Entropy, excess partial molar

Figure 6J Excess partial molar properties of jadeite component in NaAlSi206-KAlSi206 molten mixture. (A) Excess partial molar entropy. (B) Excess partial molar enthalpy. Reprinted from Eraser et al. (1983), Bulletin Mineralogique, 106, 111-117, with permission from Masson S.A., Paris, Erance.

The excess partial molar entropy, enthalpy, and volume can now be obtained from familiar partial derivatives of free energy as follows ... 

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. ... 

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... 

It is of interest to compare the relative partial molar entropy at infinite dilution exhibited by TiMo/H2 with that exhibited by /J-Ti/H2. Gallagher and Oates (48) reported ASh values for absorption of hydrogen by 0-Ti ASff, the excess entropy, is obtained via Equation 4, where Xh refers to the atom frac-... 

As already pointed out, Yu is 1 if a compound forms an ideal solution. In this rather rare case, the term RTkiyu, which we denote as partial molar excess free energy of compound i in solution t, Gpe, is 0. This means that the difference between the chemical potential of the compound in solution and its chemical potential in the reference state is only due to the different concentration of the compound i in the two states. The term R In xtf=S 1 expresses the partial molar entropy of ideal mixing (a purely statistical term) when diluting the compound from its pure liquid (xiL =1) into a solvent that consists of otherwise like molecules. 

Koga, Y. Siu, W. W. Y. Wong, T. Y. H. Excess partial molar free energies and entropies in aqueous tert-butyl alcohol solutions at 25 °C. /. Phys. Chem. 1990, 94, 7700-7706. 

When X = 2 th e two effects compensate each other, (/ii — / l) = 0 and the dilute polymer solution behaves ideally, i.e., as if Hrmx — 0 and the polymer chain segments were not connected. Flory used the term theta conditions to describe this ideal state of dilute polymer solutions and developed the concept further by defining the excess partial molar enthalpy,, and entropy, AS, of mixing as... 

Using Boltzmann s relation, the partial molar entropy of excess oxygen in UO2+ ,. is expressed by... 

Flory and Krigbaum defined an enthalpy (Kj) parameter and an entropy of dilution ( /i) parameter such that the thermodynamic functions used to describe these long-range effects are given in terms of the excess partial molar quantities... 

Sato, T., Chiba, A., and Nozaki, R. (1999). Dynamical aspects of mixing schemes in ethanol-water mixtures in terms of the excess partial molar activation free energy, enthalpy, and entropy of the dielectric relaxation process. J. Chem. Phys., 110, 2508-2521. 

Using data given in the previous example, calculate the values of the excess partial molar free energy of zinc and cadmium, excess integral molar free energy of solution, and excess integral molar entropy of solution at 527°C (800 K) for the equiatomic Zn-Cd solution. 

Thalium, excess entropy and partial molar enthalpy of solutions of noble metals in, 133... 

The partial molar excess entropy is obtained from the following... 

We also see that the excess free enthalpy GE is differentiated with respect to the temperature and the number of moles of the solution to give the excess entropy SF and the partial molar excess free energy of mixing RTlnyi as follows ... 

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