Simple system Gibbs energy

Gamma/Phi Approach For many XT E systems of interest the pressure is low enough that a relatively simple equation of state, such as the two-term virial equation, is satisfactoiy for the vapor phase. Liquid-phase behavior, on the other hand, may be conveniently described by an equation for the excess Gibbs energy, from which activity coefficients are derived. The fugacity of species i in the liquid phase is then given by Eq. (4-102), written... 

A simple example of the analysis of multicomponent systems will suffice for the present consideration, such as the calculation of the components in a gaseous mixture of oxygen, hydrogen and sulphur. As a first step, the Gibbs energy of formation of each potential compound, e.g. S2, H2S, SO, SO2, H2O etc. can be used to calculate the equilibrium constant for the formation of each compound from the atomic species of the elements. The total number of atoms of each element will therefore be distributed in the equilibrium mixture in proportion to these constants. Thus for hydrogen with a starting number of atoms and the final number of each species... 

To illustrate such a calculation, Balder (Bl) considered a simple case wherein he assumed that the (symmetric) excess Gibbs energy of the ternary system is given by a two-suffix Margules expansion ... 

The difference between the potential of the current peak for the desorption and the bulk deposition potential is known as the underpotential shift simple systems the value of Gibbs energies of adsorption and deposition shift both according to the Nernst equation. Deviations from this behavior may indicate coadsorption of other ions. 

The first two terms represent the Gibbs energy of f.c.c. Al Cr and Fe because the second sublattice consists entirely of unfilled interstitial sites. The next two terms represent the Gibbs energy of the CrC and FeC compounds which are formed when all of the interstitial sites of the f.c.c. Al lattice are filled with C. The second line is the ideal entropy term while the last four lines correspond to the excess term. It can be seen that, when j/ = 0, the model reduces to Eq. (5.21) for the simple substitutional mixing of Cr and Fe. This is particularly useful as thermodynamic assessments of metallic binary systems can be extended to include interstitial elements without the need for changing any of the existing parameters. 

Liquid-Solution Models. The simple-solution model has been used most extensively to describe the dependence of the excess integral molar Gibbs energy, Gxs, on temperature and composition in binary (142-144, 149-155), quasi binary (156-160), ternary (156, 160-174), and quaternary (175-181) compound-semiconductor phase diagram calculations. For a simple multicomponent system, the excess integral molar Gibbs energy of solution is expressed by... 

For the entropy and internal energy, the canonical variables consist of extensive parameters. For a simple system, the extensive properties are S, U, and V. and the fundamental equations define a fundamental surface of entropy S = S(U,V) in the Gibbs space of S, U, and V. 

The Gibbs-ensemble procedure lias also been employed to estimate adsorptionisothemis for simple systems. The approach is illustrated- by calculations for a straight cylindrical pore where both fluid/fluid and fluid/adsorbent molecular interactions can be represented by tlie Lemiard-Jones potential-energy function [Eq. (16.1)]. Simulation calculations have also been made for isothemis of methane and ethane adsorbed on a model carbonaceous slit pore. Isosteric heats of adsorption liave also been calculated. ... 

The Gibbs reactor is very useful when modeling a system that is known to come to equilibrium, in particular high-temperature processes involving simple molecules. It is less useful when complex molecules are present, as these usually have high Gibbs energy of formation consequently, very low concentrations of these species are predicted unless the number of components in the model is very restricted. 

In the case of mixtures of simple molecules, the Gibbs energy for a one-fluid system may be written as... 

On the lhs of equation (7.238), we have measurable quantities - the solvation Helmholtz (or Gibbs) energy of a solute in H20 and in D20. On the rhs, we have the quantity ((HB) — (HB) ), which measures the change in the average number of HBs in a system of N water molecules, induced by the solvation process. This may be estimated, provided we have an estimated value for the difference sD — aH. Thus, whereas in (7.234) we obtained an estimate of the structure of pure water, here we got an estimate of the structural changes induced by a simple solute. More details can be found in Ben-Naim (1992). 

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