For a reversible reaction of the type
chemical equilibrium occurs when the rate of the forward reaction equals the rate of the back reaction, so that the concentrations of products and reactants reach steady-state values. It can be shown that at equilibrium the ratio of concentrations
[C]z [D]w/[A]x [B]y
is a constant for a given reaction and fixed temperature, called the equilibrium constant Kc (where the c indicates concentrations have been used). Note that, by convention, the products on the right-hand side of the reaction are used on the top line of the expression for equilibrium constant. This form of the equilibrium constant was originally introduced in 1863 by C. M. Guldberg and P. Waage using the law of mass action. They derived the expression by taking the rate of the forward reaction
and that of the back reaction
Since the two rates are equal at equilibrium, the equilibrium constant Kc is the ratio of the rate constants kf/kb. The principle that the expression is a constant is known as the equilibrium law or law of chemical equilibrium.
The equilibrium constant shows the position of equilibrium. A low value of Kc indicates that [C] and [D] are small compared to [A] and [B]; i.e. that the back reaction predominates. It also indicates how the equilibrium shifts if concentration changes. For example, if [A] is increased (by adding A) the equilibrium shifts towards the right so that [C] and [D] increase, and Kc remains constant.
For gas reactions, partial pressures are used rather than concentrations. The symbol Kp is then used. Thus, in the example above
Kp = pCzp Dw/pAxp By
It can be shown that, for a given reaction Kp = Kc(RT)Δν, where Δν is the difference in stoichiometric coefficients for the reaction (i.e. z+w – x – y). Note that the units of Kp and Kc depend on the numbers of molecules appearing in the stoichiometric equation. The value of the equilibrium constant depends on the temperature. If the forward reaction is exothermic, the equilibrium constant decreases as the temperature rises; if endothermic it increases (see also van't Hoff's isochore).
The expression for the equilibrium constant can also be obtained by thermodynamics; it can be shown that the standard equilibrium constant K⦵ is given by exp(−ΔG⦵/RT), where ΔG⦵ is the standard Gibbs free energy change for the complete reaction. Strictly, the expressions above for equilibrium constants are true only for ideal gases (pressure) or infinite dilution (concentration). For accurate work activities are used.