Question

For a reaction, $N_2{O}_5⟶2N{O}_2+\frac{1}{2}{O}_2$
Given:
$\frac{-d\left[N_2{O}_5\right]}{dt}=k_1\left[N_2{O}_5\right]$
$\frac{d\left[N{O}_2\right]}{dt}=k_2\left[N_2{O}_5\right]$
$\frac{d\left[O_2\right]}{dt}=k_3\left[N_2{O}_5\right]$
The relation between $k_1,k_2$ and $k_3$ are:

• A. $2k_1=k_2=4k_3$
• B. $k_1=k_2=k_3$
• C. $2k_1=4k_2=k_3$
• D. $\frac{1}{2}{k}_1=k_2=\frac{1}{4}{k}_3$

Answer 1

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

For the reaction,
$N_2{O}_5⟶2N{O}_2+\frac{1}{2}{O}_2$
We can express the rate as:
$\frac{-d\left[N_2{O}_5\right]}{dt}=\frac{1}{2}\frac{d\left[N{O}_2\right]}{dt}=\frac{1}{0.5}\frac{d\left[O_2\right]}{dt}$
$=k_1\left[N_2{O}_5\right]=\frac{1}{2}{k}_2\left[N_2{O}_5\right]=2k_3\left[N_2{O}_5\right]$
Hence, we can write
$k_1=\frac{k_2}{2}=2k_3$
$\Rightarrow 2k_1=k_2=4k_3$