Electrochemical Theory: EMF, electrode potential, Nernst equation; numerical problems

EMF, Electrode Potential & Nernst Equation with Numericals

1. Electrochemical cell basics

A galvanic (voltaic) cell converts chemical energy to electrical energy: oxidation at anode (–ve), reduction at cathode (+ve), salt bridge completes circuit.

• Anode: $Zn \to Zn^{2+} + 2e^-$; cathode: $Cu^{2+} + 2e^- \to Cu$.
• Cell representation: anode | anode-ion || cathode-ion | cathode (oxidation on left by convention).

2. Electrode potential and EMF

• Standard electrode potential $E^\circ$: potential of $M^{n+}/M$ vs standard hydrogen electrode (SHE, $E^\circ = 0$ by definition), all at 1 M, 25 °C, 1 atm.
• EMF of cell: $E^\circ_{cell} = E^\circ_{cathode} - E^\circ_{anode}$.
• Daniel cell: $E^\circ_{cell} = (+0.34) - (-0.76) = 1.10$ V.
• Relation to free energy and equilibrium:

Spontaneous if $E_{cell} > 0$ ($\Delta G < 0$).

3. Nernst equation

For $aA + bB \to cC + dD$:

For metal electrode $M^{n+} + ne^- \to M$: $E = E^\circ + \frac{0.0591}{n}\log_{10}[M^{n+}]$.

• Increasing reactant ion concentration raises $E$; product build-up lowers it.
• pH electrodes, ion-selective electrodes, and corrosion-potential shifts all follow Nernst behaviour.

4. Solved numericals

Ex 1: $E^\circ_{cell}$ for $Zn + Cu^{2+}(1M) \to Zn^{2+}(1M) + Cu$: $E^\circ = 0.34 - (-0.76) = 1.10$ V; $\Delta G^\circ = -2 \times 96500 \times 1.10 = -212$ kJ/mol.
Ex 2: Zn electrode in 0.01 M $Zn^{2+}$: $E = -0.76 + \frac{0.0591}{2}\log_{10}(0.01) = -0.76 - 0.0591 = -0.819$ V.
Ex 3: Cell with $[Zn^{2+}] = 0.1$, $[Cu^{2+}] = 0.001$: $E = 1.10 - \frac{0.0591}{2}\log_{10}\frac{0.1}{0.001} = 1.10 - 0.0591 = 1.04$ V.
Ex 4: Find $K$ if $E^\circ = 0.46$ V, $n = 2$: $\log_{10}K = 2 \times 0.46/0.0591 = 15.6$ → $K \approx 4 \times 10^{15}$.

Exam Points

• Cell representation + anode/cathode reactions (2–3 marks).
• Nernst equation statement, 298 K form, and one concentration-cell numerical (5 marks favourite); $\Delta G^\circ = -nFE^\circ$ conversion is a guaranteed sub-part.