Question

Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest and which would be slowest? Explain your answer. (a) \(E_{a}=45 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-25 \mathrm{~kJ} / \mathrm{mol}\) (b) \(E_{a}=35 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-10 \mathrm{~kJ} / \mathrm{mol}\) (c) \(E_{a}=55 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=10 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

The fastest reaction will be (b) with an activation energy of \(35\, \mathrm{kJ/mol}\), while the slowest reaction will be (c) with an activation energy of \(55\, \mathrm{kJ/mol}\). This is because lower activation energy results in a faster reaction rate, and higher activation energy results in a slower reaction rate.

Step-by-step solution

Identify the activation energies

We are given the activation energies \(E_a\) for each reaction: (a) \(E_a = 45\, \mathrm{kJ/mol}\) (b) \(E_a = 35\, \mathrm{kJ/mol}\) (c) \(E_a = 55\, \mathrm{kJ/mol}\)

Compare the activation energies

Compare the activation energies to determine the relative rates of the reactions: - Reaction (a): \(E_a = 45\, \mathrm{kJ/mol}\) - Reaction (b): \(E_a = 35\, \mathrm{kJ/mol}\) - Reaction (c): \(E_a = 55\, \mathrm{kJ/mol}\) Based on this comparison, we can see that reaction (b) has the lowest activation energy, while reaction (c) has the highest activation energy.

Determine the fastest and slowest reactions

Since the reaction with the lowest activation energy proceeds the fastest, reaction (b) will be the fastest of the three. On the other hand, the reaction with the highest activation energy proceeds the slowest, which means that reaction (c) will be the slowest.