Standard Electrode Potentials: Free Energy Change (CIE A Level Chemistry)

Calculating the standard Gibbs free energy change

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

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

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