Concentration and pressure equilibrium constants

What you’ll learn

• Write Kc and Kp expressions for homogeneous and heterogeneous equilibria.
• Calculate equilibrium constants from composition.
• Separate equilibrium shifts from changes in the constant.

Understand the idea

An equilibrium constant uses equilibrium concentrations or partial pressures, raised to the powers in the balanced equation. Pure solids and pure liquids are omitted from the expression. For gas mixtures, a component's partial pressure is its mole fraction multiplied by total pressure. Use the pressure unit requested; this specification uses atmospheres for $K_p$ calculations.

At a fixed temperature, changing concentration or pressure changes the equilibrium position but does not change the constant. Only temperature changes the constant for a given equation. A catalyst speeds both directions and reaches the same equilibrium sooner. Large constants favour products, but the numerical constant must always be interpreted with its stated balanced equation and units.

Key formulae

$$K_c=\frac{[\mathrm C]^c[\mathrm D]^d}{[\mathrm A]^a[\mathrm B]^b}$$

$$p_i=\frac{n_i}{n_{\mathrm{total}}}p_{\mathrm{total}}$$

$$K_p=\frac{p_{\mathrm C}^cp_{\mathrm D}^d}{p_{\mathrm A}^ap_{\mathrm B}^b}$$

$$K_{\mathrm{reverse}}=\frac1{K_{\mathrm{forward}}}$$

Worked example

For $\mathrm{H_2(g)+I_2(g)\rightleftharpoons2HI(g)}$, the equilibrium concentrations are $0.20$, $0.10$ and $0.80\,\mathrm{mol\,dm^{-3}}$ respectively. Find $K_c$.

1. The expression is $K_c=[\mathrm{HI}]^2/([\mathrm{H_2}][\mathrm{I_2}])$.
2. Insert equilibrium values: $0.80^2/(0.20\times0.10)$.
3. The concentration powers cancel, and the numerical value is $32$.

Answer: $K_c=32$, with no units in this concentration convention.