Maxwell-Boltzmann distributionsEdexcel A-Level Chemistry: Subtopic test

1. 1
   A student sketches the Maxwell–Boltzmann distribution of molecular energies for a gas at a fixed temperature, with the number of molecules on the vertical axis and energy on the horizontal axis, and marks the activation energy of a reaction on the energy axis.

   (a)

   Which statement about the distribution is correct?

   [1 mark]

   • AThe area under the curve represents the total number of molecules
   • BThe curve meets the energy axis at a maximum energy, as no molecule can exceed it
   • CThe curve starts at a minimum energy greater than zero
   • DThe peak shows the energy of the fastest molecules

   (b)

   Which statement about the activation energy marked on the energy axis is correct?

   [1 mark]

   • AOnly molecules with energy exactly equal to the activation energy can react
   • BOnly molecules at the peak of the curve can react
   • CAll molecules to the left of the activation energy can react
   • DOnly molecules in the area to the right of the activation energy have enough energy to react on collision

   (c)

   Explain why the curve starts at the origin and why it never touches the energy axis at high energy.

   [2 marks]

   Total for question 1: 4 marks

2. 2
   A reaction mixture of gases is heated from 300 K to 310 K, and the rate of the reaction approximately doubles. The student sketches the distribution of molecular energies at the two temperatures on the same axes.

   (a)

   How does the distribution at 310 K compare with that at 300 K?

   [1 mark]

   • AThe peak is higher and moves to a lower energy, with the same area
   • BThe peak is higher and moves to a higher energy, with a larger area
   • CThe peak is lower and moves to a higher energy, and the area under the curve is unchanged
   • DThe peak is unchanged but the area is larger because there are more molecules

   (b)

   Which statement best explains why a rise of only 10 K can roughly double the rate?

   [1 mark]

   • AThe activation energy is halved
   • BThe proportion of molecules with energy equal to or greater than the activation energy increases significantly
   • CThe mean molecular energy doubles
   • DThe number of molecules in the mixture increases

   (c)

   Explain, using the distributions, why the reaction is faster at 310 K.

   [2 marks]

   Total for question 2: 4 marks

3. 3
   A car's catalytic converter contains platinum and rhodium on a solid support. At the temperature of the exhaust gases it converts carbon monoxide and nitrogen monoxide into carbon dioxide and nitrogen: 2CO(g) + 2NO(g) → 2CO₂(g) + N₂(g). Without the catalyst the reaction is far too slow at this temperature.

   (a)

   Explain, with reference to the Maxwell–Boltzmann distribution, how the catalyst increases the rate of the reaction at the same temperature.

   [3 marks]

   (b)

   Compare how raising the temperature and adding a catalyst each increase the proportion of molecules able to react.

   [4 marks]

   Total for question 3: 7 marks

4. 4
   A chemical company wants to speed up a gas-phase reaction in a reactor operating at 400 K. One option is to raise the temperature to 500 K. The other is to add a solid catalyst that lowers the activation energy from 90 kJ mol⁻¹ to 60 kJ mol⁻¹. Energy for heating is expensive.

   (a)

   Explain, with reference to the Maxwell–Boltzmann distribution, why raising the temperature from 400 K to 500 K increases the rate of the reaction.

   [6 marks]

   (b)

   Evaluate whether adding the catalyst is a better way of speeding up the reaction than raising the temperature, with reference to the distribution of molecular energies.

   [6 marks]

   Total for question 4: 12 marks

End of questions