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

Explanation

Half life of the reaction `=120` min.
We know that
`k=(0.693)/(t_(1//2))=(0.693)/(120)`
If `a=100, x=90` ,
`a-x=10`
`=5.77xx10-3"min"-1`
Applying first order rate equation.
`R=(2.303)/(t) log. (a)/(a-x)`
If `a=100, x=90, a-x=10`
`=(2.303)/(5.77xx10^(-3))log10`
`=(2.303)/(5.77xx10^(-3))=399` min.