The equilibrium law and equilibrium constant

The equilibrium law states that for a chemical system at equilibrium, the ratio of the equilibrium concentrations of products and reactants, each raised to the power of their stoichiometric coefficient, is a constant (K). This constant is called the equilibrium constant. Its value depends on temperature but is independent of the initial concentrations of reactants and products.

For the general chemical equilibrium:

aA + bB ⇌ dD + eE

The equilibrium constant expression is:

$\text{K }=\frac{[D]^d[E]^e}{[A]^a[B]^b}$

Where the lower case letters represent the coefficients in the balanced chemical equation and square brackets denote equilibrium concentrations in mol dm^-3.

K values are unitless when equilibrium concentrations are expressed in consistent units.

For example, for the reaction:

H_2(g)_ + I_2(g)_ ⇌ 2HI_(g)_

The equilibrium constant expression would be:

$\text{K }=\frac{\text{[HI]}^2}{\text{[H}_2\text{][I}_2\text{]}}$

Writing equilibrium constant expressions

When writing equilibrium constant expressions, keep the following points in mind:

• Include only concentrations of species whose amounts change significantly during the reaction.
• Omit concentrations of pure liquids and solids as they remain essentially constant throughout the reaction.
• For reactions in aqueous solution, omit the concentration of water as it does not change significantly in aqueous solutions.

For instance, the K expression for the formation of an ester in aqueous solution is:

HCOOH_(aq) + CH₃OH_(aq) ⇌ HCOOCH_3(aq) + H₂O_(l) $K = \frac{\text{[HCOOCH}_3\text{]}}{\text{[HCOOH][CH}_3\text{OH]}}$

However, if the reaction occurs in a non-aqueous solvent, include the water concentration as it would be treated like any other reactant.

Calculating K from equilibrium concentrations

If the equilibrium concentrations of reactants and products are known, the value of K can be calculated by substituting these values into the equilibrium constant expression.

Worked example 1 - Calculating K from equilibrium concentrations

Calculate the value of K for the reaction H_2(g)_ + I_2(g)_ ⇌ 2HI_(g)_ at 580 K using the equilibrium concentrations given in the table below. Give your answer to 2 significant figures.

Step 1: Write the equilibrium constant (K) expression

$K=\frac{[HI]^2}{[H_2][I_2]}$

Step 2: Substitution and correct evaluation

$K = \frac{(0.60)^2} {0.20\times0.20}=9.0$

Interpreting K values

The magnitude of K indicates the relative amounts of reactants and products present at equilibrium, thus revealing which direction of the reaction is favoured under the given conditions:

Reactions with very large or very small K values are essentially irreversible:

• If K >> 1 - The forward reaction is heavily favoured, resulting in predominantly products at equilibrium.
• If K << 1 - The reverse reaction is heavily favoured, resulting in predominantly reactants at equilibrium.

Changing reaction stoichiometry and K

Changing the stoichiometric coefficients in a balanced chemical equation affects the value of the equilibrium constant:

K represents the equilibrium constant for the original reaction, while K' represents the equilibrium constant for the modified reaction.

Worked example 2 - Calculating K after changing stoichiometry

For the reaction 2NO_2(g)_ ⇌ N_2_O_4(g)_, K = 0.36 at 298 K.

Calculate the value of the equilibrium constant (K') for the reaction 1⁄2N_2_O_4(g)_ ⇌ NO_2(g)_ at the same temperature. Give your answer to 2 significant figures.

Step 1: Identify changes to original equation

The equation has been reversed and all stoichiometric coefficients halved.

Step 2: Equation

$K'=\frac{1}{\sqrt{K}}$

Step 3: Substitution and correct evaluation

$K'=\frac{1}{\sqrt{0.36}}=1.7$