Free Energy and Equilibrium

The standard free energy change equals negative RT times the natural logarithm of the equilibrium constant. When ΔG° is negative, the equilibrium constant is greater than 1, favoring product formation. Conversely, when ΔG° is positive, K is less than 1, favoring reactants. This relationship allows you to predict reaction favorability from either thermodynamic property.

A negative ΔG represents a driving force for the process in the forward direction, indicating the reaction is spontaneous and product-favored at equilibrium. The more negative the free energy, the larger the equilibrium constant and the greater the tendency for reactants to convert to products. This thermodynamic property predicts whether a reaction will proceed spontaneously under given conditions.

Temperature changes alter the equilibrium constant according to the relationship ln K equals negative ΔH over RT plus ΔS over R. Plotting the natural log of K against inverse temperature yields a straight line with slope negative ΔH over R and y-intercept ΔS over R. This temperature dependence allows calculation of enthalpy changes from equilibrium data measured at two different temperatures.

The reaction quotient Q measures the current ratio of products to reactants. When Q is less than the equilibrium constant K, the reaction proceeds forward until equilibrium is reached and Q equals K. When Q exceeds K, the reaction shifts in reverse. At equilibrium, Q equals K and the free energy change is zero, meaning forward and reverse driving forces are equal.

The free energy change under nonstandard conditions is calculated as ΔG equals ΔG° plus RT times the natural log of Q, where Q is the reaction quotient. This equation applies to reactants and products at pressures other than 1 bar or concentrations other than 1 M. It allows prediction of reaction spontaneity under any given set of conditions by comparing actual conditions to standard states.

When ΔG° equals zero, the system is at equilibrium with reactants and products comparably abundant. The equilibrium constant K equals 1, and the forward and reverse reaction rates are equal. At this point, the reaction quotient Q equals the equilibrium constant, and there is no net driving force for the reaction to proceed in either direction.

The Van't Hoff equation, expressed as ln K equals negative ΔH over RT plus ΔS over R, creates a linear relationship between ln K and inverse temperature. This straight-line form enables graphical determination of enthalpy and entropy changes from experimental equilibrium constants measured at different temperatures, assuming enthalpy remains constant over the limited temperature range studied.