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Question

Two substances A and B are present such that [A0]=4[B0] and half life of A is 5 min and that of B is 15 min. If they start decaying at the same time following first order kinetics how much time later will take if the concentration of both of them would be same?

A
15 min
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B
10 min
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C
5 min
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D
12 min
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Solution

The correct option is C 15 min
Amount of A left in n1 halves = (12)n1[A0]
Amount of A left in n2 halves = (12)n2[B0]
At the end, according to the question
[A0]2n1=[B0]2n242n1=12n2,([A0]=4[B0])
2n12n2=42n1n2=(2)2n1n2=2
n2=(n12)
Also t = n1t1/2(A);t=n2t1/2(B)
(Let concentration of both become equal after time t)
n1×t1/2(A)n2×t1/2(B)=1n1×5n2×15=1n1n2=3 ...(II)
From equations (i) and (ii), we get
n1=3,n2=1
t = 3 × 5 = 15 min

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