The reaction CH32O(g)→CH4(g)+H2(g)+CO(g)follows first-order kinetics. The reaction is studied at constant volume with p0 as the initial pressure of CH32O. If p is the pressure at time t, then a linear plot will be observed between

# The reaction ${\left({\mathrm{CH}}_{3}\right)}_{2}\mathrm{O}\left(\mathrm{g}\right)\to {\mathrm{CH}}_{4}\left(\mathrm{g}\right)+{\mathrm{H}}_{2}\left(\mathrm{g}\right)+\mathrm{CO}\left(\mathrm{g}\right)$follows first-order kinetics. The reaction is studied at constant volume with ${p}_{0}$ as the initial pressure of ${\left({\mathrm{CH}}_{3}\right)}_{2}\mathrm{O}$. If p is the pressure at time t, then a linear plot will be observed between

1. A

$\mathrm{ln}\left(p/{p}_{0}\right)$ versus t

2. B

$\mathrm{ln}\left\{\left(p-{p}_{0}\right)/{p}_{0}\right\}$ versus t

3. C

$\mathrm{ln}\left\{\left(2p-{p}_{0}\right)/{p}_{0}\right\}$ versus t

4. D

$\mathrm{ln}\left\{\left(3p-{p}_{0}\right)/\left(2{p}_{0}\right)\right\}$ versus t

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### Solution:

For a gaseous reaction at constant volume the rate constant is $\mathrm{ln}\left\{\left(\mathrm{\Delta }{v}_{\mathrm{g}}+1\right){p}_{0}-p\right\}/\left(\mathrm{\Delta }{v}_{\mathrm{g}}{p}_{0}\right)}$ versus t is a straight line for the first-order kinetics. In the present case, $\mathrm{\Delta }{v}_{\mathrm{g}}=2$. Hence the plot of $\mathrm{ln}\left\{3\left({p}_{0}-p\right)/2{p}_{0}\right\}$ versus twill a straight line

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