Problem 80 - Chemistry The Central Science In Si Units

Question

The addition of NO accelerates the decomposition of \(\mathrm{N}_{2} \mathrm{O},\) possibly by the following mechanism: $$ \begin{aligned} \mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) & \longrightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g) \\ 2 \mathrm{NO}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ (a) What is the chemical equation for the overall reaction? Show how the two steps can be added to give the overall equation. (b) Is NO serving as a catalyst or an intermediate in this reaction? (c) If experiments show that during the decomposition of \(\mathrm{N}_{2} \mathrm{O}, \mathrm{NO}_{2}\) does not accumulate in measurable quantities, does this rule out the proposed mechanism?

Step-by-Step Solution

Answer

(a) \(\text{N}_2\text{O}(g) \to \text{N}_2(g) + \text{O}_2(g)\); (b) NO is a catalyst; (c) No, the mechanism is not ruled out.

Step 1: Identifying Components of the Mechanism

Begin by listing the reactions given in each step of the mechanism: \(\text{NO}(g) + \text{N}_2\text{O}(g) \to \text{N}_2(g) + \text{NO}_2(g)\) and \(2 \text{NO}_2(g) \to 2 \text{NO}(g) + \text{O}_2(g)\). These are two sequential reactions that together create the overall reaction.

Step 2: Adding the Reactions

To find the overall reaction, add the two steps together. Cancel out any identical species that appear on both the reactant and product sides. Here, \(\text{NO}\) is both a reactant in the first step and a product in the second step. Also, \(\text{NO}_2\) is produced in the first step and consumed in the second step. The resulting overall reaction is \(\text{N}_2\text{O}(g) \to \text{N}_2(g) + \text{O}_2(g)\).

Step 3: Identifying the Role of NO

Assess the role of \(\text{NO}\) by observing its behavior through the mechanism. Initially, it acts as a reactant in the first step and is regenerated in the second step. Since it is not consumed in the overall reaction, \(\text{NO}\) acts as a catalyst.

Step 4: Analyzing NO2 Accumulation

Determine whether the proposed mechanism aligns with the observed data: the non-accumulation of \(\text{NO}_2\). In the mechanism, \(\text{NO}_2\) is produced in the first step and consumed immediately in the second step, meaning \(\text{NO}_2\) does not accumulate. This supports the validity of the proposed mechanism.

Key Concepts

Understanding Catalysts

A catalyst is a substance that speeds up a chemical reaction without undergoing any permanent change itself. In many reactions, catalysts lower the energy required for reactants to transform into products, known as the activation energy. This makes reactions proceed faster and more efficiently. In the decomposition of \(\text{N}_2\text{O}\), \(\text{NO}\) acts as a catalyst. Even though it participates in the first step of the mechanism, it is regenerated in a later step. Therefore, it is not consumed by the overall reaction. This recycling feature is a hallmark of catalysts. They often appear in both the reactants and the products of reaction steps, but not in the overall balanced chemical equation.

The Role of Chemical Equations

Chemical equations represent chemical reactions using symbols and formulas. They provide a concise way to convey information about reactants and products. For the given decomposition of \(\text{N}_2\text{O}\), the chemical equations outline how molecules interact in each step of the proposed mechanism. By adding the equations of each step and canceling out common species on both sides, we arrive at the overall equation: \(\text{N}_2\text{O} \to \text{N}_2 + \text{O}_2\). This final equation focuses only on the initial reactants and final products, ignoring the intermediates and catalysts that facilitate the process.

Decomposition Reactions Explained

Decomposition reactions involve breaking down a compound into two or more simpler substances. These reactions are the reverse of synthesis reactions. In our context, \(\text{N}_2\text{O}\) decomposes through a series of steps facilitated by a catalyst. The complexity of decomposition reactions can vary, but they often require external factors like heat or a catalyst to proceed. In this mechanism, \(\text{N}_2\text{O}\) breaks down into \(\text{N}_2\) and \(\text{O}_2\) via two steps: interaction with \(\text{NO}\) and regeneration of \(\text{NO}\). This sequential breakdown showcases how catalysts work to keep reactions moving smoothly.

The Significance of Intermediates

Intermediates are species that appear in the steps of a reaction mechanism but not in the overall balanced equation. They are produced in one step and consumed in another, helping convert reactants to final products without being present in the end. \(\text{NO}_2\) in our mechanism is an example of an intermediate. It forms when \(\text{NO}\) reacts with \(\text{N}_2\text{O}\), and then reacts further to regenerate \(\text{NO}\). Its quick formation and consumption prevent its accumulation, aligning with experimental observations. Intermediates are crucial as they often provide insight into the reaction pathway, helping scientists validate or revise proposed mechanisms.