Thermodynamic Description of the Equilibrium State

In this section we use thermodynamics to demonstrate why the mass action law takes its special mathematical form and why the thermodynamic equilibrium constant fC is a dimensionless quantity. This demonstration justifies the procedures we presented in Section 14.2 for writing down the mass action law by inspection for any chemical reaction. In addition, thermodynamics gives a method for calculating the value of K from tabulated properties of the reactants and products. Consequently, the value of K can be obtained for a reaction, even if the empirical equilibrium constant Kq or has not been measured. Thermodynamics also explains how K changes when the reaction is run under different experimental conditions. With this information, we can manipulate reaction conditions to obtain maximum yield from the reaction. 

Thermodynamics views a chemical reaction as a process in which atoms flow from reactants to products. If the reaction is spontaneous and is carried out at constant T and P, thermodynamics requires that AG 0 for the process (see Section 13.7). Consequently, G always decreases during a spontaneous chemical reaction. When a chemical reaction has reached equilibrium, AG = 0 that is, there is no further tendency for the reaction to occur in either the forward or the reverse direction. We will use the condition AG = 0 in the following three subsections to develop the mass action law and the thermodynamic equilibrium constant for gaseous, solution, and heterogeneous reactions. 

Before we develop the mass action law, it is necessary to investigate how the Gibbs free energy changes with pressure at constant temperature, because in chemical equilibria, the partial pressures of gases can differ from 1 atm. 

The last equality is true because AH = 0 when the pressure of an ideal gas is changed at constant temperature. The entropy change for an ideal gas in an isothermal process was calculated in Section 13.5  

FIGURE 14.4 A three-step process (red arrows) to calculate AG of a reaction (blue arrow) for which reactants and products are not in their standard states of 1 atm. 

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