What determines chemical equilibrium and how is the equilibrium constant related to thermodynamics?

At chemical equilibrium, forward and reverse reaction rates are equal, and Gibbs energy is minimized. The equilibrium constant K is related to standard Gibbs energy change: dG_standard = -RT*ln(K). Temperature dependence follows van't Hoff equation: d(ln K)/dT = delta_H_rxn/(R*T^2). Exothermic reactions: K decreases with temperature; endothermic: K increases. Pressure affects equilibrium position through Le Chatelier's principle but doesn't change K. Understanding these relationships guides reactor design and operating condition selection.