1‑Chloropentane ($C{H}_{3}C{H}_{2}C{H}_{2}C{H}_{2}C{H}_{2}Cl$) reacts with excess NaI in dry acetone at 298 K. The standard Gibbs free energy change for the reaction ${\mathrm{C}}_5{\mathrm{H}}_{11}\mathrm{Cl}+\mathrm{NaI}\to {\mathrm{C}}_5{\mathrm{H}}_{11}\mathrm{I}+\mathrm{NaCl}$ is $\Delta G^{\circ }=-4.2{\text{kJ mol}}^{-1}$. Calculate the equilibrium constant $K$ at this temperature.

Step-by-step solution

1. Convert $\Delta G^{\circ }$ to joules: $-4.2{\text{kJ mol}}^{-1}=-4200{\text{J mol}}^{-1}$.
2. Use the relation $\Delta G^{\circ }=-RT\ln K$.
3. Substitute $R=8.314{\text{J mol}}^{-1}{\text{K}}^{-1}$ and $T=298\text{K}$:
4. $\ln K=-\Delta G^{\circ }/(RT)=4200/(8.314\times 298)=1.694$.
5. Exponentiate: $K=e^{1.694}\approx 5.44$.
6. Round to two significant figures: $K\approx 5.4$.

Concept tested: Thermodynamics of Finkelstein reaction

Published 16 September 2026 · How this solution was prepared and checked