For a first order reaction , the initial concentration of the reactant is `[A]_(0)` . How much time is required for the concentration of the reactant to decrease to decrease to `([A]_(0))/(e)` ? (Where e = base of natural log).

Explanation

For a first order reaction , the concentration of the reactant time t is given by `[A]_(t)=[A]_(0)e^(-kt), `(k=rate constant).
If the concentration of the reactant at time `'t_(1)' " is " [A]_(1)` , then `[A]_(1) = ([A]_(0))/(e). " Therefore", ([A]_(0))/(e)=[A]_(0)^(-kt_(1))" or, " e^(-1)=e^(-kt_(1))`
or, `kt_(1)=1 thereforet_(1) = (1)/(k) `