Calculating E°cell
HL Extension
Spontaneity Criteria: E°cell and ΔG°
\[\mathbf{E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}}\]
\[\mathbf{\Delta G^\circ = -nFE^\circ_{\text{cell}}}\]
- \(E^\circ_{\text{cell}} > 0 \implies \Delta G^\circ < 0 \implies\) Spontaneous under standard conditions.
- \(E^\circ_{\text{cell}} < 0 \implies \Delta G^\circ > 0 \implies\) Non-spontaneous (requires external electrical energy).
- \(E^\circ_{\text{cell}} = 0 \implies \Delta G^\circ = 0 \implies\) System at equilibrium.
Link to Gibbs energy
Worked Example
Worked Example
Calculating E°cell and ΔG° for Zn-Cu
Problem: Will zinc reduce \(\text{Cu}^{2+}\) spontaneously? (\(E^\circ_{\text{Cu}} = +0.34\text{ V}, E^\circ_{\text{Zn}} = -0.76\text{ V}\))
\[E^\circ_{\text{cell}} = +0.34 - (-0.76) = +1.10\text{ V}\] \[\Delta G^\circ = -(2)(96500)(+1.10) = -212300\text{ J mol}^{-1} = \mathbf{-212.3\text{ kJ mol}^{-1}} \implies \text{Spontaneous}\]
Examiner Trap
Sign Reversal Error in E°cell
When calculating \(E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}\), do not manually change the sign of \(E^\circ_{\text{anode}}\) before substituting. The minus sign in the formula already accounts for the reversal!
Exam Tip
Thermodynamics vs Kinetics in Redox
Thermodynamic Spontaneity vs Kinetic Rate: A reaction may have \(E^\circ_{\text{cell}} > 0\) (\(\Delta G^\circ < 0\)) but proceed imperceptibly slowly at room temperature due to a high activation energy (\(E_{\text{a}}\)).
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