Introducing the equilibrium constant

When a reversible reaction reaches a state of dynamic equilibrium, we can calculate a value called the equilibrium constant (K_c_) using the molar concentrations of the reactants and products at equilibrium.

K_c_ gives us a quantitative measure of where the equilibrium lies - whether there are more products or more reactants present at equilibrium.

• A large K_c_ value indicates the equilibrium position favours the products.
• A small K_c_ value indicates the equilibrium position favours the reactants.

A K_c_ value of 1 indicates that the reaction is at equilibrium, and the concentrations of reactants and products are equal when raised to their respective stoichiometric coefficients.

Writing an expression for K_c_

For the general equilibrium reaction:

aA + bB ⇌ dD + eE

The equilibrium constant K_c_ is given by:

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

Where the lower case letters represent the coefficients in the balanced chemical equation.

For example, for the reaction:

H_2(g)_ + I_2(g)_ ⇌ 2HI_(g)_

The K_c_ expression would be:

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

Calculating values for K_c_

If we know the equilibrium concentrations of all reactants and products, we can substitute them into the K_c expression to calculate a value for K_c_.

Worked example 1 - Determining the equilibrium constant (K_c_)

For the reaction H_2(g)_ + I_2(g)_ ⇌ 2HI_(g)_ at 580 K, the equilibrium concentrations are:

[HI] = 0.60 mol dm^−3^

[H_2_] = 0.20 mol dm^−3^

[I_2_] = 0.20 mol dm^−3^

Determine the equilibrium constant (K_c_).

Step 1: Write the equilibrium constant (K_c_) expression

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

Step 2: Substitution and correct evaluation

$K_c=\frac{{(0.60)}^2}{0.20\times 0.20}=9$