15.2.3 Gibbs Free Energy

Gibbs free energy

• 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:

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)

Calculating ΔG^ꝋ

• There are two ways you can calculate the value of ΔG^ꝋ
  1. From the Gibbs equation, using enthalpy change, ΔH^ꝋ, and entropy change, ΔS^ꝋ, values
  2. From ΔG^ꝋ values of all the substances present

Answer:

Step 1: Convert the entropy value in kilojoules

• • • ΔS^ꝋ = +344 J K^-1 mol^-1  ÷ 1000 = +0.344 kJ K^-1 mol^-1 

Step 2: Substitute the terms into the Gibbs Equation

• • • ΔG^ꝋ = ΔH_reaction^ꝋ – TΔS_system^ꝋ
      • = +135 – (298 x 0.344)
      • = +32.49 kJ mol^-1 

The temperature is 298 K since standard values are quoted in the question

Answer:

• • This can be calculated in the same way as you complete enthalpy calculations
  • ΔG^ꝋ = ΣΔG_products^ꝋ – ΣΔG_reactants^ꝋ
    • ΔG^ꝋ = [(2 x CO₂ ) + (3 x H₂O )] – [(C₂H₅OH) + (3 x O₂)]
    • ΔG^ꝋ = [(2 x -394 ) + (3 x -229 )] – [-175 + 0]
    • ΔG^ꝋ = -1300 kJ mol^-1 

  • This can also be done by drawing a Hess cycle - find the way that is best for you