Question

The first-order reaction k = 4.6 s–1. If [A]o = 0.500 M, how long will it take to reach [A] = 0.125 M?

Answer 1

Given :

The rate constant of the first order reaction = 4.6 /s

Initial concentration of reaction = 0.500 M

To find :

Time taken by the reaction to reduce the concentration of the reactant to 0.125 M .

Solution :

The Integral representation of the first order reaction is given by -

ln ( A$_t$ / A$_o$ ) = -kt

where , A$_t$ is the concentration of the reactant at any time t ,

A$_o$ is  the initial concentration ,

k is rate constant ,

and t is time .

now ,

ln ( 0.125 / 0.500 ) = - ( 4.6 ) t

=> ln ( 1 / 4 ) = - ( 4.6 ) t

=> t = ( 1.386 ) / 4.6

=> t = 0.3 s  {approx}

Time taken by the reaction to reduce the concentration of the reactant to 0.125 M is 0.3 seconds .