Two substances, 'A' and 'B' are initially present as [A0] = 8[B0] and t1/2 for the first-order decomposition of 'A' and 'B' are 10 and 20 min, respectively. If they start decomposing at the same time,

Question

Two substances, 'A' and 'B' are initially present as [A0] = 8[B0] and t1/2 for the first-order decomposition of 'A' and 'B' are 10 and 20 min, respectively. If they start decomposing at the same time, after how much time, the concentration of both of them would be same?

Prashant Kotian · Accepted Answer

Correct answer: C. [A] = 8B0 e^(-k1 t), [B] = B0 e^(-k2 t). Setting them equal: 8 = e^((k1-k2)t). Taking ln: ln(8) = 3 ln(2) = (ln(2)/10 - ln(2)/20)t = (ln(2)/20)t. Solving for t gives 3 = t/20, so t = 60 min. Therefore, correct answer is C.

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