Consider the following first order gas phase reaction at constant temperature $\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ If the total pressure of the gases is found to be 200 torr after $23 \mathrm{sec}$. and 300 torr upon the complete decomposition…

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Consider the following first order gas phase reaction at constant temperature $\mathrm{A}(\mathrm{g}) \rightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g})$ If the total pressure of the gases is found to be 200 torr after $23 \mathrm{sec}$. and 300 torr upon the complete decomposition of A after a very long time, then the rate constant of the given reaction is ______ $\times 10^{-2} \mathrm{~s}^{-1}$ (nearest integer) [Given : $\log _{10}(2)=0.301$]

Aicharya · Accepted Answer

$\begin{aligned} & \mathrm{A}(\mathrm{g}) ightarrow 2 \mathrm{~B}(\mathrm{~g})+\mathrm{C}(\mathrm{g}) \ & \mathrm{P}_{23}=\mathrm{P}_0+2 \mathrm{x}=200 \ & \mathrm{P}_{\infty}=3 \mathrm{P}_0=300 \ & \mathrm{P}_0=100 \ & \mathrm{~K}=\frac{1}{\mathrm{t}} \ln \frac{\mathrm{P}_{\infty}-\mathrm{P}_0}{\mathrm{P}_{\infty}-\mathrm{P}_{\mathrm{t}}} \ & \mathrm{K}=\frac{2.3}{23} \log \frac{300-100}{300-200} \ & =\frac{2.3 	imes 0.301}{23}=0.0301=3.01 	imes 10^{-2} \mathrm{sec}^{-1} \ & \end{aligned}$

Consider the following first order gas phase reaction at constant temperature \(\mathrm{A}(\mathrm{g})…

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