Chemical equilibrium and Le Chatelier

What you'll learn

Many chemical reactions do not go to completion. Instead, they reach a state of dynamic equilibrium, where the forward and reverse reactions continue at equal rates and the concentrations of reactants and products stay constant. Understanding equilibrium lets chemists control the yield of industrial processes — such as the production of ammonia and methanol at Point Lisas in Trinidad — by choosing the right temperature, pressure and catalyst. This guide covers the features of dynamic equilibrium, Le Chatelier's principle, the equilibrium constants K_c and K_p, calculations of equilibrium concentrations and partial pressures, the effect of changing conditions on the position of equilibrium and on the value of K, and the compromise conditions used in industry.

CAPE equilibrium questions mix qualitative explanations (predicting shifts) with quantitative work (writing expressions, calculating K and its units). Learn to separate clearly what changes the position of equilibrium from what changes the value of K.

Key terms and definitions

Reversible reaction — A reaction that can proceed in both the forward and reverse directions.

Dynamic equilibrium — A state in a closed system where the rates of the forward and reverse reactions are equal and the concentrations of reactants and products remain constant.

Closed system — A system in which no substances enter or leave.

Position of equilibrium — The relative proportions of reactants and products at equilibrium.

Le Chatelier's principle — If a system at equilibrium is subjected to a change, the position of equilibrium shifts to oppose that change.

Equilibrium constant, K_c — The ratio of product concentrations to reactant concentrations at equilibrium, each raised to the power of its stoichiometric coefficient.

Partial pressure — The pressure a gas in a mixture would exert if it alone occupied the container.

Mole fraction — The amount of one gas divided by the total amount of gas.

K_p — The equilibrium constant expressed in terms of partial pressures of gases.

Homogeneous equilibrium — All species are in the same phase.

Heterogeneous equilibrium — Species are in different phases.

Core concepts

Features of dynamic equilibrium

At equilibrium:

• the forward and reverse rates are equal;
• concentrations are constant (but not necessarily equal);
• the system must be closed;
• equilibrium can be reached from either direction — starting with reactants or with products;
• reactions continue at the molecular level — it is dynamic, not static.

Evidence that equilibrium is dynamic comes from isotope labelling: adding radioactive iodine to an equilibrium mixture of iodine in two solvents leads to radioactivity in both layers, showing particles continue to move in both directions.

Le Chatelier's principle

Concentration: increasing the concentration of a reactant shifts the equilibrium to the right, using up the added reactant and producing more product. Removing a product also shifts it right.

Pressure (gases): increasing pressure shifts the equilibrium towards the side with fewer moles of gas, reducing the pressure. If both sides have equal moles of gas, pressure has no effect on position.

Temperature: increasing temperature shifts the equilibrium in the endothermic direction, absorbing the added heat. Decreasing temperature favours the exothermic direction.

Catalyst: speeds up the forward and reverse reactions equally, so equilibrium is reached faster but its position does not change.

The equilibrium constant K_c

For aA + bB ⇌ cC + dD:

K_c = [C]ᶜ[D]ᵈ ÷ ([A]ᵃ[B]ᵇ)

Square brackets mean equilibrium concentrations in mol dm⁻³. Units depend on the expression: cancel units from top and bottom.

The magnitude of K_c indicates position: a large K_c (much greater than 1) means products predominate; a small K_c means reactants predominate.

In heterogeneous equilibria, pure solids and pure liquids are omitted from the expression, because their concentrations are effectively constant.

K_p

For gaseous equilibria, partial pressures are used:

partial pressure of A, p_A = mole fraction of A × total pressure

For N₂(g) + 3H₂(g) ⇌ 2NH₃(g):

K_p = p(NH₃)² ÷ (p(N₂) × p(H₂)³), with units of atm⁻² or Pa⁻² (depending on the pressure unit used).

What changes K?

