For the reaction, $2 \mathrm{NO}_{2(\mathrm{~g})} \rightarrow 2…

For the reaction, $2 \mathrm{NO}_{2(\mathrm{~g})} \rightarrow 2 \mathrm{NO}_{(\mathrm{g})}+\mathrm{O}_{2(\mathrm{~g})}, \frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}$ is $1.3 \times 10^{-5} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{sec}^{-1}$, What is rate of $\mathrm{O}_2$ ?
  1. $1.3 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{sec}^{-1}$
  2. $3.25 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{sec}^{-1}$
  3. $1.62 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{sec}^{-1}$
  4. $6.5 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{sec}^{-1}$

Solution

$\begin{aligned} & -\frac{1}{2} \frac{\mathrm{d}\left[\mathrm{NO}_2\right]}{\mathrm{dt}}=\frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}} \\ & \frac{1}{2}\left(1.3 \times 10^{-5}\right)=\frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}} \\ & \frac{\mathrm{d}\left[\mathrm{O}_2\right]}{\mathrm{dt}}=6.5 \times 10^{-6} \frac{\mathrm{mo} 1}{\mathrm{~L}-\mathrm{sec}}\end{aligned}$

Asked in: MHT CET 2022 (11 Aug Shift 1)

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