5.5.4 Electrode Potential Calculations

• Once the E^ꝋ of a half-cell is known, the potential difference or voltage or emf of an electrochemical cell made up of any two half-cells can be calculated
  • These could be any half-cells and neither have to be a standard hydrogen electrode

• The standard cell potential (E_cell^ꝋ) can be calculated by subtracting the less positive E^ꝋ from the more positive E^ꝋ value
  • The half-cell with the more positive E^ꝋ value will be the positive pole
    • By convention this is shown on the right hand side in a conventional cell diagram, so is termed  E_right^ꝋ

  • The half-cell with the less positive E^ꝋ value will be the negative pole
    • By convention this is shown on the left hand side in a conventional cell diagram, so is termed  E_left^ꝋ

E_cell^ꝋ = E_right^ꝋ - E_left^ꝋ   

• • Since oxidation is always on the left and reduction on the right, you can also use this version

E_cell^ꝋ = E_reduction^ꝋ - E_oxidation^ꝋ

   Answer

   Step 1: Calculate the standard cell potential. The copper is more positive so must be the right hand side.

E_cell^ꝋ = E_right^ꝋ - E_left^ꝋ   

E_cell^ꝋ = (+0.34) - (-0.76)

= +1.10 V

   The voltmeter will therefore give a value of +1.10 V

   Step 2: Determine the positive and negative poles

   The Cu²⁺ / Cu  half-cell is the positive pole as its E^ꝋ is more positive than the E^ꝋ value of the Zn²⁺ / Zn half-cell

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

Limitations of E^θ to predict reactions

• 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
• Another, more basic limitation is the fact that many redox reactions are not aqueous