Only temperature changes the value of K. Changing concentration or pressure shifts the position of equilibrium, but the system readjusts so that K stays the same. Catalysts do not change K.

• For an exothermic forward reaction, increasing temperature decreases K (less product at equilibrium).
• For an endothermic forward reaction, increasing temperature increases K.

Calculating equilibrium concentrations

Use an ICE table: Initial, Change, Equilibrium.

1. Write initial amounts.
2. Use the stoichiometry to write changes in terms of x (or use given data).
3. Write equilibrium amounts.
4. Convert to concentrations by dividing by volume.
5. Substitute into the K_c expression.

Industrial equilibria and compromise conditions

The Haber process (ammonia), N₂ + 3H₂ ⇌ 2NH₃, ΔH = −92 kJ mol⁻¹:

• Low temperature would favour ammonia (exothermic forward reaction), but the rate would be too slow; a compromise of about 400–450 °C is used.
• High pressure favours ammonia (4 moles of gas → 2 moles), but very high pressures are expensive and dangerous; around 200 atm is typical.
• An iron catalyst increases the rate.
• Ammonia is removed by liquefaction, and unreacted gases are recycled.

Trinidad and Tobago is one of the world's major exporters of ammonia, produced from natural gas at Point Lisas, so these principles have direct economic importance in the Caribbean.

The Contact process (sulfuric acid), 2SO₂ + O₂ ⇌ 2SO₃, ΔH negative: a compromise temperature of about 450 °C, pressure slightly above atmospheric (the equilibrium already lies well to the right), and a vanadium(V) oxide catalyst.

Worked examples

Example 1: Predicting shifts

For 2SO₂(g) + O₂(g) ⇌ 2SO₃(g), ΔH = −197 kJ mol⁻¹, predict the effect of (a) increasing pressure, (b) increasing temperature.

(a) The right-hand side has fewer moles of gas (2 vs 3), so equilibrium shifts right, increasing the yield of SO₃. (b) The forward reaction is exothermic, so increasing temperature shifts equilibrium left and decreases K.

Example 2: Calculating K_c

For H₂(g) + I₂(g) ⇌ 2HI(g), equilibrium concentrations are [H₂] = 0.10, [I₂] = 0.10 and [HI] = 0.70 mol dm⁻³. Calculate K_c.

K_c = [HI]² ÷ ([H₂][I₂]) = 0.70² ÷ (0.10 × 0.10) = 0.49 ÷ 0.010 = 49 (no units, because they cancel).

Example 3: ICE table

1.00 mol of PCl₅ is placed in a 1.00 dm³ flask. At equilibrium, 0.40 mol of PCl₃ is present. PCl₅ ⇌ PCl₃ + Cl₂. Calculate K_c.

K_c = (0.40 × 0.40) ÷ 0.60 = 0.267 mol dm⁻³.

Example 4: K_p

At equilibrium in the Haber process, the partial pressures are p(N₂) = 50 atm, p(H₂) = 150 atm and p(NH₃) = 20 atm. Calculate K_p.

K_p = 20² ÷ (50 × 150³) = 400 ÷ (50 × 3 375 000) = 400 ÷ 168 750 000 = 2.37 × 10⁻⁶ atm⁻².

Example 5: K_p from mole fractions

A mixture at equilibrium in the Haber process contains 0.20 mol N₂, 0.60 mol H₂ and 0.20 mol NH₃ at a total pressure of 10 atm. Calculate K_p.

Total moles = 1.00, so mole fractions are 0.20, 0.60 and 0.20. Partial pressures: p(N₂) = 0.20 × 10 = 2.0 atm; p(H₂) = 0.60 × 10 = 6.0 atm; p(NH₃) = 0.20 × 10 = 2.0 atm. K_p = 2.0² ÷ (2.0 × 6.0³) = 4.0 ÷ (2.0 × 216) = 9.26 × 10⁻³ atm⁻².

