Problem 105 - Chemistry The Science in Context

Question

Mechanism of NO, Destruction Which of the following mechanisms are possible for the thermal decomposition of \(\mathrm{NO}_{2},\) given that the rate \(=k\left[\mathrm{NO}_{2}\right]^{2} ?\) a. \(\quad \mathrm{NO}_{2}(g) \stackrel{\text { then }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}(g)\) \(\mathrm{O}(g)+\mathrm{NO}_{2}(g) \stackrel{\mathrm{Gist}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) b. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { fait }}{\longrightarrow} \mathrm{N}_{2} \mathrm{O}_{4}(g)\) \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \stackrel{\text { thow }}{\mathrm{fist}} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\longrightarrow}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \stackrel{\text { thm }}{\longrightarrow} \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) \(\mathrm{NO}_{3}(g) \stackrel{\mathrm{fitit}}{\longrightarrow} \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Step-by-Step Solution

Answer

The possible mechanisms are mechanism (b) and mechanism (c).

Step 1: Review the Given Mechanisms

Let's go over each of the three proposed mechanisms for the thermal decomposition of \(\mathrm{NO}_{2}(g)\) a. 1. \(\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}(g)\) 2. \(\mathrm{O}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) b. 1. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2}\mathrm{O}_{4}(g)\) 2. \(\mathrm{N}_{2}\mathrm{O}_{4}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) 3. \(\mathrm{NO}_{3}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\) c. 1. \(\mathrm{NO}_{2}(g)+\mathrm{NO}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{NO}_{3}(g)\) 2. \(\mathrm{NO}_{3}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Step 2: Evaluate Mechanism (a)

First, we describe mechanism (a) using rate laws. The overall rate law should be \(rate = k\left[\mathrm{NO}_{2}\right]^{2}\) 1. For the first reaction: \(r_{1} = k_{1}[\mathrm{NO}_{2}]\) 2. For the second reaction: \(r_{2} = k_{2}[\mathrm{O}][\mathrm{NO}_{2}]\) Since the overall rate law doesn't match the given rate law, mechanism (a) is not valid.

Step 3: Evaluate Mechanism (b)

Next, we will evaluate mechanism (b) using rate laws. The overall rate law should be \(rate = k\left[\mathrm{NO}_{2}\right]^{2}\). 1. For the first reaction: \(r_{1} = k_{1}[\mathrm{NO}_{2}][\mathrm{NO}_{2}] = k_{1}\left[\mathrm{NO}_{2}\right]^{2}\) 2. For the second reaction: \(r_{2} = k_{2}[\mathrm{N}_{2}\mathrm{O}_{4}]\) 3. For the third reaction: \(r_{3} = k_{3}[\mathrm{NO}_{3}]\) Since the first reaction has the same rate law as the given rate law \(k\left[\mathrm{NO}_{2}\right]^{2}\), mechanism (b) can be a valid mechanism.

Step 4: Evaluate Mechanism (c)

Finally, we will evaluate mechanism (c) using rate laws. The overall rate law should be \(rate = k\left[\mathrm{NO}_{2}\right]^{2}\) 1. For the first reaction: \(r_{1} = k_{1}[\mathrm{NO}_{2}][\mathrm{NO}_{2}] = k_{1}\left[\mathrm{NO}_{2}\right]^{2}\) 2. For the second reaction: \(r_{2} = k_{2}[\mathrm{NO}_{3}]\) Similar to mechanism (b), the first reaction has the same rate law as the given rate law \(k\left[\mathrm{NO}_{2}\right]^{2}\). Therefore, mechanism (c) can also be a valid mechanism.

Step 5: Conclusion

Based on the analysis, the two possible mechanisms for the thermal decomposition of \(\mathrm{NO}_{2}(g)\) are mechanism (b) and mechanism (c).

Key Concepts

Rate Law

In chemical kinetics, the rate law is a mathematical expression that describes the relationship between the concentration of reactants and the rate of a chemical reaction. The rate law is crucial as it helps chemists understand how variations in concentration affect the speed at which a reaction proceeds. When known, the rate constant specifically indicates how quickly a reaction occurs at a given temperature.

For the decomposition of \(\mathrm{NO}_{2} \), the given rate law is:

• \(\text{rate} = k[\mathrm{NO}_{2}]^{2}\)

This means the rate of reaction is proportional to the square of the concentration of \(\mathrm{NO}_{2} \). This type of rate law is called second-order because the sum of the powers of the concentration terms is two.

Understanding the rate law helps us determine which reaction mechanism among the proposed alternatives aligns with the experimental data. Mechanisms where the initial step aligns with this rate law, such as mechanisms b and c in our exercise, are more likely to reflect the true process taking place in the reaction.

Reaction Mechanism

A reaction mechanism outlines the sequence or pathway through which a chemical reaction occurs, from reactants to products. It details the elementary steps and intermediates involved, which collectively form the overall reaction.

The purpose of studying reaction mechanisms is to provide a detailed picture of how chemical transformations occur and to help make predictions about the effects of changing conditions like temperature and concentration.

• Mechanism (b): This involves \(\mathrm{NO}_2\) reacting in a dimerization step to form \(\mathrm{N}_2\mathrm{O}_4\), which then decomposes through successive stages to produce \(\mathrm{NO}\) and \(\mathrm{O}_2\).
• Mechanism (c): Involves an initial bimolecular reaction forming intermediates that eventually yields the final products \(\mathrm{NO}\) and \(\mathrm{O}_2\).

Both mechanisms b and c match the given rate law \([\mathrm{NO}_2]^2\), an indication they could represent valid pathways for the decomposition of \(\mathrm{NO}_2\). Understanding which mechanism is correct can shed light on the specific steps and intermediates involved, further illuminating the reaction's dynamics.

Thermal Decomposition

Thermal decomposition refers to the breakdown of chemical substances into simpler elements or compounds through the application of heat. It's a type of chemical reaction where a single compound breaks down into two or more different substances.

In the context of \(\mathrm{NO}_2\), thermal decomposition involves heating \(\mathrm{NO}_2\) until it breaks down into \(\mathrm{NO}\) and \(\mathrm{O}_2\). During this process, energy in the form of heat is absorbed by the \(\mathrm{NO}_2\) molecule, providing enough energy to overcome activation barriers and break chemical bonds.

• Mechanisms involve successive steps that may involve short-lived intermediates like \(\mathrm{NO}_3\) before eventually yielding final stable molecules.
• This process occurs until the compound reaches a sufficient level of energy to break into the products noted above.

Understanding thermal decomposition is essential for industries relying on heat to process materials and also for the safe handling of reactive substances. Such reactions are fundamental, not only in chemistry but also in fields involving material science, environmental technology, and safety engineering.