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)

$t_{1/3}=23$min
$\therefore k=\frac{0.693}{t_{1/2}}=\frac{0.693}{23}$
Further, for a reaction to complete $90\%$ of reaction,
$t=\frac{2.303}{k}log\frac{a}{a-0.9a}$
$=\frac{2.303}{0.693}\times 23log10$
$=76.4$ minutes