Molar excess entropy

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

For an ideal mixture, the enthalpy of mixing is zero and so a measured molar enthalpy of mixing is the excess value, HE. The literature concerning HE -values is more extensive than for GE-values because calorimetric measurements are more readily made. The dependence of HE on temperature yields the excess molar heat capacity, while combination of HE and GE values yields SE, the molar excess entropy of mixing. The dependences of GE, HE and T- SE on composition are conveniently summarized in the same diagram. The definition of an ideal mixture also requires that the molar volume is given by the sum, Xj V + x2 V2, so that the molar volume of a real mixture can be expressed in terms of an excess molar volume VE (Battino, 1971). 

Entropy Data for Pd Alloys. Information on the distribution of H atoms in alloys can also be obtained from entropy data. The relevant entropy term is the relative partial molar excess entropy, A5, defined by... 

This chapter deals with experimental methods for determining the thermodynamic excess functions of binary liquid mixtures of non-electrolytes. Most of it is concerned with techniques suitable for measurements in the temperature range 250 to 400 K and the pressure range 0 to 100 kPa. Techniques suitable for lower temperatures will be briefly reviewed. Techniques for measuring the molar excess Gibbs function G, the molar excess enthalpy and the molar excess volume will be discussed. The molar excess entropy can only be determined indirectly from either measurements of (7 and at a specific temperature = (If — C /T], or from the temperature dependence of G m [ S m = The molar excess functions have been defined by... 

Similarly the entropic interaction parameter, xs-> is obtained from the partial molar excess entropy changes on mixing and is given by... 

All the other thermodynamic excess functions are obtained by differentiation of with respect to T or P. The most important are the molar excess entropy 5 , enthalpy Pf, and volume ... 

It is expected from simple kinds of solution theories that AG will be reasonably independent of temperature over a range of a few hundred to several hundred degrees. If this is so, as the Wood (1975) data suggest, then the analogous molar excess entropy of mixing, AS , given by - AG, will be nearly zero. 

In general exothermic heats and negative partial molar excess entropies of solution indicate that the solution process involves strong interactions between Y and the ions in the melt. ... 

Solubility parameters are generally tabulated, together with the corresponding liquid molar volumes, only at 25°C. Although solubility parameters are themselves temperature-dependent, the combination of quantities in Eq. 70 is not. Differentiating Eq. 70 with respect to temperature gives — the excess entropy, a quantity which has been assumed to be zero in accord with the definition of a regular solution. Thus only data at 25°C are needed. Solubility parameters may be... 

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

A direct quantitative comparison between AG theory and measurements requires the resolution of two issues. First, the excess entropy Sexc must be normahzed by the molar volume. We suggest that the lack of this normalization is partly responsible for previous claims [15, 49] that AG theory breaks down for small molecule fluids. Second, the vibrational contribution to which is absent in s, must be subtracted reliably. While the first correction can readily be introduced, the inclusion of the second correction requires further investigation [63, 240]. 

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. 

Where V2/V1 (r) is the ratio of the molar volume of the polymer to that of the solvent and x is the Flory parameter which depends primarily on the intermolec-ular forces between solute and solvent. According to the original formulation, this parameter is zero for athermal mixtures. However, subsequent work has shown that both the excess entropy and the excess enthalpy contribute to x ... 

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 ... 

This reaction stops when the liquid composition reaches point J, where SiC becomes stable in contact with the liquid and precipitated C. At this point, the equilibrium molar fraction of Si dissolved in M, X (Figure 7.2), is related to the partial enthalpy of mixing of Si in M, AHsi(M) (neglecting the partial excess entropy of mixing), and to the molar Gibbs energy of formation of SiC, AGf(SiC), by the equation ... 

Number of independent chemical reactions, phase rale Molar or specific entropy Partial entropy, species i in solution Excess entropy = S —... 

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