AQA A-Level Chemistry Paper 2, 2019: Question 5

Calculating the Arrhenius Constant (A) and Units

WHAT THIS QUESTION TESTS

This question assesses quantitative mastery of reaction kinetics and temperature dependence using the exponential form of the Arrhenius equation:

Unit Conversions: Converting temperature from Celsius to Kelvin ( T + 273 ) and activation energy from kilojoules to joules ( kJ mol⁻¹ → J mol⁻¹ ).
Algebraic Manipulation: Rearranging k = Ae^(-Ea/RT) to make A the subject.
Calculator Proficiency: Managing negative exponential powers ( e^(-x) ) and standard form without rounding prematurely.
Deducing Units: Recognising that the exponential term is dimensionless, meaning A shares the identical units of k .

⚠️ Historical Exam Note (AQA Official Mark Scheme):
On the original examination paper, a typographical error printed the fraction slash as an uppercase letter 'I' ( k = Ae^-EaIRT ). Because this prevented some candidates from correctly identifying the standard formula, all students were awarded the full 4 marks. However, below is the intended standard AQA chemistry calculation that you must master for future exams.

Question 05 Walkthrough (4 Marks)

Calculate a value for the Arrhenius constant, A, and give its units.

📐 Step-by-Step Calculation

Convert all units to SI standards:
• T = 25 + 273 = 298 K
• Ea = 96.2 kJ mol⁻¹ = 96 200 J mol⁻¹
• R = 8.31 J K⁻¹ mol⁻¹
Evaluate the exponential term power (-Ea / RT):
-Ea / RT = -96 200 / (8.31 × 298)
-Ea / RT = -96 200 / 2476.38 = -38.847
Calculate e^(-Ea / RT):
e^(-38.847) = 1.3458 × 10⁻¹⁷
Rearrange for A and solve:
A = k / e^(-Ea/RT)
A = (3.46 × 10⁻⁸) / (1.3458 × 10⁻¹⁷)
A = 2.57 × 10⁹ (to 3 sig figs)
Determine units of A:
Since e^(-Ea/RT) is a pure number without units, units of A = units of k = s⁻¹ .

✅ Expected Answers & Mark Breakdown

Value for A: 2.57 × 10⁹ (allow 2.56 × 10⁹ to 2.58 × 10⁹ )

Units for A: s⁻¹

Intended 4-Mark Allocation:
• Mark 1: Unit conversions: 298 K and 96 200 J mol⁻¹ .
• Mark 2: Correct value of -Ea / RT (-38.8) or e^(-Ea/RT) (1.35 × 10⁻¹⁷) .
• Mark 3: Final calculated value of A ( 2.57 × 10⁹ , matching 3 significant figures).
• Mark 4: Correct unit for A ( s⁻¹ ).

💡 Key Knowledge

Arrhenius Constant (A): Also known as the pre-exponential factor or frequency factor. It is related to the frequency of collisions and the probability that collisions have favorable orientation.
The Factor e^(-Ea/RT): Represents the fraction of collisions that have sufficient energy ( E ≥ Ea ) to react. It is strictly dimensionless.
Matching Units: The units of A are always identical to the units of the rate constant k . If k is in mol⁻¹ dm³ s⁻¹ , A would also be in mol⁻¹ dm³ s⁻¹ .

🧠 Exam Technique & Alternative Method

Logarithmic Alternative: You can take natural logs of both sides first:
ln k = ln A - (Ea / RT)
ln A = ln k + (Ea / RT)
ln A = ln(3.46 × 10⁻⁸) + 38.847
ln A = -17.18 + 38.847 = 21.667
A = e^(21.667) = 2.57 × 10⁹ s⁻¹
This log method prevents extreme powers on older calculators and avoids floating-point errors.
Significant Figures: Data is given to 3 significant figures ( 3.46 × 10⁻⁸ , 96.2 , 8.31 ); quote your answer to 3 sig figs.

❌ Common Errors & Traps to Avoid

Energy Unit Mismatch: Using 96.2 directly without multiplying by 1000. Because R is in J K⁻¹ mol⁻¹ , Ea must be converted to J mol⁻¹ . Leaving it in kJ gives a massive exponent error.
Forgetting to Convert Temperature: Substituting 25 instead of 298 K . The Arrhenius equation requires absolute temperature in Kelvin.
Losing the Minus Sign: Entering e^(+Ea/RT) into the original formula instead of e^(-Ea/RT) . Note that when rearranging, A = k × e^(+Ea/RT) or A = k / e^(-Ea/RT) .
Inventing Rate Constant Units: Overcomplicating the units of A by writing complex concentration terms. Simply look at the unit given for k ( s⁻¹ ) and copy it directly.

AQA A-Level Chemistry Paper 2, 2019: Question 5

Question

Mark scheme

How to answer it