While Mia is playing in a sandbox, Mike, a biochem major, is sitting in a lab and trying to solve a problem about the law of mass action (poor Mike!). Ac- cording to this law, a chemical reaction...

While Mia is playing in a sandbox, Mike, a biochem major, is sitting in a lab and trying to solve a problem about the law of mass action (poor Mike!). Ac- cording to this law, a chemical reaction proceeds at a rate proportional to the product of the concentrations of involved reactants. If two reactants have the same initial concentration of a moles/L, and the concentration of the reaction product

at time t is y(t), then dy/dt = k(a−y)², where k is a constant.

(a) Help Mike to solve the differential equation assuming that the initial concentration of the reaction product is 0. He has to give the answer in explicit form, that is as a function y = y(t) containing constants a and k. Verify that the solution is correct.

(b) What happens to the concentration y(t) as t → ∞? Is the answer plausible from the point of view of chemistry?

(c) What happens to the rate of the reaction as t → ∞? Is the answer plausible from the point of view of chemistry?