Example 6: Esterification equilibrium

1.00 mol of ethanoic acid and 1.00 mol of ethanol are mixed and allowed to reach equilibrium. 0.667 mol of ethyl ethanoate is formed. Calculate K_c.

CH₃COOH + C₂H₅OH ⇌ CH₃COOC₂H₅ + H₂O

Because there are equal numbers of moles on each side, the volume cancels: K_c = (0.667 × 0.667) ÷ (0.333 × 0.333) = 4.0 (no units).

This classic result also shows why using an excess of one reactant (often the cheaper alcohol) increases the yield of ester: the equilibrium shifts to the right to keep K_c constant.

Example 7: Temperature and K

For the reaction 2NO₂(g) ⇌ N₂O₄(g), ΔH = −58 kJ mol⁻¹. Predict how the colour of the mixture and the value of K_c change when it is heated.

NO₂ is brown and N₂O₄ is colourless. The forward reaction is exothermic, so heating shifts the equilibrium to the left, producing more brown NO₂ — the mixture becomes darker. Because the position has shifted towards the reactants, K_c decreases.

Summary: what changes what?

Learning this table thoroughly prevents the most common equilibrium errors.

Common mistakes and how to avoid them

• Saying concentrations are equal at equilibrium — they are constant, not equal.
• Saying a catalyst shifts equilibrium — it does not.
• Thinking pressure or concentration changes K — only temperature does.
• Including solids or liquids in K expressions for heterogeneous equilibria.
• Using initial instead of equilibrium amounts in K calculations.
• Forgetting units, or giving units when they cancel.

Self-test questions

1. 1.00 mol of H₂ and 1.00 mol of I₂ are heated in a 1.00 dm³ flask until equilibrium is reached; 1.56 mol of HI is present. Calculate K_c. Answer: 0.78 mol of each reactant has reacted, leaving 0.22 mol H₂ and 0.22 mol I₂. K_c = 1.56² ÷ (0.22 × 0.22) = 50 (no units).
2. State the effect of adding a catalyst on (a) the position of equilibrium, (b) K_c, (c) the time taken to reach equilibrium. Answer: (a) no change; (b) no change; (c) shorter time, because forward and reverse rates both increase.
3. For CaCO₃(s) ⇌ CaO(s) + CO₂(g), write the K_p expression. Answer: K_p = p(CO₂) — the solids are omitted.
4. Why is the yield of ammonia in the Haber process not increased by using a lower temperature in practice? Answer: Although a lower temperature increases the equilibrium yield, the rate would be too slow to be economic, even with a catalyst.

How this links to your Internal Assessment

Equilibrium can be investigated practically by observing colour changes: the cobalt(II) chloride equilibrium between pink [Co(H₂O)₆]²⁺ and blue [CoCl₄]²⁻ responds visibly to added chloride ions and to temperature, and the iron(III) thiocyanate equilibrium changes colour as concentrations change. An SBA might also determine K_c for an esterification reaction by titrating the acid remaining at equilibrium. Record observations precisely, explain them using Le Chatelier's principle, and evaluate any limitations, such as difficulty judging colour.

Exam technique for Chemical equilibrium and Le Chatelier's principle

• For shift questions, state the direction, the reason (oppose the change) and the effect on yield.
• Distinguish position from value of K.
• Show ICE tables clearly and convert to concentrations before substituting.
• Work out units of K step by step.
• In industrial questions, explain the compromise between rate, yield and cost.

Quick revision summary

• Dynamic equilibrium: closed system, equal forward and reverse rates, constant concentrations.
• Le Chatelier: concentration, pressure and temperature changes shift the position to oppose the change; catalysts do not.
• K_c = [products]^coefficients ÷ [reactants]^coefficients; omit solids and liquids.
• K_p uses partial pressures = mole fraction × total pressure.
• Only temperature changes K; for exothermic reactions, higher temperature lowers K.
• Haber process: ~400–450 °C, ~200 atm, iron catalyst — a compromise of rate, yield and cost.