1.

In a first order reaction `A rarr` product, 80% of the given sample of compound decomposes in 40 min. What is the half life period of the reaction ?

Answer» Given, 80% of sample decomposes
Time = 40 min.
`t_(1//2)` (half life = ? )
Consider, initial concentration of sample is 100.
`:.[A]_(o)=100`
`:.[A]_(t)=100-80`
`=20 ` Final concentration
`:.k=(2.303)/(t)log_(10).([A]_(o))/([A]_(t))`
`=(2.303)/(40)log_(10).(100)/(20)`
`=(2.303)/(40) log_(10)5`
`=(2.303)/(40)xx0.6989`
`k=0.04024`
`:.` Half life `t_(1//2)=(0.693)/(k)`
`=(0.693)/(0.04024)=17.22`
Half-life is `17.22` min.


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