Relationship Between Equilibrium Constant K, Reaction Quotient Q, and Gibbs Energy, G

Full Notes

Introduction

This section brings together three major ideas from chemistry:

• The equilibrium constant (K)
• The reaction quotient (Q)
• The Gibbs free energy change (ΔG)

These can help us determine whether a reaction is spontaneous, whether it is at equilibrium or in which direction it will proceed.

Note - for more of Gibbs Free Energy and its role in chemistry, please see Gibbs Free Energy (5.6).

Gibbs Energy and Equilibrium Constant

For a general reaction: aA + bB ⇌ cC + dD

We define the Gibbs free energy at any point as:

(Equation 6.21)

This equation tells us how the free energy changes as the concentrations of reactants and products shift – it reflects how far the system is from equilibrium.

At Equilibrium, Q = K and ΔG = 0

so when substituted into the equation:

0 = ΔG⁰ + RT ln K

Rewriting:

This tells us how strongly a reaction favors products or reactants, just by looking at ΔG°.

Interpretation of ΔG⁰ and K

• If K > 1, then ln K > 0 and ΔG⁰ < 0
  Reaction is product-favoured, spontaneous under standard conditions.
• If K < 1, then ln K < 0 and ΔG⁰ > 0
  Reaction is reactant-favoured, non-spontaneous under standard conditions.

Think of it this way:

• A large K means a reaction wants to go forward – it produces a lot of product.
• A small K means the reaction prefers to stay with the reactants.

Summary of Relationships

Summary

• Use ΔG = ΔG⁰ + RT ln Q to assess spontaneity at any composition.
• At equilibrium Q equals K and ΔG equals 0.
• Standard link: ΔG⁰ equals −RT ln K.
• Large K means product favoured and small K means reactant favoured.