Problem 80 - Chemistry: The Central Science in SI Units, Global Edition

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) The overall chemical equation for the reaction is: \(\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g)\) (b) NO is serving as a catalyst in this reaction. (c) The absence of measurable NO₂ accumulation does not rule out the proposed mechanism, as it might suggest that the second step of the mechanism is much faster than the first step.

Step 1: Find the overall reaction equation

To determine the overall chemical equation, we will add the two steps of the reaction mechanism: \[ \begin{aligned} \mathrm{NO}(g)+\mathrm{N}_{2} \mathrm{O}(g) & \longrightarrow \mathrm{N}_{2}(g)+\mathrm{NO}_{2}(g) \\ 2 \mathrm{NO}_{2}(g) & \longrightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \end{aligned} \] Add both equations together and cancel any species that appear on both sides of the equation (in this case, NO and NO₂): \[ \begin{aligned} \cancel{\mathrm{NO}(g)}+\cancel{\mathrm{N}_{2} \mathrm{O}(g)} + 2 \cancel{\mathrm{NO}_{2}(g)} & \longleftrightarrow \mathrm{N}_{2}(g)+\cancel{\mathrm{NO}_{2}(g)} + 2 \cancel{\mathrm{NO}(g)}+\mathrm{O}_{2}(g) \end{aligned} \] This simplifies to: \[ \mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \]

Step 2: Determine the role of NO

To understand whether NO is serving as a catalyst or an intermediate, we should analyze how it behaves in the reaction mechanism. A catalyst speeds up the reaction by participating in the reaction steps but is not consumed in the overall reaction. An intermediate is formed and consumed during the reaction steps. In the mechanism, NO is consumed in the first step and then regenerated in the second step. Since it is not consumed in the overall reaction, NO is acting as a catalyst.

Step 3: Discuss the effect of non-accumulating NO₂ on the proposed mechanism

The fact that experiments do not show measurable accumulation of NO₂ during the decomposition of N₂O does not necessarily rule out the proposed mechanism. It might indicate that the second step of the reaction mechanism (the decomposition of NO₂) is much faster than the first step (the reaction between NO and N₂O). In this case, the intermediate NO₂ would be rapidly consumed as soon as it is produced, making it difficult to detect its accumulation experimentally. In conclusion: (a) The overall chemical equation for the reaction is: \(\mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g)\) (b) NO is serving as a catalyst in this reaction. (c) The absence of measurable NO₂ accumulation does not rule out the proposed mechanism, as it might suggest that the second step of the mechanism is much faster than the first step.

Key Concepts

Catalyst

In chemical reactions, a catalyst is a substance that increases the reaction rate without being consumed in the process. In the decomposition of \(\mathrm{N}_2\mathrm{O}\), NO acts as a catalyst. This means it participates in the reaction steps but emerges unchanged at the end of the overall process.
A catalyst works by providing an alternative reaction pathway with a lower activation energy. This allows more reactant particles to collide effectively, speeding up the reaction.

• Catalysts can be homogeneous (in the same phase as the reactants) or heterogeneous (in a different phase).
• They are vital in many industrial processes, making reactions more efficient and economical.
• Importantly, because NO is regenerated in the process, it is not present in the overall reaction equation.

Intermediate

Reaction intermediates are species that are formed during a reaction mechanism but do not appear in the overall balanced equation. In the mechanism for the \(\mathrm{N}_2\mathrm{O}\) decomposition, \(\mathrm{NO}_2\) is identified as an intermediate.
Intermediates are crucial because they help bridge the gap between reactants and products by forming transient species that facilitate the reaction pathway.

• They are typically unstable and short-lived.
• Evidence of intermediates often involves detecting them during the course of the reaction, although they might not accumulate if their consumption rate is high.
• Intermediates are important for understanding reaction kinetics and helping chemists design better catalysts.

Reaction Rate

The reaction rate is a measure of how quickly reactants are converted into products in a chemical reaction. In this context, the presence of NO as a catalyst affects the reaction rate by providing a pathway with a lower activation energy.
Factors affecting reaction rate include the nature of the reactants, temperature, concentration, and the presence of a catalyst.

• Catalysts significantly alter reaction rates without being consumed themselves.
• The concentration of the catalyst can affect how much the reaction rate is increased.
• Understanding reaction rates is essential in both laboratory and industrial settings to control the speed of reactions and optimize output.

Overall Reaction Equation

The overall reaction equation sums up the reactants and products of a chemical process, discounting any intermediates or catalysts involved in the multiple steps. In the decomposition of \(\mathrm{N}_2\mathrm{O}\), the overall reaction is simplified to:
\[\mathrm{N}_2 \mathrm{O}(g) \longrightarrow \mathrm{N}_2(g) + \mathrm{O}_2(g)\]
The process to obtain this involves adding up the individual steps of a reaction mechanism and canceling out species that appear on both sides of the equation.

• Catalysts like NO do not appear in the final equation, even though they are involved in intermediate steps.
• The overall equation provides a simplified view of the chemical transformation occurring between reactants and products.
• This simplification is essential for stoichiometric calculations and predicting the yields of reactants and products.