Equilibrium constant and Gibbs energy

Gibbs energy tells us which way a reaction goes, and so does K. The two are connected:

∆G = ∆G⊖ + RT ln Q

At equilibrium, ∆G = 0 and Q = K, so:

∆G⊖ = –RT ln K, or K = e^(–∆G⊖/RT).

What this means:

• ∆G⊖ < 0 gives K > 1: products are favoured.
• ∆G⊖ > 0 gives K < 1: reactants are favoured.
• At any moment, if ∆G is negative the reaction moves forward; if positive, the reverse reaction is spontaneous; if zero, the system is at equilibrium.

An example: a reaction with ∆G⊖ = –5.7 kJ mol⁻¹ at 298 K has log K = 5700 ÷ (2.303 × 8.314 × 298) ≈ 1.0, so K ≈ 10. A small negative ∆G⊖ gives a modest K; a large negative ∆G⊖ gives a huge K.

This link is used even in biology: the energy changes of reactions in our cells (such as those that break down sugar) are understood through their ∆G⊖ and K values.