Question

The decomposition reaction $2\mathrm{N}{}_2\mathrm{O}{}_5(\mathrm{g})\stackrel{\mathrm{\Delta }}{\to }2\mathrm{N}{}_2\mathrm{O}{}_4(\mathrm{g})+\mathrm{O}{}_2(\mathrm{g})$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After $Yx10^3$ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is $5x10^{-4}$ $s^{-1}$, assuming ideal gas behavior, the value of Y is_____

Answer 1

Answer: 2.30

$2\mathrm{N}{}_2\mathrm{O}{}_5(\mathrm{g})\stackrel{\mathrm{\Delta }}{\to }2\mathrm{N}{}_2\mathrm{O}{}_4(\mathrm{g})+\mathrm{O}{}_2(\mathrm{g})$ at constant $V,T$
$\begin{array}{cccc}t=0& 1& & \\ t=y\times 10^{3}sec& \left(1-2P\right)& 2P& P\end{array}$
$P_T=\left(1+P\right)=1.45$
$P=0.45$ atm
$\left(2K\right)t=2.303log\left(\frac{1}{1-2P}\right)$
$\left(2\times 5\times 10^{-4}\right)\times y\times 10^3=2.303$log $\frac{1}{0.1}$
$y=2.303=2.30$