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?

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: \[ \mathrm{N}_{2} \mathrm{O}(g) \longrightarrow \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \]

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.

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.