The standard free energy change G is related to K (equilibrium constant) as — Thermodynamics and Thermochemistry Chemistry Question

💡 Solution & Explanation

# Relationship between ΔG° and K **The correct relationship is:** $$\Delta G° = -RT \ln K$$ **Step-by-step derivation:** 1. **Start with the fundamental equation:** At equilibrium, the total free energy change is zero: $$\Delta G° = -RT \ln Q$$ 2. **Apply equilibrium condition:** When the system reaches equilibrium, $Q = K$ (the reaction quotient equals the equilibrium constant) 3. **Substitute:** $$\Delta G° = -RT \ln K$$ where: - $R$ = gas constant (8.314 J mol⁻¹ K⁻¹) - $T$ = absolute temperature (in Kelvin) - $K$ = equilibrium constant - $\ln$ = natural logarithm **Physical interpretation:** - If $K > 1$: $\ln K > 0$, so $\Delta G° < 0$ (reaction is spontaneous forward) - If $K < 1$: $\ln K < 0$, so $\Delta G° > 0$ (reaction is non-spontaneous forward) - If $K = 1$: $\ln K = 0$, so $\Delta G° = 0$ (system at equilibrium) This equation is fundamental in thermodynamics and connects the spontaneity of a reaction (through ΔG°) to its position of equilibrium (through K).