Gibbs Free Energy, ΔG
Gibbs free energy
- As we have seen in the previous sections, the feasibility of a reaction is determined by two factors, the enthalpy change and the entropy change
- The two factors come together in a fundamental thermodynamic concept called the Gibbs free energy (G)
- The Gibbs equation is:
ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ
- The units of ΔGꝋare in kJ mol-1
- The units of ΔHreactionꝋare in kJ mol-1
- The units of T are in K
- The units of ΔSsystemꝋare in J K-1 mol-1(and must therefore be converted to kJ K-1 mol-1 by dividing by 1000)
- There are two ways you can calculate the value of ΔGꝋ
- From ΔHꝋand ΔSꝋ values
- From ΔGꝋ values of all the substances present
Worked example
Calculate the free energy change for the following reaction:
2NaHCO3 (s) → Na2CO3 (s) + H2O (l) + CO2 (g)
ΔHꝋ= +135 kJ mol-1 ΔS = +344 J K-1 mol-1
Answer
Step 1: Convert the entropy value in kilojoules
ΔSꝋ = +344 J K-1 mol-1 ÷ 1000 = +0.344 kJ K-1 mol-1
Step 2: Substitute the terms into the Gibbs Equation
ΔGꝋ = ΔHreactionꝋ - TΔSsystemꝋ
= +135 - (298 x 0.344)
= +32.49 kJ mol-1
The temperature is 298 K since standard values are quoted in the question
Worked example
What is the standard free energy change, ΔGꝋ, for the following reaction?
C2H5OH(l) + 3O2(g) → 2CO2(g) + 3H2O(g)
Answer
ΔGꝋ = ΣΔGproductsꝋ - ΣΔGreactantsꝋ
ΔGꝋ = [(2 x CO2 ) + (3 x H2O )] - [(C2H5OH) + (3 x O2)]
ΔGꝋ = [(2 x -394 ) + (3 x -229 )] - [-175 + 0]
ΔGꝋ = -1300 kJ mol-1