Gibbs free energy changes with pressure

Before we develop the mass action law, it is necessary to investigate how the Gibbs free energy changes with pressure at constant temperature, because in chemical equilibria, the partial pressures of gases can differ from 1 atm. 

In its most general form, the fullerene synthesis could be treated as a complex kinetic scheme described by a huge number of kinetic differential equations. The equilibrium composition comes as the limiting case for infinite time. If we treat the problem from a thermodynamic point of view, we should realize that the conventional standard pressure of 1 atm is considerably different from the actual fullerene synthesis conditions. We should expect lower cluster pressures in the carbon-arc synthesis. The actual entropy and Gibbs free energy change with pressure as can be demonstrated [208-212] on the Cgo and C70 cases based on computed or observed [213] data. For example, the equilibrium constant Xgo/yo for an interconversion between the two clusters, expressed in partial pressures p, offers a deeper insight into the problem [208-212] ... 

The variation in Gibbs-free-energy change with temperature at constant pressure is given by... 

The subject of interest is a gel swollen by solvent. Let F be the Gibbs free energy change after mixing of solvent and an initially unstrained polymer network [1]. When the gel is isotropic and is immersed in a pure solvent with a fixed pressure Po, F is a thermodynamic potential dependent on the temperature T, the pressure p inside the gel, and the solvent particle number Ns inside the gel. It satisfies... 

The Gibbs free energy change during a reaction is a measure of the reversible work (other than pressure-volume work) that can be obtained from the process at constant T and p. Since cellular processes are isothermal and isobaric, free energies are the quantities of choice in studying metabolic processes with respect to their ability to carry out the work of cells. 

The transformation from graphite to diamond under low pressure, i.e. reaction 1, is a nonspontaneous reaction with positive molar Gibbs free energy change, which should never occur spontaneously toward the right side. 

Assume the shape of the nucleus to be spherical with a radius of S. The free energy of nucleus formation, A<(i is related to the Gibbs free energy change Af per unit volume, Af, accompanied by phase separation (under constant pressure and temperature T), and the Intersurface energy per unit area, a, at the surface of the nuclei in the form ... 

As with all chemical reactions, the standard state Gibbs free energy change for an isotope exchange reaction at a given pressure and temperature is related to the equilibrium constant by ... 

The change in Gibbs free energy varies with bofli temperature and pressure,... 

Although this process shows similarities to the Monsanto process for the carbonylation of methanol to produce acetic acid (Sec. 5.1.1), there are some important differences. In addition to the difference in the catalysts and the corresponding mechanistic aspect of the reactions, the methyl acetate carbonylation reaction [Eq. (25)] has a much smaller Gibbs free energy change than the methanol carbonylation reaction [Eq. (1)]. Thus, to maintain a substantial net rate of reaction, the methyl acetate carbonylation process is operated at 175190°C up to a conversion between 50 and 70% and at over 5 MPa pressure (50 atm). Acetic anhydride is separated from the rest of the material in the effluent of the reactor by a series of distillation steps. Acetic acid is a by-product. Most of the other material in the reactor effluent is recycled back to the reactor. A small amount of tar is removed. In this process, acetic anhydride with purity up to 99.7% could be obtained. The main impurity is acetic acid. 

Fig. 12.4 Standard Gibbs free energy change of carbonation reactions of alkaline earth cerates and zirconates as a function of temperature calculated from a thermodynamic database [20] standard pressure, p°=l X 10 Pa. (Reprinted from [24] with permission from Springer Science and Business Media)...

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