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 fundamental thermodynamic equation:** $$\Delta G° = -RT \ln K$$ where: - $\Delta G°$ = standard free energy change - $R$ = gas constant (8.314 J·mol⁻¹·K⁻¹) - $T$ = absolute temperature (in Kelvin) - $K$ = equilibrium constant - $\ln$ = natural logarithm **Why this relationship holds:** At equilibrium, $\Delta G = 0$. The equation $\Delta G° = -RT \ln K$ connects the standard state free energy to the equilibrium position: - If $K > 1$: $\ln K > 0$, so $\Delta G° < 0$ (reaction spontaneous forward) - If $K < 1$: $\ln K < 0$, so $\Delta G° > 0$ (reaction non-spontaneous forward) - If $K = 1$: $\ln K = 0$, so $\Delta G° = 0$ (system at equilibrium) This is the **standard form** expected in chemistry courses (JEE/NEET/AP Chemistry).