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

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a

\ln (p / p_{0})

versus t

b

\ln \{(p - p_{0}) / p_{0}\}

versus t

c

\ln \{(2 p - p_{0}) / p_{0}\}

versus t

d

\ln \{(3 p - p_{0}) / (2 p_{0})\}

versus t

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detailed solution

Correct option is D

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

moderate

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