Question

A first order reaction completes $60\%$ in $20$ minutes. The time required for the completion of $90\%$ of the reaction is approx

• A. 30 minutes
• B. 40 minutes
• C. 50 minutes
• D. 60 minutes

Answer 1

Answer: (C)

$K=\frac{2.303}{t}\log \frac{100}{100-x}$
$K=\frac{2.303}{20}\log \frac{100}{100-60}...(i)$
$K=\frac{2.303}{t}\log \frac{100}{100-90}...(ii)$
$(i)(ii)$
$\frac{K=\frac{2.303}{20}\log \frac{100}{40}}{K=\frac{2.303}{t}\log \frac{100}{10}}\to \frac{1}{t}\log 10=\frac{1}{20}[\log 10-\log 4]$
$\Rightarrow \frac{1}{t}\times 1=\frac{1}{20}[1-0.6020]$
$\therefore t=50$ minutes