A first order reaction is `20%` complete in 5 minutes. Calculate the time taken for the reaction to go to `60%` complete.

Explanation

For a first order reaction: `t=2.303/k log (a)/(a-x)`
I case : `a=100%, (a-x)=80%, t=5 min`
`5 min =2.303/k log 100/80 = 2.303/klog1.25`………….(i)
Iind case: `a=100%, (a-x)=40%`
`t=(2.303)/k log (100)/(40) = 2.303/k log 2.50`…………….(ii)
Dividing eqn. (ii) by eqn. (i)
`(t/5 "min") = (log2.5)/(log 1.25) = (0.3979)/(0.0969)` or `t=(0.3979)/(0.0969) xx (5 "min")` = 20.53 min.