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Question

A flask contains a mixture of two compounds AB and XY. Both of these decompose on heating by first order reactions. If the half-life of AB is 30 min and that of XY is 10 min, how long will it take for the concentration of AB to be four times that of XY? Assume the initial concentration of both AB and XY to be the same.

A
30 min
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B
40 min
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C
50 min
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D
60 min
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Solution

The correct option is A 30 min
lna0a=kt for a first order reaction.
Let t1 and t2 be half lives of AB and XY respectively.
k1=ln2t1,k2=ln2t2
lna0aAB=ln230t
lna0aXY=ln210t
And aAB=4aXY
lna04aXY=ln230t
Removing logs (taking exponents on LHS and RHS):
2t10t30=22
t10t30=2
20t=600
t=30 min

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