Question

The rate of the reaction
$2 N_2 O_5 \rightarrow 4 NO_2 + O_2$
can be written in three ways:
$\frac{-d [N_2 O_5]}{dt} = k [N_2 O_5]$
$\frac{d[NO_2]}{dt} = k' [N_2 O_5]$
$\frac{d[O_2]}{dt} = k" [N_2 O_5]$
The relationship between k and k′ and between k and k′′ are-

• A. k' = k, k′′= k
• B. k′= 2k; k′′= k
• C. k′= 2k, k′′= k/2
• D. k′ = 2k; k′′= 2k

Answer 1

Answer: (C)

Rate $ = - \frac{1}{2} \frac{d\left[N_{2}O_{5}\right]}{dt} = + \frac{1}{4} \frac{d\left[NO_{2}\right]}{dt} = \frac{d\left[O_{2}\right]}{dt} $
$ \frac{1}{2} K\left[N_{2} O_{5}\right] = \frac{1}{4} K' \left[N_{2}O_{5}\right] $
$ K' = 2 K$ and $ K" = \frac{K}{2} $