Arrhenius equationAQA A-Level Chemistry: Subtopic test

1. 1
   A food scientist is studying how quickly a vitamin breaks down in fruit juice during storage. The breakdown is a first order reaction with an activation energy of 85.0 kJ mol⁻¹. Take the gas constant R as 8.31 J K⁻¹ mol⁻¹.

   (a)

   Which statement best explains why the rate constant for the breakdown increases when the juice is stored at a higher temperature?

   [1 mark]

   • AThe activation energy of the reaction decreases as the temperature rises
   • BThe collisions become more frequent, and this alone accounts for the increase in k
   • CA greater fraction of the molecules has energy equal to or greater than the activation energy
   • DThe concentration of the vitamin increases

   (b)

   What is the value of the term e^(−Ea/RT) at 298 K?

   [1 mark]

   • A1.2 × 10⁻¹⁵
   • B1.2 × 10¹⁵
   • C0.97
   • D3.8 × 10⁻¹⁵

   (c)

   The storage temperature of the juice rises from 298 K to 308 K. Calculate the factor by which the rate constant increases.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student measures the rate constant, k, for the hydrolysis of an ester (reaction X) at five temperatures and plots ln k on the vertical axis against 1/T on the horizontal axis, where T is in kelvin. The line is straight, with a gradient of −8.9 × 10³ K. For a second reaction, Y, the equivalent line has a gradient of −5.2 × 10³ K. Take the gas constant R as 8.31 J K⁻¹ mol⁻¹.

   (a)

   Which pair of quantities gives a straight line for reaction X?

   [1 mark]

   • Ak against T
   • Bln k against T
   • Ck against 1/T
   • Dln k against 1/T

   (b)

   Which comparison of reactions X and Y is correct?

   [1 mark]

   • AY has the larger activation energy because its gradient is less steep
   • BX has the larger activation energy, so its rate constant is more sensitive to a change in temperature
   • CX and Y have the same activation energy because both lines are straight
   • DY is faster at every temperature because its gradient is smaller

   (c)

   Calculate the activation energy of reaction X in kJ mol⁻¹.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   The first order decomposition of compound Z in solution has an Arrhenius constant, A, of 4.5 × 10¹³ s⁻¹ and an activation energy, Ea, of 110 kJ mol⁻¹. Take the gas constant R as 8.31 J K⁻¹ mol⁻¹.

   (a)

   Calculate the value of the rate constant for the decomposition of Z at 350 K.

   [3 marks]

   (b)

   Calculate the temperature, in K, at which the rate constant for the decomposition of Z is 1.0 × 10⁻² s⁻¹.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A chemist studies the first order decomposition of a compound in solution at several temperatures. The rate constant, k, is in s⁻¹ and the temperature, T, is in kelvin. Take the gas constant R as 8.31 J K⁻¹ mol⁻¹.

   (a)

   A rise in temperature of only 10 K often causes the rate constant to roughly double or triple. Explain, with reference to the Maxwell–Boltzmann distribution and the Arrhenius equation, why a small increase in temperature has such a large effect on k.

   [6 marks]

   (b)

   The chemist plots ln k against 1/T. Two points on the straight line are (1/T = 3.30 × 10⁻³ K⁻¹, ln k = −5.10) and (1/T = 2.90 × 10⁻³ K⁻¹, ln k = −2.12). Determine the activation energy in kJ mol⁻¹ and the Arrhenius constant, A, including its units.

   [6 marks]

   Total for question 4: 12 marks

End of questions