Question

For the reaction A → products, successive half-lives are observed to be 12.4, 24.8, and 49.6 min for an experiment in which [A]₀ = 0.15 M. Calculate the concentration of A at the following times.

a) 99.2 min

b) 37.2 min

Answer 1

Half life is time need for initital concentraion to become half.As in our case we can see that time doubles each time, and follows a particular order of getting twice and the rate of reaction associated with this should be second order rate. The equation for this half-life is:

and rate equation for 2nd order reaction is rate eq. is:

1/[A] = 1/[A]0 + kt ------#

using 1st half life value we obtain raection constant (k) :

k = 1/( t_.5 * [A]0) = 1/(12.4 min * 0.15 M) = 0.537 min^-1M-1

k value from equation # we can be used to obtain concentraion at
(a) 99.2 min
1/[A] = 1/(.15 M) + .537min^-1M^-1*99.2 min

1/[A] = 6.666 M^-1+ 53.27 M^-1 =59.94 M^-1
[A] = 0.0167 M

(b) 37.2
   1/[A] = 1/(.15 M) + .537min^-1M^-137.2 min

1/[A] = 6.666 M^-1+ 19.976 M^-1

   [A] = 0.0375 M