Question

One pathway for the destruction of ozone in the upper atmosphere is $$\begin{array}{l}\mathrm{O}_{3}(g)+\mathrm{NO}(g) \longrightarrow \mathrm{NO}_{2}(g)+\mathrm{O}_{2}(g) \quad \text { Slow } \\\\\mathrm{NO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g) \quad \text { Fast } \\ \text { Overall reaction: } \mathrm{O}_{3}(g)+\mathrm{O}(g) \rightarrow 2 \mathrm{O}_{2}(g)\end{array}$$ a. Which species is a catalyst? b. Which species is an intermediate? c. The activation energy \(E_{\mathrm{a}}\) for the uncatalyzed reaction $$\mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2 \mathrm{O}_{2}(g)$$ is \(14.0 \mathrm{~kJ} . E_{\mathrm{a}}\) for the same reaction when catalyzed by the presence of \(\mathrm{NO}\) is \(11.9 \mathrm{~kJ} .\) What is the ratio of the rate constant for the catalyzed reaction to that for the uncatalyzed reaction at \(25^{\circ} \mathrm{C}\) ? Assume that the frequency factor \(A\) is the same for each reaction. d. One of the concerns about the use of Freons is that they will migrate to the upper atmosphere, where chlorine atoms can be generated by the reaction $$\mathrm{CCl}_{2} \mathrm{~F}_{2} \stackrel{\mathrm{hr}}{\longrightarrow} \mathrm{CF}_{2} \mathrm{Cl}+\mathrm{Cl}$$ Freon- 12 Chlorine atoms also can act as a catalyst for the destruction of ozone. The first step of a proposed mechanism for chlorinecatalyzed ozone destruction is $$\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)$$ Slow Assuming a two-step mechanism, propose the second step in the mechanism and give the overall balanced equation. e. The activation energy for Cl-catalyzed destruction of ozone is \(2.1 \mathrm{~kJ} / \mathrm{mol}\). Estimate the efficiency with which \(\mathrm{Cl}\) atoms destroy ozone as compared with NO molecules at \(25^{\circ} \mathrm{C}\). Assume that the frequency factor \(A\) is the same for each catalyzed reaction and assume similar rate laws for each catalyzed reaction.

Short answer

a. The catalyst in this mechanism is \(\mathrm{NO}\). b. The intermediate in this mechanism is \(\mathrm{NO}_2\). c. The ratio of the rate constant for the catalyzed reaction to that of the uncatalyzed reaction at \(25^{\circ}\mathrm{C}\) is approximately 5.48. d. The second step of the proposed mechanism is \(\mathrm{ClO}(g)+\mathrm{O}(g) \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_{2}(g)\) (fast), giving the overall balanced equation: \(\mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2\mathrm{O}_{2}(g)\). e. The efficiency of \(\mathrm{Cl}\) atoms to destroy ozone is approximately 60.9 times more than that of \(\mathrm{NO}\) molecules at \(25^{\circ}\mathrm{C}\).

Step-by-step solution

a. Identifying catalyst

In a reaction mechanism, a catalyst is a substance that is involved in the elementary steps of the reaction but is not used up. It is the substance that appears in the initial steps and is regenerated in the final steps. In this mechanism, \(\mathrm{NO}\) is involved in both steps 1 and 2 but is not present in the overall reaction. Therefore, \(\mathrm{NO}\) is the catalyst.

b. Identifying intermediate

An intermediate is a species that is formed and consumed during the reaction mechanism but does not appear in the overall reaction. In this mechanism, \(\mathrm{NO}_2\) is formed in the first step and consumed in the second step. Therefore, \(\mathrm{NO}_2\) is the intermediate.

c. Calculating rate constant ratio

The ratio of the rate constant for the catalyzed reaction to the uncatalyzed reaction can be calculated using the Arrhenius equation: \[\frac{k_{\text{catalyzed}}}{k_{\text{uncatalyzed}}} = \frac{e^{-E_{a,\text{catalyzed}}/RT}}{e^{-E_{a,\text{uncatalyzed}}/RT}}\] Given, \(E_{a,\text{catalyzed}} = 11.9\mathrm{~kJ}, E_{a,\text{uncatalyzed}} = 14.0\mathrm{~kJ}, T= 25^{\circ} \mathrm{C} = 298\mathrm{~K}.\) We know that \(R = 8.314\mathrm{~J~mol^{-1}~K^{-1}}\). So: \[\frac{k_{\text{catalyzed}}}{k_{\text{uncatalyzed}}} = \frac{e^{-(11.9\times10^3)/(8.314\times298)}}{e^{-(14.0\times10^3)/(8.314\times298)}} \approx 5.48\] Hence, the ratio of rate constant for catalyzed reaction to that of the uncatalyzed reaction at \(25^{\circ}\mathrm{C}\) is approximately 5.48.

