The emf of an electrochemical cell

1. Definition

• Electromotive Force $(emf)$ is the potential difference (voltage) between the two electrodes in an electrochemical cell.
• It represents the maximum voltage the cell can produce under standard conditions.
• Measured using a voltmeter connected across the electrodes.

2. Calculating emf of a Galvanic Cell

The emf $(E^\circ_{\text{cell}})$ is calculated using:

$E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$

or

$E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} + E^\circ_{\text{oxidation}}$

Example: Zinc-Copper Cell

• $Zn/Zn²⁺$ Half-reaction: $Zn(s) \rightarrow Zn^{2+}(aq) + 2e^- \quad (E^\circ = :highlight[-0.76V])$

• $Cu²⁺/Cu$ Half-reaction: $Cu^{2+}(aq) + 2e^- \rightarrow Cu(s) \quad (E^\circ = :highlight[+0.34V])$

• Calculate $E^\circ_{\text{cell}}:$ $E^\circ_{\text{cell}} = 0.34V - (-0.76V) = :highlight[1.10V]$

• Since $E^\circ_{\text{cell}}$ is positive, the reaction is spontaneous.

3. Factors Affecting emf

1) Concentration of Electrolytes

• Increasing reactant concentration → Increases emf (favours forward reaction).
• Decreasing reactant concentration → Decreases emf (shifts equilibrium back).

2) Temperature

• Higher temperature can increase or decrease emf, depending on the reaction.
• Exothermic reactions: emf decreases at higher temperatures.
• Endothermic reactions: emf increases at higher temperatures.

3) Surface Area of Electrodes

• Increasing electrode size does not change emf but increases current flow.

4. Predicting if a Reaction Will Occur

• A reaction is spontaneous if $E^\circ_{\text{cell}} > 0$.
• A reaction is non-spontaneous if $E^\circ_{\text{cell}} < 0$ , meaning external energy is needed (e.g., electrolysis).

5. Key Takeaways

• Emf measures the voltage difference between electrodes.
• Use $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$ to calculate emf.
• If $E^\circ_{\text{cell}}$ is positive → spontaneous reaction.
• Emf is affected by concentration, temperature, and electrode materials.