Consider the following reaction, $2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow…
Consider the following reaction,
$2 \mathrm{H}_2(\mathrm{~g})+2 \mathrm{NO}(\mathrm{g}) \rightarrow \mathrm{N}_2(\mathrm{~g})+2 \mathrm{H}_2 \mathrm{O}(\mathrm{g})$
which follows the mechanism given below:
$2 \mathrm{NO}(\mathrm{g}) \stackrel{k_1}{\underset{k_{-1}}{\rightleftharpoons}} \mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})$ $\quad$ (fast equlibrium)
$\mathrm{N}_2 \mathrm{O}_2(\mathrm{~g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_2} \mathrm{~N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ $\quad$(slow reaction)
$\mathrm{N}_2 \mathrm{O}(\mathrm{g})+\mathrm{H}_2(\mathrm{~g}) \xrightarrow{k_3} \mathrm{~N}_2(\mathrm{~g})+\mathrm{H}_2 \mathrm{O}(\mathrm{g})$ $\quad$ (fast reaction)
The order of the reaction is_____
Solution
Rate law $=\mathrm{k}_2\left[\mathrm{~N}_2 \mathrm{O}_2\right]\left[\mathrm{H}_2\right] \quad[\because$ slowest step of reaction is RDS $]$
$\because \frac{\mathrm{k}_1}{\mathrm{k}_{-1}}=\frac{\left[\mathrm{N}_2 \mathrm{O}_2\right]}{[\mathrm{NO}]^2}$
$\therefore \quad\left[\mathrm{N}_2 \mathrm{O}_2\right]=\frac{\mathrm{k}_1}{\mathrm{k}_{-1}}[\mathrm{NO}]^2$
$\therefore \quad$ Rate $=\mathrm{k}_2 \times \frac{\mathrm{k}_1}{\mathrm{k}_{-1}}[\mathrm{NO}]^2\left[\mathrm{H}_2\right]$
$\therefore$ Order of reaction is (3)