Question

For the reaction A → products, successive half-lives are observed to be 11.4, 22.8, and 45.6 min for an experiment in which [A]0 = 0.18 M. Calculate the concentration of A at the following times.

b) 34.2

Answer 1

As you can see, in this case that time doubles each time

so it is a second order reaction

half life equation for the second order reaction

t_1/2 = 1/([A₀] x k)

first find out the rate constant using

using first half life find out the rate constant

11.4 = 1/ (0.18 x k)

k = 1/2.052

k = 0.4873 M-1 min-1

now integrated rate equation for the second order is

1/[A] = 1/[A0] + kt

[A] need t calculate at t = 34.2

[A0] = 0.18 M, k = 0.4873 M-1min-1

1/[A] = 1/ 0.18 + 0.4873 x 34.2

1/[A] = 5.55 + 16.66

1/[A] = 22.21566

[A] = 1/ 22.21566

[A] = 0.045 M