Energy, Gibbs

Gibbs free energy is a potential for reversible work in constant T-P processes, and always decreases in spontaneous processes. By comparison with (5.26) it is clear that G is a measure of the net work or non-PAV work. This function therefore contrasts with the Helmholtz work function, which measures total work, including mechanical PY work. The Gibbs free energy is a particularly useful measure of the electrical or chemical work attainable from a process and is used a great deal with chemical systems where PY work is often unimportant. 

If this reaction proceeds to the right, the mineral is dissolving. If it proceeds to the left, it is precipitating. In most cases, the dissolved form of the mineral is ionized, so we write, say, for calcite, 

Some minerals do not form ions on dissolving, at least under normal conditions. For example, for quartz we write 

Having written the reaction of interest, we now need to know which way it will go under our chosen conditions. This is done by determining the energy per mole of each product and reactant. If the products have more energy than the reactants, the reaction goes to the left, and vice versa. However, a special kind of energy is required. 

It can be shown that, because we always consider reactions at a given temperature (T) and pressure (P), the appropriate energy is the Gibbs energy, G. So for (3.2), if 

Unfortunately, it is not possible to measure values of G of any substance. Only differences in G are measurable. Therefore, for every substance of interest, solid, liquid, gas, or solute, we measure, usually by calorimetric methods, the quantity A/G°, which is the difference between G of a compound substance, and the sum of the G values of its constituent elements, each in its most stable state. For example, for calcite, 

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Since the accuracy of experimental data is frequently not high, and since experimental data are hardly ever plentiful, it is important to reduce the available data with care using a suitable statistical method and using a model for the excess Gibbs energy which contains only a minimum of binary parameters. Rarely are experimental data of sufficient quality and quantity to justify more than three binary parameters and, all too often, the data justify no more than two such parameters. When data sources (5) or (6) or (7) are used alone, it is not possible to use a three- (or more)-parameter model without making additional arbitrary assumptions. For typical engineering calculations, therefore, it is desirable to use a two-parameter model such as UNIQUAC. 

Null (1970) discusses some alternate models for the excess Gibbs energy which appear to be well suited for systems whose activity coefficients show extrema. 

In most cases only a single tie line is required. When several are available, the choice of which one to use is somewhat arbitrary. However, our experience has shown that tie lines which are near the middle of the two-phase region are most useful for estimating the parameters. Tie lines close to the plait point are less useful, since no common models for the excess Gibbs energy can adequately describe the flat region near the... 

Guffey and Wehe (1972) used excess Gibbs energy equations proposed by Renon (1968a, 1968b) and Blac)c (1959) to calculate multicomponent LLE. They concluded that prediction of ternary data from binary data is not reliable, but that quarternary LLE can be predicted from accurate ternary representations. Here, we carry these results a step further we outline a systematic procedure for determining binary parameters which are suitable for multicomponent LLE. 

A liquid-phase model for the excess Gibbs energy provides... 

VLE data are correlated by any one of thirteen equations representing the excess Gibbs energy in the liquid phase. These equations contain from two to five adjustable binary parameters these are estimated by a nonlinear regression method based on the maximum-likelihood principle (Anderson et al., 1978). 

The most important themiodynamic property of a substance is the standard Gibbs energy of fomiation as a fimetion of temperature as this infomiation allows equilibrium constants for chemical reactions to be calculated. The standard Gibbs energy of fomiation A G° at 298.15 K can be derived from the enthalpy of fomiation AfT° at 298.15 K and the standard entropy AS° at 298.15 K from... 

The enthalpy of fomiation is obtained from enthalpies of combustion, usually made at 298.15 K while the standard entropy at 298.15 K is derived by integration of the heat capacity as a function of temperature from T = 0 K to 298.15 K according to equation (B 1.27.16). The Gibbs-FIehiiholtz relation gives the variation of the Gibbs energy with temperature... 

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.

Table 2.10 shows the effect of substituents on the endo-exo ratio. Under homogeneous conditions there is hardly any substituent effect on the selectivity. Consequently the substituents must have equal effects on the Gibbs energies of the endo and the exo activated complex. 

Figure 3.5. Gibbs energies of complexation of 3.8a-g to the copper(II)(Lr tryptophan) complex versus those for complexation to copper aquo ion.

The enthalpies of complexation of 3.8c to the copper(lf) - amino acid ligand complexes have been calculated from the values of at 20 C, 25 1C, 30 1C, 40 1C and 50 1C using the van t Hoff equation. Complexation entropies have been calculated from the corresponding Gibbs energies and enhalpies. 

Solid angle over which lumi- F(P,DF) Standard Gibbs energy of ac- ag ... 

Table 6.1 Enthalpies and Gibbs Energies of Formation, Entropies, and Heat...

ENTHALPIES AND GIBBS ENERGIES OF FORMATION, ENTROPIES, AND HEAT CAPACITIES... 

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