# How To Calculate Equilibrium Constant

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

### Cite This Article

#### MLA

Beck, Kevin. "How To Calculate Equilibrium Constant" *sciencing.com*, https://www.sciencing.com/how-to-calculate-equilibrium-constant-13710478/. 23 March 2018.

#### APA

Beck, Kevin. (2018, March 23). How To Calculate Equilibrium Constant. *sciencing.com*. Retrieved from https://www.sciencing.com/how-to-calculate-equilibrium-constant-13710478/

#### Chicago

Beck, Kevin. How To Calculate Equilibrium Constant last modified March 24, 2022. https://www.sciencing.com/how-to-calculate-equilibrium-constant-13710478/