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Consider the reaction of nitrogen dioxide and carbon monoxide.

[tex]\[
NO_2(s) + CO(s) \rightarrow NO(s) + CO_2(s)
\][/tex]

The reaction is believed to be a two-step process represented by the following mechanism.

[tex]\[
\begin{array}{l}
\text{Step 1: } NO_2 + NO_2 \rightarrow NO_3 + NO \\
\text{Step 2: } NO_3 + CO \rightarrow NO_2 + CO_2
\end{array}
\][/tex]

Quantitative studies have found that increasing the concentration of CO had no effect on the rate of the reaction, but increasing that of NO[tex]\(_2\)[/tex] increased the rate of the reaction.

Choose the correct answer to complete the following sentence.

The slowest step is [tex]$\square$[/tex] 1, and it is called the rate [tex]$\square$[/tex] determining step.



Answer :

GinnyAnswer
To determine the slowest and rate-determining step in the given reaction mechanism, we consider the following points:

1. The overall reaction combines [tex]\( \text{NO}_2 \)[/tex] and [tex]\( \text{CO} \)[/tex] to produce [tex]\( \text{NO} \)[/tex] and [tex]\( \text{CO}_2 \)[/tex].

2. The reaction mechanism proposed consists of two steps:
[tex]\[ \begin{array}{l} \text { Step 1: } \text{NO}_2 + \text{NO}_2 \rightarrow \text{NO}_3 + \text{NO} \\ \text { Step 2: } \text{NO}_3 + \text{CO} \rightarrow \text{NO}_2 + \text{CO}_2 \end{array} \][/tex]

3. Experimental findings have shown that increasing the concentration of [tex]\( \text{CO} \)[/tex] has no effect on the rate of reaction, while increasing the concentration of [tex]\( \text{NO}_2 \)[/tex] increases the rate of the reaction.

Given these points, we can deduce the following:

- Since increasing the concentration of [tex]\( \text{CO} \)[/tex] does not affect the rate of the reaction, step 2 involving [tex]\( \text{CO} \)[/tex] is not the rate-determining step. This implies that step 2 is relatively fast.

- Conversely, since increasing the concentration of [tex]\( \text{NO}_2 \)[/tex] increases the reaction rate, it suggests that [tex]\( \text{NO}_2 \)[/tex] directly influences the rate-determining step. This information points towards step 1 as the slower step which involves [tex]\( \text{NO}_2 \)[/tex].

Therefore, we can conclude that the slowest step is step 1, and it is called the rate-determining step.

In summary:
The slowest step is 1, and it is called the rate-determining step.

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