The rate constant for a first order reaction is `60 s^(-1).` How much time will it take to reduce the initial concentration of the reactant to its `1//6^(th)` value ?

Explanation

For `1 ^(st)` order reaction
`t=(2.303)/(k)log ""(a)/((a-x))-(i)`
Given `(a-x) =(a)/(16), k =60s^(-1)`
Placing the values in eq. (i)
`t=(2.303)/(60s^(-1))log ""(axx 16)/(a) =(2.303)/(60s^(-1))log 16`
`=(2.303)/(60s^(-1))log 2^(4)`
`=(2.303)/(60s^(-1))xx4 log 2=(2.303)/(60s^(-1))xx4xx0.3010=4.62xx10^(-2)s`
Time `=4.62 xx10^(-2)s.`