Extend the analysis conducted in Problem 11.8 by relaxing the assumption that the solute concentration C_{A, s} remains constant. In a practical applications, C_{A, s} will vary as a result of adsorption when, for example, a volume of adsorbent particles, V, is added to a finite volume, V_f , of solution with an initial concentration C_{A, 0} in a well-mixed tank. In order to find the solution of this problem, we need to combine the expression for the rate of adsorption obtained in Problem 11.8 with a transient material balance for the solute A in the fluid phase. Note that the rate of mass transfer will be equal to the rate at which the solute A disappears from the solution. Using this approach, develop an expression to predict the concentration of A in the fluid phase as a function of time.