Standard Electrode Potentials: Free Energy Change (Cambridge International A-Level Chemistry)

Free Energy Change Calculations Using Standard Electrode Potentials

Calculating Free Energy Change Using Standard Electrode Potentials

• The standard free energy change can be calculated using the standard cell potential of an electrochemical cell

ΔG ^ꝋ = - n x E_cell^ꝋ x F

• ΔG^ꝋ = standard Gibbs free energy

  • n = number of electrons transferred in the reaction
  • E_cell^ꝋ = standard cell potential (V)
  • F = Faraday constant (96 500 C mol^-1)

Worked Example Calculating the standard Gibbs free energy change

Calculate the standard Gibbs free energy change for the following electrochemical cell:

2Fe³⁺ (aq) + Cu (s) ⇌ 2Fe²⁺ (aq) + Cu²⁺ (aq)

Answer

• **Step 1: **Determine the two half-equations and their E^ꝋ using the Data booklet:

Fe³⁺** (aq) + e**^- ⇌ Fe²⁺(aq) E^ꝋ = +0.77 V **

Cu²⁺** (aq) + 2e - ⇌ Cu (s) E^ꝋ = +0.34 V

• **Step 2: **Calculate the E_cell^ꝋ

  • E_cell^ꝋ** = E_red^ꝋ** - E_ox^ꝋ
  • E_cell^ꝋ****= (+0.77) - (+0.34)
  • E_cell^ꝋ**** = +0.43 V

• Step 3: Determine the number of electrons transferred in the reaction

  • The Cu²⁺/Cu has a smaller E^ꝋ value which means that it gets oxidised
  • It **transfers **two electrons to **two **Fe³⁺ ions
  • Each Fe³⁺ ion accepts one electron so the total number of electrons transferred is two

• **Step 4: **Substitute the values in for the standard Gibbs free energy equation

  • ΔG**^ꝋ** = - n x E_cell^ꝋ** x F
  • ΔG**^ꝋ** **= -2 x (+0.43) x 96 500
  • ΔG**^{** ꝋ} = -82 990 J mol^-1 = -83 kJ mol^-1