Question

$50\%$ of a first order reaction is complete in $23$ minutes. Calculate the time required to complete $90\%$ of the reaction

• A. $70.4$ minutes
• B. $76.4$ minutes
• C. $38.7$ minutes
• D. $35.2$ minutes

Answer 1

Answer: (B)

$76.4$ minutes

Answer 2

$t_{1/3} = 23\,$min
$\therefore k = \frac{0.693}{t_{1/2}} = \frac{0.693}{23}$
Further, for a reaction to complete $90\%$ of reaction,
$t = \frac{2.303}{k} log \frac{a}{a-0.9 a}$
$= \frac{2.303}{0.693}\times 23 \,log \,10$
$= 76.4$ minutes