Effect of tempature on reaction rates and the concept of activation energy

a. Sketch a graph to show the Boltzmann distribution of molecular energies. Label the axes.

b. Comment on the shape of the distribution curve

a.

b. Not all molecules have the same energy and are distributed about a mean.

Explain the meaning of the term activation energy

The activation energy of a reaction is the minimum energy required by colliding particles for a reaction to occur. Enthalpy profile diagrams show how the activation energy provides a barrier to reaction.

Draw a second curve on your graph to show the Boltzmann distribution of molecular energies at a slightly higher temperature.

Assume the initial temperature is T and the higher temperature is T + t

This question is about the following general reaction

A + B ⇌ C + D

The reaction pathway diagram for the reaction is shown in the Figure below

a. Explain whether the forward reaction is exothermic or endothermic.

b. Calculate the activation energy for the forward and backward reactions.

a. The forward reaction is endothermic because the energy level of the products is higher than energy level of the reactants

b. The activation energy for the forward reaction = 150 + 180 = 330 kJ mol^-1 

The activation energy for the backward reaction = 180 kJ mol^-1 

One important remark: In reversible reactions, the endothermic reaction will always have a higher activation energy than the exothermic reaction.

The Boltzmann distribution curve of molecular energies for a general reaction at a given temperature is shown in the Figure below

a. State what will happen to the curve when the temperature of the reaction is decreased.

b. Comment on how, if at all, the total area under a Boltzmann distribution curve changes with temperature.

a. When decreasing the temperature, the curve will shift to the left and be higher. In addition, curve finishes below the level of the original curve.

b. The total area under a Boltzmann distribution curve won’t change because it represents the number of molecules within the sample

The Boltzmann distribution of energies for a gas is shown in the Figure below

State what the shaded area represents

The number of molecules that do not have enough energy to react (E≤Ea)

The diagram represents the reaction pathway for the following reaction:

Z (g) + Y (g) → X (g) + W (g)

What statement is true about the reverse reaction?

A. It will have a smaller activation energy and a negative ∆H

B. It will have a smaller activation energy and a positive ∆H

C. It will have a larger activation energy and a negative ∆H

D. It will have a larger activation energy and a positive ∆H

The answer is D.

The forward reaction is exothermic and the backward reaction is endothermic.

An exothermic reaction has a negative ∆H and an endothermic reaction has a positive ∆H.

A is incorrect because it is an endothermic reaction

B is incorrect because the endothermic reaction will always have a higher activation energy than the exothermic reaction

C is incorrect because it is an endothermic reaction

The distribution of molecular energies in a sample of a gas at a given temperature is shown by the Boltzmann distribution graph below.

If the temperature is increased, what will happen to the position of point X?

A. Fewer molecules possess the most probable energy value so X will shift to the right.

B. Fewer molecules possess the most probable energy value so X will shift to the left.

C. More molecules possess the most probable energy value so X will shift to the left.

D. The position of X will stay the same but the area under the distribution curve increases.

The answer is A.

The Boltzmann distribution curve shows the peak as the most probable energy.

When the temperature is increased, the number of particles with enough energy for a successful collision is increased, leading to shift the peak of the graph down and to the right.

B is incorrect because when the temperature increases, X will shift to the right

C is incorrect because when the temperature increases, X will shift to the right

D is incorrect because the area under the graph would only change if the number of particles changed

The diagram shows a reaction pathway for an endothermic reaction.

Which arrow represents the activation energy for the forward reaction?

A. A

B. B

C. C

D. D

The answer is B.

The activation energy in an endothermic reaction is the energy required for the reactants to react. 

A is incorrect because this does not correspond to the activation energy

C is incorrect because this is the activation energy for the reverse reaction

D is incorrect because this is the ∆H of the forward reaction

The dotted-line curve on each graph below represents the corresponding distribution for a gas at 300 K. 

Which solid-line curve most accurately represents the distribution of molecular energies in the same gas at 500 K?

A. 

B. 

C. 

D. 

The answer is D.

When the temperature is increased, the number of particles with enough energy for a successful collision is increased, leading to shift the peak of the graph down and to the right.

A, B and C are incorrect because all the other graphs do not move down and to the right