Cyclopropane rearranges to form propene

This follows first order kinetics. The rate constant is $2.714 \times 10^{- 3} s e c^{- 1}$ . The initial concentration of cyclopropane is 0.29 M. What will be the concentration of cyclopropane after 100 sec?

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$0.035 M$

$0.145 M$

$0.22 M$

$0.0018 M$

answer is B.

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Detailed Solution

$k = \frac{2.303}{t} \log \frac{a}{(a - x)}$
$(a - x)$ is the concetration left after 100 sec.
$2.714 \times 10^{- 3} = \frac{2.303}{100} \log \frac{0.29}{(a - x)}$
$\begin{array}{l} \Rightarrow \frac{0.2714}{2.303} = \log \frac{0.29}{(a - x)} \Rightarrow 0.118 = \log \frac{0.29}{(a - x)} \\ \Rightarrow (a - x) = 0.22 M \end{array}$