Question

The decomposition reaction $\ce{2N2O5(g) ->[\Delta] 2N2O4(g) + O2(g)}$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After $Y x 10^3$ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is $5 x 10^{-4}$ $s^{-1}$, assuming ideal gas behavior, the value of Y is_____

Answer 1

$\ce{2N2O5(g) ->[\Delta] 2N2O4(g) + O2(g)}$ at constant $V, T$
$\begin{matrix}t=0&1&&\\ t=y\times10^{3}\,sec&\left(1-2P\right)&2P&P\end{matrix}$
$P_{T}=\left(1+P\right)=1.45$
$P=0.45$ atm
$\left(2K\right)t=2.303\,log\left(\frac{1}{1-2P}\right)$
$\left(2 × 5 × 10^{-4}\right)\times y\times10^{3}=2.303$log $\frac{1}{0.1}$
$y=2.303=2.30$