Part 2: Equilibrium amounts and Kp calculations

Use a mole table before calculating pressure, then solve for Kp, total pressure or the extent of reaction.

Keep initial and equilibrium amounts separate

Start with a balanced equation and an initial–change–equilibrium table. Use one reaction extent so all changes follow the coefficients. Add the equilibrium amounts to obtain the equilibrium total; it need not equal the initial total. Convert to mole fractions, then partial pressures, then substitute into Kp.

Check that all equilibrium amounts are non-negative and no amount consumed exceeds the starting amount. Carry unrounded fractions through the calculation. Early rounding is especially damaging when partial pressures are cubed.

Worked ammonia mixture

A closed vessel initially contains 1.50 mol N₂ and 4.50 mol H₂ with no NH₃. At equilibrium, 0.300 mol of nitrogen has reacted. Total pressure is 200 kPa.

Rearrange to find total pressure

For N₂O₄(g) ⇌ 2NO₂(g), substitute p = xP to get Kp = x(NO₂)²P/x(N₂O₄). If the equilibrium mole fractions are 0.400 NO₂ and 0.600 N₂O₄ and Kp = 12.0 kPa, then P = 12.0 × 0.600/0.400² = 45.0 kPa.

Check by substitution: p(NO₂) = 18.0 and p(N₂O₄) = 27.0 kPa; 18.0²/27.0 = 12.0 kPa. In ammonia calculations the net power of P is −2, so recovering P requires a square root. Derive the power from the equation instead of memorising one rearrangement.

Solve for dissociation

Begin with 1.00 mol N₂O₄ and no NO₂. Let α be the fraction dissociated. At equilibrium there are (1 − α) mol N₂O₄ and 2α mol NO₂, total (1 + α) mol. Hence Kp = 4α²P/(1 − α²).

At P = 100 kPa and Kp = 25.0 kPa: 25.0(1 − α²) = 400α², giving α² = 25/425 and α = 0.2425. The physical root is positive and below one. Equilibrium amounts are 0.7575 mol N₂O₄ and 0.4851 mol NO₂. The fraction dissociated is 24.3%, but the NO₂ mole fraction is 0.390; those are different quantities.

Catch errors before submitting

Check the pressure sum, the Kp units and the equilibrium amount bounds. If a question supplies an equilibrium mass, convert it with the correct molar mass before finding the reaction extent. If products were present initially, include them in the initial row; do not assume every final product molecule was made during the experiment.

Use the stated ideal-gas assumption. Industrial mixtures at high pressure can deviate from ideal behaviour, but do not introduce unprovided corrections into an A-level calculation.

Quick checks

Original Finesse questions. Reveal the indicative worked solutions after attempting each question; these are not official AQA mark allocations.

Sources