A and B decompose via first order kinetics with half-lives 54 . 0 min and 18 . 0 min respectively. Starting from an equimolar non-reactive mixture of A and B , the time taken for the concentration of A to become 16 times that of B is ______ min . (Round off to the Nearest Integer).

Step-by-step solution

Given A = t 1 / 2 = 54   min B = t 1 / 2 = 18   min t = 0 ' x ' M t = 0 ' x ' M ⇒ To calculate : A t = 16 × B t time = ? ⇒ For I order kinetic : A t = A 0 2 n n → no. of Half lives ⇒ Now from the relation ( 1 ) ⇒ x 2 n 1 = x 2 n 2 × 16 ⇒ 2 n 2 = 2 n 1 × 2 4 ⇒ n 2 = n 1 + 4 ⇒ t t 1 / 2 2 = t t 1 / 2 1 + 4 ⇒ t 1 18 - 1 54 = 4 ⇒ t = 4 × 18 × 54 36 ⇒ t = 108   min