# D22.3 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:

ΔrG° = −RT(lnK°)        or        K° = erG°/RT

Note that in these equations the equilibrium constant is represented by K°. The standard equilibrium constant, Kº, is formulated like Kc or Kp, 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. Hence, Kº is truly unitless. Dividing by the standard-state concentration or pressure means that if concentrations in Kc are expressed in M (mol/L) the numerical values of Kº and Kc are the same. Similarly, if partial pressures in Kp are expressed in bar, the numerical values of Kº and Kp are the same.

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 