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^??= ΔH_reaction^??- TΔS_system^?

• The units of ΔG^??are in kJ mol^-1
• The units of ΔH_reaction^??are in kJ mol^-1
• The units of T are in K
• The units of ΔS_system^??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^??= ΔH_reaction^??-? TΔS_system^?

• The equation can also be rearranged to find values of ΔH_reaction^?, ΔS_system^??or the temperature, T
• For example, if for a given reaction, the values of ΔG^?,?ΔH_reaction^??and ΔS_system^??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^?

ΔS_system^??= ΣΔS_products^??- ΣΔS_reactants^?

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

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

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

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

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

• ?Step 3 -?Calculate ΔG^?

ΔG^??= ΔH_reaction^??- TΔS_system^?

= -47 - (298 x -0.023)

= -40.146 kJ mol^-1

= -40.1 kJ mol^-1