Question

A particular reactant decomposes with a half-life of 169 s when its initial concentration is 0.293 M. The same reactant decomposes with a half-life of 245 s when its initial concentration is 0.202 M. What is the value and the unit of the rate constant for this reaction?

Answer 1

To calculate the rate constant K value and its units , we need to calculate first the order of the reaction.

We know the half time is proportional to (initial concentration)^1-n where n is the order of reaction.

        t_1/2 propotional to a^1-n

Thus t₁/t₂ = (a₂/a₁)^n-1
Substituting the given values we have 169/245 =[ 0.202/0.293]^n-1

which gives n= 2 that is second order reaction.

For second order reaction the integrated rate expression is Kt = 1/[A_t] - 1/[A] and half time and K are related as           k = 1/ [a.t_1/2]

Substituting the given values half time = 169s and a= 0.293 we get k = 0.02019M^-1 s^-1