Question

The decomposition of nitrogen dioxide, 2 \(\mathrm{NO}_{2} \longrightarrow\) \(2 \mathrm{NO}+\mathrm{O}_{2},\) occurs in a two-step sequence at elevated temperatures. The first step is \(\mathrm{NO}_{2} \longrightarrow \mathrm{NO}+\mathrm{O}\) . Predict a possible second step that, when combined with the first step, gives the complete reaction.

Short answer

The second step is \(\text{O} + \text{O} \rightarrow \text{O}_2\).

Step-by-step solution

Identify the Given Reaction

The given overall reaction for the decomposition is: 2 \(\text{NO}_2 \rightarrow 2 \text{NO} + \text{O}_2\).

Analyze the First Step

The first step of the reaction is given as: \(\text{NO}_2 \rightarrow \text{NO} + \text{O}\). In this step, one molecule of \(\text{NO}_2\) decomposes into one molecule of \(\text{NO}\) and one oxygen atom \(\text{O}\).

Determine the Role of the Oxygen Atom

After the first step, the oxygen atom (\(\text{O}\)) must react with other species to complete the overall reaction. Since we need \(\text{O}_2\) in the final products, consider a reaction that can produce \(\text{O}_2\).

Propose a Possible Second Step

Conclude that the oxygen atom \(\text{O}\) must combine with another oxygen atom to form \(\text{O}_2\). Therefore, the second step could be: \(\text{O} + \text{O} \rightarrow \text{O}_2\).

Combine the Two Steps

Verify the combination of the two steps to ensure it matches the overall reaction: 1. \(\text{NO}_2 \rightarrow \text{NO} + \text{O}\)2. \(\text{O} + \text{O} \rightarrow \text{O}_2\)Adding these two steps gives the complete reaction: 2 \(\text{NO}_2 \rightarrow 2 \text{NO} + \text{O}_2\).

Key concepts

Reaction Mechanisms

To understand complex chemical reactions, we often break them down into simpler steps. These steps are collectively known as the reaction mechanism. Each step details a part of the overall reaction and helps explain how reactants transform into products. This breakdown is especially useful in multi-step reactions, like the decomposition of nitrogen dioxide \(\text{NO}_2\), because it provides insight into intermediate products and their transformations.

A reaction mechanism consists of several elementary steps. Each step involves the making or breaking of bonds and produces intermediates, which are species that appear in the steps but not in the overall reaction. By combining these steps, we get the full picture of how the reaction proceeds from start to finish. In the case of \(2\,\text{NO}_2 \rightarrow 2 \text{NO} + \text{O}_2\), the mechanism involves two steps. The first step produces an intermediate oxygen atom, which then reacts in the second step to form molecular oxygen O2.

Chemical Kinetics

Chemical kinetics is the study of the rates at which chemical processes occur. It helps us understand the speed of reactions and the factors that affect this speed. By studying the kinetics of a reaction, we can gather data about each step's speed in the mechanism. This is crucial for reactions like the decomposition of nitrogen dioxide, which involves multiple steps and intermediates.

The rate of a reaction depends on several factors including concentration, temperature, and catalysts. For example, the first step in the \(\text{NO}_2\) decomposition reaction is \(\text{NO}_2 \rightarrow \text{NO} + \text{O}\). The rate at which this step occurs depends on the concentration of \(\text{NO}_2\), and the energy required to break its bonds. The faster this step occurs, the sooner the intermediate oxygen atom will be available for the next step.

The second step \(\text{O} + \text{O} \rightarrow \text{O}_2\), which forms molecular oxygen, also has its own rate and depends on the availability of intermediate oxygen atoms. Studying the kinetics of each step helps scientists manipulate conditions to control the reaction speed.

Reaction Steps

Breaking down complex reactions into simpler, manageable steps is essential for understanding and predicting reaction behavior. Each step in a reaction mechanism must follow two main rules: they must add up to the overall reaction, and they must obey the laws of conservation of mass and energy.

For the decomposition of nitrogen dioxide, we start with the given overall reaction: \(2 \text{NO}_2 \rightarrow 2 \text{NO} + \text{O}_2\). The process involves two key reaction steps:

• **Step 1:** \(\text{NO}_2 \rightarrow \text{NO} + \text{O}\) – In this step, one molecule of nitrogen dioxide decomposes into one nitrogen monoxide (NO) molecule and one oxygen atom (O),
• **Step 2:** \(\text{O} + \text{O} \rightarrow \text{O}_2\) – Here, two oxygen atoms combine to form an oxygen molecule (\(\text{O}_2\)).

By combining these steps, we recreate the overall reaction: \(2 \text{NO}_2 \rightarrow 2 \text{NO} + \text{O}_2\). This stepwise analysis helps us understand how individual bond-breaking and bond-forming events lead to the products. It also ensures that both mass and energy are conserved in each step, providing a complete and accurate picture of the reaction process.