Edexcel A-Level Chemistry Paper 2, November 2020: Question 9

11 marks · Hard difficulty · Calculations

Calculate the activation energy for the decomposition of nitrogen(V) oxide using Arrhenius equation and rate constants at two temperatures, and interpret Maxwell-Boltzmann distribution curves.

Practise this question

Question

The question presents a kinetics problem about the decomposition of nitrogen(V) oxide. Part (a) includes a Maxwell-Boltzmann distribution curve labelled T1 with activation energy Ea on the horizontal energy axis, asking students to label the vertical axis, draw a second curve for a lower temperature T2, explain the effect of lower temperature on rate in terms of collisions and energy, and label an activation energy for a catalyzed reaction (Ecat). Part (b) provides a table of rate constants at 328 K and 338 K, giving the Arrhenius equation, and asks students to calculate the activation energy including units and appropriate significant figures without using a graphical method.
Question text

9 This question is about the effect of temperature on the rate of decomposition of

nitrogen(V) oxide.

2N2O5(g) → 2N2O4(g) + O2(g)

(a) The diagram shows the Maxwell-Boltzmann distribution of molecular energies for

nitrogen(V) oxide at a temperature T1.

Ea is the activation energy of this reaction.

T1

Ea

Energy, E

(i) Give the label for the vertical axis.

(1)

(ii) Draw a second curve on the same set of axes for the same gas at a lower

temperature, T2.

(2)

(iii) Explain, in terms of collisions and energy, why lowering the temperature

decreases the rate of reaction.

(2)

(iv) A catalyst is added to the gas.

Label the diagram above with the symbol Ecat to show a possible activation

energy for the reaction in the presence of a catalyst.

(1)

(b) The rate constant for the decomposition of nitrogen(V) oxide was determined at*P62669A02832*

two temperatures.

Temperature / K Rate constant / s−1

328 1.50 × 10−3

338 4.87 × 10−3

Calculate the activation energy for this reaction.

Include units and give your answer to an appropriate number of significant figures.

You should not attempt to use any graphical method to answer this question.

The Arrhenius equation relating two rate constants, k1 and k2, at two different

temperatures, T1 and T2, can be expressed as

k2 Ea 1 1

ln = − −

k1 R T2 T1

(5)

(Total for Question 9 = 11 marks)

Mark scheme

Show the mark scheme The mark scheme provides the answers for each part. For 9(a)(i), it accepts fraction, proportion, or number of molecules/particles with energy E. For 9(a)(ii), it awards marks for a peak for T2 to the left and higher than T1 with an asymptote lower than T1. For 9(a)(iii), it awards marks for stating that particles have lower kinetic energy at lower temperature and fewer have energy greater than Ea. For 9(a)(iv), it shows Ecat labelled between the peak and Ea. For 9(b), it details the 5-mark calculation for activation energy using the Arrhenius equation, requiring correct substitution, evaluation of terms, rearrangement, correct numerical value with units (J mol-1 or kJ mol-1), and 2 to 3 significant figures.

How to answer it

Effect of Temperature on the Rate of Decomposition

🔍 What this question tests

This question tests your understanding of Maxwell-Boltzmann distribution curves, the qualitative effect of temperature and catalysts on reaction rates, and quantitative problem-solving using the Arrhenius equation. You are required to manipulate natural logarithms, rearrange algebraic expressions, handle units correctly, and apply significant figure rules.

Part (a)(i) — Vertical Axis Label

Maxwell-Boltzmann Distribution Basics

✅ Correct Answer

Fraction / proportion / number of molecules (or particles) with energy, E

❌ Common Errors

Writing just "number of molecules" without referencing energy or probability. The vertical axis represents a distribution relative to energy, not a static count.

Marks: 1 mark

Part (a)(ii) — Lower Temperature Curve

Sketching Maxwell-Boltzmann Curves

✅ Correct Answer

  • Peak for T₂ shifted to the left (lower modal energy) compared to T₁ .
  • Peak for T₂ must be higher than T₁ (maintaining area under the curve).
  • Asymptotic tail on the right must be lower than T₁ and MUST NOT touch or cross the x-axis.

🧠 Exam Technique

When drawing a lower temperature curve, remember: taller peak, shifted left, lower right-hand tail. Examiners strictly penalize curves that cross the original curve at unusual angles or touch the axis at the high-energy end.

Marks: 2 marks

Part (a)(iii) — Explaining Temperature Effect

Collisions and Energy Explanation

💡 Key Knowledge

  • At a lower temperature, molecules have lower kinetic energy / move more slowly.
  • Fewer molecules have energy greater than or equal to the activation energy ( E ≥ Eₐ ).
  • Consequently, fewer successful/effective collisions occur per unit time.

❌ Common Errors

Students often lose marks by simply stating "there are fewer collisions overall". Examiners require specific reference to the activation energy and the proportion of molecules possessing sufficient energy to react.

Marks: 2 marks

Part (a)(iv) — Catalyst Activation Energy

Effect of Catalysts on Activation Energy

✅ Correct Answer

Label Eₙₜ marked clearly to the left of the original Eₐ , specifically positioned underneath the falling curve (between the highest point of the peak and the original Eₐ ).

🧠 Exam Technique

Ensure your label is clearly placed on the energy axis. A catalyst provides an alternative reaction pathway with a lower activation energy, shifting the threshold to the left.

Marks: 1 mark

Part (b) — Arrhenius Equation Calculation

Determining Activation Energy ( Eₐ ) from Rate Constants

📐 Step-by-Step Calculation

Step 1: Substitute values into the provided Arrhenius expression

ln(4.87 × 10⁻³ / 1.50 × 10⁻³) = (-Eₐ / 8.31) × ((1 / 338) - (1 / 328))

Step 2: Evaluate both sides

ln(3.2467) = 1.1776

(1 / 338) - (1 / 328) = -9.0201 × 10⁻⁵ K⁻¹

Step 3: Rearrange to isolate Eₐ

Eₐ = (1.1776 × 8.31) / (9.0201 × 10⁻⁵)

Step 4: Calculate final value

Eₐ = +108 493 J mol⁻¹

Step 5: Apply significant figures and units

108 000 J mol⁻¹ OR 108 kJ mol⁻¹ (to 3 SF) or 110 kJ mol⁻¹ (to 2 SF)

❌ Common Calculation Traps

  • Sign Errors: Forgetting that subtracting inverted temperatures (1/T₂ - 1/T₁) yields a negative value, which cancels out the negative sign in the Arrhenius formula -Eₐ/R . Never report a negative activation energy!
  • Unit Omission: Failing to include J mol⁻¹ or kJ mol⁻¹ loses the final mark.
  • Significant Figures: Data is provided to 3 SF, so answers should be given to 2 or 3 significant figures.
Marks: 5 marks

Topics

Physical Chemistry · Topic 9: Kinetics I · Topic 16: Kinetics II

Question and mark scheme from the Edexcel A-Level Chemistry examination, Paper 2, November 2020. QuestionVault is an independent revision resource; questions remain the copyright of the awarding body.