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

💡 Solution & Explanation

# Relationship Between Standard Free Energy and Equilibrium Constant **Step 1: Recall the fundamental thermodynamic equation** The standard free energy change is directly connected to the equilibrium constant through: $$\Delta G° = -RT \ln K$$ where: - $\Delta G°$ = standard free energy change - $R$ = universal gas constant (8.314 J/mol·K) - $T$ = absolute temperature (Kelvin) - $K$ = equilibrium constant - $\ln$ = natural logarithm **Step 2: Derive the relationship from first principles** At equilibrium, $\Delta G = 0$, and the relationship between $\Delta G$ and $\Delta G°$ is: $$\Delta G = \Delta G° + RT \ln Q$$ When $Q = K$ (at equilibrium), $\Delta G = 0$: $$0 = \Delta G° + RT \ln K$$ $$\Delta G° = -RT \ln K$$ **Step 3: Interpret the significance** - If $K > 1$: $\ln K > 0$, so $\Delta G° < 0$ (spontaneous forward reaction) - If $K < 1$: $\ln K < 0$, so $\Delta G° > 0$ (non-spontaneous forward reaction) - If $K = 1$: $\ln K = 0$, so $\Delta G° = 0$ (at equilibrium) **The correct answer is:** $$\boxed{\Delta G° = -RT \ln K}$$