Given a balanced reaction aA+bB ⇋ cC+dD, the equilibrium constant Kc, sometimes written K_{eq} or just K, is defined as

[C]^{c}[D]^{d} ÷ [A]^{a}[B]^{b},

where [C] and [D] are the equilibrium molar concentrations of the products and [A] and [B] are the equilibrium molar concentrations of the reactants, with concentrations in moles per liter (mol/L). K itself has no units.

Large values of K, such as 1,000 or greater, mean that a reaction has gone nearly to completion at equilibrium and little of the reactants remains. Conversely, a small value of K, 0.001, implies that the reaction has not proceeded to a significant extent. Importantly, K is temperature-dependent.

## Example of an Equilibrium Constant Calculation

A mixture of 0.200 M NO, 0.050 M H_{2}, and 0.100 M H_{2}O is allowed to reach equilibrium. At equilibrium, the concentration of NO is found to be 0.080 M.

The value of the equilibrium constant K_{c} for the reaction

2 NO + 2 H_{2} ⇋ N_{2}+2 H_{2}O

is [N_{2}][H_{2}O]^{2} ÷ [NO]^{2}[H_{2}]^{2}

Create an ICE chart:

NO H_{2} N_{2} H_{2}O

Initial 0.100 0.050 0 0.100

Change -2x -2x +x +2x

Equilibrium 0.070 ? ? ?

First, solve for x:

0.100 - 2x = 0.070, so x = 0.015. This means the equilibrium concentrations of H_{2}, N_{2}, and H_{2}O are 0.020, 0.015 and 0.130 respectively (read down the columns).

Substitute these into the equation for K:

[0.015][0.130]^{2}÷ [0.070]^{2}[0.020]^{2} = 0.0002535 ÷ 0.00000196 = 129.3 or 1.29 x 10^{2}

References

About the Author

Kevin Beck holds a bachelor's degree in physics with minors in math and chemistry from the University of Vermont. Formerly with ScienceBlogs.com and the editor of "Run Strong," he has written for Runner's World, Men's Fitness, Competitor, and a variety of other publications. More about Kevin and links to his professional work can be found at www.kemibe.com.