Molar entropy partial

The configurational entropy (sQ conf) can be determined by using a model proposed by Mizusaki.20,24 The configurational entropy, partial molar enthalpy, and partial molar entropy can be expressed in terms of 8, a, n, and p values as follows... 

The following development is in terms of enthalpy, but the same can be done for free energy, entropy, partial molar volume and so on. The reaction energetics are defined by Figure 3.2, where it should be apparent that... 

The partial molar entropy of adsorption AI2 may be determined from q j or qsi through Eq. XVII-118, and hence is obtainable either from calorimetric heats plus an adsorption isotherm or from adsorption isotherms at more than one temperature. The integral entropy of adsorption can be obtained from isotherm data at more than one temperature, through Eqs. XVII-110 and XVII-119, in which case complete isotherms are needed. Alternatively, AS2 can be obtained from the calorimetric plus a single complete adsorption isotherm, using Eq. XVII-115. This last approach has been recommended by Jura and Hill [121] as giving more accurate integral entropy values (see also Ref. 124). 

When the film thickens beyond two or three molecular layers, the effect of surface structure is largely smoothed out. It should therefore be possible, as Hill and Halsey have argued, to analyse the isotherm in the multilayer region by reference to surface forces (Chapter 1), the partial molar entropy of the adsorbed film being taken as equal to that of the liquid adsorptive. By application of the 6-12 relation of Chapter 1 (with omission of the r" term as being negligible except at short distances) Hill was able to arrive at the isotherm equation... 

We may define, say, partial molar volume, enthalpy, or entropy by analogy with Eq. (8.5) ... 

P rtl IMol r Properties. The properties of individual components in a mixture or solution play an important role in solution thermodynamics. These properties, which represent molar derivatives of such extensive quantities as Gibbs free energy and entropy, are called partial molar properties. For example, in a Hquid mixture of ethanol and water, the partial molar volume of ethanol and the partial molar volume of water have values that are, in general, quite different from the volumes of pure ethanol and pure water at the same temperature and pressure (21). If the mixture is an ideal solution, the partial molar volume of a component in solution is the same as the molar volume of the pure material at the same temperature and pressure. 

Corresponding to the integral heat and entropy of formation of the solution are the partial molar heats A//, and entropies AS, of solution of the components where... 

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

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

Chapter 4 presents the Third Law, demonstrates its usefulness in generating absolute entropies, and describes its implications and limitations in real systems. Chapter 5 develops the concept of the chemical potential and its importance as a criterion for equilibrium. Partial molar properties are defined and described, and their relationship through the Gibbs-Duhem equation is presented. 

The chemical potential difference —ju may be resolved into its heat and entropy components in either of two ways the partial molar heat of dilution may be measured directly by calorimetric methods and the entropy of dilution calculated from the relationship A i = (AHi —AFi)/T where AFi=/xi —/x or the temperature coefficient of the activity (hence the temperature coefficient of the chemical potential) may be determined, and from it the heat and entropy of dilution can be calculated using the standard relationships... 

ASiy ASt Corresponding partial molar entropies of dilution. 

Besides the partial molar and the relative partial molar free energies of the components, some other important thermodynamic properties are the partial molar and the relative partial molar enthalpies and entropies. The partial molar enthalpy and entropy of the component A are defined by... 

The relative partial molar enthalpy, AHa, and the relative partial molar entropy, A,S a, are defined as... 

The corresponding expressions for the relative partial molar enthalpy and entropy of the component A are... 

The relationships presented thus far for partial, integral and relative partial molar free energies are applicable in a similar manner to entropy, enthalpy and also volume. 

In open systems consisting of several components the thermodynamic properties of each component depend on the overall composition in addition to T and p. Chemical thermodynamics in such systems relies on the partial molar properties of the components. The partial molar Gibbs energy at constantp, Tand rij (eq. 1.77) has been given a special name due to its great importance the chemical potential. The corresponding partial molar enthalpy, entropy and volume under the same conditions are defined as... 

The partial molar entropy, enthalpy or volume of mixing can be derived from eq. (3.21) and are given by the relations... 

The same type of polynomial formalism may also be applied to the partial molar enthalpy and entropy of the solute and converted into integral thermodynamic properties through use of the Gibbs-Duhem equation see Section 3.5. 

Partial molar availability, 24 692 Partial molar entropy, of an ideal gas mixture, 24 673—674 Partial molar Gibbs energy, 24 672, 678 Partial molar properties, of mixtures, 24 667-668... 

Recently, the Pitzer equation has been applied to model weak electrolyte systems by Beutier and Renon ( ) and Edwards, et al. (10). Beutier and Renon used a simplified Pitzer equation for the ion-ion interaction contribution, applied Debye-McAulay s electrostatic theory (Harned and Owen, (14)) for the ion-molecule interaction contribution, and adoptee) Margules type terms for molecule-molecule interactions between the same molecular solutes. Edwards, et al. applied the Pitzer equation directly, without defining any new terms, for all interactions (ion-ion, ion-molecule, and molecule-molecule) while neglecting all ternary parameters. Bromley s (1) ideas on additivity of interaction parameters of individual ions and correlation between individual ion and partial molar entropy of ions at infinite dilution were adopted in both studies. In addition, they both neglected contributions from interactions among ions of the same sign. 

Partial differentiation of Eqns (4.17a) and (4.17b) with respect to x allows us easily to relate the variation in the preexponential term with the variation in partial molar entropy of MY, and the variation in activation energy with the variation in partial molar enthalpy by the relationships (Fig. 4.5)... 

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