Given t1/2 of (A) = 5 min
t1/2 of (B) = 15 min.
and initially = [A] = 4[B]
using hit and trial method -
Let after 15 min the concentration of [A]5 = [B]15
using formula -
N = N0 (1/2)n
where,
N = concentration after n half life time
N0 = initial concentration
n = Number of half life time.
Therefore,
concentration of A after 15 min -
[A]15 = [A]0 (1/2)3 where [B]0 = initial concentration
[A]15 = [A]0/8
concentration of B after 15 min -
[B]15 = [B]0 (1/2)1
[B]15 = [B]0/2
∴ [A]15 = [B]15
⇒ [A]0/8 = [B]0/2
∵ Given [A] = 4[B]
∴ 4[B]0/8 = [B]0/2
⇒ [B]0/2 = [B]0/2
Hence, after 15 min. the concentration of A and B become equal.