The tendency of a chemical reaction to go to completion can be expressed as an equilibrium constant. For the reaction aA + bB
the equilibrium constant, Keq, is given by
[Ceq]C[Deq]d [Aeq]a[Beq]b where [Aeq] is the concentration of A, [Beq] the concentration of B, and so on, when the system has reached equilibrium. A large value of Keq means the reaction tends to proceed until the reactants have been almost completely converted into the products.
Gibbs showed that AG for any chemical reaction is a function of the standard free-energy change, AG°— a constant that is characteristic of each specific reaction—and a term that expresses the initial concentrations of reactants and products:
where [AJ is the initial concentration of A, and so forth; R is the gas constant; and T is the absolute temperature.
When a reaction has reached equilibrium, no driving force remains and it can do no work: AG = 0. For this special case, [AJ = [Aeq], and so on, for all reactants and products, and
[C¡]c[D¡]d = [Ceq]c[Deq]d = K [A¡]a[B¡]b [Aeq]a[Beq]b eq
Substituting 0 for AG and Keq for [Ci]c[Di]7[Ai]a[Bi]b in Equation 1-1, we obtain the relationship
RT ln Ke from which we see that AG° is simply a second way (besides Keq) of expressing the driving force on a reaction. Because Keq is experimentally measurable, we have a way of determining AG°, the thermodynamic constant characteristic of each reaction.
The units of AG° and AG are joules per mole (or calories per mole). When Keq >> 1, AG° is large and negative; when Ke
1, AG° is large and positive.
From a table of experimentally determined values of either Keq or AG°, we can see at a glance which reactions tend to go to completion and which do not.
One caution about the interpretation of AG°: thermodynamic constants such as this show where the final equilibrium for a reaction lies but tell us nothing about how fast that equilibrium will be achieved. The rates of reactions are governed by the parameters of kinetics, a topic we consider in detail in Chapter 6.
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