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

In conclusion, based on their activation energies, Reaction (b) is the fastest, and Reaction (c) is the slowest. This is because Reaction (b) has the lowest activation energy of 35 kJ/mol, and Reaction (c) has the highest activation energy of 55 kJ/mol.

Step-by-step solution

Understand the relationship between activation energy and reaction rate

To analyze the given reactions, we must first understand how activation energy affects the rate of a reaction. Activation energy is the minimum amount of energy required for a reaction to occur. Reactions with a lower activation energy require less energy to proceed and therefore are more likely to occur, meaning that they are faster. In contrast, reactions with a higher activation energy require more energy, making them slower.

Compare activation energies

To determine which reaction is the fastest and which is the slowest, we need to compare the activation energies of the three reactions: (a) Activation Energy (Ea) = 45 kJ/mol (b) Activation Energy (Ea) = 35 kJ/mol (c) Activation Energy (Ea) = 55 kJ/mol

Determine the fastest and slowest reactions

Based on the comparisons in Step 2, we can determine the following: - Fastest reaction: Since the reaction with the lowest activation energy is the fastest one, Reaction (b) has the lowest activation energy of 35 kJ/mol, making it the fastest reaction. - Slowest reaction: Since the reaction with the highest activation energy is the slowest, Reaction (c) has the highest activation energy of 55 kJ/mol, making it the slowest reaction. In conclusion, Reaction (b) is the fastest, and Reaction (c) is the slowest. This is because Reaction (b) has the lowest activation energy, and Reaction (c) has the highest activation energy.

Key concepts

Activation Energy

Activation energy is a key concept in reaction kinetics. It represents the minimum energy required for reactants to transform into products. Think of it as a hill that reactants need to climb before they can slide down to form products.
In simpler terms, if a reaction has a low activation energy, it's like a short hill—easy to climb, allowing the reaction to proceed quickly once the climb is conquered. Conversely, a high activation energy is akin to a steep hill—difficult to surmount, slowing down the reaction speed.
In the context of the given reactions, comparing their activation energies provides insight into their relative speeds. Lower activation energy results in faster reactions, as less energy is needed to reach the transition state. This crucial factor helps chemists predict which reactions will occur quickly and which will lag.

Reaction Rate

The rate of a chemical reaction is an expression of how quickly or slowly reactants turn into products. It's influenced by factors such as temperature, concentration, surface area, and importantly, activation energy.
In the exercise, we compare reactions with different activation energies to determine their speeds, assuming all other factors are identical. Reaction rates tend to be higher when activation energy is lower. This is because molecules can more readily meet the energy threshold for the reaction to proceed.
Understanding reaction rates is vital in many fields, from industrial manufacturing to biological processes. It allows scientists and engineers to control and optimize processes to meet desired outcomes efficiently.

Energy Changes

Energy changes in a reaction usually refer to the difference in energy between reactants and products, often denoted as ΔE. This can indicate whether a reaction is exothermic (releasing energy) or endothermic (absorbing energy).
For the reactions in the exercise, ΔE helps us understand not only the direction of energy flow but also potential energy barriers. Though ΔE isn't directly related to the speed of a reaction, it provides context for the thermodynamics alongside kinetics.
While kinetic factors like activation energy determine how fast a reaction occurs, the energy change tells us how much energy will be exchanged with the surroundings during the reaction. In essence, reaction kinetics and energy changes together help in predicting the overall feasibility and characteristics of a chemical reaction.

• Exothermic reactions have a negative ΔE, indicating energy release.
• Endothermic reactions have a positive ΔE, indicating energy absorption.