Gibbs energy mixing

In this appendix, we shall discuss a system of ideal gases. We shall examine the suitability of the terms mixing entropy and mixing Gibbs energy, and the validity of the statement that the mixing process is essentially reversible , see, for example, Denbigh (1966). 

The reference to NAkT In xA as a mixing Gibbs energy term is so ubiquitous that it is really difficult to find exceptions. This erroneous interpretation of the term kT In xA also leads to an erroneous interpretation of the term p°A — pA, which is very common in solution chemistry. 

Sketch G versus for a reaction for which AG° < 0. What are the roles of both AG° and the mixing Gibbs energy in determining the equilibrium position ... 

Figure C2.1.10. (a) Gibbs energy of mixing as a function of the volume fraction of polymer A for a symmetric binary polymer mixture = Ag = N. The curves are obtained from equation (C2.1.9 ). (b) Phase diagram of a symmetric polymer mixture = Ag = A. The full curve is the binodal and delimits the homogeneous region from that of the two-phase stmcture. The broken curve is the spinodal.

A.ctivity Coefficients. Activity coefficients in Hquid mixtures are directiy related to the molar excess Gibbs energy of mixing, AG, which is defined as the difference in the molar Gibbs energy of mixing between the real and ideal mixtures. It is typically an assumed function. Various functional forms of AG give rise to many of the different activity coefficient models found in the Hterature (1—3,18). Typically, the Hquid-phase activity coefficient is a function of temperature and composition expHcit pressure dependence is rarely included. 

The heat of mixing (excess enthalpy) and the excess Gibbs energy are also experimentally accessible, the heat of mixing by direcl measurement and G (or In Yi) indirectly as a prodiicl of the reduction of vapor/hqiiid eqiiihbriiim data. Knowledge of H and G allows calculation of by Eq. (4-13) written for excess properties. 

The well-known Flory treatment [50-52] of the en-thropic contribution to the Gibbs energy of mixing of polymers with solvents is still the simplest and most reliable theory developed. It is quite apparent, however, that the Flory-Huggins theory was established on the basis of the experimental behavior of only a few mixtures investigated over a very narrow range of temperature. Strict applications of the Flory-Huggins approach... 

Two liquids are miscible in all proportions if Ag, the molar Gibbs energy of mixing at constant temperature and pressure, satisfies the relations... 

There are other ways of estimating inner potential differences. Gi rault and Schiffrin [4] assume that the difference in the inner potential is negligible at the pzc, because the interface consists of an extended layer where both solvents mix, so that any dipole potentials will be small. The resulting scale of Gibbs energies of transfer agrees reasonably well with the TPAs+/TPB scale, if the small difference in the radii of these ions is accounted for. 

The last two terms give the change AGM in the Gibbs energy that occurs during mixing. Using x2 = 1 — aq we write this as ... 

Prove that for a > 2 the Gibbs energy of mixing has one maximum and two minima. 

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