Thermal decomposition of compound `x` is a first order reaction. If `75%` of `x` is decomposed in `100 min`. How long will it take for `90%` of the compound to decompose ? Given `log 2=0.30`

Options

A. `190 min`
B. `176.66 min`
C. `166.66 min`
D. `156.66 min`

Answer

C

Explanation

`K = (1)/(t)ln[(1)/(1-3//4)] = (1)/(100)ln(4)`
`K = (ln4)/(100)` and `t._(9) = (1)/(k)ln[10] = (100)/(ln4)ln 10`
`= (100)/(.6) = 166.66 min`.