A-Level Chemistry May/June 2024 Q2(c)(ii): Equilibrium mixture D is made when 1.0mol of N₂(g) and 3.0mol of H2(g) are added to a s…

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  Step 1: Determine the moles of each substance at equilibrium.

  We can use an ICE table based on the reaction: $N_2(g) + 3H_2(g) \rightleftharpoons 2NH_3(g)$

  Species	Initial Moles (mol)	Change in Moles (mol)	Equilibrium Moles (mol)
  $N_2$	1.0	$-x$	$1.0 - x$
  $H_2$	3.0	$-3x$	$3.0 - 3x$
  $NH_3$	0	$+2x$	$2x$

  We are given that the equilibrium moles of $NH_3$ is 1.16 mol. So, $2x = 1.16 \implies x = 1.16 / 2 = 0.58$

  Now, calculate the equilibrium moles of the reactants:

  • Moles of $N_2 = 1.0 - x = 1.0 - 0.58 = 0.42$ mol
  • Moles of $H_2 = 3.0 - 3x = 3.0 - 3(0.58) = 3.0 - 1.74 = 1.26$ mol

  Step 2: Calculate the total moles of gas at equilibrium.

  Total moles ($n_{total}$) = moles($N_2$) + moles($H_2$) + moles($NH_3$) $n_{total} = 0.42 + 1.26 + 1.16 = 2.84$ mol

  Step 3: Calculate the mole fraction of $NH_3$.

  Mole fraction of $NH_3$ ($x_{NH_3}$) = moles($NH_3$) / Total moles $x_{NH_3} = \frac{1.16}{2.84} = 0.40845...$

  mole fraction of $NH_3(g) = 0.408$ (to 3 s.f.)

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  How the marks are awarded

  • M1 — Correctly calculating the equilibrium moles of both N₂ (0.42 mol) and H₂ (1.26 mol) by using the stoichiometry of the reaction based on the 1.16 mol of NH₃ formed.
  • M2 — Correctly calculating the total moles at equilibrium (2.84 mol) and using this to find the mole fraction of NH₃ by dividing the moles of NH₃ by the total moles, giving the final answer 0.408 or 0.41.

  Common mistakes

  • Using incorrect stoichiometric ratios to find the change in moles of reactants. For example, subtracting 1.16 mol from the initial moles of N₂ and H₂ instead of using the 1:2 and 3:2 ratios.
  • Calculating the total moles using the initial amounts (1.0 + 3.0 = 4.0 mol) instead of the calculated equilibrium amounts.
  • Forgetting to include one of the species in the calculation for total moles at equilibrium, e.g., calculating total moles as just the sum of the reactants (0.42 + 1.26).
  • Inverting the mole fraction formula, i.e., calculating total moles / moles of NH₃.

  Examiner tip: Always use an ICE (Initial, Change, Equilibrium) table to methodically calculate equilibrium amounts, ensuring you use the correct stoichiometric ratios from the balanced equation for the 'Change' row.

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