Q. 75% of a first order reaction was completed in 32 minutes. When was 50% of the reaction completed

Solution:

$k=\dfrac{2.303}{t}log_{10} \left(\dfrac{a}{a-x}\right)$
$k=\dfrac{2.303}{t}log \left(\dfrac{100}{100-75}\right)....(i)$
$k= \dfrac{2.303}{t}log \left(\dfrac{100}{100-50}\right).....(ii)$
From the two eqns. (i) and (ii), t = 16 minutes.

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