Gibbs Free-Energy Change, ∆G, & Entropy Change, ∆S (Oxford AQA International A Level Chemistry)

Gibbs Free-Energy Change, ∆G

• The feasibility of a reaction does not only depend on the entropy change of the reaction but can also be affected by the enthalpy change

  • Therefore, using the entropy change of a reaction only to determine the feasibility of a reaction is inaccurate

• The Gibbs free energy (G) is the energy change that takes into account both the entropy change of a reaction and the enthalpy change

• The Gibbs equation is:

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

• Where the units for each term are:

  • ΔG^ꝋ = kJ mol^-1

  • ΔH_reaction^ꝋ = kJ mol^-1

  • T = K

  • ΔS_system^ꝋ = J K^-1 mol^-1

Calculating Gibbs Free-Energy Change

• The Gibbs equation can be used to calculate the Gibbs free energy change of a reaction

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

• The equation can also be rearranged to find values of ΔH_reaction^ꝋ, ΔS_system^ꝋ or the temperature, T

• For example, if for a given reaction, the values of ΔG^ꝋ, ΔH_reaction^ꝋ and ΔS_system^ꝋ are given, the temperature can be found by rearranging the Gibbs equation as follows:

T = 

Feasible Reactions

• The feasibility of a reaction can be affected by the temperature

• The Gibbs equation will be used to explain what will affect the feasibility of a reaction for exothermic and endothermic reactions

Exothermic reactions

• In exothermic reactions, ΔH_reaction^θ is negative

• If the ΔS_system^θ is positive:

  • Both the first and second term will be negative

  • Resulting in a negative ΔG^θ so the reaction is feasible

  • Therefore, regardless of the temperature, an exothermic reaction with a positive ΔS_system^θ will always be feasible

• If the ΔS_system^θ is negative:

  • The first term is negative and the second term is positive

  • At high temperatures, the -TΔS_system^θ will be very large and positive and will overcome ΔH_reaction^θ

  • Therefore, at high temperatures ΔG^θ is positive and the reaction is not feasible

  • The reaction is more feasible at low temperatures, as the second term will not be large enough to overcome ΔH_reaction^θ resulting in a negative ΔG^θ

• This corresponds to Le Chatellier’s principle which states that for exothermic reactions an increase in temperature will cause the equilibrium to shift position in favour of the reactants, i.e. in the endothermic direction

  • In other words, for exothermic reactions, the products will not be formed at high temperatures

  • The reaction is not feasible at high temperatures

Summary of factors affecting Gibbs free energy for exothermic reactions

Endothermic reactions

• In endothermic reactions, ΔH_reaction^θ is positive

• If the ΔS_system^θ is negative:

  • Both the first and second term will be positive

  • Resulting in a positive ΔG^θ so the reaction is not feasible

  • Therefore, regardless of the temperature, endothermic with a negative ΔS_system^θ will never be feasible

• If the ΔS_system^ꝋ is positive:

  • The first term is positive and the second term is negative

  • At low temperatures, the -TΔS_system^θ will be small and negative and will not overcome the larger ΔH_reaction^θ

  • Therefore, at low temperatures ΔG^θ is positive and the reaction is less feasible

  • The reaction is more feasible at high temperatures as the second term will become negative enough to overcome the ΔH_reaction^θ resulting in a negative ΔG^θ

• This again corresponds to Le Chatellier’s principle which states that for endothermic reactions an increase in temperature will cause the equilibrium to shift position in favour of the products

  • In other words, for endothermic reactions, the products will be formed at high temperatures

  • The reaction is therefore feasible

Summary of factors affecting Gibbs free energy for endothermic reactions