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.

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 K_c 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