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Equilibrium ConstantAuthor: John Hutchinson
Thermodynamics can also provide a quantitative understanding of the equilibrium constant. Recall that the condition for equilibrium is that ΔG = 0. As noted before, ΔG depends on the pressures of the gases in the reaction mixture, because ΔS depends on these pressures. Though we will not prove it here, it can be shown by application of equation 5 to a reaction that the relationship between ΔG and the pressures of the gases is given by the following equation:
(Recall again that the superscript ° refers to standard pressure of 1 atm. ΔG° is the difference between the free energies of the products and reactants when all gases are at 1 atm pressure.) In this equation, Q is a quotient of partial pressures of the gases in the reaction mixture. In this quotient, each product gas appears in the numerator with an exponent equal to its stoichiometic coefficient, and each reactant gas appears in the denominator also with its corresponding exponent. For example, for the reaction
It is important to note that the partial pressures in Q need not be the equilibrium partial pressures. However, if the pressures in Q are the equilibrium partial pressures, then Q has the same value as K_{p}, the equilibrium constant, by definition. Moreover, if the pressures are at equilibrium, we know that ΔG=0. If we look back at equation 7, we can conclude that
This is an exceptionally important relationship, because it relates two very different observations. To understand this significance, consider first the case where ΔG°<0. We have previously reasoned that, in this case, the reaction equilibrium will favor the products. From equation 10 we can note that, if ΔG°<0, it must be that K_{p} > 1. Furthermore, if ΔG° is a large negative number, K_{p} is a very large number. By contrast, if ΔG° is a large positive number, K_{p} will be a very small (though positive) number much less than 1. In this case, the reactants will be strongly favored at equilibrium. Note that the thermodynamic description of equilibrium and the dynamic description of equilibrium are complementary. Both predict the same equilibrium. In general, the thermodynamic arguments give us an understanding of the conditions under which equilibrium occurs, and the dynamic arguments help us understand how the equilibrium conditions are achieved.


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