δg and equilibrium

Question

For a reaction at 298 K, ΔG° = -9.9 kJ mol⁻¹. The equilibrium constant K is approximately (R = 8.314 J mol⁻¹ K⁻¹):

RankGuru · Accepted Answer

1. **Formula**: $\Delta G^\circ = -RT \ln K$.
2. **Rearrangement**: $\ln K = -\frac{\Delta G^\circ}{RT}$.
3. **Calculation**:
   - $\Delta G^\circ = -9,900$ J/mol.
   - $RT = 8.314 	imes 298 \approx 2,477.5$ J/mol.
   - $\ln K = -(-9,900) / 2,477.5 \approx 3.996 \approx 4.0$.
4. **Solve for K**: $K = e^4$.
5. **Estimation**: Since $e \approx 2.718$, $e^4 \approx (2.7)^4 \approx 50	ext{--}60$.
6. **Result**: The closest option is **$50$**.

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δg and equilibrium

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