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.

Explanation

Half life of reaction =120 min
We know that,
`k'(0.693)/(t_(1//2))=(0.693)/(120)=5.77xx10^(-3)"min"^(-1)`
Applying firs order reaction equation,
`t=(0.303)/(k)"log"_(10)(a)/(a-x)`
If `a=100,x=9 or (a-x)=10`
`So" " t=(2.030)/(5.77xx10^(-3))."log"10=(2.303)/(5.77xx10^(-3))=399` min