Question

Based on their activation energies and energy changes and assuming that all collision factors are the same, rank the following reactions from slowest to fastest. (a) \(E_{a}=75 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-20 \mathrm{~kJ} / \mathrm{mol}\) (b) \(E_{a}=100 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=+30 \mathrm{~kJ} / \mathrm{mol}\) (c) \(E_{a}=85 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-50 \mathrm{~kJ} / \mathrm{mol}\)

Short answer

The ranking of the reactions from slowest to fastest, based on their activation energies and energy changes, is: (b), (c), (a).

Step-by-step solution

Comparing Activation Energies

To rank the reactions from slowest to fastest, we can first look at their activation energies. The reaction with the highest activation energy is expected to be the slowest because it requires more energy for the reaction to proceed. Recall that the activation energies for the three reactions are: (a) \(E_{a}=75 \mathrm{~kJ} / \mathrm{mol}\) (b) \(E_{a}=100 \mathrm{~kJ} / \mathrm{mol}\) (c) \(E_{a}=85 \mathrm{~kJ} / \mathrm{mol}\) From these values, we can see that reaction (b) has the highest activation energy, followed by reaction (c) and then reaction (a).

Considering Energy Changes

Now let's consider the energy changes for each reaction. The energy change indicates whether the reaction is endothermic (positive \(\Delta E\)) or exothermic (negative \(\Delta E\)). In general, exothermic reactions tend to be faster than endothermic reactions, as they release energy and promote more particle collisions. The energy changes for the three reactions are: (a) \(\Delta E=-20 \mathrm{~kJ} / \mathrm{mol}\) (b) \(\Delta E=+30 \mathrm{~kJ} / \mathrm{mol}\) (c) \(\Delta E=-50 \mathrm{~kJ} / \mathrm{mol}\) From these values, we can see that reaction (a) and (c) are exothermic while reaction (b) is endothermic. Since exothermic reactions are generally faster, we can tentatively rank the reactions as: (c) > (a) > (b).

Combining Activation Energies and Energy Changes

Finally, we can combine the rankings from the activation energies and energy changes to determine the overall ranking from slowest to fastest. Taking into account the activation energy ranking from Step 1 and the energy change ranking from Step 2, we have: Slowest to Fastest: (b) > (c) > (a) Therefore, the ranking of the reactions from slowest to fastest is: (b), (c), (a).

Key concepts

Activation Energy

Activation energy is a key concept in understanding chemical reaction rates. It represents the minimum amount of energy required to initiate a chemical reaction. Think of it as the energy barrier that reactants must overcome for a reaction to proceed. The size of this barrier influences how quickly a reaction occurs. A higher activation energy means that it takes more time and energy for reactants to transform into products, thus slowing down the reaction rate.

In the context of the given exercise, reaction (b) has the highest activation energy at 100 kJ/mol, meaning it requires the most energy to initiate, making it the slowest among the three. On the other hand, reaction (a), with an activation energy of 75 kJ/mol, has the lowest barrier, making it faster than the others when considering this factor alone. Reaction (c) falls in between these two with an activation energy of 85 kJ/mol.

Exothermic and Endothermic Reactions

Chemical reactions are often categorized into two types based on energy changes: exothermic and endothermic reactions. In exothermic reactions, energy is released, usually in the form of heat, as the reaction proceeds. This release of energy often makes the reactions more spontaneous and sometimes more rapid due to the increased likelihood of particle collisions.

Endothermic reactions, by contrast, absorb energy from their surroundings. This energy input is necessary to sustain the reaction, typically making such reactions slower compared to exothermic reactions since energy must continually be supplied.

From the exercise, reaction (a) and (c) are exothermic, having negative \( \Delta E \) values of -20 kJ/mol and -50 kJ/mol, respectively. Reaction (b) is endothermic with a positive \( \Delta E \) of +30 kJ/mol. The negative \( \Delta E \) values indicate energy is being released, thereby supporting faster reaction rates than that of reaction (b).

Energy Changes in Reactions

Energy changes in reactions are crucial to understanding the overall dynamics and rate of a chemical process. These changes are represented by the differences in energy content between the reactants and the products.\

• A negative \( \Delta E \) value signifies that the reaction is exothermic, as it results in a net release of energy.
• A positive \( \Delta E \) indicates an endothermic reaction, where energy is absorbed.

In the given exercise, we notice distinct energy changes:

• Reaction (a) releases 20 kJ/mol of energy, making it an exothermic process.
• Reaction (b) requires an additional 30 kJ/mol of energy, identifying it as endothermic, thus needing more energy to drive the reaction forward.
• Reaction (c) releases a significant 50 kJ/mol of energy, the largest energy release among the three, favoring it as the fastest due to the ease in maintaining the reaction dynamics.

These energy changes give insight into not just the speed of reactions but also their feasibility under given environmental conditions.