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