How the equilibrium constant varies with the energy change of a reaction

The equilibrium constant of a reaction is related to the difference in energy between reactants and products by this equation:

ΔG° = The standard Gibbs energy of the reaction, the difference between two states in kJ / mol. The ° represents standard conditions.

T = Temperature in kelvin
R = Molar gas constant
K = Equilibrium constant of the reaction

For example, this equation can be used to work out the energy change in the addition of water to isobutyraldehyde:

The equilibrium concentrations of hydrate and water can be measure by comparing UV adsorptions of the compound dissolved in water and the compound dissolved in hexane. As usual, approximately constant concentrations such as H₂O are set to 1.

These experiments reveal K_eq at 25° to be around 0.5.

So ∆G° = –8.314 × 298 × ln(0.5) = +1.7 kJmol^–1

The sign of G tells us about the direction the equilibrium favors. At K = 1, there is a 50:50 mixture of products:reactants, and ln(1) = 0, so ∆G° = 0.

At K > 1, ln(K) gives a positive number. At K < 1, ln(K) is negative.

In other words, equilibrium concentration is shifted in favor of the side with the lowest energy - in favor of the reaction with a negative ∆G. This should be pretty intuitive even without working it out from the equation. 

A small change in ∆G makes a big difference in K, which you might notice by considering the log term. Also have a look at this table:

Every reaction is theoretically at equilibrium. But a typical C-C bond is 350 kJ mol^-1. You might want to input that and see what percentage of products you get... it gives you an appreciation for why we consider these reactions to only operate in one direction.

The point of using Gibbs energy instead of enthalpy is that the Gibbs energy takes entropy into account.