AQA A-Level Chemistry Paper 3, 2019: Question 10

1 mark · Medium difficulty · Multiple Choice

Calculate the initial concentration of Q in experiment 2 using the given rate equation and initial rates data.

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Question

A multiple choice question containing a table of results for two experiments between reactants P and Q. Experiment 1 lists initial [P] as 0.200 mol dm⁻³, initial [Q] as 0.500 mol dm⁻³, and initial rate as 0.400 mol dm⁻³ s⁻¹. Experiment 2 lists initial [P] as 0.600 mol dm⁻³, initial [Q] as 'To be calculated', and initial rate as 0.800 mol dm⁻³ s⁻¹. The rate equation is given as rate = k[P][Q]². The options are A 0.167, B 0.333, C 0.408, and D 0.612.
Question text

10 The results of an investigation of the reaction between P and Q are shown in this

table.

Initial [P] Initial [Q] Initial rate

Experiment –3 –3 –3 –1

/ mol dm / mol dm / mol dm s

1 0.200 0.500 0.400

To be

2 0.600 0.800

calculated

The rate equation is: rate = k [P] [Q]2

What is the initial concentration of Q in experiment 2?

[1 mark]

A 0.167

B 0.333

C 0.408

D 0.612

Mark scheme

Show the mark scheme Mark scheme table row showing question number 10, the correct answer option C, and 1 mark.

10 C 1

How to answer it

Rate Equations: Calculating an Unknown Concentration

What this question tests

Core syllabus skills:

  • Rearranging the rate equation: rate = k [P][Q]²
  • Calculating the rate constant ( k ) with correct substitution
  • Solving for a reactant concentration when the reaction order is non-linear (second order)
  • Identifying mathematical trap options in multiple-choice questions

Question 10 Walkthrough

AQA A-Level Chemistry • Multiple Choice • 1 Mark

Experiment Initial [P] / mol dm⁻³ Initial [Q] / mol dm⁻³ Initial rate / mol dm⁻³ s⁻¹
1 0.200 0.500 0.400
2 0.600 To be calculated 0.800

✅ Correct Answer

C — 0.408 mol dm⁻³

Awarded 1 mark for selecting option C.

💡 Key Knowledge

  • The rate equation expresses the mathematical relationship:
    rate = k [P][Q]²
  • The rate constant, k , is invariant between experiments at the same temperature.
  • Because [Q] is raised to the power of 2 (second order), isolating [Q] requires taking the square root:
    [Q] = √(rate / (k [P]))

📐 Step-by-Step Calculation

Method 1: Finding the Rate Constant (k) First

  1. Calculate the rate constant ( k ) using Experiment 1:
    Rearrange: k = rate / ([P][Q]²)
    k = 0.400 / (0.200 × 0.500²)
    k = 0.400 / (0.200 × 0.250) = 0.400 / 0.0500 = 8.00 mol⁻² dm⁶ s⁻¹
  2. Substitute values from Experiment 2 into the rate equation:
    rate₂ = k [P]₂ [Q]₂²
    0.800 = 8.00 × 0.600 × [Q]₂²
    0.800 = 4.80 × [Q]₂²
  3. Solve for [Q]₂² :
    [Q]₂² = 0.800 / 4.80 = 0.1667 mol² dm⁻⁶
  4. Take the square root to determine [Q]₂ :
    [Q]₂ = √(0.1667) = 0.4082... ≈ 0.408 mol dm⁻³

Method 2: Ratio Comparison (Fast Exam Shortcut)

Compare Experiment 2 directly to Experiment 1:

  • Rate change: 0.800 / 0.400 = 2×
  • [P] change: 0.600 / 0.200 = 3×
  • Since Rate factor = (Factor in [P]) × (Factor in [Q])² :
    2 = 3 × (Factor in [Q])²
    (Factor in [Q])² = 2 / 3 ≈ 0.6667
    Factor in [Q] = √(2 / 3) = 0.8165
  • [Q]₂ = 0.500 × 0.8165 = 0.408 mol dm⁻³

❌ Common Calculation Traps & Distractors

  • Option A (0.167): The most common student error. This is the value of [Q]² ( 0.800 / 4.80 ). The student forgot to take the square root at the final step!
  • Option B (0.333): Forgetting that [Q] is squared and treating the reaction as first order with respect to Q ( 0.500 × (2/3) ).
  • Option D (0.612): Inverting the ratio when scaling, taking √(3/2) × 0.500 instead of √(2/3) × 0.500 .

🧠 Exam Technique & Examiner Tips

  • Sense-check your working: While the overall rate doubled, the concentration of P tripled. For the rate to only double despite a larger increase in P , [Q] must have decreased below its initial value of 0.500 mol dm⁻³ . This immediately eliminates Option D!
  • Highlight powers in the rate equation: Circle the power ² on the exam paper to prompt yourself to square-root at the end.

Topics

Physical Chemistry · 3.1.9 Rate Equations

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.