The half-life period of a first-order chemical reaction is `6.93 min`. The time required for the completion of `99%` of the chemical reaction will be `(log 2 = 0.301)`

Options

A. `230.3 min`
B. `23.03 min`
C. `46.06 min`
D. `460.6 min`

Answer

C

Explanation

Half-life `= 6.93 min, k_(1) = (0.693)/(0.693) = 0.1 "min"^(-1)`
Rate constant for the first-order reaction is given by
`k = (2.303)/(t)"log"([A_(0)])/([A])`
Where `[A_(0)] =` initial concentration
`[A] =` final concentration
`0.1 = (2.303)/(t) xx "log"(100)/(1)`
`0.1 = (2.303)/(t) xx log10^(2)`
`t = (2.303 xx 2)/(0.1) xx 2 log10 = 46.06 min`