Question

The reaction The reactionA -> B+C is second order with respect to A. When [A]0= 0.290 M the reaction is 43.0% complete at 64.5 min. calculate the half life for this reaction.

The reaction A B+C is second order with respect to A. When [Alo 0.290 M, the reaction is 43.0 % complete at 64.5 min. Calculate the half-life for this reaction.

Answer 1

we have:

[A]o = 0.29 M

43 % is complete.

So, remaining is 57 %

[A] = 57 * of 0.29 M

= 57*0.29/100

= 0.1653 M

t = 64.5 min

use integrated rate law for 2nd order reaction

1/[A] = 1/[A]o + k*t

1/(0.1653) = 1/(0.29) + k*64.5

6.05 = 3.448 +k*64.5

k*64.5 = 2.601

k = 4.033*10^-2 M-1.min-1

Given:

k = 4.033*10^-2 M-1.min-1

use relation between rate constant and half life of 2nd order reaction

t1/2 = 1/([A]o*k)

= 1/(0.29*4.033*10^-2)

= 85.5 min

Answer: 85.5 min