AQA A-Level Chemistry Paper 3, 2019: Question 11

1 mark · Medium difficulty · Multiple Choice

Calculate the mole fraction of sulfur trioxide at equilibrium given initial amounts of reactants and the total moles of gas at equilibrium.

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Question

Question 11 presents the chemical equation: 2SO2(g) + O2(g) equilibrium arrow 2SO3(g). An experiment mixes 2.00 mol of sulfur dioxide with 2.00 mol of oxygen, resulting in a total of 3.40 mol of gas at equilibrium. Four multiple choice options are provided for the mole fraction of sulfur trioxide: A (0.176), B (0.353), C (0.600), and D (1.200).
Question text

11 The equation for the reaction between sulfur dioxide and oxygen is shown.

2SO2(g) + O2(g) ⇌ 2SO3(g)

In an experiment, 2.00 mol of sulfur dioxide are mixed with 2.00 mol of oxygen.

The total amount of the three gases at equilibrium is 3.40 mol

What is the mole fraction of sulfur trioxide in the equilibrium mixture?

[1 mark]

A 0.176

B 0.353

C 0.600

D 1.200

Mark scheme

Show the mark scheme Mark scheme table row showing Question 11 with correct answer B and 1 mark.

11 B 1

How to answer it

Equilibrium Amounts & Mole Fraction Calculation

📋 What this question tests

This question assesses your mastery of gas-phase homogeneous equilibria and mole fraction determination:

  • Setting up an ICE table (Initial, Change, Equilibrium) using stoichiometric ratios.
  • Using total equilibrium moles to solve for an algebraic unknown.
  • Applying the formula for mole fraction: Mole fraction (x) = Moles of gas / Total gas moles .
  • Recognising impossible values (a mole fraction cannot be greater than 1).
Question 11 • 1 Mark

Determining the Mole Fraction of SO₃ at Equilibrium

Reaction: 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)

✅ Correct Answer

B — 0.353

📐 Step-by-Step Calculation

Step 1: Construct an ICE table
Let 2x be the amount (in mol) of SO₃ formed at equilibrium. According to stoichiometry ( 2 : 1 : 2 ), 2x mol of SO₂ and x mol of O₂ will react:
Species 2SO₂(g) + O₂(g) ⇌ 2SO₃(g)
Initial / mol 2.00 2.00 0.00
Change / mol −2x −x +2x
Equilibrium / mol 2.00 − 2x 2.00 − x 2x
Step 2: Form an equation for total equilibrium moles
The question states total equilibrium moles = 3.40 mol .
Total moles = n(SO₂) + n(O₂) + n(SO₃)
Total moles = (2.00 − 2x) + (2.00 − x) + 2x = 4.00 − x
Step 3: Solve for x
4.00 − x = 3.40
x = 0.60 mol
Step 4: Find equilibrium moles of SO₃
n(SO₃) = 2x = 2 × 0.60 = 1.20 mol
Step 5: Calculate mole fraction of SO₃
Mole fraction of SO₃ = n(SO₃) / Total moles
Mole fraction = 1.20 / 3.40 = 0.3529... ≈ 0.353 (Option B)

💡 Key Knowledge

  • Mole fraction: Defined as xA = nA / ntotal . The sum of all mole fractions in a mixture always equals 1.
  • Stoichiometry awareness: The change line must always strictly follow the molar coefficients from the balanced symbol equation ( 2 : 1 : 2 ).
  • Gas mole change: Notice that for every 2 moles of SO₃ formed, 3 moles of reactants are consumed. Net change = −1 mole of gas per 2 moles of SO₃ produced.

🧠 Exam Technique (The 20-Second Shortcut)

In multiple-choice papers, speed is essential:

  • Initial gas moles: 2.00 + 2.00 = 4.00 mol.
  • Equilibrium gas moles: 3.40 mol.
  • Overall mole decrease: 4.00 − 3.40 = 0.60 mol.
  • Looking at the equation: (2 + 1) → 2 moles of gas represents a decrease of 1 mole of gas for every 2 moles of SO₃ formed.
  • Therefore, SO₃ formed = 2 × 0.60 = 1.20 mol.
  • Mole fraction = 1.20 / 3.40 = 0.353.

❌ Common Errors & Distractor Traps

  • Trap D (1.200): Calculating the moles of SO₃ ( 1.20 mol ) and stopping there without dividing by total moles. Note that a mole fraction can never be greater than 1.0!
  • Trap C (0.600): Solving for x = 0.60 and forgetting that n(SO₃) = 2x , or mistaking the mole reduction for moles of product.
  • Trap A (0.176): Dividing x (0.60) by 3.40 directly ( 0.60 / 3.40 = 0.176 ), forgetting the coefficient of 2 in front of SO₃.

Topics

Physical Chemistry · 3.1.2 Amount of Substance · 3.1.10 Equilibrium Constant Kp

Question and mark scheme from the AQA A-Level Chemistry examination, Paper 3, 2019. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.