Q.Explain what is meant by the 'criterion for equilibrium' in terms of Gibbs free energy. Using the relation $\Delta G = \Delta H - T\Delta S$, explain briefly why $\Delta G < 0$ signals a spontaneous process, $\Delta G > 0$ a non-spontaneous one, and $\Delta G = 0$ a system at equilibrium.

[!TLDR] Equilibrium is the state of minimum Gibbs free energy, where $\Delta G = 0$. [!ANSWER] $\Delta G<0$ means the forward process is spontaneous (G still decreasing); $\Delta G>0$ means it is non-spontaneous (the reverse is spontaneous instead); $\Delta G=0$ mean …

Gibbs free energy, $G=H-TS$, provides a single criterion, based only on the system, for predicting the direction of a process at constant temperature and pressure. As a process proceeds, if it is thermodynamically favourable, $G$ decreases; equilibrium is reached specifically at the composition where $G$ has fallen to its lowest possible value and can decrease no further in either direction — the minimum of the free-energy curve as a function of the extent of reaction. At any point where $G$ could still decrease by proceeding further in the forward direction, $\Delta G < 0$ for that further step, and the process continues spontaneously forward; conversely, wherever proceeding further forward would actually increase $G$ (i.e. $\Delta G > 0$ for the forward step), that forward step does not happen spontaneously — instead, the reverse process, for which $\Delta G$ would be negative, is what proceeds spontaneously. Exactly at the minimum of the curve, the instantaneous slope is zero: neither moving further forward nor further backward decreases $G$, so $\Delta G = 0$ and the system remains at that fixed composition indefinitely (until conditions such as temperature or pressure are changed) — this is the equil …

Explain equilibrium as the minimum-G composition using the shape of the free-energy-versus-extent-of-reaction curve, then connect the sign of ΔG at any point on that curve to whether the forward process …

Describing equilibrium as 'nothing happening' rather than as the specific minimum-G composition; failing to explain WHY ΔG=0 specif …