Gibbs Free Energy and Equilibrium

The final and most powerful description of equilibrium connects it to thermodynamics through the Gibbs free energy. The standard Gibbs free energy change, $\Delta G^{\circ}$, determines both the spontaneity of a reaction and the value of its equilibrium constant. The two are linked by the central equation

$$\Delta G^{\circ} = -RT\ln K,$$

where $R$ is the gas constant, $8.31$ J K$^{-1}$ mol$^{-1}$, $T$ is the absolute temperature in kelvin, and $K$ is the equilibrium constant. This equation unifies the thermodynamic and equilibrium pictures of a reaction.

The sign and magnitude of $\Delta G^{\circ}$ tell us about the position of equilibrium. If $\Delta G^{\circ}$ is negative, then $\ln K$ is positive, so $K > 1$ and products are favored; the reaction is spontaneous under standard conditions