A flask contains a mixture of compounds A and B . Both compounds decompose by first-order kinetics. The half-lives for A and B are 300 s and 180 s , respectively. If the concentrations of A and B are equal initially, the time required for the concentration of A to be four times that of B (in s) is : ( Use ln 2 = 0 . 693 )

Step-by-step solution

C t = C 0 e - kt k A = ln 2 300 k = ln 2 T 1 / 2 k B = ln 2 180 C t A = C 0 A e - k A t C t B = C 0 B e - k B t C t , B C t , A = C 0 , B C 0 , A × e k A - k B t 1 4 = e k A - k B t   ln 1 4 = ln 2 300 - ln 2 180 t   - 2 ln 2 = ln 2 300 - ln 2 180 t 2 = 120 180 × 300 t t = 2 × 180 × 300 120 = 900   sec