Question

Dinitropentaoxide decomposes as follows :
$N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$
Given that

${}_d\left[N_2{O}_5\right]/dt=k_1\left[N_2{O}_5\right]$
$d\left[N{O}_2\right]/dt=k_2\left[N_2{O}_5\right]$
$d\left[O_2\right]/dt=k_3\left[N_2{O}_5\right]$
What is the relation between $k_1,k_{2}and{k}_3$?

• A. $2k_1=k_2=4k_3$
• B. $2k_2=k_1=4k_3$
• C. $2k_3=k_2=4k_1$
• D. $2k_1=k_2=4k_2$

Answer 1

The correct option is A $2k_1=k_2=4k_3$

$N_2{O}_5\left(g\right)\to 2N{O}_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)$
$-d\left[N_2{O}_5\right]/dt=k_1\left[N_2{O}_5\right]$
$d\left[N{O}_2\right]/dt=k_2\left[N_2{O}_5\right]$
$d\left[O_2\right]/dt=k_3\left[N_2{O}_5\right]$
$-\frac{d{N}_2{O}_5}{dt}=\frac{1}{2}\frac{dN{O}_2}{dt}=2\frac{d{O}_2}{dt}$
$k_1=\frac{k_2}{2}=2k_3$
$2k_1=k_2=4k_3$