`75%`. of a first order reaction is complete is 30 min. Calculate (a) half life, (b) rate constant and (c) time required for `99.9%` completion of the reaction.

Explanation

Time required for `75%` completion of the reaction is `2` half - lives=30 min .
(a) Half-life `(t_(1//2))=15` min (b) Rate constant,
`k=(0.693)/(t_(1//2))=(0.693)/(15)=0.046 "min"^(-1)("or") 7.7xx10^(-4)s^(-1)`
(c ) Time required for `99.9%` of the reaction (t)
`t=(2.303)/(k)log.(a)/(a-x)=(2.303)/(0.046)log.(100)/(0.1)=149"min"`