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A first order reaction takes 40 min for ...

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

A

`33.2 m i n `

B

`77.7 m i n`

C

`22.7 m i n`

D

`40 m i n `

Text Solution

Verified by Experts

The correct Answer is:
2
`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`
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