6.1.5 Thermodynamics & Electrode Potential

Feasibility

• The E^ꝋ values of a species indicate how easily they can get oxidised or reduced
• The more positive the value, the easier it is to reduce the species on the left of the half-equation
  • The reaction will tend to proceed in the forward direction

• The less positive the value, the easier it is to oxidise the species on the right of the half-equation
  • The reaction will tend to proceed in the backward direction
  • A reaction is feasible (likely to occur) when the E_cell^ꝋ is positive

• For example, two half-cells in the following electrochemical cell are:

Cl₂ (g) + 2e^- ⇌ 2Cl^- (aq)        E^ꝋ = +1.36 V

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

• Cl₂ molecules are reduced as they have a more positive E^ꝋ value
• The chemical reaction that occurs in this half cell is:

Cl₂ (g) + 2e^- → 2Cl^- (aq)          

• Cu²⁺ ions are oxidised as they have a less positive E^ꝋ value
• The chemical reaction that occurs in this half cell is:

Cu (s) → Cu²⁺ (aq) + 2e^-

• The overall equation of the electrochemical cell is (after cancelling out the electrons):

Cu (s) + Cl₂ (g) → 2Cl^- (aq) + Cu²⁺ (aq)

OR

Cu (s) + Cl₂ (g) → CuCl₂ (s)

• The forward reaction is feasible (spontaneous) as it has a positive E^ꝋ  value of +1.02 V ((+1.36) - (+0.34))
• The backward reaction is not feasible (not spontaneous) as it has a negative E^ꝋ value of -1.02 ((+0.34) - (+1.36))

A reaction is feasible when the standard cell potential E^ꝋ is positive

• Cell potential is related to both entropy, S, and the equilibrium constant, K
• A larger cell potential means a bigger change in total entropy
  • Therefore, we can say that cell potential is directly proportional to total entropy change

E^θ ∝ ΔS_total  

• The use of two equations for Gibbs free energy change can also show that:

E^θ ∝ lnK

• • ΔG = –nF E^θ_cell
  • ΔG = –RT ln K

• The thermodynamic feasibility of a reaction can be deduced from the electrode potential, however, it gives no information about the rate of reaction
• As standard electrode potentials are measured using solutions, we have to consider the le Châtelier's effect on concentration using non-standard conditions
  • For example, the redox equilibrium equation and standard electrode potential for the V³⁺ | V²⁺ system are:

V³⁺ (aq) + e^- ⇌ V²⁺ (aq)       E^θ = +0.26 V

• • If the concentration of V³⁺ (aq) is greater than 1.0 mol dm^-3, then the equilibrium will shift to the right
    • This will remove electrons from the system, therefore, making the electrode potential less negative 
  • If the concentration of V²⁺ (aq) is greater than 1.0 mol dm^-3, then the equilibrium will shift to the left 
    • This will add electrons to the system, therefore, making the electrode potential more negative 
  • Any change to the concentration will cause a change to the electrode potential and, therefore, to the overall cell potential
    • This is true of any change to the conditions that results in non-standard conditions
• Reaction kinetics can also affect the prediction
  1. The rate of reaction may simply be so slow that it looks like the reaction isn't happening, when it is
  2. The reaction may have a high activation energy which inhibits the reaction, for example:

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

            2H⁺ (aq) + 2e^- ⇌ H₂ (g)   E^θ = 0.00 V

• • • The reaction of Cu²⁺ (aq) + H₂ (g) → Cu (s) + 2H⁺ (aq) is thermodynamically feasible with an electromotive force of +0.34 V
    • However, this reaction does not occur as the activation energy is so high which means that the reactants are kinetically stable
• Another, more basic limitation is the fact that many redox reactions are not aqueous