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

Options

A. 5 hours
B. `7.5` hours
C. 10 hours
D. 20 hours

Answer

B

Explanation

`k=(0.693)/(45)min^(-1)`
`=(2.303)/(t_(99.9%))log.(a)/(a-0.999a)` or `t_(99.9%)=(2.303xx45)/(0.693)log10^(3)`
`=448min~~7.5` hrs.