Question

For a first order reaction, the time required for $99.9\%$ of the reaction to take place is nearly

• A. 10 times that required for half of the reaction
• B. 100 times that required for two-third of the reaction
• C. 10 times that required for one-fourth of the reaction
• D. 20 times that required for half of the reaction

Answer 1

Answer: (A)

Time required to complete $99.9\%$ of reaction
$t_{99.9}=\frac{2.303}{k}\log \frac{100}{100-99.9}$
$=\frac{2.303}{k}\log 1000=\frac{6.909}{k}$
and $t_{1/2}=\frac{2.303}{k}\log \frac{100}{100-50}$
$=\frac{2.303}{k}\log 2=\frac{0.693}{k}$
So, $t_{99.9}$ is $10$ times that of required for half of the reaction.