free energy and equilibrium
Imagine a ball rolling around the inside of a curved bowl. It keeps moving as long as the surface tilts, and it finally comes to rest at the lowest point. A reacting mixture does exactly this in a landscape of Gibbs free energy: it shifts forward or backward, always heading downhill, until it settles in the valley bottom. That resting place is chemical equilibrium — the point where free energy is at its minimum and ΔG has fallen to zero.
This gives the deep link between thermodynamics and the equilibrium constant K. The standard Gibbs energy ΔG° fixes exactly where the valley bottom lies: a large negative ΔG° pushes the minimum far toward products, giving a big K, while a positive ΔG° leaves the minimum near the reactants, giving a small K. The relation ΔG° = −RT ln K turns one into the other, with R the gas constant and T the temperature.
Why it matters: this is what lets chemists predict how complete a reaction will be, just from tabulated free energies — no need to run it. The honest subtlety is that equilibrium is not 'nothing happening.' It is a dynamic balance, with forward and reverse reactions racing along at equal rates so the amounts stay constant. Equilibrium also doesn't mean fifty-fifty; the mix can sit far toward one side.
At 25 °C, a reaction with ΔG° = −40 kJ/mol gives an equilibrium constant of about ten million — so at rest the mixture is overwhelmingly product, with only a trace of reactant left over.
Every extra few kJ/mol of −ΔG° pushes equilibrium far toward products.
Keep two things distinct: ΔG° = 0 means K = 1 (a fifty-fifty balance under standard conditions), whereas ΔG = 0 means the mixture has actually reached equilibrium right now. The first is a fixed property of the reaction; the second is a momentary state of the system.