The rate of reaction $2 \mathrm{~N}_2 \mathrm{O}_5 \longrightarrow 4 \mathrm{NO}_2+\mathrm{O}_2$ can be written in three ways $\begin{aligned} \frac{-d\left[\mathrm{~N}_2 \mathrm{O}_5 ight]}{d t} & =k\left[\mathrm{~N}_2 \mathrm{O}_5 ight] \ \frac{d\left[\mathrm{NO}_2 ight]}{d t} &…

Question

The rate of reaction $2 \mathrm{~N}_2 \mathrm{O}_5 \longrightarrow 4 \mathrm{NO}_2+\mathrm{O}_2$ can be written in three ways $\begin{aligned} \frac{-d\left[\mathrm{~N}_2 \mathrm{O}_5ight]}{d t} & =k\left[\mathrm{~N}_2 \mathrm{O}_5ight] \ \frac{d\left[\mathrm{NO}_2ight]}{d t} & =k^{\prime}\left[\mathrm{N}_2 \mathrm{O}_5ight] \ \frac{d\left[\mathrm{O}_2ight]}{d t} & =k^{\prime \prime}\left[\mathrm{N}_2 \mathrm{O}_5ight] \end{aligned}$ The relationship between $k$ and $k^{\prime}$ and between $k$ and $k^{\prime \prime}$ are

Aicharya · Accepted Answer

$\begin{aligned} & 	ext { Rate }=-\frac{1}{2} \frac{d\left[\mathrm{~N}_2 \mathrm{O}_5ight]}{d t}=\frac{1}{4} \frac{d\left[\mathrm{NO}_2ight]}{d t}=\frac{d\left[\mathrm{O}_2ight]}{d t} \ & \Rightarrow \frac{1}{2} k\left[\mathrm{~N}_2 \mathrm{O}_5ight]=\frac{1}{4} k^{\prime}\left[\mathrm{N}_2 \mathrm{O}_5ight]=k^{\prime \prime}\left[\mathrm{N}_2 \mathrm{O}_5ight] \end{aligned}$ $\begin{array}{llrl} \Rightarrow & \frac{k}{2} & =\frac{k^{\prime}}{4}=k^{\prime \prime} \ & 	herefore & k^{\prime} & =2 k ; k^{\prime \prime}=\frac{k}{2} \end{array}$

The rate of reaction $2 \mathrm{~N}_2 \mathrm{O}_5 \longrightarrow 4 \mathrm{NO}_2+\mathrm{O}_2$ can be…

Solution