For a first order reaction the rate constant is 6.909 min^-1. The time taken for 75% conversion in minutes is:

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$\frac{3}{2} \log \frac{3}{4}$

$\frac{2}{3} \log 2$

$\frac{3}{2} \log 2$

$\frac{2}{3} \log 3$

answer is C.

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Detailed Solution

$\begin{array}{l} k = \frac{2 .303}{t} \log \frac{R_{o}}{R} \\ t = \frac{2 .303}{6 .909} \log \frac{100}{25} = \frac{1}{3} \log 4 \\ t = \frac{1}{3} \log 2^{2} \Rightarrow \frac{2}{3} \log 2 \end{array}$

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