How Do You Calculate Standard Cell Potential From Electrode Potentials? (HL)

Subtract the standard reduction potential of the anode from that of the cathode: $E_{\text{cell}}^\ominus = E_{\text{cathode}}^\ominus - E_{\text{anode}}^\ominus$. A positive value indicates that the cell reaction is spontaneous under standard conditions.

The Method

A standard electrode potential, $E^\ominus$, measures the tendency of a half-cell to undergo reduction relative to the standard hydrogen electrode. Values in the IB Chemistry data booklet are written as reduction potentials.

Under standard conditions, dissolved species are at one mole per cubic decimetre, gases are at 100 kPa, and measurements are normally made at 298 K.

1. Write both half-equations as reductions.
2. Identify which reduction has the more positive $E^\ominus$. This occurs at the cathode.
3. The other half-equation is reversed in the operating cell, so oxidation occurs at the anode.
4. Substitute the data-booklet values into the formula.

Cell potential is the potential difference between the two electrodes. The subtraction accounts for using one listed reduction half-equation in reverse as an oxidation.

For a zinc-copper voltaic cell:

$\text{Cu}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Cu}(\text{s})\qquad E^\ominus = +0.34\text{ V}$

$\text{Zn}^{2+}(\text{aq}) + 2e^- \rightarrow \text{Zn}(\text{s})\qquad E^\ominus = -0.76\text{ V}$

Copper is reduced at the cathode, while zinc is oxidized at the anode. Therefore:

$$E_{\text{cell}}^\ominus = (+0.34)-(-0.76)=+1.10\text{ V}$$

The positive result means electrons flow spontaneously from zinc to copper through the external circuit. Zinc is therefore negative and copper positive in this voltaic cell.

The overall reaction is:

$\text{Zn}(\text{s}) + \text{Cu}^{2+}(\text{aq}) \rightarrow \text{Zn}^{2+}(\text{aq}) + \text{Cu}(\text{s})$

A common misconception is multiplying $E^\ominus$ by a stoichiometric coefficient when balancing electrons. Do not do this: electrode potential is an intensive property, so doubling a half-equation does not double its potential.

Exam Technique

This is AHL content from Reactivity 3.2.13. In a calculation, identify the cathode and anode, show the substitution with signs, and give the answer in volts. State that $E_{\text{cell}}^\ominus>0$ predicts a spontaneous reaction under standard conditions. Always connect the sign to the predicted direction of the overall redox reaction.