Assume that a bimolecular, irreversible reaction A + B -> C takes place at steady state in a liquid film of thickness L. Reactant A is introduced at x = 0 and reactant B at x = L. The liquid solution is dilute everywhere with respect to solutes A, B, and C. The volumetric rate of formation of C is given by R = k * C * C, where k is the second-order, homogeneous rate constant. If the reaction kinetics are extremely fast, A and B cannot coexist in the liquid. In this limit, the reaction occurs at a plane x = R, dividing the liquid film into two parts, and forms a boundary between the part of the film that contains A (but not B) and the part that contains B (but not A). Determine xR, C(x), C(x), and the reaction rate. NOTE: The problem should be modeled as a one-dimensional system.