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Question

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).

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Solution

A1storder−−−t1/2(A)=54 minB1storder−−−t1/2(B)=18 min

A0=B0=N0
At=A02t54

Bt=B02t18

according to question,
At=16.Bt

A02t54=16×B02t18

2t/18t/54=16

22t/54=16=24
2t54=4
t=108 min

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