The Bridge: $\Delta G^\circ = -RT\ln K$

This single equation connects the macroscopic thermodynamic quantity $\Delta G^\circ$ to the equilibrium constant $K$ that describes chemical equilibrium.

What This Means Physically

Temperature Dependence of $K$

For exothermic reactions ($\Delta H < 0$): increasing $T$ → $K$ decreases (Le Chatelier: equilibrium shifts left) For endothermic reactions ($\Delta H > 0$): increasing $T$ → $K$ increases (Le Chatelier: equilibrium shifts right)

This is described mathematically by the Van't Hoff equation: $\frac{d\ln K}{dT} = \frac{\Delta H^\circ}{RT^2}$

Connection to Kinetics

Thermodynamics: tells us WHERE equilibrium lies (the destination) Kinetics: tells us HOW FAST we get there (the journey) A reaction can be thermodynamically spontaneous ($\Delta G < 0$) but kinetically so slow as to be practically impossible. Example: C(diamond) → C(graphite) is thermodynamically spontaneous but immeasurably slow.