The following mechanism has been proposed for the reaction of $\mathrm{NO}$ with $\mathrm{Br}_2$ to form…

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
  1. 1
  2. 0
  3. 3
  4. 2

Solution

$ \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} $

Asked in: JEE Main 2006

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