A first order reaction completes 25% of the reaction in 100 mins. What are the rate constant and half life values of the reactions ?

Explanation

Given data : Time taken for 25% completion of the reaction = 100 mins
a = 100, x = 25 and a - x = 75 , t = 100 min
Formula : `k=(2.303)/(t)"log"(a)/(a-x), t_(1//2)=(0.693)/(k)`
Solution : `k=(2.303)/(100)"log"(100)/(100-25)`
`=(2.303)/(100)"log"(100)/(75)=(2.303)/(100)"log"(4)/(3)`
`= (2.303)/(100)xx0.1249`
Rate constant `(k)=2.8773xx10^(-3)"min"^(-1)`
`t_(1//2)=(0.693)/(k)=(0.693)/(2.8773xx10^(-3)"min"^(-1))`
`=(693)/(2.8773)=240.85`
Half - life period `(t_(1//2))= 240.85` minutes.