Cell Potential & Thermodynamic Favorability (College Board AP Chemistry)

Standard electrode potential

• The position of equilibrium and therefore the electrode potential depends on factors such as:
  • Temperature
  • Pressure of gases
  • Concentration of reagents

• So, to be able to compare the electrode potentials of different species, they all have to be measured against a common reference or standard
• Standard conditions also have to be used when comparing electrode potentials
• These standard conditions are:
  • An ion concentration of 1.00 mol dm^-3
  • A temperature of 298 K
  • A pressure of 100 kPa

• Standard measurements are made using a high resistance voltmeter so that no current flows and the maximum potential difference is achieved
• The electrode potentials are measured relative to a standard hydrogen electrode
• The standard hydrogen electrode is given a value of 0.00 V, and all other electrode potentials are compared to this standard
• This means that the electrode potentials are always referred to as standard electrode potential (E^o)
• The standard electrode potential (E^o) is the potential difference ( sometimes called voltage) produced when a standard half-cell is connected to a standard hydrogen cell under standard conditions
  • For example, the standard electrode potential of bromine suggests that relative to the hydrogen half-cell it is more likely to get reduced, as it has a more positive E^o value

Br₂ (l) + 2e^– ⇌ 2Br^– (aq)   E^o = +1.09 V

2H⁺ (aq) + 2e^– ⇌ H₂ (g)   E^o = 0.00 V

• • The standard electrode potential of sodium, on the other hand, suggests that relative to the hydrogen half-cell it is less likely to get reduced as it has a more negative E^o value

Na⁺ (aq) + e^– ⇌ Na (s)   E^o = -2.71 V

2H⁺ (aq) + 2e^– ⇌ H₂ (g)   E^o = 0.00 V

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

How to calculate E_cell^o

• Voltmeters measure potential on the right-hand side of the cell and subtract it from the potential on the left-hand side of the cell
• If both E° values are known, the E_cell° of the cell formed can be calculated if the right-hand electrode and left-hand electrode are specified
  • For example, if in a cell the E_right^o = silver electrode (+0.80V) and LHS is copper electrode (+0.34 V), then

E_cell^o = E_right^o - E_left^o   

E_cell^o = +0.80 - 0.34 = +0.46 V

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

E_cell^o = E_reduction^o - E_oxidation^o

Feasibility

• The E^o values of a species indicate how easily they can get oxidised or reduced
• The reaction will tend to proceed in the forward direction
  • 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 backward direction
• A reaction is feasible (likely to occur) when the E_cell^o is positive
• The less positive the value, the easier it is to oxidise the species on the right of the half-equation
• For example, two half-cells in the following electrochemical cell are:

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

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

• Cl₂ molecules are reduced as they have a more positive E^o 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^o 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^o  value of +1.02 V
  • Calculated from (+1.36) - (+0.34)
• The backward reaction is not feasible (not spontaneous) as it has a negative E^o value of -1.02
  • Calculated from (+0.34) - (+1.36)

A cell containing Cu²⁺/Cu and Cl₂/2Cl^– 

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

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

ΔG^o = - n x E_cell^o x F

• • ΔG^o = standard Gibbs free energy
  • n = number of electrons transferred in the reaction
  • E_cell^o = standard cell potential (V)
  • F = Faraday constant (96,485 C mol^-1)