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The following mechanism has been proposed for the reaction of $\mathrm{NO}$ with $\mathrm{Br}_2$ to form $\mathrm{NOBr}$ : $\mathrm{NO}(\mathrm{g})+\mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons \mathrm{NOBr}_2(\mathrm{~g})$
$$
\mathrm{NOBr}_2(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})
$$
If the second step is the rate determining step, the order of the reaction with respect to $N O(g)$ is
Options:
$$
\mathrm{NOBr}_2(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})
$$
If the second step is the rate determining step, the order of the reaction with respect to $N O(g)$ is
Solution:
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Verified Answer
The correct answer is:
2
2
$$
\mathrm{NO}(\mathrm{g})+\mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons \mathrm{NOBr}_2(\mathrm{~g})
$$
$$
\mathrm{NOBr}_2(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})
$$
$$
\begin{aligned}
\mathrm{R} & =\mathrm{K}\left[\mathrm{NOBr}_2\right][\mathrm{NO}] \\
& =\mathrm{K} \cdot \mathrm{K}_{\mathrm{c}}[\mathrm{NO}]\left[\mathrm{Br}_2\right][\mathrm{NO}], \text { where } \mathrm{K}_{\mathrm{c}}=\frac{\left[\mathrm{NOBr}_2\right]}{\left[\mathrm{NO}_2\right]\left[\mathrm{Br}_2\right]} \\
& =\mathrm{K}^{\prime}[\mathrm{NO}]^2\left[\mathrm{Br}_2\right]
\end{aligned}
$$
\mathrm{NO}(\mathrm{g})+\mathrm{Br}_2(\mathrm{~g}) \rightleftharpoons \mathrm{NOBr}_2(\mathrm{~g})
$$
$$
\mathrm{NOBr}_2(\mathrm{~g})+\mathrm{NO}(\mathrm{g}) \longrightarrow 2 \mathrm{NOBr}(\mathrm{g})
$$
$$
\begin{aligned}
\mathrm{R} & =\mathrm{K}\left[\mathrm{NOBr}_2\right][\mathrm{NO}] \\
& =\mathrm{K} \cdot \mathrm{K}_{\mathrm{c}}[\mathrm{NO}]\left[\mathrm{Br}_2\right][\mathrm{NO}], \text { where } \mathrm{K}_{\mathrm{c}}=\frac{\left[\mathrm{NOBr}_2\right]}{\left[\mathrm{NO}_2\right]\left[\mathrm{Br}_2\right]} \\
& =\mathrm{K}^{\prime}[\mathrm{NO}]^2\left[\mathrm{Br}_2\right]
\end{aligned}
$$
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