For a first order reaction, it takes 5 minutes for the initial concentration of 0.6 mol `L^(-1)` to become `0.4` mol `L^(-1)`. How long in all will it take for the initial concentration to become 0.3 mol `L^(-1)`?

Explanation

For a first order reaction: `t=(2.303)/k log (a)/(a-x)`
Ist case: a`=0.6 mol L^(-), (a-x) mol L^(-1), t=5 min`
`5 min =(2.303)/(k) log (0.6)/(0.4)` or `5 min = (2.303)/(k) log1.5`………..(i)
IInd case: a=`0.6 mol L^(-), (a-x)=0.3 mol L^(-1)`
`t=(2.303)/k log (0.6)/(0.3) = (2.303)/k log 0.6/0.4` or `5 min = (2.303)/k log 2`
Dividing equn (ii) by eqn. (i),
`t/(5 "min") = (log 2.5)/(log 1.25) = (0.3979)/(0.0969)` or `t=(0.3979)/(0.0969) xx (5 "min")=20.53 min`