Deducing Kc Expressions

Equilibrium expression & constant

The equilibrium constant expression is an expression that links the equilibrium constant, K, to the concentrations of reactants and products at equilibrium taking the stoichiometry of the equation into account
So, for a given reaction:

aA + bB ⇌ cC + dD

The corresponding equilibrium constant expression is written as:

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

- Where:
  - [A] and [B] = equilibrium reactant concentrations (mol dm^-3)
  - [C] and [D] = equilibrium product concentrations (mol dm^-3)
  - a, b, c and d = number of moles of corresponding reactants and products

The K_c of a reaction is specific and only changes if the temperature of the reaction changes

Homogeneous systems and K_c

A homogeneous system is where all of the reactants and products are in the same physical state, e.g.

CH₃COOH (l) + C₂H₅OH (l) ⇌ CH₃COOC₂H₅ (l) + H₂O (l)

For this reaction, all of the reactants and products are in the same, liquid state / phase and will, therefore, all feature in the K_c expression
- K_c = $\frac{[{CH}_{3} {COOC}_{2} H_{5}] [H_{2} O]}{[{CH}_{3} COOH] [C_{2} H_{5} OH]}$

Heterogeneous systems and K_c

A heterogeneous system is where not all of the reactants and products are in the same physical state, e.g.

CaCO₃ (s) ⇌ CaO (s) + CO₂ (g)

Solids are ignored in equilibrium expressions
- This leads to a K_c expression of K_c = [CO₂]

Examiner Tip

For K_c expressions, it is important that you use square brackets as sometimes examiners are instructed to be strict about the appearance of brackets in expressions

Square brackets implies concentration

Worked example

Deducing equilibrium expressions

Deduce the equilibrium constant expression for the following reactions

Ag⁺ (aq) + Fe²⁺ (aq) ⇌ Ag (s) + Fe³⁺ (aq)
N₂ (g) + 3H₂ (g) ⇌ 2NH₃ (g)
2SO₂ (g) + O₂ (g) ⇌ 2SO₃ (g)

Answer 1:

$K = \frac{[{Fe}^{3 +} (aq)]}{[{Fe}^{2 +} (aq)] [{Ag}^{+} (aq)]}$

[Ag (s)] is not included in the equilibrium constant expression as it is a solid

Answer 2:

$K = \frac{[{NH}_{3} (g)]}{[N_{2} (g)] {[H_{2} (g)]}^{3}}$

Answer 3:

$K = \frac{{[{SO}_{3} (g)]}^{2}}{{[{SO}_{2} (g)]}^{2} [O_{2} (g)]}$

Examiner Tip

The value of K_c indicates the position of equilibrium:

K_c = 1 - the position of equilibrium is halfway between the reactants and products

K_c < 1 - the position of equilibrium lies towards the left-hand side, i.e. the reactants

K_c > 1 - the position of equilibrium lies towards the right-hand side, i.e. the products

Deducing Kc Expressions (Edexcel AS Chemistry)

Revision Note