# Enduring Understanding 6.D: Gibbs Free Energy and Equilibrium

• The equilibrium constant, K, specifies the relative proportions of reactants and products present at chemical equilibrium.
• K can be directly related to temperature and the difference in free energy between reactants and products, by the equation:
• K = e-ΔG/RT
• And the rearranged version:
• ΔG = -RT ln K
• This equation implies:
• If ΔG° is positive, the overall exponent will be negative and K will be less than 1. i.e., in an endergonic reaction (ΔG° is positive), reactants are favored over products.
• If ΔG° is negative, the overall exponent will be positive and K will be greater than 1. i.e., in an exergonic reaction (ΔG° is negative), reactants are favored over products.
• If the magnitude of ΔG° is large relative to RT, the equilibrium constant will be strongly in favor of reactants or products.
• If the magnitude of ΔG° is close to RT, the equilibrium constant will be near 1 and there will be similar concentrations of reactants and products at equilibrium.
• RT is a measure of 'thermal energy'. At room temperature, RT is approximately 2.4 kJ/mol. So when the reaction A⇆B has a ΔG° = -2.4 kJ/mol:
• K = e +1 = 2.72
[B]/[A] = 2.72 at equilibrium
• Therefore, a ΔG° of -2.4 kJ/mol in a A⇆B reaction results in an equilibrium of about 3:1 B:A (products to reactants).
• Sample Question 1: In an equilibrium reaction A⇆B with equilibrium constant Keq, the initial concentration of [A] was 0.2M and the final concentration was 0.5M. Which of the following correctly describes the mixture:
• 1. Q = Keq
2. Q < Keq
3. Q > Keq
• The answer is (3), Q > Keq. The reaction proceeds in the reverse direction (more A is formed) so the starting ratio of product to reactant (reaction quotient, Q, [B]/[A]) must have been greater than the equilibrium constant Keq.
• Sample Question 2: If a chemical reaction at room temperature has a Keq of 0.02, which of the following is the most reasonable value for ΔG°? -1000, -10, +10, or +1000 kJ/mol?
• The answer is +10 kJ/mol. ΔG = -RT ln K, which would be -2.4 x ln(0.02). ln(0.02) is about -4 (i.e. e-4 □ 0.02), so ΔG = -2.4 x -4 □ 10 kJ/mol.

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