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  • Nitric oxide (NO) reacts with oxygen to produce nitrogen dioxide. If the mechanism of reaction is        <img alt="\mathrm{NO}+\mathrm{O}_2 \stackrel{\mathrm{K}}{\rightle

Nitric oxide (NO) reacts with oxygen to produce nitrogen dioxide. If the mechanism of reaction is
       \mathrm{NO}+\mathrm{O}_2 \stackrel{\mathrm{K}}{\rightleftharpoons} \mathrm{NO}_3 \text { (fast) } \\

       \mathrm{NO}_3+\mathrm{NO} \stackrel{\mathrm{K}_1}{\longrightarrow} \mathrm{NO}_2+\mathrm{NO}_2 \text { (slow) }

Which among the following represents rate law?

Option: 1

\mathrm{Rate} =\mathrm{K}^{\prime}[\mathrm{NO}]\left[\mathrm{O}_2\right]


Option: 2

\mathrm{Rate =\mathrm{K}^{\prime}[\mathrm{NO}]\left[\mathrm{O}_2\right]^2}


Option: 3

\mathrm{ Rate =K^{\prime}\left[\mathrm{NO}^2\left[\mathrm{O}_2\right]\right.}


Option: 4

\mathrm{ Rate =\mathrm{K}^{\prime}[\mathrm{NO}]^3\left[\mathrm{O}_2\right]}


Answers (1)

\mathrm{ Rate=\mathrm{K}_1\left[\mathrm{NO}_3\right][\mathrm{NO}]}   .....(i)


Since ther is no such option, we shall see if we can replace \mathrm{\left[\mathrm{NO}_3\right]}  in terms of  \mathrm{ [NO]}.
For that we shall use the given fast reaction.
\mathrm{\mathrm{K} =\left[\mathrm{NO}_3\right] /\left([\mathrm{NO}]\left[\mathrm{NO}_2\right]\right) }
\mathrm{ \Rightarrow\left[\mathrm{NO}_3\right]=\mathrm{K}\left([\mathrm{NO}]\left[\mathrm{NO}_2\right]\right) }


Putting it in Eq. (i)
\mathrm{\text { Rate } =\mathrm{K}_1 \mathrm{~K}\left([\mathrm{NO}]\left[\mathrm{NO}_2\right]\right)[\mathrm{NO}] }

\mathrm{\Rightarrow \text { Rate }=\mathrm{K}^{\prime}[\mathrm{NO}]^2\left[\mathrm{NO}_2\right]}

Posted by

Ramraj Saini

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