Equilibrium constants (Kp and Kc)

Applying the law of mass action to a general reversible reaction

(where A, B are reactants; C, D are products; and x, y, l, m are their respective stoichiometric coefficients), the forward rate is $r_f \propto [A]^x[B]^y$, i.e. $r_f = k_f[A]^x[B]^y$, and the backward rate is $r_b \propto [C]^l[D]^m$, i.e. $r_b = k_b[C]^l[D]^m$, where $k_f$ and $k_b$ are the forward and backward rate constants.

At equilibrium, the forward rate equals the backward rate:

where $K_C$ is the equilibrium constant in terms of concentration (active mass). In words: at a fixed temperature, the ratio of the product of the active masses of the products (each raised to its stoichiometric coefficient) to the product of the active masses of the reactants (likewise raised to their coefficients) is a constant -- the equilibrium constant. (This simple picture, tying $K_C$ directly to the ratio of rate constants, turns out to be only approximately true once the more detailed machinery of chemical kinetics is studied -- but it is exactly right as a statement about the equilibrium concentrations themselves.) …