Exploring the Equilibrium Constant $K$
Definition
Equilibrium constant
The equilibrium constant $K$ is a ratio that provides a snapshot of the relative concentrations of products and reactants at equilibrium for a reversible chemical reaction.
- It is derived from the stoichiometry of the reaction and remains constant as long as the temperature is unchanged.
- Consider the general reaction: $$
aA + bB \rightleftharpoons cC + dD
$$ - At equilibrium, the concentrations of $ A $, $ B $, $ C $, and $ D $ remain constant.
- The equilibrium constant $ K $ is expressed as: $$
K = \frac{[C]^c[D]^d}{[A]^a[B]^b}
$$ where:- $[X]$ represents the equilibrium concentration of species $ X $ in $ \text{mol dm}^{-3} $.
- $ a, b, c, d $ are the stoichiometric coefficients from the balanced chemical equation.
- Before writing the $ K $ expression, ensure the chemical equation is balanced.
- The stoichiometric coefficients directly determine the exponents in the $ K $ expression.
Deriving the Expression for $ K $: Step-by-Step
- Let’s illustrate this with an example: the synthesis of ammonia. $$
N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)
$$ - Identify the Reactants and Products:
- Reactants: $ N_2 $ and $ H_2 $
- Product: $ NH_3 $
- Write the General Form of $ K $:
- According to the equilibrium law, the concentrations of the products are placed in the numerator, while the concentrations of the reactants are placed in the denominator.
- Each species is raised to the power of its stoichiometric coefficient: $$
K = \frac{[NH_3]^2}{[N_2][H_2]^3}
$$
- Interpret the Expression:
- If $ K $ is large ($ K > 1 $), the numerator dominates, indicating that the equilibrium mixture contains more products than reactants.
- If $ K $ is small ($ K < 1 $), the denominator dominates, meaning the equilibrium mixture contains more reactants than products.
Example question
Write the $ K $ expression for the reaction:$$
2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)
$$
Solution
The equilibrium constant expression is:$$
K = \frac{[SO_3]^2}{[SO_2]^2[O_2]}
$$
Properties of the Equilibrium Constant
- Temperature Dependence:
