Problem 59 - Chemistry The Central Science In Si Units

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) \(E_{a}=85 \mathrm{~kJ} / \mathrm{mol} ; \Delta E=-50 \mathrm{~kJ} / \mathrm{mol}\)

Step-by-Step Solution

Answer

Rank: (b) slowest, (c), (a) fastest.

Step 1: Understanding Activation Energy and Rate

The rate of a chemical reaction depends on the activation energy (Ea). A lower activation energy means the reaction is faster, while a higher activation energy means the reaction is slower. Since the collision factors are the same for all reactions, we only need to consider the activation energies for this ranking.

Step 2: Analysis of Reaction A

For reaction (a), the activation energy is \(E_a = 75\, \text{kJ/mol}\) and the energy change \(\Delta E\) is \(-20\, \text{kJ/mol}\). Since \(E_a\) is relatively low, this reaction would be faster than reactions with higher \(E_a\).

Step 3: Analysis of Reaction B

For reaction (b), the activation energy is \(E_a = 100\, \text{kJ/mol}\) and \(\Delta E\) is \(+30\, \text{kJ/mol}\). This reaction has the highest activation energy, suggesting it will be the slowest unless another reaction also has an overlapping factor that surpasses this activation energy.

Step 4: Analysis of Reaction C

For reaction (c), the activation energy is \(E_a = 85\, \text{kJ/mol}\) and \(\Delta E\) is \(-50\, \text{kJ/mol}\). Since the activation energy is higher than (a) but lower than (b), this reaction is predicted to be slower than (a) but faster than (b).

Step 5: Ranking Reactions

Based on the activation energies alone, the reactions can be ranked from slowest to fastest as follows: Reaction (b) \((E_a = 100\, \text{kJ/mol})\), Reaction (c) \((E_a = 85\, \text{kJ/mol})\), Reaction (a) \((E_a = 75\, \text{kJ/mol})\).

Key Concepts

Reaction Rates

In the world of chemistry, reaction rates tell us how fast or slow a chemical reaction occurs. Reaction rate is influenced mainly by the activation energy, represented as \(E_a\). Activation energy is the minimum amount of energy that reacting particles must have to successfully collide and cause a chemical change.

A reaction with a lower activation energy is typically faster because particles need less energy to start the reaction. For example, based on the given activation energies, Reaction (a) with \(E_a = 75\, \text{kJ/mol}\) is the fastest, while Reaction (b) with \(E_a = 100\, \text{kJ/mol}\) is the slowest. This is because it takes more energy to overcome the starting energy barrier in Reaction (b) compared to Reaction (a).

Factors like temperature and concentration can also affect reaction rates, but assuming collision factors are equal, activation energy becomes the major determining factor in our case. This fundamental understanding helps chemists control and predict chemical processes effectively.

Energy Change in Reactions

Energy change in reactions can either be positive or negative, indicating whether the reaction is endothermic or exothermic. An exothermic reaction releases energy, usually in the form of heat, causing the energy change \(\Delta E\) to be negative. Conversely, an endothermic reaction absorbs energy, leading to a positive \(\Delta E\).

For instance, Reaction (a) and Reaction (c) are exothermic with energy changes of \(\Delta E = -20\, \text{kJ/mol}\) and \(\Delta E = -50\, \text{kJ/mol}\) respectively. This means they release energy, contributing to a potentially energetically favorable situation. On the other hand, Reaction (b) is endothermic with \(\Delta E = +30\, \text{kJ/mol}\), meaning it requires an input of energy, which is less favorable from an energy change perspective.

Although energy change itself doesn't directly affect the speed of reaction as much as the activation energy, it gives insights into the overall energy dynamic and favorability of the reaction.

Collision Theory

According to collision theory, for a reaction to occur, reactant molecules must collide with enough energy and the correct orientation. This theory underpins the concept of activation energy, as only collisions that exceed this energy threshold will result in products being formed.

The collision theory also states that the frequency of collisions between effective reactants can affect reaction rates. More frequent and energetic collisions can lead to a higher chance of overcoming the activation barrier, thus speeding up the reaction.

Consider our reactions: while all collisions are assumed to be equally likely or frequent (the collision factor is the same), the variation in reaction rates due to differences in activation energy can be explained by collision theory. Reactions with lower \(E_a\) transform more effectively because the necessary energy is lower, allowing more collisions to initiate the process successfully.

This understanding of molecular collisions helps chemists manipulate and design conditions for achieving desired reaction rates.