Consider an electrochemical cell: A(s) | An+ (aq, 2 M) || B2n+ (aq, 1 M) | B(s). The value of ΔH° for the cell reaction is twice that of ΔG° at 300 K. If the emf of the cell is zero, the ΔS° (in J K–1 mol–1) of the cell reaction per mole of B formed at 300 K is ____.[Given: ln(2) = 0.7, R (universal gas constant) = 8.3 J K–1 mol–1. H, S and G are enthalpy, entropy and Gibbs energy respectively.]

Engineering

Chemistry

Cell Potential Free Energy and Equilibrium Constant

Question

Consider an electrochemical cell: A(s) | Aⁿ⁺ (aq, 2 M) || B²ⁿ⁺ (aq, 1 M) | B(s). The value of ΔH° for the cell reaction is twice that of ΔG° at 300 K. If the emf of the cell is zero, the ΔS° (in J K^–1 mol^–1) of the cell reaction per mole of B formed at 300 K is ____.

[Given: ln(2) = 0.7, R (universal gas constant) = 8.3 J K^–1 mol^–1. H, S and G are enthalpy, entropy and Gibbs energy respectively.]

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A(s) $\to_{}^{}$ Aⁿ⁺ [(aq, 2M) + ne^–) × 2

2ne^– + B²ⁿ⁺ (aq, 1M) $\to_{}^{}$ B(s)

2A(s) + B²ⁿ⁺ (aq, 1M) $\to_{}^{}$ B(s) + 2Aⁿ⁺ (aq, 2M)

$ΔG ° = ΔH ° - TΔS °$

$ΔG ° = 2 ΔG ° - TΔS °$

$TΔS ° = ΔG °$

$∆$ G° = – nFE° = – RT ln K

$∆$ G° = – RT ln $\frac{4}{1}$

$∆$ G° = – 2RT × 0.7 = –1.4 RT

⇒ T $∆$ S° = – 1.4 RT

$∴ Δ$ S° = – 1.4 × R = – 1.4 × 8.3 J mol–1 K^–1

= – 11.62 J mol^–1 K^–1