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Question

A first order reaction has a specific reaction rate of 10-2 s-1. How much time will it take for 20 g of the reactant to reduce to 5 g?


A

238.6 s

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B

138.6s

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C

346.6s

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D

693.0s

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Solution

The correct option is B

138.6s


For a first order reaction,
Rate constant (k)=2.303tlogaax
Where, a =initial concentration
a–x =concentration after time ‘t’
t =times in sec.
Given, a =20 g, a - x =5 g, k=102
t=2.303102log205
=138.6s
Alternatively,
Half –life for the first order reaction,
t12=0.693k=0.693102=69.3s
Two half –lives are required for the reduction of 20 g of reactant into 5 g.
20gt1210gt125g.
Total time =2t12=2×69.3=138.6s


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