A first order reaction takes 40 minutes for `30%` decomposition of rectants. Calculate its half life period.

Explanation

Step-I: Calculation of rate constant:
a=`100%, (a-x)=70%, t=40` min
For first order reaction,
`k=(2.303)/t log (a)/(a-x) =(2.303)/(40"min") log 100/70=(2.303 xx 0.1549)/(40"min") =0.0089 min^(-1)`
Step-II Calculation of half life period `(t_(1//2))`
`t_(1//2) = 0.693/k =(0.693)/(0.0089 min^(-1)) = 78 min`