A first order reaction takes 40 minutes for 30% decomposition. Calculate `t_(1//2)` for this reaction (Given log 1.428 = 0.1548)

Explanation

For a first order reaction,
` k=( 2.303 )/( t) log ""(a)/((a-x))`
Let .a. be 100, then x = 30 and (a - x) = 100 - 30 = 70 when t=40 min.
Substituting the values in equation (1)
` k=( 2.303 )/( 40 min ) log "" (100)/(70 ) = ( 2.303 )/( 40 min ) log "" 1.428`
`=( 2.303 )/( 40 ) xx 0.1528 = 8.91 xx 10^(-3) min""^(-1)`
` t_(1//2) = ( 0.693 )/( k ) = ( 0.693 )/( 8.91 xx 10^(-3) min""^(-1) ) = 77.78 min `.