Problem 56 - Chemistry: The Central Science in SI Units, Global Edition

Question

For the elementary process \(\mathrm{N}_{2} \mathrm{O}_{5}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{NO}_{3}(g)\) the activation energy \(\left(E_{a}\right)\) and overall \(\Delta E\) are \(154 \mathrm{~kJ} / \mathrm{mol}\) and \(136 \mathrm{~kJ} / \mathrm{mol}\), respectively. (a) Sketch the energy profile for this reaction, and label \(E_{a}\) and \(\Delta E\). (b) What is the activation energy for the reverse reaction?

Step-by-Step Solution

Answer

The energy profile for the given reaction can be sketched by drawing the reactants and products at different energy levels, and an arc representing the activation energy (Ea = 154 kJ/mol). The overall change in energy (ΔE) is labeled as 136 kJ/mol. To find the activation energy for the reverse reaction, we first calculate the energy difference between the peak and product energy levels (18 kJ/mol) and add it to the given ΔE. Thus, the activation energy for the reverse reaction is 154 kJ/mol.

Step 1: Determine the reactants and products

In the given reaction, the reactants are N2O5 (g) and the products are NO2 (g) and NO3 (g).

Step 2: Draw the energy profile

Draw a horizontal axis labeled "Reaction Progress," and a vertical axis labeled "Energy." Start by drawing a horizontal line at a certain height representing the reactant's energy level, and another horizontal line at a higher height representing the product's energy level. Draw an arc above the reactant's energy level, indicating the transition state where the activation energy (Ea) is at its maximum.

Step 3: Label the activation energy and overall change in energy

Label the distance between the reactant's energy level and the peak of the arc as the activation energy, "Ea = 154 kJ/mol". Label the difference in energy between the reactant and product energy levels as "ΔE = 136 kJ/mol". #b. Finding the activation energy for the reverse reaction#

Step 1: Calculate the energy difference between the peak and product energy level

Determine the energy difference between the peak level (maximum energy) and the product energy level. Since we already know that Ea (forward) is 154 kJ/mol and ΔE is 136 kJ/mol, we can calculate this difference by subtracting ΔE from Ea. Energy difference = Ea - ∆E = 154 kJ/mol - 136 kJ/mol = 18 kJ/mol

Step 2: Calculate the activation energy for the reverse reaction

Now, to find the activation energy for the reverse reaction (Ea_reverse), add the energy difference obtained in Step 1 to the overall change in energy (∆E). Ea_reverse = energy difference + ΔE = 18 kJ/mol + 136 kJ/mol = 154 kJ/mol Thus, the activation energy for the reverse reaction is 154 kJ/mol.

Key Concepts

Elementary Process

In chemistry, an elementary process is a fundamental step in a reaction that cannot be broken down into simpler processes. This makes it different from overall reactions that may consist of several elementary steps.
For instance, in the reaction \[\text{N}_2\text{O}_5(g) \longrightarrow \text{NO}_2(g) + \text{NO}_3(g)\]this transformation from reactants to products occurs in one go. There's no intermediary step in an elementary process.
Thus, these reactions feature only one transition state, and they are singular, step-based changes in the structure of molecules. Understanding elementary processes helps in comprehending how reactions proceed at a molecular level.

Energy Profile

An energy profile graph is a visual representation illustrating the changes in energy as a reaction proceeds.
The plot typically has:

• A horizontal axis labeled as "Reaction Progress", indicating the steps of the reaction over time.
• A vertical axis indicating "Energy", which shows the energy levels of the reactants, products, and the highest energy state.

For the given reaction, the energy profile displays a starting energy level for \(\text{N}_2\text{O}_5(g)\) and a higher energy level for its products \(\text{NO}_2(g) + \text{NO}_3(g)\).
At the peak of the energy profile, we see the transition state, portraying the moment in the reaction where the system requires maximum energy before proceeding to form products.

Energy Difference

The energy difference, often denoted as \(\Delta E\), is essential in understanding the "net energy" change of a chemical reaction. It represents the difference in energy between reactants and products.
For the transformation from \(\text{N}_2\text{O}_5(g)\) to \(\text{NO}_2(g) + \text{NO}_3(g)\), \(\Delta E\) is the energy change from the reactant level to the product level and it is measured at \(136\text{ kJ/mol}\).This means that the products are at a higher energy state compared to the reactants and energy is absorbed during the reaction.
Energy difference helps to determine whether a reaction is endothermic (absorbing energy) or exothermic (releasing energy). In this case, since \(\Delta E\) is positive, the reaction is endothermic.

Transition State

The transition state in a reaction is an extremely unstable and ephemeral phase, characterized by the highest energy point along the reaction path. It is not something you'd see or hold, but rather a fleeting moment where old bonds break, and new ones begin to form.

• This is marked on the energy profile by the peak between energy levels of reactants and products.
• The difference between the energy level of the reactants and this peak gives the activation energy \( (E_a) \) of the reaction, which is \(154\text{ kJ/mol}\).

Understanding the transition state is crucial because it tells us about the reaction's rate. A higher peak equates to a larger \(E_a\), indicating that more energy is needed for the reaction to occur, making it slower. Conversely, a lower peak and lower \(E_a\) mean a faster reaction.
The studied reaction involves overcoming this energy barrier before the reactants can transform into the products.