Question

For the reaction,
$ N_2O_5 \rightarrow 2NO_2 + \frac{1}{2} O_2 $
$ \frac{-d\left[N_{2}O_{5}\right]}{dt} = k_{1}\left[N_{2}O_{5}\right] $
$ \frac{d\left[NO_{2}\right]}{dt} = k_{2}\left[N_{2}O_{5}\right] $
$ \frac{d\left[O_{2}\right]}{dt} = k_{3} \left[N_{2}O_{5}\right] $
The relation in between $ k_1 $ , $ k_2 $ and $ k_3 $ is

• A. $ 2k_1 = k_2 = 4k_3 $
• B. $ k_1 = k_2 = k_3 $
• C. $ 2k_1 = 4k_2 = k_3 $
• D. None of these

Answer 1

Answer: (A)

The rate of reaction is given by
$\frac{-d\left[N_{2}O_{5}\right]}{dt} = + \frac{1}{2} \frac{d\left[NO_{2}\right]}{dt} = +\frac{2d\left[O_{2}\right]}{dt} $
Substituting the given values, we get
$k_{1}\left[N_{2}O_{5}\right] = \frac{1}{2}k_{2}\left[N_{2}O_{5}\right] = 2k_{3} \left[N_{2}O_{5}\right] $
or $k_{1} = \frac{k_{2}}{2} = 2 k_{3} $
or $2k_{1} = k_{2} = 4k_{3}$