Question

If the $t_{1/2}$ for a first order reaction is $0.4$ min, the time of or $99.9$% completion of the reaction is about ________ min.

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is D $4$

$t_{1/2}=\frac{In2}{k}=0.4$min

for $99.9\%$, $a_t=\frac{0.1a_0}{100}=\frac{a_0}{1000}$

$kt=In\frac{a_0}{a_t}=In1000$

$(\frac{In2}{0.4}.t=3In10$

$t=1.2\times \frac{In10}{in2}=4$ min