Question

Half life of a First order reaction is 45 minutes. How long does it need to complete 99.9% of the reaction?

• A. 5 hours
• B. 7.5 hours
• C. 7 3/10 hours
• D. 20 hours

Answer 1

Answer: (C)

$t_{1/2}=45$ minutes
For 1st order reaction $t_{1/2}=\frac{0.693}{k}$
$\therefore k=\frac{0.693}{45}mi{n}^{-1}=0.0154mi{n}^{-1}$
Again for 1st order reaction we have
$k=\frac{2.303}{t}\log \left[\frac{100}{100-99.9}\right]$
(considering original concentration to be 100)
$t=\frac{2.303}{k}\log \left[\frac{100}{0.1}\right]$
$t=\frac{2.303}{0.0154}\log 1000$
$t=\frac{2.303}{0.0154}\times 3=448.636$ minutes
$t=7\frac{3}{10}\text{ hours. }$