D23.4 ΔG° and K°
We know that there is a qualitative relationship between ΔrG° and equilibrium constant for a given reaction. The standard Gibbs free energy change for a reaction indicates whether a reaction is product-favored at equilibrium (ΔrG° < 0) or reactant-favored at equilibrium (ΔrG° > 0). A strongly product-favored reaction (large negative ΔrG°) has a large equilibrium constant (K>> 1) and a strongly reactant-favored reaction (large positive ΔrG°) has a very small equilibrium constant (K<<1, a very small fraction because K cannot be negative).
Quantitatively, this relationship between the equilibrium constant and ΔrG° is expressed by the equation:
where R is the ideal gas constant (8.314 J/K·mol) and T is absolute temperature in kelvin. Note that in these equations the equilibrium constant is represented by K°, the standard equilibrium constant. It is formulated like K, but with all solution phase substance concentrations divided by the standard state concentration of 1 M and all gas phase substance pressures divided by the standard state pressure of 1 bar. Dividing by the standard-state concentration or pressure means that if concentrations in K are expressed in M (mol/L) or partial pressures in bar, the numerical values of Kº and K are the same.
| Kº | ΔrG° | |
|---|---|---|
| > 1 | < 0 | Product-favored at equilibrium. |
| < 1 | > 0 | Reactant-favored at equilibrium. |
| = 1 | = 0 | Reactants and products are equally abundant at equilibrium. |
Exercise: Gibbs Free Energy and Equilibrium
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