Maxwell-Boltzmann distribution and temperatureAQA A-Level Chemistry: Subtopic test

1. 1
   The distribution of molecular energies in a sample of a gas at 300 K is described by a Maxwell–Boltzmann distribution curve, in which the number of molecules is plotted against their energy. The same sample is then heated to 310 K. A reaction of this gas has an activation energy that is much greater than the most probable molecular energy.

   (a)

   Which statement about the Maxwell–Boltzmann distribution curve is correct?

   [1 mark]

   • AThe curve is symmetrical about the most probable energy
   • BThe curve touches the energy axis at high energies, showing that no molecules have very high energy
   • CThe area under the curve is equal to the total number of molecules in the sample
   • DThe peak of the curve shows the activation energy of the reaction

   (b)

   Which statement describes the curve at 310 K compared with the curve at 300 K?

   [1 mark]

   • AThe peak is lower and moves to a higher energy, and the area under the curve is unchanged
   • BThe peak is higher and moves to a lower energy, and the area under the curve is unchanged
   • CThe peak is lower and moves to a higher energy, and the area under the curve is greater
   • DThe peak stays at the same energy, and the area under the curve is greater

   (c)

   Explain the significance of the area under the curve to the right of the activation energy.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A student investigates how temperature affects the rate of the reaction between sodium thiosulfate solution and dilute hydrochloric acid, which forms a precipitate of sulfur. She mixes 50.0 cm³ of 0.10 mol dm⁻³ sodium thiosulfate solution with 5.0 cm³ of 1.0 mol dm⁻³ hydrochloric acid and measures the time taken for a cross viewed through the mixture to disappear. At 20 °C the time is 64 s and at 30 °C the time is 31 s.

   (a)

   By what factor is the rate of reaction greater at 30 °C than at 20 °C, taking the rate as proportional to 1/t?

   [1 mark]

   • A0.48
   • B1.0
   • C33
   • D2.1

   (b)

   Which variables must be kept constant so that only the effect of temperature is investigated?

   [1 mark]

   • AThe time taken for the cross to disappear
   • BThe volumes and concentrations of both solutions
   • CThe temperature of the mixture
   • DThe rate of the reaction

   (c)

   Suggest two ways in which the reliability of the investigation could be improved.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A gas-phase reaction between two gases is carried out at constant volume at 300 K and at 310 K. At 300 K, 1.0 × 10⁻⁸ of the molecules in the mixture have energy equal to or greater than the activation energy. At 310 K the proportion is 1.8 × 10⁻⁸.

   (a)

   Calculate the factor by which the proportion of molecules with energy equal to or greater than the activation energy increases, and use it to estimate the effect on the rate of reaction.

   [3 marks]

   (b)

   A rise of 10 K is only about 3% of 300 K, yet the rate increases by about 80%. Explain why a small increase in temperature has such a large effect on the rate.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   The same gas-phase reaction is studied at a range of temperatures. A student reports that raising the temperature from 300 K to 310 K increases the rate of reaction by a factor of 1.9, but raising the temperature from 600 K to 610 K increases the rate by a factor of only 1.2.

   (a)

   Describe how the Maxwell–Boltzmann distribution of molecular energies for the gas at 400 K differs from that at 300 K, and explain how these differences account for an increase in the rate of reaction.

   [6 marks]

   (b)

   Explain why the same 10 K increase in temperature has a much smaller effect on the rate of reaction at 600 K than at 300 K.

   [6 marks]

   Total for question 4: 12 marks

End of questions