A first order reaction takes 40 min for `30%` decomposition. Calculate `t_(1//2)`. (Given `log 7 =0.845)`

Options

A. `33.2 m i n `
B. `77.7 m i n`
C. `22.7 m i n`
D. `40 m i n `

Answer

2

Explanation

`30%` decomposition means that `x=30%` of `a=0.30a`
As reaction is of 1st order,
`k-(2.303)/(t)log.(a)/(a-x)=(2.303)/(40 min )log.(a)/(a-0.30a)=(2.303)/(40)xxlog.(10)/(7)"min"^(-1)`
For a 1st order reaction
`t_(1//2)=(0.693)/(k)=(0.693)/(8.918xx10^(-3)"min"^(-1))=77.7min`