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

see full answer

Talk to JEE/NEET 2025 Toppers - Learn What Actually Works!

Real Strategies. Real People. Real Success Stories - Just 1 call away

An Intiative by Sri Chaitanya

$\ln (p / p_{0})$ versus t

$\ln \{(p - p_{0}) / p_{0}\}$ versus t

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

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

answer is D.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

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