Question

Consider the decomposition of $N _{2} O _{5}$ as $N _{2} O _{5} \longrightarrow 2 NO _{2}+\frac{1}{2} O _{2}$ The rate of reaction is given by $\frac{-d\left[ N _{2} O _{5}\right]}{d t}=\frac{1}{2} \frac{d\left[ NO _{2}\right]}{d t}=2 \frac{d\left[ O _{2}\right]}{d t}=k_{1}\left[ N _{2} O _{5}\right]$ Therefore, $\frac{-d\left[ N _{2} O _{5}\right]}{d t}=k_{1}\left[ N _{2} O _{5}\right]$ $\frac{+d\left[ NO _{2}\right]}{d t} =2 k_{1}\left[ N _{2} O _{5}\right]$ $=k_{1}'\left[ N _{2} O _{5}\right] \frac{+d\left[ O _{2}\right]}{d t} =\frac{1}{2} k_{1}\left[ N _{2} O _{5}\right]=k_{1}'' \left[N _{2} O _{5}\right]$ Choose the correct option.

• A. $k_{1}=k_{1}'=k_{1}''$
• B. $k_{1}=2 k_{1}'=k_{1}''$
• C. $4 k_{1}=k_{1}'=2 k_{1}''$
• D. $4 k_{1}=2 k_{1}'=k_{1}''$

Answer 1

Answer: (A)

$k_{1}=k_{1}'=k_{1}''$

Answer 2

Given,
$\frac{-d\left[ N _{2} O _{5}\right]}{d t}=\frac{1}{2} \frac{d\left[ NO _{2}\right]}{d t}=\frac{2 d\left[ O _{2}\right]}{d t}=k_{1}\left[ N _{2} O _{5}\right]$
$\therefore k_{1}\left[ N _{2} O _{5}\right]=2 k_{1}\left[ N _{2} O _{5}\right]=\frac{1}{2} k_{1}\left[ N _{2} O _{5}\right]$
or $k_{1}\left[ N _{2} O _{5}\right]=k_{1}'\left[ N _{2} O _{5}\right]=k_{1}''\left[ N _{2} O _{5}\right]$
$k_{1}=k_{1}'=k_{1}''$