogously as E m = T x mf... 

The partial molar excess properties vary with composition. They can be derived directly from the curvature of the excess enthalpies or excess volumes as a function of the mole fraction. How the partial molar properties can be determined by the tangent line for the excess enthalpy and a composition of xi = 0.252 is shown in Figure 5.17. Using the partial molar excess values h, and the activity coefficient at a different temperature or pressure can be determined. But it has to be considered that these partial molar excess properties do not only depend on composition but also on temperature and pressure. 

Excess properties, the difference between the property in a real solution and in an ideal solution, are generally expressed as a relative or relative partial molar properties, such as the relative enthalpy, L, or relative partial molar enthalpy, L. The Gibbs energy is treated differently. The fact that Gj-p is a thermodynanoic potential leads naturally to the definition of a relative partial molar Gibbs energy (q. - /a°) which is not the difference from an ideal solution (/A — pL° is not zero even for an ideal solution) but the difference from a standard state, which in this chapter is a pure phase, but may also be some hypothetical state. The form of the equation relating q, - to composition then... 

Keywords Aqueous systems bibliography biochemical systems enthalpy data entropy data equilibrium data excess properties Gibbs energy data heat capacHy data partial molar properties review articles thermochemistry thermodynamics. 

The scope of the present work remains essentially that of Special Publication 454, The general aim 1 to assist the reader in locating those publications which contain thermochemical data which can best serve his needs. Equilibrium data Is taken in its most general sense and includes equilibrium constants, enthalpies, entropies, heat capacities, volumes, and partial molar and excess property data. To a much lesser extent, transport and other properties have been included. Unfortunately, much of the data on biochemical systems is scattered throughout much of the literature and there is a need for... 

Many of the theories and models described in this section were developed for the excess thermodynamic properties of solutions, including not only the excess partial molar volume, but also other excess properties. In the following subsections we have restricted the discussion to the volumetric properties of aqueous systems. 

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