The problem is to find the rate of change of the reactant in
a 2nd order chemical reaction which can be modelled
by the given by the differential equation, ,
where [A] is the concentration of the reactant at time
*t* in minutes, and *k* is the reaction constant.

If [ *A* ] = 0.500 M when *t* = 0 minutes, and [ *A* ] = 0.435 M when *t*
= 38.5 minutes, find *k* .

We need to solve the differential equation:

Separate the variables, [ *A* ] and
*t* , to get:

Then integrate over the given limits for each variable, to get:

∴ And *k* ≅0.00776