5.4.6 Standard Electrode Potentials: Free Energy Change

• 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

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

= (+0.77) - (+0.34)

= +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

= -2 x (+0.43) x 96 500

 = -82 990 J mol^-1

= -83 kJ mol^-1