Gibbs Free Energy & Equilibrium Constant (HL) (HL IB Chemistry)

• When ΔG < 0 for a reaction at constant temperature and pressure, the reaction is spontaneous
• When a reversible reaction reaches equilibrium, the Gibbs free energy is changing as the ratio of reactants to products changes
• For non-reversible reactions:
  • As the amount of products increases, the reaction moves towards completion
  • This leads to a decrease in Gibbs free energy
• For reversible reactions:
  • As the amount of products increases, the reaction moves towards equilibrium
  • This causes a decrease in Gibbs free energy
• At the point of equilibrium, Gibbs free energy is at its lowest as shown on the graph:

Gibbs free energy and equilibrium relationship

Gibbs free energy changes as the reaction proceeds

• In section 1 of the graph, the forward reaction is favoured and the reaction proceeds towards a minimum value
• Having reached a point of equilibrium, the Gibbs free energy increases
  • This is when the reaction becomes non-spontaneous (section 2)
• The reverse reaction now becomes spontaneous and the Gibbs free energy again reaches the minimum value, so heads back towards equilibrium

• The reaction will be spontaneous in the direction that results in a decrease in free energy (becomes more negative)
• When the equilibrium constant, K, is determined for a given reaction, its value indicates whether the products or reactants are favoured at equilibrium
• ΔG is an indication of whether the forward or backward reaction is favoured

Free energy graph for a spontaneous reaction

Free energy graph for a non-spontaneous reaction

• The quantitative relationship between standard Gibbs free energy change, temperature and the equilibrium constant is represented by:

$\mathbf{∆}{\mathit{G}}^{\mathbf{\theta }}\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{-}\mathit{R}\mathit{T}\mathbf{ }\mathbf{ln}\mathbf{ }\mathit{K}$

The rearrangement of this equation makes it possible to:

• Calculate the equilibrium constant
• Deduce the position of equilibrium for the reaction

$\mathbf{ln}\mathit{ }\mathit{K}\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{ }\mathbf{-}\frac{\mathbf{∆}{\mathit{G}}^{\mathbf{\theta }}}{\mathit{R}\mathit{T}}$

• The reaction quotient, Q, is calculated using the same equation as the equilibrium constant expression, but with non-equilibrium concentrations of reactants and products
• It is a useful concept because the size of Q can tell us how far a reaction is from equilibrium and in which direction the reaction proceeds

So how is the reaction quotient related to Gibbs free energy?

• They are related by the following expression:

ΔG = ΔG^θ + RT ln Q

• At non-equilibrium conditions ΔG and ΔG^θ are not the same; ΔG is the driver that pushes a reaction toward equilibrium
• When a reaction reaches equilibrium, Q = K and  ΔG = 0, so 

0 = ΔG^θ + RT ln K

ΔG^θ = - RT ln K