The equilibrium constant Kc

For a general reaction aA + bB ⇌ cC + dD at equilibrium, the law of chemical equilibrium says:

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Square brackets mean molar concentration at equilibrium. Products go on top, reactants below, and each concentration is raised to the power of its coefficient in the balanced equation. For N₂(g) + 3H₂(g) ⇌ 2NH₃(g): Kc = [NH₃]² / [N₂][H₂]³.

Kc has one value at a given temperature, whatever amounts you start with. Different starting mixtures reach different equilibrium concentrations, but they always give the same Kc.

Kc depends on how the equation is written:

• Reversing the equation gives 1/Kc.
• Multiplying the equation by n gives Kcⁿ.
• Dividing it by n gives the nth root of Kc.

So if Kc for P ⇌ Q is 5, then for Q ⇌ P it is 1/5 = 0.2, and for 2P ⇌ 2Q it is 5² = 25.

That is why a value of K must always be quoted together with its balanced equation.

The units of Kc depend on ∆n, the change in the number of moles: (mol L⁻¹)^∆n. If ∆n = 0, Kc has no units. When concentrations are expressed relative to a standard state (1 mol L⁻¹), K becomes dimensionless.