⚖️ Chemical Equilibrium — Free Energy, Reaction Quotient & Le Chatelier

K = exp(−ΔG°/RT). A negative ΔG° (spontaneous forward reaction) gives K > 1, favouring products at equilibrium; a positive ΔG° gives K < 1, favouring reactants. Since ΔG° = ΔH° − TΔS°, both enthalpy and entropy — and temperature — jointly determine which side wins.

Free energy as a function of Q combines the fixed ΔG° term with a mixing-entropy term (RT ln Q) that diverges at both Q→0 and Q→∞, guaranteeing an interior minimum. Setting the derivative dG/dQ to zero and solving reproduces exactly ΔG° + RT ln K = 0, i.e. the minimum is the equilibrium point by construction.

The van't Hoff equation ln K = −ΔH°/(RT) + ΔS°/R predicts a straight line when ln K is plotted against 1/T, with slope −ΔH°/R and intercept ΔS°/R. This is exactly how ΔH° and ΔS° are measured experimentally: run the reaction at several temperatures, plot ln K vs 1/T, and read off the slope and intercept.

ICE stands for Initial, Change, Equilibrium — a bookkeeping method where each species' concentration changes by its stoichiometric coefficient times a single reaction extent ξ. Solving for the ξ that satisfies K = Q at equilibrium gives every species' equilibrium concentration in one step, which is exactly what the simulation's ICE table displays live.

Changing [A]₀ or [B]₀ shifts Q away from K, and the simulation immediately recomputes ξ so the system relaxes back toward K — visibly consuming the added species and forming more of the other side, or vice versa. This is Le Chatelier's principle made computable rather than just a qualitative rule of thumb.