Question

Calculate the time required for the completion of 90% of a reaction of first order kinetics. T1/2= 44.1 minutes.

Answer 1

Concept:

For first order reaction the half life and the rate constant are related with each other as

$k = \frac{0.693}{t_{1/2} }$

$t = \frac{2.303}{k}*log\frac{[A_{0}] }{[A_{t}] }$

Solution:

Given that,

$t_{1/2} = 44.1 min$

$A_{0} = 100$

$A_{t} = (100-90) = 10$

$k = \frac{0.693}{44.1} = 0.0157$

On substituting all these values in above formula of first order reaction

We get ,

$t = \frac{2.303}{0.0157}*log\frac{100}{10}$

$t = \frac{2.303}{0.0157}*1 =  146.7 min.$

Conclution:

Time required to complete the given reaction = 146.7 minutes