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Question

A first order reaction is half completed in 45 minutes. How long does it need for 99.9% of the reaction to be completed?

A
20 hours
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B
10 hours
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C
7.5 hours
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D
5 hours
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Solution

The correct option is C 7.5 hours
Each half life would reduce the concentration to half of its original value. So, 99.9% completion takes place in 10 half-lives. Remember 210=1024 and 1/10240.001

Hence time taken = 45 × 10 minutes = 450 minutes = 7.5 hours.

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