Chemical Reactions. A second order chemical reaction

Chapter 2, Problem 28

(choose chapter or problem)

Chemical Reactions. A second order chemical reaction involves the interaction (collision)of one molecule of a substance P with one molecule of a substance Q to produceone molecule of a new substance X; this is denoted by P + Q X. Suppose that p andq, where p = q, are the initial concentrations of P and Q, respectively, and let x(t) be theconcentration of X at time t. Then p x(t) and q x(t) are the concentrations of P andQ at time t, and the rate at which the reaction occurs is given by the equationdx/dt = (p x)(q x), (i)where is a positive constant.(a) If x(0) = 0, determine the limiting value of x(t) as t without solving thedifferential equation. Then solve the initial value problem and find x(t) for any t.(b) If the substances P and Q are the same, then p = q and Eq. (i) is replaced bydx/dt = (p x)2. (ii)If x(0) = 0, determine the limiting value of x(t) as t without solving the differentialequation. Then solve the initial value problem and determine x(t) for any t.