Question

Calculate the \(E^\circ_{{Mg^{2+}/Mg}}\) potential for the following half-cell at 25°C:
Mg/Mg²⁺(1 × 10⁻⁴ M), E⁰ _Mg²⁺/Mg = +2.36 V

Answer 1

Electrode Potential Calculation via Nernst Equation

The Nernst equation is employed:

\[ E = E^\circ - \frac{0.0592}{n} \log Q \]

Parameters:

• Standard electrode potential: \(E^\circ = 2.36\ \text{V}\)
• Number of electrons: \(n = 2\)
• Reaction quotient: \(Q = \frac{1}{[{Mg^{2+}}]} = 10^4\), given \( [{Mg^{2+}}] = 1 \times 10^{-4}\ \text{M}\)

Substitution into Nernst equation:

\[ E = 2.36 - \frac{0.0592}{2} \log (10^4) \]

\[ E = 2.36 - \frac{0.0592}{2} \times 4 \]

\[ E = 2.36 - 0.1184 = 2.2416\ \text{V} \]

Result: The calculated electrode potential is 2.2416 V.