Chemical Equilibria

This lesson covers dynamic equilibrium, the equilibrium constants Kc and Kp, le Chatelier's principle, homogeneous and heterogeneous equilibria, ICE tables, and the industrial importance of equilibrium. Understanding equilibrium is essential for predicting the composition of reaction mixtures and optimising industrial processes.

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Dynamic Equilibrium

Key Definition: A dynamic equilibrium is established in a closed system when the rate of the forward reaction equals the rate of the reverse reaction, so that the concentrations of reactants and products remain constant.

At equilibrium:

• The concentrations of reactants and products remain constant (but not necessarily equal).
• Both the forward and reverse reactions continue to occur — the equilibrium is dynamic, not static.
• There is no change in macroscopic properties (colour, pressure, concentration) even though molecules are constantly reacting.

Dynamic equilibrium can only be established in a closed system — one where no substances can enter or leave.

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The Equilibrium Constant Kc

For the general equilibrium: aA + bB ⇌ cC + dD

The equilibrium constant in terms of concentration is:

Kc = [C]ᶜ[D]ᵈ / [A]ᵃ[B]ᵇ

Key Definition: Kc is the equilibrium constant expressed in terms of the equilibrium concentrations of the reactants and products, each raised to the power of their stoichiometric coefficients.

Key points about Kc:

• It has a fixed value at a given temperature.
• A large Kc (>> 1) means the equilibrium lies to the right (products are favoured).
• A small Kc (<< 1) means the equilibrium lies to the left (reactants are favoured).
• Only temperature changes the value of Kc. Changing concentration, pressure, or adding a catalyst does not change Kc.
• Units of Kc depend on the stoichiometry and must be worked out for each equilibrium.

Worked Example: Calculating Kc Using an ICE Table

For the equilibrium: H₂(g) + I₂(g) ⇌ 2HI(g)

0.50 mol of H₂ and 0.50 mol of I₂ are placed in a 1.0 dm³ container at 700 K. At equilibrium, 0.40 mol of HI is present. Calculate Kc.

Solution:

Set up an ICE (Initial, Change, Equilibrium) table:

	H₂	I₂	2HI
Initial moles	0.50	0.50	0
Change	−0.20	−0.20	+0.40
Equilibrium moles	0.30	0.30	0.40

(Since 0.40 mol of HI forms, and the ratio is 1:1:2, we need 0.20 mol each of H₂ and I₂ to react.)

Convert to concentrations (volume = 1.0 dm³, so moles = concentration):

[H₂] = 0.30 mol dm⁻³, [I₂] = 0.30 mol dm⁻³, [HI] = 0.40 mol dm⁻³

Kc = [HI]² / ([H₂][I₂])

Kc = (0.40)² / (0.30 × 0.30)

Kc = 0.16 / 0.09

Kc = 1.78 (no units — the powers of mol dm⁻³ cancel in this case because there are equal numbers of moles on each side)

Exam Tip: Always set up an ICE table systematically. Define x if you need to, and remember the stoichiometric ratios. Check your units of Kc by substituting (mol dm⁻³) raised to each power and cancelling.

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The Equilibrium Constant Kp

For gaseous equilibria, Kp is expressed in terms of partial pressures.

Key Definition: The mole fraction of a gas is the number of moles of that gas divided by the total number of moles of gas: xₐ = nₐ / n(total). The partial pressure of a gas is its mole fraction multiplied by the total pressure: pₐ = xₐ × P(total).

For the equilibrium aA(g) + bB(g) ⇌ cC(g) + dD(g):

Kp = pCᶜ × pDᵈ / (pAᵃ × pBᵇ)

Like Kc, the value of Kp is only affected by temperature.

Worked Example: Calculating Kp

For the equilibrium: N₂O₄(g) ⇌ 2NO₂(g)

At equilibrium at 400 K and a total pressure of 100 kPa, the mixture contains 0.40 mol of N₂O₄ and 0.80 mol of NO₂. Calculate Kp.

Solution:

Step 1: Calculate total moles.

Total moles = 0.40 + 0.80 = 1.20 mol

Step 2: Calculate mole fractions.

x(N₂O₄) = 0.40 / 1.20 = 1/3

x(NO₂) = 0.80 / 1.20 = 2/3

Step 3: Calculate partial pressures.

p(N₂O₄) = (1/3) × 100 = 33.3 kPa

p(NO₂) = (2/3) × 100 = 66.7 kPa

Step 4: Calculate Kp.

Kp = p(NO₂)² / p(N₂O₄)

Kp = (66.7)² / 33.3

Kp = 4448.9 / 33.3

Kp = 133.6 kPa

(Units: kPa² / kPa = kPa, since there are 2 moles of gas on the right and 1 on the left, giving an excess of 1 power of pressure.)

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Homogeneous vs Heterogeneous Equilibria

Key Definition: A homogeneous equilibrium is one in which all reactants and products are in the same phase. A heterogeneous equilibrium is one in which reactants and products are in different phases.

In heterogeneous equilibria, pure solids and pure liquids are not included in the expression for Kc or Kp because their concentrations (or activities) are constant and are incorporated into the value of K.

For example, for the equilibrium:

CaCO₃(s) ⇌ CaO(s) + CO₂(g)

Kp = p(CO₂) only — the solids are omitted.