Question

if rate constant of a first order reaction is 3×10^-2S^-1 then the half life period of the reaction will be​

Answer 1

Given:

Rate constant for a first order reaction = 3 × 10⁻² s⁻¹

To find:

Half life period for a first order reaction

Solution:

For a first order reaction,

The rate constant and half life period can be relate to each other by formula -

            $t_\frac{1}{2} = \frac{1}{K}$

or,        $K = \frac{1}{t_\frac{1}{2} }$

here, K = rate constant

         $t_\frac{1}{2}$ = half life time period

so, by substituting all the values we get,

             $t_\frac{1}{2} = \frac{1}{3 \times 10^-^2 s^-^1}$

             $t_\frac{1}{2} = \frac{1}{3} \cdot 10^2 s$

             $t_\frac{1}{2}$ = 0.33 × 10² s

             $t_\frac{1}{2}$ = 33.33s

Therefore, half life time for a first order reaction is 33.33s with rate constant 3 × 10⁻² s⁻¹.