A first order reaction takes 40 min for 30% decomposition. Calculate t1/2.

Question 4.19: A first order reaction takes 40 min for 30% decomposition. Calculate t_1/2.
Answer
Given that
Order of reaction = first
Let Initial amount = 100 g
Amount in % after 30 % decomposition = 100 - 30 = 70%
Amount in g [R]= 70% of 100g = 70g
Use the formula of first order reaction

Time required for the decomposition of 30% of reaction
After calculation we get
t = 8.918 x 10 ^{– 3} min^-1
use the formula of t_1/2 of reaction

t_1/2 = 78 min (approx)
Answer
Half life is 78 approx