Gibbs Energy and Reaction Equilibrium

CHAPTER 11 REACTIONS AND OTHER CHEMICAL PROCESSES 11.7 Gibbs Energy and reaction Equilibrium... 

Fig. 4.4 The relation between standard reaction Gibbs energy and the equilibrium constant of the reaction.

Say we have a system in which the species undergo chemical reaction by rearranging their bonds to minimize the total Gibbs energy and obtain equilibrium. While we have identified the significant species at play and their phases, we do not know what the reaction mechanism is. In fact, there may be many simultaneous reactions that describe these molecular rearrangements. We may be concerned with questions about how to set up the chemical reaction equilibrium problem, such as What equations should I use to describe the reactions and How do I know if I have included enough reactions ... 

The chemical potential pi plays a vital role in both phase and chemical-reaction equilibria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence pi, is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, pi approaches negative infinity when either P or Xi approaches zero. While these characteristics do not preclude the use of chemical potentials, the application of equilibrium criteria is facilitated by introduction of the fugacity, a quantity that takes the place of p. but which does not exhibit its less desirable characteristics. 

Measurements of the rate of reaction of the hydrated electron with water and the reverse process have given a value for the change in Gibbs energy for the equilibrium ... 

A distinguishing aspect in electrode kinetics is that the heterogeneous rate constants, kred and kox, can be controlled externally by the difference between the inner potential in the metal electrode (V/>M) and in solution (7/>so1) that is, through the interfacial potential difference E = electrode setup (typically, a three-electrode arrangement and a potentiostat), the E-value can be varied in order to distort the electrochemical equilibrium and favor the electro-oxidation or electro-reduction reactions. Thus, the molar electrochemical Gibbs energy of reaction Scheme (l.IV), as derived from the electrochemical potentials of the reactant and product species, can be written as (see Eqs. 1.32 and 1.33 with n = 1)... 

Since the hydrolysis of ATP evolves heat, Le Chatelier s principle says raising the temperature will cause the reaction to go less far to the right. But at 313 K the transformed Gibbs energy of reaction is more negative. To apply Le Chatelier we have to look at the apparent equilibrium constants. At pH 7 and ionic strength 0, we obtain... 

Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

Example 3.15 Gibbs energy and distance from global equilibrium Discuss the effect of the distance from global equilibrium for a chemical reaction system R = P. 

Using Eqs. (8.5) and (8.9), we relate the Gibbs energy of reaction and equilibrium constant K... 

Example 8.3 Temperature effect on equilibrium conversion Consider the elementary reversible reaction B P with no initial product P, while the initial concentration of B is B0. The standard Gibbs energy and standard enthalpy of the reaction are AG° (298.15K) = -14.1kJ/mol and A//" (298.15K) = -83.6kJ/mol. Assume that the specific heats of solutions are equal to that of water. Estimate the equilibrium conversion of B between 25°C and 120°C. 

Fig. 4-1. One-dimensional Gibbs energy diagram for an equilibrium reaction A B in the solvents 1 and 11. Ordinate standard molar Gibbs energies of the reactants A and B in solvents 1 and 11 Abscissa not defined. AG°(1) and AG°(11) standard molar Gibbs energies of reaction in solvents 1 and 11, respectively AGj°(A, 1 11) and AGj°(B, 1 11) standard molar Gibbs energies of transfer of the solutes A and B from solvent 1 to solvent 11, respectively [AGj°(A, 1 11) = G°(A in 1) - G°(A in 11), and AG°(B, 1 11) = G°(B in 1) - G°(B in 11)], cf. Eq. (2-12a) in Section 2.3 = transition state.

Note that these apparent equilibrium constants are the products of the apparent equilibrium constants of the reactions that are coupled. The standard transformed Gibbs energies of reaction and change in the binding of hydrogen ions in the reaction are sums of the properties of the reactions being coupled. 

Standard Transformed Gibbs Energies of Reaction, Changes in Binding of Hydrogen Ions, and Apparent Equilibrium Constants of Lyase Reactions... 

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