Chemistry - Chemical Kinetics Question with Solution | TestHub

Consider the decomposition of${\mathrm{N}}_2{\mathrm{O}}_5$as
${\mathrm{N}}_2{\mathrm{O}}_5\to 2\mathrm{N}{\mathrm{O}}_2+\frac{1}{2}{\mathrm{O}}_2$
The rate of reaction is given by
$\frac{-\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{d}\mathrm{t}}=\frac{1}{2}\frac{\mathrm{d}\left[\mathrm{N}{\mathrm{O}}_2\right]}{\mathrm{d}\mathrm{t}}=2\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{d}\mathrm{t}}={\mathrm{k}}_1\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]$
Therefore,$\frac{-\mathrm{d}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]}{\mathrm{d}\mathrm{t}}={\mathrm{k}}_1\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]$
$\frac{+\mathrm{d}\left[\mathrm{N}{\mathrm{O}}_2\right]}{\mathrm{d}\mathrm{t}}=2{\mathrm{k}}_1\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]={\mathrm{k}}_1^{\mathrm{\text{'}}}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]$
$\frac{\mathrm{d}\left[{\mathrm{O}}_2\right]}{\mathrm{d}\mathrm{t}}=\frac{1}{2}{\mathrm{k}}_1\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]={\mathrm{k}}_1^{"}\left[{\mathrm{N}}_2{\mathrm{O}}_5\right]$
Choose the correct option.