Partial molar entropy, definition

The relative partial molar enthalpies of the species are obtained by using Eqs. (70) and (75) in Eq. (41). When the interaction coefficients linear functions of T as assumed here, these enthalpies can be written down directly from Eq. (70) since the partial derivatives defining them in Eq. (41) are all taken at constant values for the species mole fractions. Since the concept of excess quantities measures a quantity for a solution relative to its value in an ideal solution, all nonzero enthalpy quantities are excess. The total enthalpy of mixing is then the same as the excess enthalpy of mixing and a relative partial molar enthalpy is the same as the excess relative partial molar enthalpy. Therefore for brevity the adjective excess is not used here in connection with enthalpy quantities. By definition the relation between the relative partial molar entropy of species j, Sj, and the excess relative partial molar entropy sj is... 

Similar arguments and definitions can be applied to the other partial molar thermodynamic functions and properties of the components in solution. By differentiation of Equation (8.71), the following expressions for the partial molar entropy, enthalpy, volume, and heat capacity of the kth component are obtained ... 

Partial molar entropies of ions can, for example, be calculated assuming S (H+) = 0. Alternatively, because K+ and Cl ions are isoelectronic and have similar radii, the ionic properties of these ions in solution can be equated, e.g. analysis of B-viscosity coefficients (Gurney, 1953). In other cases, a particular theoretical treatment which relates solvation parameters to ionic radii indicates how the subdivision could be made. For example, the Bom equation requires that AGf (ion) be proportional to the reciprocal of the ionic radius (Friedman and Krishnan, 1973b). However, this approach involves new problems associated with the definition of ionic radius (Stem and Amis, 1959). In another approach to this problem, the properties of a series of salts in solution are plotted in such a way that the value for a common ion is obtained as the intercept. For example, when the partial molar volumes of some alkylammonium iodides, V (R4N+I ) in water (Millero, 1971) are plotted against the relative molecular mass of the cation, M+, the intercept at M + = 0 is equated to Ve (I-) (Conway et al., 1966). This procedure has been used to... 

Some care must be exercised in the interpretation of this statement. We saw in Section 7.7 that part of the structural changes (defined in a very broad sense) can be absorbed in the static part of the partial molar entropies and enthalpies of a solute. The above statement applies to any particular definition of the structure which has been adopted for the present purpose. 

The partial molar entropy of solution AS of hydrogen in a metal is,by definition,... 

Based on the definition we have just given, it is obvious that the excess entropy of a regular solution is null, as are the excess partial molar entropies of each it its components - i.e. ... 

In an earlier section the free energy of a phase and the free energy of a total system were discussed generally in terms of the potentials (e.g., equation 48). With the definition of the chemical potential as a function of activity in hand, we will now consider the Gibbs energy of a system. In a similar fashion, the enthalpy and entropy of a system can be computed using the partial molar quantities and the mole numbers of each phase. 

Here the first two derivatives follow from Eqs. 6.2-12 for the pure fluid, and the last from the definition of the partial molar Gibbs energy. Historically, the partial molar Gibbs energy has been called the chemical potential and designated by the symbol Since the enthalpy can be written as a function of entropy and pressure (see Eq. 

You can divide the partial molar free energy- into its partial molar enthalpy and entropy components by using the definition G = H - TS ... 

The random motion of molecules causes all thermodynamic quantities such as temperature, concentration and partial molar volume to fluctuate. In addition, due to its interaction with the exterior, the state of a system is subject to constant perturbations. The state of equilibrium must remain stable in the face of all fluctuations and perturbations. In this chapter we shall develop a theory of stability for isolated systems in which the total energy U, volume V and mole numbers Nk are constant. The stability of the equilibrium state leads us to conclude that certain physical quantities, such as heat capacities, have a definite sign. This will be an introduction to the theory of stability as was developed by Gibbs. Chapter 13 contains some elementary applications of this stability theory. In Chapter 14, we shall present a more general theory of stability and fluctuations based on the entropy production associated with a fluctuation. The more general theory is applicable to a wide range of systems, including nonequilibrium systems. 

As the excess entropy is null by definition, the excess enthalpy is equal to the excess Gibbs energy, and thus for the partial molar values, we would have ... 

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