A first order reaction is half-completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed ?

A first order reaction is half-completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed ?

A
20 hours
B
10 hours
C
$7 \frac{1}{2}$ hours
D
5 hours

Solution:

For the $1^{st}$ order reaction $t_{50 %} = t_{1 / 2} = 45 \min$

$t_{99.9 %} =_____\min$

$t_{99.9 %} = 10 . t_{1 / 2}$

$t_{99.9 %} = (10) (45) = 450 \min$

=7.50 hrs

= $7 \frac{1}{2}$ hrs

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