The conversion of vinyl allyl ether to pent-4-enol follows first order kinetics. The following plot is obtained for such a reaction:
The rate constant for the reaction is

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$2.3 \times 10^{- 2} s^{- 1}$

$1.2 \times 10^{- 2} s^{- 1}$

$8.4 \times 10^{- 2} s^{- 1}$

Ā $4.6 \times 10^{- 2} s^{- 1}$

answer is C.

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Detailed Solution

$\begin{array}{l} k = \frac{2 .303}{t} \log \frac{a}{a - x} \\ \frac{kt}{2 .303} = \log a - \log (a - x) \\ ∴ \log (a - x) = \log a - \frac{kt}{2 .303} \\ \log (a - x) = \log a - \frac{k}{2 .303} t \end{array}$

(Equation of straight line)

y = mx + c

$Slope = \frac{- k}{2 .303} = \frac{- 6}{10 \times 60}$

$∴ k = 2.30 \times 10^{- 2} s^{- 1}$

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