A concentration equilibrium constant (K_c ) is a ratio of equilibrium concentrations of products and reactants that is constant for a given reaction at a given temperature. For example, consider this generic reaction:

For this reaction, the concentration equilibrium constant, K_c, is:

This mathematical expression is called the equilibrium constant expression. Square brackets represent concentration in M (mol/L), so “[A]” represents the equilibrium concentration of reactant A. Each concentration is raised to the power of its coefficient. Sometimes, a subscript “e” (as in [A]_e) can be used to explicitly indicate that the concentration correspond to concentration at equilibrium.

In general, K_c expressions include only substances whose concentrations change as a reaction proceeds. In other words, K_c expressions do not contain terms for pure solids or pure liquids. For example, consider the equilibrium constant expression for the following reaction:

Because HgO is a solid, the number of HgO per unit volume depends only on the density of HgO at the temperature of the reaction. In other words, HgO(s) concentration is the same throughout the reaction, and does not change when HgO are consumed or produced. Similarly, the number of Hg atoms per unit volume of Hg(ℓ) is constant throughout the reaction. Thus, these concentrations are not included in the K_c expression. It is necessary for some HgO(s) and some Hg(ℓ) to be present for the equilibrium to be maintained, but the total quantity of each does not affect the equilibrium.

In addition, for dilute solutions, the concentration of the solvent remains constant throughout the reaction and is also not included in the K_c expression, even though the solvent sometimes appear in the reaction equation.

A homogeneous equilibrium is one in which all of the reactants and products are present in a single phase. Examples of homogeneous equilibria are reactions in the gas phase and reactions in liquid solutions. For example:

C₂H₂(g) + 2 Br₂(g) ⇌ C₂H₂Br₄(g)         

I₂(aq) + I⁻(aq) ⇌ I₃⁻(aq)        

Hg₂²⁺(aq) + NO₃⁻(aq) + 3 H₃O⁺(aq) ⇌ 2 Hg²⁺(aq) + HNO₂(aq) + 4H₂O(ℓ)     

HF(aq) + H₂O(ℓ) ⇌ H₃O⁺(aq) + F⁻(aq)         

NH₃(aq) + H₂O(ℓ) ⇌ NH₄⁺(aq) + OH⁻(aq)         

In the aqueous equilibrium systems, H₂O(l) is the solvent. Its concentration does not appear in the K_c expression.

A heterogeneous equilibrium is a system in which reactants and products are found in two or more phases. Some heterogeneous equilibria involve chemical changes, for example:

CaO(s) + CO₂(g) ⇌ CaCO₃(s)         

C(s) + 2S(g) ⇌ CS₂(g)         

Other heterogeneous equilibria involve phase changes, for example:

Working with K_c

There are a few things to keep in mind when working with equilibrium constant expressions.

When all the coefficients in a balanced chemical equation are multiplied by some factor n, then the new K_c is the original K_c raised to the n^th power. For example:

2 NO₂(g) ⇌ N₂O₄(g)         

NO₂(g) ⇌ ½ N₂O₄(g)         

When a reaction’s direction is reversed, the K_c for the new reaction is the reciprocal (inverse) of the original reaction K_c. For example:

A + 2B ⇌ AB₂         

AB₂ ⇌ A + 2B         

When two reactions occur sequentially to yield a new overall reaction, the K_c for the overall reaction is the product of the K_c values for the individual steps. For example:

A + C ⇌ AC         

AC + C ⇌ AC₂          

A + 2 C ⇌ AC₂