Free Energy, Equilibrium, and Reaction Direction

The sign of AG allows us to predict reaction direction, but you already know that it is not the only way to do so. In Chapter 17, we predicted direction by comparing the values of the reaction quotient (Q) and the equilibrium constant (K). Recall that 

As you might expect, these two ways of predicting reaction spontaneity—the sign of AG and the magnitude of QjK—are related. Their relationship emerges when we compare the signs of In QjK with AG  

Note that the signs of AG and In QjK are identical for a given reaction direction. 

In fact, AG and In QjK are proportional to each other and made equal through the constant RT. 

What does this central relationship mean As you know, Q represents the concentrations (or pressures) of a system s components at any time during the reaction, whereas K represents them when the reaction has reached equilibrium. Therefore, Equation 20.11 says that AG depends on how different the ratio of concentrations, Q, is from the equilibrium ratio, K. 

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Free Energy, Equilibrium, and Reaction Direction 676 CHAPTER REVIEW GUIDE 681 PROBLEMS 682... 

TABLE 10.1 The numerical relationship between the equilibrium constant of biochemical reactions, standard free-energy change and the direction of a reaction at pH 7.0 and 25°C... 

It is important to note that, for any given temperature, the [thermodynamic] equilibrium constant is directly related to the standard change in free energy. Since, at any given temperature, the free energy in the standard state for each reactant and product, G°, is independent of the pressure, it follows that the standard change in free energy for the reaction, AfG°, is independent of the pressure.g Therefore, at constant temperature, the equilibrium constant K. .. is also independent of the pressure. That is,... 

Equation (3.3) gives the potential dependence of the reaction free energy of Reaction (3.2). Since this reaction equilibrium defines the standard hydrogen electrode potential, we now have a direct fink between quite simple DFT calculations and the electrode potential. In a similar way, we can now calculate potential-dependent reaction free energies for other reactions, such as O - - H" " + e OH or OH - -+ e HzO. 

Arguments based on the second law which are given in standard text books [3,4] lead to the conclusion that, on its own, a chemical reaction will proceed in the direction in which the Gibbs free energy decreases and, when equilibrium is reached, this quantity has a minimum value. More precisely, for a system undergoing some small change... 

Thermodynamics is a powerful tool. It states that at constant temperature and pressure, the system always moves to a state of lower Gibbs free energy. Equilibrium is achieved when the lowest Gibbs free energy of the system is attained. Given an initial state, thermodynamics can predict the direction of a chemical reaction, and the maximum extent of the reaction. Macroscopically, reactions... 

Equations (11) and (13) are two of the most important thermodynamic relationships for biochemists to remember. If the concentrations of reactants and products are at their equilibrium values, there is no change in free energy for the reactions going in either direction. Living cells, however, maintain some compounds at concentrations far from the equilibrium values, so that their reactions are associated with large changes in free energy. We expand on this point in chapter 11. 

Chemical equilibrium state corresponds to the minimum value of the Gibbs free energy. Hence, the chemical equilibrium composition and the reaction direction can be predicted from the dependence of the Gibbs free energy on the reaction extend. For the reaction... 

Once the principal net reaction and equilibrium constant are established, standard total free energies, entropies, and heat contents become corollary. In the case of the cadmium vapor pressure one can therefore calculate total thermodynamic quantities from the established reactions as well as partial thermodynamic quantities from the vapor pressures directly. 

The similarity coefficient of Hammett and other Class II free energy correlations often bears no direct relationship to the transition structure because of dissimilarity between the model equilibrium and the reaction being studied. The closer the model is to the reaction under investigation the more reliable is any mechanistic conclusion from the value of the similarity coefficient. Some representative free energy relationships and their similarity coefficients are collected in Appendix 4. 

The equilibrium constant is fixed and characteristic for any given chemical reaction at a specified temperature. It defines the composition of the final equilibrium mixture, regardless of the starting amounts of reactants and products. Conversely, we can calculate the equilibrium constant for a given reaction at a given temperature if the equilibrium concentrations of all its reactants and products are known. As we will show in Chapter 13, the standard free-energy change (AG°) is directly related to ifeq. 

Hence, there is little need to consider free-energy changes and to calculate equilibriums. Catalysts are generally used in an effort to obtain the oxidation reaction at as low a temperature as possible and to direct the reaction to the desired products. Where any one or more of several products may result from the oxidation, the predominant ones are determined generally by reaction mechanism rather than equilibrium phenomena. 

In this chapter we have seen that a system at constant temperature and pressure will proceed spontaneously in the direction that lowers its free energy. This is why reactions proceed until they reach equilibrium. The equilibrium position represents the lowest free energy value available to a particular reaction system. The free energy of a reaction system changes as the reaction proceeds, because free energy is dependent on the pressure... 

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