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3.1.5.2 Maxwell-Boltzmann

distribution

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Time: 144 min. Marks: 141 marks

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Q1. The Maxwell–Boltzmann distribution of molecular energies in a sample of gas at a fixed temperature is shown. Which letter represents the mean energy of the molecules? A B C D (Total 1 mark) Q2. The graph shows the Maxwell−Boltzmann distribution of molecular energies in a sample of gas at a fixed temperature.

(Total 1 mark) Q4. Nitryl chloride reacts with nitrogen monoxide according to the equation: ClNO 2 (g) + NO (g) ⟶ NO 2 (g) + ClNO(g) The Maxwell–Boltzmann distribution curve in Figure 1 shows the distribution of molecular energies in 1 mol of this gaseous reaction mixture (sample 1 ) at 320 K. (a) On the same axes, draw a curve for sample 1 at a lower temperature. (2) (b) Explain the effect that lowering the temperature would have on the rate of reaction.

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(2) (c) A Maxwell–Boltzmann distribution curve was drawn for a second sample of the reaction mixture in the same reaction vessel. Figure 2 shows the results.

Deduce the change that was made to the reaction conditions. Explain the effect that this change has on the rate of reaction. Change ____________________________________________________________

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Explanation _________________________________________________________

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(3) (Total 7 marks) Q5. The question below is about the Maxwell–Boltzmann distribution shown for a sample of a gas, X, at two different temperatures.

Which statement is correct for the higher temperature? A The area under the curve to the left of E a decreases. B The total area under the curve increases. C The activation energy decreases. D More molecules have the mean energy. (Total 1 mark) Q7. This question is about the Maxwell–Boltzmann distribution of molecular energies in a sample of a gas shown in the figure below.

Which letter best represents the mean energy of the molecules? A B C D (Total 1 mark) Q8. This question is about the Maxwell–Boltzmann distribution of molecular energies in a sample of a gas shown in the following figure. What does the area under the curve represent? A The total energy of the particles. B The total number of particles. C The number of particles that can react with each other. D The total number of particles that have activation energy. (Total 1 mark) Q9. The graph below shows a typical energy distribution for particles of an ideal gas in a sealed container at a fixed temperature.

(i) Sketch a second curve on the graph to show the distribution of molecular energies in this mixture at a higher temperature. (1) (ii) Explain with reference to both curves on the graph how a small change in temperature leads to a large change in the rate of reaction.

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(2) (b) Both the rate of production and equilibrium yield of methanol are considered when choosing the most appropriate conditions for the operation of this process on an industrial scale. (i) State and explain the effect of a higher pressure on the equilibrium yield of methanol.

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(3) (ii) By considering both rate and yield, state why the reaction is carried out at a temperature of 300 °C rather than at a higher temperature.

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(2) (Total 8 marks) Q11. The following figure shows the Maxwell.Boltzmann distribution of molecular energies in a

sample of gas at temperature T. (a) One of the axes is labelled. Label the other axis. (1) (b) State why the curve starts at the origin.

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(1) (c) Which of the following, A , B or C , describes what the value of Y represents in the figure? Write the correct letter, A , B or C , in the box. A The energy needed for a successful collision B The minimum energy needed for a reaction to occur C The most probable energy (1) (d) On the figure above, draw a distribution of molecular energies in this sample of gas at a higher temperature. (2) (e) The pressure of the original sample of gas is doubled at temperature T. State the effect, if any, of this change on the value of Y.

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(2) (Total 5 marks) Q13. The diagram shows the Maxwell-Boltzmann distribution of molecular energies in a gas at two different temperatures. (a) One of the axes is labelled. Complete the diagram by labelling the other axis. (1) (b) State the effect, if any, of a solid catalyst on the shape of either of these distributions.

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(1) (c) In the box, write the letter, V , W , X or Y , that represents the most probable energy of the molecules at the lower temperature. (1) (d) Explain what must happen for a reaction to occur between molecules of two different gases.

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(e) Explain why a small increase in temperature has a large effect on the initial rate of a reaction.

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(1) (Total 6 marks) Q14. The rate of a chemical reaction is influenced by the size of the activation energy. Catalysts are used to increase the rates of chemical reactions but are not used up in the reactions. (a) Give the meaning of the term activation energy.

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(2) (b) Explain how a catalyst increases the rate of a reaction.

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(2) (c) The diagram below shows the Maxwell–Boltzmann distribution of molecular energies, at a constant temperature, in a gas at the start of a reaction. On this diagram the most probable molecular energy at this temperature is shown by the symbol E mp The activation energy is shown by the symbol E a

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(2) (ii) The hydration of but-2-ene. Catalyst _______________________________________________________ Name of organic product __________________________________________

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(2) (Total 12 marks) Q15. The diagram below shows a Maxwell–Boltzmann distribution for a sample of gas at a fixed temperature. E a is the activation energy for the decomposition of this gas. (a) (i) On this diagram, sketch the distribution for the same sample of gas at a higher temperature. (2) (ii) With reference to the Maxwell–Boltzmann distribution, explain why an increase in temperature increases the rate of a chemical reaction.

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(2) (b) Dinitrogen oxide (N 2 O) is used as a rocket fuel. The data in the table below show how the activation energy for the decomposition of dinitrogen oxide differs with different catalysts. 2N 2 O(g) 2N 2 (g) + O 2 (g)

Ea / kJ mol– Without a catalyst 245 With a gold catalyst 121 With an iron catalyst 116 With a platinum catalyst 136 (i) Use the data in the table to deduce which is the most effective catalyst for this decomposition.

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(1) (ii) Explain how a catalyst increases the rate of a reaction.

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(2) (Total 7 marks) Q16. The diagram below shows the Maxwell–Boltzmann energy distribution curve for a sample of gas at a fixed temperature. Ea is the activation energy for the decomposition of this gas. (a) On this diagram sketch the distribution curve for the same sample of gas at a higher temperature. (3) (b) (i) What is the effect of an increase in temperature on the rate of a chemical reaction? Explain your answer with reference to the Maxwell–Boltzmann distribution.

(b) On the diagram above, sketch a curve to show the distribution of molecular energies in the same sample of gas at a higher temperature. (2) (c) (i) Explain why, even in a fast reaction, a very small percentage of collisions leads to a reaction.

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(ii) Other than by changing the temperature, state how the proportion of successful collisions between molecules can be increased. Explain why this method causes an increase in the proportion of successful collisions. Method for increasing the proportion of successful collisions ______________

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Explanation ____________________________________________________

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(4) (Total 9 marks) Q18. (a) Define the term activation energy for a chemical reaction.

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(2) (b) Draw, with labelled axes, a curve to represent the Maxwell–Boltzmann distribution of molecular energies in a gas. Label this curve T 1. On the same axes, draw a second curve to represent the same sample of gas at a lower temperature. Label this curve T 2. Use these curves to explain why a small decrease in temperature can lead to a large decrease in the rate of a reaction.

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(8) (c) Give one reason why most collisions between gas-phase reactants do not lead to a reaction. State and explain two ways of speeding up a gas-phase reaction other than by changing the temperature.

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(5) (Total 15 marks) Q19. Gas G decomposes as shown in the equation below. G(g) → X(g) + Y(g) (a) Draw, on the axes below, a Maxwell–Boltzmann distribution curve for a sample of G