Question

Thermal decomposition of $N_2{O}_5$ occurs as per the equation below
$2N_2{O}_5\to 4N{O}_2+O_2$
The correct statement is

• A. $O_2$ production rate is four times the $N{O}_2$ production rate
• B. $O_2$ production rate is the same as the rate of disappearance of $N_2{O}_5$
• C. Rate of disappearance of $N_2{O}_5$ is one-fourth of $N{O}_2$ production rate
• D. Rate of disappearance of $N_2{O}_5$ is twice the $O_2$ production rate

Answer 1

The correct option is D Rate of disappearance of $N_2{O}_5$ is twice the $O_2$ production rate

$2N_2{O}_5\to 4N{O}_2+O_2$
$rate=\frac{1}{2}\left(\frac{-d\left[N_2{O}_5\right]}{dt}\right)=\frac{1}{4}\left(\frac{d\left[N{O}_2\right]}{dt}\right)=\frac{d\left[O_2\right]}{dt}$
a) $\frac{d\left[N{O}_2\right]}{dt}=4\frac{d\left[O_2\right]}{dt}$
Thus $N{O}_2$ production rate is four times the $O_2$ production rate.
b) We know,
$\frac{1}{2}\left(\frac{-d\left[N_2{O}_5\right]}{dt}\right)=\frac{d\left[O_2\right]}{dt}$
So $O_2$ production rate is half the rate of disappearance of $N_2{O}_5$.
c)$\frac{1}{2}\left(\frac{-d\left[N_2{O}_5\right]}{dt}\right)=\frac{1}{4}(\frac{d\left[N{O}_2\right]}{dt}$
$\left(\frac{-d\left[N_2{O}_5\right]}{dt}\right)=\frac{1}{2}\left(\frac{d\left[N{O}_2\right]}{dt}\right)$
So, Rate of disappearance of $N_2{O}_5$ is one-half of $N{O}_2$ production rate.
d) $\frac{1}{2}\left(\frac{-d\left[N_2{O}_5\right]}{dt}\right)=\frac{d\left[O_2\right]}{dt}$
$\Rightarrow \left(\frac{-d\left[N_2{O}_5\right]}{dt}\right)=2\frac{d\left[O_2\right]}{dt}$
So, rate of disappearance of $N_2{O}_5$ is twice the $O_2$ production rate.