Problem 53 - Chemistry: The Central Science

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) \(E_{a}=55 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=10 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

The fastest reaction is (b) with an activation energy of \(35 \mathrm{~kJ/mol}\) and the slowest reaction is (c) with an activation energy of \(55 \mathrm{~kJ/mol}\). This is because lower activation energy leads to a faster reaction rate, assuming all collision factors are the same. The energy changes (ΔE) do not directly affect the reaction speed.

Step 1: Understand the role of activation energy in reaction rates

Activation energy is the minimum amount of energy required for the reactants to overcome the energy barrier and form products. A lower activation energy means that it is easier for the molecules to react and, therefore, the reaction occurs at a faster rate. Given that the collision factors are the same for all reactions, the lower the activation energy, the faster the reaction, and vice-versa.

Step 2: Compare the activation energies of the given reactions

We have three reactions with the following activation energies: (a) \(E_{a} = 45 \mathrm{~kJ/mol}\) (b) \(E_{a} = 35 \mathrm{~kJ/mol}\) (c) \(E_{a} = 55 \mathrm{~kJ/mol}\) Comparing these values, we can see that reaction (b) has the lowest activation energy and reaction (c) has the highest activation energy.

Step 3: Determine the fastest and slowest reactions

Since reaction (b) has the lowest activation energy, this reaction will be the fastest among the three options. On the other hand, reaction (c) has the highest activation energy, so it will be the slowest reaction.

Step 4: Justification based on Energy Changes

While the energy changes (ΔE) can provide information about the spontaneity of a reaction, they do not have a direct impact on the speed of the reaction. Therefore, in this case, the energy changes do not affect our determination of the fastest and slowest reactions. However, it is important to note that the most favorable reactions (based on ΔE) would be those with large negative energy changes: reaction (a) being the most favorable and reaction (c) being the least favorable.