Question

The decomposition reaction $2N_2{O}_5\left(g\right)\stackrel{\Delta }{\to }2N_2{O}_4\left(g\right)+O_2\left(g\right)$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of $1atm$. After $Y\times {10}^{3}s$, the pressure inside the cylinder is found to be $1.45atm$. If the rate constant of the reaction is $5\times {10}^{-4}{s}^{-1}$, assuming ideal gas behaviour, the value of Y is

Answer 1

Unit of rate constant (k) represent it is a first order reaction.

$2N_2{O}_5\to 2N_2{O}_4+O_2$

t=0 1atm 0 0

t=t 1−p p p/2

Total pressure
$1-P+P+\frac{P}{2}=1.45$

$\frac{P}{2}=0.45$, $P=0.9$
Now,
$t=\frac{2.303}{2\times 5\times {10}^{-4}}log\frac{1}{1-P}$

$y\times {10}^3=\frac{2.303}{2\times 5\times {10}^{-4}}log\frac{1}{1-0.9}=\frac{2.303}{2\times 5\times {10}^{-4}}log10$

$\therefore y=2.30$