d. Proposing the second step and overall balanced equation

Considering a two-step mechanism involving \(\mathrm{Cl}\) as a catalyst, the first step is already given: \[\mathrm{Cl}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \text{ (slow)}\] To regenerate the catalyst (\(\mathrm{Cl}\)) and balance the overall reaction, we can propose the second step to be: \[\mathrm{ClO}(g)+\mathrm{O}(g) \longrightarrow \mathrm{Cl}(g)+\mathrm{O}_{2}(g) \text{ (fast)}\] Adding these two steps and canceling the intermediate (\(\mathrm{ClO}\)), we obtain the overall balanced equation: \[\mathrm{O}_{3}(g)+\mathrm{O}(g) \longrightarrow 2\mathrm{O}_{2}(g)\]

e. Estimating efficiency of Cl compared to NO

Given the activation energy for the Cl-catalyzed destruction of ozone is \(2.1\mathrm{~kJ/mol}\). We can calculate the ratio of rate constants using Arrhenius equation with the same temperature: \[\frac{k_\text{Cl-catalyzed}}{k_\text{NO-catalyzed}} = \frac{e^{-(2.1\times10^3)/(8.314\times298)}}{e^{-(11.9\times10^3)/(8.314\times298)}} \approx 60.90\] The efficiency of \(\mathrm{Cl}\) atoms to destroy ozone is approximately 60.9 times more than that of \(\mathrm{NO}\) molecules at \(25^{\circ}\mathrm{C}\).

Key concepts

Catalysis

Catalysis is a process where a catalyst speeds up a chemical reaction without being consumed. In the ozone destruction pathway, a catalyst is something that makes the reaction happen faster or at a lower energy. Here, nitrogen oxide (NO) serves as a catalyst in the reactions involving ozone (O extsubscript{3}). NO participates in both steps: it helps in one reaction and is regenerated in another, ending in the same form it started.

• A catalyst reduces activation energy, making the reaction easier to start.
• It appears in the initial steps and reappears unchanged at the end.

Emphasizing that catalysts are crucial for environmental chemistry, NO and other such catalysts play significant roles in both creation and destruction of atmospheric compounds.

Activation Energy

Activation energy (E extsubscript{a}) is the minimum energy required for a chemical reaction to occur. It acts as the energy barrier that reactants need to overcome to convert into products. Every reaction has its own unique activation energy.

• For uncatalyzed ozone destruction: E extsubscript{a} = 14.0 kJ/mol.
• With NO as a catalyst: E extsubscript{a} is reduced to 11.9 kJ/mol.

The reduction in activation energy by NO exemplifies how catalysts work. This smaller energy barrier allows more ozone molecules to convert into products, as more of the ozone molecules can surpass the lowered energy requirement. By changing the activation energy, we can alter the rate constants and thus the speed of reactions.

Reaction Kinetics

Reaction kinetics involves studying the rate at which reactions occur and the steps they take to transform reactants into products. By understanding these processes, we can predict how fast a reaction proceeds. In the given ozone destruction, the reaction rate is affected by the presence of NO:

• Arrhenius equation: relates the rate constant (k) to activation energy and temperature.
• By calculating the ratio of rate constants with and without a catalyst, we observe how much faster the reaction becomes with a lower E extsubscript{a}.

For example, the calculation showed the NO-catalyzed reaction increases the rate constant by approximately 5.48 times compared to the uncatalyzed reaction at room temperature. Such kinetic studies highlight how catalysts like NO enhance reaction rates significantly.

Reaction Intermediates

Reaction intermediates are species that are formed and consumed during the course of a reaction mechanism. They are not found in the overall reaction equation because they exist only transiently. In the ozone destruction pathway:

• NO extsubscript{2} is generated in the first slow step.
• It is then consumed in the second fast step, leading to the final products.

These intermediates are essential for energy-efficient pathways, and they provide insights into the intricacies of reaction mechanisms. Studying intermediates helps scientists to decipher complex processes like atmospheric reactions, improving our understanding of phenomena such as ozone depletion.