In a well-mixed batch system, the following reactions are taking place: A + S → X, X + S → Y . The rate constant for the first reaction is k1 and the one for the other is k2. k2/k1 = 2, and these reactions have elementary, bimolecular rate expressions. Initially, CA0 = 1 M and CS0 = 2 M, and the concentrations of X and Y are zero. In this system, kinetics, i.e. the change in composition with respect to time, is not critical, but the product distribution is desired to be known. Further reaction of X into Y is undesired.

(a). Write the balance equations for A and X. Are those differential equations linear or nonlinear?

(b). Divide dCX /dt by dCA/dt, in order to get a differential equation that describes CX as a function of CA. That is, eliminate time and make CA the independent variable.

(c) .Solve the ODE you derived in part (b) to get an expression for CX in terms of CA.

( d). Find the mole fraction of X when CA = CA0/2