The thermal decomposition of a compound is of first order. If `50%` of a sample of the compound is decomposed in 120 minutes, how long it take for `90%` of the compounds to decompose.

Options

A. Nearly `240` minutes
B. Nearly `480` minutes
C. Nearly `450` minutes
D. Nearly `400` minutes

Answer

D

Explanation

`k=(0.693)/(t_(1//2))=(0.693)/(120)`
`k=(2.303)/(t)log.(a)/(a-x)`
`(0.693)/(120)=(2.303)/(t)log.(100)/(100-90)`
`t=(120xx2.303)/(0.693)`min
`t=400` min