Calculating Free-Energy Change

Reactions (1) and (2) above are actually greatly simplified. In reality, it is likely that subchlorides such as TiCl3 and TiCl2 will be formed in Reaction (1) and higher boranes in Reaction (2). Such factors are not revealed by the simple free-energy change calculations. 

Consider the thermodynamic data on the formation of a few transition metal silicides presented in Table 3.1. The values of AfG° were taken from the work by V.N. Yeremenko et al. When comparing the free energy changes calculated per mole of the compound, the silicides of the Me5Si3 type should be regarded as most stable. However, in none of the systems under consideration the compound of such a composition was found to form first. 

The integral free energy changes, calculated on the basis of equations (11) and (12) together with the experimental values, per mole of bound water, are given in Figure 6. 

The principles of Hess s law (Chapter 8) also apply to free energy change calculations. 

Experimentation shows that the best, fully dense, and homogeneous carbon deposits are produced at an optimum negative value of AG. For smaller negative values, the reaction rate is very low and, for higher negative values, vapor-phase precipitation and the formation of soot can occur. Such factors are not revealed in the simple free-energy change calculation. A more complete analysis is often necessary. 

The enthalpy, entropy and free energy changes for an isothennal reaction near 0 K caimot be measured directly because of the impossibility of carrying out the reaction reversibly in a reasonable time. One can, however, by a suitable combination of measured values, calculate them indirectly. In particular, if the value of... 

Having calculated the standai d values AyW and S" foi the participants in a chemical reaction, the obvious next step is to calculate the standard Gibbs free energy change of reaction A G and the equilibrium constant from... 

Free energy simulations are a useful means of quantitating whether the free energy and not simply the energy is shifting in the predicted manner for the mutant (see Chapter 9). The difference in the free energy changes upon reduction between a wild-type and a mutant, AAG = AG — AG, where the asterisk indicates the mutant, can be calculated in two ways via the thennodynamic cycle shown in Scheme 2,... 

Procedures to compute acidities are essentially similar to those for the basicities discussed in the previous section. The acidities in the gas phase and in solution can be calculated as the free energy changes AG and AG" upon proton release of the isolated and solvated molecules, respectively. To discuss the relative strengths of acidity in the gas and aqueous solution phases, we only need the magnitude of —AG and — AG" for haloacetic acids relative to those for acetic acids. Thus the free energy calculations for acetic acid, haloacetic acids, and each conjugate base are carried out in the gas phase and in aqueous solution. 

Estimation of the free-energy change associated with a reaction permits the calcula-aon of the equilibrium position for a reaction and indicates the feasibility of a given chemical process. A positive AG° imposes a limit on the extent to which a reaction can x cur. For example, as can be calculated using Eq. (4.2), a AG° of 1.0 kcal/mol limits conversion to product at equilibrium to 15%. An appreciably negative AG° indicates that e reaction is thermodynamically favorable. 

If the heat capacity can be evaluated at all temperatures between 0 K and the temperature of interest, an absolute entropy can be calculated. For biological processes, entropy changes are more useful than absolute entropies. The entropy change for a process can be calculated if the enthalpy change and free energy change are known. 

The equilibrium constants determined by Brandts at several temperatures for the denaturation of chymotrypsinogen (see previous Example) can be used to calculate the free energy changes for the denaturation process. For example, the equilibrium constant at 54.5°C is 0.27, so... 

Calculate the free energy change for acetyl phosphate hydrolysis in a solution of 2 mM acetate, 2 mM phosphate, and 3 iiM acetyl phosphate. 

Hexokinase catalyzes the phosphorylation of glucose from ATP, yielding glncose-6-P and ADR Using the values of Table 3.3, calculate the standard-state free energy change and equilibrium constant for the hexokinase reaction. 

We have already noted that the standard free energy change for a reaction, AG°, does not reflect the actual conditions in a ceil, where reactants and products are not at standard-state concentrations (1 M). Equation 3.12 was introduced to permit calculations of actual free energy changes under non-standard-state conditions. Similarly, standard reduction potentials for redox couples must be modified to account for the actual concentrations of the oxidized and reduced species. For any redox couple. 

Calculate the value of A l,/ for the glyceraldehyde-3-phos-phate dehydrogenase reaction, and calculate the free energy change for the reaction under standard-state conditions. 

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