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
• B. 10 hours
• C. 7.5 hours
• D. 5 hours

Answer 1

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 $2^{10}=1024$ and $1/1024\approx 0.001$

Hence time taken = 45 $\times$ 10 minutes = 450 minutes = 7.5 hours.