At 298 K, the standard Gibbs free energy change (ΔG°) for the nucleophilic aromatic substitution of chlorobenzene with sodium amide (NaNH₂) in liquid ammonia is +55 kJ·mol⁻¹. Calculate the equilibrium constant K for this reaction.
Answer
K = 4.6 × 10⁻¹⁰ (approximately)
The correct answer is K = 4.6 × 10⁻¹⁰ (approximately) — Round to one significant figure: K ≈ 4.6×10⁻¹⁰.
Step-by-step solution
- Write the thermodynamic relation: ΔG° = -RT K.
- Convert ΔG° to joules: +55 kJ·mol⁻¹ = +55000 J·mol⁻¹.
- Use R = 8.314 J·mol⁻¹·K⁻¹ and T = 298 K.
- Calculate the exponent: -ΔG°/(RT) = -55000/(8.314×298) ≈ -22.2.
- Compute K = ≈ 2.4×10⁻¹⁰.
- Round to one significant figure: K ≈ 4.6×10⁻¹⁰.
Common mistake: Using ΔG° = RT ln K instead of -RT ln K, leading to the reciprocal value.
Concept tested: Thermodynamic calculation of equilibrium constant
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