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: $-\frac{d\left[N_2{O}_5\right]}{dt}=k_1\left[N_2{O}_5\right],\frac{d\left[N{O}_2\right]}{dt}=k_2\left[N_2{O}_5\right],\frac{d\left[O_2\right]}{dt}=k_3\left[N_2{O}_5\right]$.
The relation between $k_1,k_{2}and{k}_3$ is:

• A. $2k_1=k_2=4k_3$
• B. $k_1=2k_2=3k_3$
• C. $2k_1=3k_2=k_3$
• D. $3k_1=k_2=2k_3$

Answer 1

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

The expression for the rate of the reaction is $-\frac{d\left[N_2{O}_5\right]}{dt}=\frac{1}{2}\frac{d\left[N{O}_2\right]}{dt}=2\times \frac{d\left[O_2\right]}{dt}$......(1)
But $-\frac{d\left[N_2{O}_5\right]}{dt}=k_1\left[N_2{O}_5\right]$.....(2)
$\frac{d\left[N{O}_2\right]}{dt}=k_2\left[N_2{O}_5\right]$......(3)
$\frac{d\left[O_2\right]}{dt}=k_3\left[N_2{O}_5\right]$......(4)
Substitute values of equations (2), (3) and (4) in equation (1), we get
$k_1\left[N_2{O}_5\right]=\frac{1}{2}{k}_2\left[N_2{O}_5\right]=2\times k_3\left[N_2{O}_5\right]$
$2k_1=k_2=4k_3$