The decomposition reaction,\ $2 \mathrm{~N}_{2} \mathrm{O}_{5(\mathrm{~g})} \xrightarrow{\Delta} 2

Question

The decomposition reaction,\ $2 \mathrm{~N}_{2} \mathrm{O}_{5(\mathrm{~g})} \xrightarrow{\Delta} 2 \mathrm{~N}_{2} \mathrm{O}_{4(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$\ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm . After $Y 	imes 10^{3} \mathrm{~s}$, the pressure inside the cylinder is found to be 1.45 atm . If the rate constant of the reaction is $5 	imes 10^{-4} \mathrm{~s}^{-1}$, assuming ideal gas behaviour, the value of $Y$ is _______.\

Professor PC Thomas Classes · Answer

(2.30) :\ $2 \mathrm{~N}_{2} \mathrm{O}_{5(\mathrm{~g})} \xrightarrow{\Delta} 2 \mathrm{~N}_{2} \mathrm{O}_{4(\mathrm{~g})}+\mathrm{O}_{2(\mathrm{~g})}$\ Given : rate constant of the reaction $=$ $5 	imes 10^{-4} \mathrm{~s}^{-1}$\ rate $=-\frac{1}{2} \frac{d\left[\mathrm{~N}_{2} \mathrm{O}_{5}ight]}{d t}=k_{	ext {overall }} P_{\mathrm{N}_{2} \mathrm{O}_{5}}$\ $\Rightarrow-\frac{d\left[\mathrm{~N}_{2} \mathrm{O}_{5}ight]}{d t}=2 k_{	ext {overall }} P_{\mathrm{N}_{2} \mathrm{O}_{5}}$\ $\underset{1-P}{2 \mathrm{~N}_{2} \mathrm{O}_{5(\mathrm{~g})}} \longrightarrow \underset{P}{2 \mathrm{~N}_{2} \mathrm{O}_{4(\mathrm{~g})}}+\underset{P / 2}{\mathrm{O}_{2(\mathrm{~g})}}$ After $Y 	imes 10^{3} \mathrm{~s}$, the total pressure\ $=1+\frac{P}{2}=1.45 \mathrm{~atm}$\ $P=0.90 \mathrm{~atm}$ $$ t=\frac{2.303}{2 k_{	ext {overall }}} \log \left(\frac{1}{1-P}ight) $$ $\Rightarrow Y 	imes 10^{3}=\frac{2.303}{2 	imes 5 	imes 10^{-4}} \log \frac{1}{0.1}$\ $Y=2.303 \approx 2.30$\