The Equilibrium Constant Kc

This lesson covers the equilibrium constant Kc, writing Kc expressions, ICE tables, calculating Kc, its units, and the effect of changing conditions on Kc.

The Equilibrium Constant Kc

For a general reaction: aA + bB ⇌ cC + dD

The equilibrium constant in terms of concentrations is:

Kc = [C]^c [D]^d / ([A]^a [B]^b)

where [X] represents the equilibrium concentration of species X in mol dm⁻³.

Only species in aqueous solution or gaseous phase are included.
Pure solids and pure liquids are omitted (their concentrations are constant).
Kc is only valid at a specified temperature.

Writing Kc Expressions

Example 1: N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Kc = [NH₃]² / ([N₂][H₂]³)

Example 2: CH₃COOH(l) + C₂H₅OH(l) ⇌ CH₃COOC₂H₅(l) + H₂O(l)

Kc = [CH₃COOC₂H₅][H₂O] / ([CH₃COOH][C₂H₅OH])

Note: Although these are liquids, they are in a homogeneous mixture (not pure liquids), so all species are included.

ICE Tables

An ICE table (Initial, Change, Equilibrium) is used to track concentrations through a reaction reaching equilibrium.

Example 3: 1.0 mol of N₂O₄ is placed in a 1.0 dm³ container at 25°C. At equilibrium, 0.20 mol of N₂O₄ has dissociated. Calculate Kc for: N₂O₄(g) ⇌ 2NO₂(g)

	N₂O₄	NO₂
Initial (mol)	1.0	0
Change (mol)	−0.20	+0.40
Equilibrium (mol)	0.80	0.40

Since volume = 1.0 dm³: [N₂O₄] = 0.80 mol dm⁻³, [NO₂] = 0.40 mol dm⁻³

Kc = [NO₂]² / [N₂O₄] = (0.40)² / 0.80 = 0.16 / 0.80 = 0.20 mol dm⁻³

Units of Kc

The units of Kc depend on the balanced equation. Substitute the units (mol dm⁻³) for each concentration term.

For Kc = [NO₂]² / [N₂O₄]:

Units = (mol dm⁻³)² / (mol dm⁻³) = mol dm⁻³

For Kc = [NH₃]² / ([N₂][H₂]³):

Units = (mol dm⁻³)² / ((mol dm⁻³)(mol dm⁻³)³) = (mol dm⁻³)² / (mol dm⁻³)⁴ = mol⁻² dm⁶

Exam Tip: Always work out the units of Kc. If the total powers of concentration on top and bottom are equal, Kc has no units.

The Equilibrium Constant Kc

The Equilibrium Constant Kc