5.2.3 Gibbs Free Energy Change & Gibbs Equation

Gibbs free energy

• 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

• The units of ΔG^ꝋ are in kJ mol^-1
• The units of ΔH_reaction^ꝋ are in kJ mol^-1
• The units of T are in K
• The units of ΔS_system^ꝋ are in J K^-1 mol^-1 (and must therefore be converted to kJ K^-1 mol^-1 by dividing by 1000)

• 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:

Worked example: Calculating Gibbs free energy

Answer

• Step 1 - Calculate ΔS_system^ꝋ

ΔS_system^ꝋ = ΣΔS_products^ꝋ - ΣΔS_reactants^ꝋ

ΔS_system^ꝋ = (ΔS^ꝋ [CH₃Br(g)] + ΔS^ꝋ [H₂O(l)]) -  (ΔS^ꝋ [CH₃OH(l)] + ΔS^ꝋ [HBr(g)])

= (246 + 70.0) - (240 + 99.0)

= -23.0 J K^-1 mol^-1

• Step 2 - Convert ΔS^ꝋ into kJ K^-1 mol^-1

= -0.023 kJ K^-1 mol^-1

•  Step 3 - Calculate ΔG^ꝋ

ΔG^ꝋ = ΔH_reaction^ꝋ - TΔS_system^ꝋ

= -47 - (298 x -0.023)

= -40.146 kJ mol^-1

= -40.1 kJ mol^-1