A first order reaction takes 40 min for 30% completion. Calculate `t_(1/2)`.

Explanation

For a first order reaction `K = ( 2. 303)/( t ) log "" ([R]_(0))/( R)`
When = 40 minutes `= ([ R _(0) ] )/( [R] ) = (100)/( 100 - 30) = (10)/(7)`
`K = ( 2 . 303)/( 40 ) log "" (10)/(7) , K = ( 2. 303)/( 40) log 1. 4 28 = ( 2. 303)/( 40 ) xx 0 . 1548.`
`K = 8. 91 xx 10 ^(-3)min^(-1)`
`t _(1//2) = ( 0. 693)/( K ) = ( 0. 69 3)/( 8. 91 xx 10 ^(-3)) , t _(1//2) = 77. 78 ` min.