The law of mass action states that

*K*_{c}is defined as the concentrations of products divided by the concentrations of reactants raised to correct powers.*K*_{p}is defined as the partial pressures of products divided by the partial pressures of reactants, raised to respective powers. The chemical coefficients become exponents in the expressions for*K*_{c}and*K*_{p}.
In the late 19th century, Norwegian chemists Cato Guldberg and Peter Waage proposed the **law of mass action**, a chemical law that states that when a reaction reaches equilibrium, the product concentrations multiplied together divided by the reactant concentrations multiplied together, with each term raised to the power of its coefficient in the balanced equation, is a constant.

${a{\rm{A}}+b{\rm{B}}}\rightleftarrows{c{\rm{C}}+d{\rm{D}}}$

*a, b, c,*and

*d*are the coefficients for a balanced chemical equation. For a chemical system at equilibrium and at a certain temperature, the

**equilibrium constant (**is the product concentrations multiplied together divided by the reactant concentrations multiplied together, with each term raised to the power of its coefficient in the balanced equation.

*K*_{c})${K_{\rm{c}}} = \frac{{{{\left[ {\rm{C}} \right]}^c}{{\left[ {\rm{D}} \right]}^d}}}{{{{\left[ {\rm{A}} \right]}^a}{{\left[ {\rm{B}} \right]}^b}}}$

*K*

_{c}, can be dimensionless or can have a unit, depending on whether the solution (mixture of aqueous or gaseous reactants and products) is highly concentrated, and the unit used for

*K*

_{c}depends on the degree of concentration. For calculations in practice,

*K*

_{c}is often treated as dimensionless. Note that the equilibrium constant,

*K*

_{c}, is calculated using concentrations. Solids and pure liquids do not have a concentration and are not used in calculating the equilibrium constant.

*K*

_{c}describes the forward reaction in which A and B are the reactants. In the reverse reaction, C and D are the reactants and A and B are the products. The equilibrium constant for the reverse reaction,

*K*

_{c}', is the reciprocal of

*K*

_{c}.

${K'_{\rm{c}}} = \frac{{{{\left[ {\rm{A}} \right]}^a}{{\left[ {\rm{B}} \right]}^b}}}{{{{\left[ {\rm{C}} \right]}^c}{{\left[ {\rm{D}} \right]}^d}}}=\frac{1}{K_{\rm{c}}}$

**reaction quotient (**, a ratio that can be used to predict how a system not in equilibrium will change to reach equilibrium. The reaction quotient is calculated in the same way as the equilibrium constant, as the product concentrations multiplied together divided by the reactant concentrations multiplied together, with each term raised to the power of its coefficient in the balanced equation. The reaction quotient, however, uses concentrations for the system not at equilibrium. If

*Q*)*Q*is less than

*K*

_{c}, the reaction will continue in the forward direction. If

*Q*is greater than

*K*

_{c}, the reaction will proceed in the reverse direction. Consider the following example. This equilibrium reaction forms the basis of the Haber-Bosch process, used for the synthesis of ammonia.

${{\rm{N}}_2}(g) + 3{{\rm{H}}_2}(g) \rightleftharpoons 2{\rm{N}}{{\rm{H}}_3}(g)$

${K_{\rm{c}}} = \frac{{{{\left[ {{\rm{N}}{{\rm{H}}_3}} \right]}^2}}}{{\left[ {{{\rm{N}}_2}} \right]{{\left[ {{{\rm{H}}_2}} \right]}^3}}}$

$P_{\rm{total}}=P_{\rm{A}}+P_{\rm{B}}$

$a{\rm{A}} + b{\rm{B}} \rightleftarrows c{\rm{C}} + d{\rm{D}}$

${P_{{\rm{total}}}} = {P_{\rm{A}}} + {P_{\rm{B}}} + {P_{\rm{C}}} + {P_{\rm{D}}}$

*K*

_{p}

*,*can be defined based on the partial pressure of each gas.

$K_{\rm{p}}=\frac{({P_{\rm{C}}}^c)({P_{\rm{D}}}^d)}{({P_{\rm{A}}}^a)({P_{\rm{B}}}^b)}$

*K*

_{p}from

*K*

_{c}. The temperature must be a constant, or the value of

*K*

_{p}will change. Also, this relation holds true only at equilibrium. Just as $K^{\prime}_{\rm{c}}=K^{-1}_{\rm{c}}$ for the reverse reaction, the equilibrium constant based on pressure for the reverse reaction is the reciprocal of the equilibrium constant based on pressure for the forward reaction.

$K^\prime_{\rm{p}}=\frac{{({{P_{\rm{A}}}^a})({{P_{\rm{B}}}^b} )}}{{({{P_{\rm{C}}}^c})({{P_{\rm{D}}}^d})}}=\frac{1}{K_{\rm{p}}}$

$\begin{aligned}P_{\rm{A}}&=(\text{mole fraction of }{\rm{A})\text{(total pressure)}}\\&=(\chi_{\rm{A}})(P_{\rm{total}})\end{aligned}$

${K_{\rm{p}}} = \frac{{{{{\rm{(}}{\chi _{\rm{C}}}{P_{{\rm{total}}}}{\rm{)}}}^c}{{{\rm{(}}{\chi _{\rm{D}}}{P_{{\rm{total}}}}{\rm{)}}}^d}}}{{{{{\rm{(}}{\chi _{\rm{A}}}{P_{{\rm{total}}}}{\rm{)}}}^a}{{{\rm{(}}{\chi _{\rm{B}}}{P_{{\rm{total}}}}{\rm{)}}}^b}}}$

*P*terms may or may not cancel, depending on the coefficients of the balanced chemical equation. Once again consider the Haber-Bosch process for the synthesis of ammonia.

${{\rm{N}}_2}(g) + 3{{\rm{H}}_2}(g) \rightleftharpoons 2{\rm{N}}{{\rm{H}}_3}(g)$

${K_{\rm{p}}}=\frac{{{P_{\rm{NH_3}}}^2}}{{P_{\rm{N_2}}}\times{{P_{\rm{H_2}}}^3}}$