Mathematical definition of an equilibrium constant

For a reversible reaction,

${\displaystyle a{\mbox{A}}+b{\mbox{B}}\rightleftharpoons c{\mbox{C}}+d{\mbox{D}}\,\!}$

the equilibrium constant K is defined as

${\displaystyle K={\frac {[{\mbox{C}}]^{c}[{\mbox{D}}]^{d}}{[{\mbox{A}}]^{a}[{\mbox{B}}]^{b}}}}$

where [X] denotes the concentration of chemical species X.

For example, for the Haber process reaction,

${\displaystyle {\mbox{N}}_{2}({\mbox{g}})+3{\mbox{H}}_{2}({\mbox{g}})\rightleftharpoons 2{\mbox{NH}}_{3}({\mbox{g}})\,\!}$

the equilibrium constant can be calculated by

${\displaystyle K={\frac {[{\mbox{NH}}_{3}({\mbox{g}})]^{2}}{[{\mbox{N}}_{2}({\mbox{g}})][{\mbox{H}}_{2}({\mbox{g}})]^{3}}}}$