Chapter D1.3, Problem 48E

Chemical rate equations Let y(t) be the concentration of a substance in a chemical reaction (typical units are moles/liter). The change in the concentration, under appropriate conditions, is modeled by the equation $\frac{dy}{dt}=-k{y}^n$ where k > 0 is a rate constant and the positive integer n is the order of the reaction.

1. a. Show that for a first-order reaction (n = 1), the concentration obeys an exponential decay law.
2. b. Solve the initial value problem for a second-order reaction (n = 2) assuming y(0) = y₀.
3. c. Graph the concentration for a first-order and second-order reaction with k = 0.1 and y₀ = 1