How to Calculate Equilibrium Constant

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Given a balanced reaction aA+bB ⇋ cC+dD, the equilibrium constant Kc, sometimes written Keq 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 H2, and 0.100 M H2O is allowed to reach equilibrium. At equilibrium, the concentration of NO is found to be 0.080 M.

The value of the equilibrium constant Kc for the reaction

2 NO + 2 H2 ⇋ N2+2 H2O

is [N2][H2O]2 ÷ [NO]2[H2]2

Create an ICE chart:

NO H2 N2 H2O

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 H2, N2, and H2O 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 102

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.

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