A first order reaction takes 40 min for 30% decomposition . Calculate `t_(1//2)`.

Explanation

30% completion means, x = 30% of a = 0.3a
For a first order reaction , `k=(2.303)/(t)log.(a)/(a-x)=(2.303)/(40)log.(10)/(7)`
`therefore" "k=(2.303)/(t)xx0.1549=8.918xx10^(-3)" min"^(-1)`
For first order reaction,
`t_(1//2)=(0.693)/(k)=(0.693)/(8.918xx10^(-3))=77.7min`