Problem 3. In water treatment systems, adsorption processes are often designed as packed columns: the columns are filled with adsorbent particles, and contaminants are removed from the feed solution as it passes through the column. The fate of contaminant in a single batch of fluid in such a system can be simulated, to a first approximation, by treating the system as a series of batch reactors. That is, movement of water downstream through the packed column can be represented as movement of the water from one batch reactor to the next in a series. The taste-and-odor compound methyl-isoborneol (MIB) can give water an earthy musty odor, even when the compound is present in solution at concentrations of just a few nanograms per liter. The MIB can be removed from solution by adsorption onto activated carbon (AC). Gillogly et al. (Journal American Water Works Association, 90(1): 98-108) reported that MIB sorption from a solution of pure water (no competing adsorbates) can be characterized by the Freundlich isotherm q=9.6c0.5, where c, the aqueous concentration at equilibrium, is in micrograms per liter and q, the adsorbed concentration at equilibrium, is in micrograms of MIB per milligram of AC. Compare the final soluble concentration of MIB in two systems each receiving an influent containing 100 g/L MIB, and in each of which a total dose of 5mgAC per liter is applied to remove the MIB. In one system, the activated carbon is all added to a single batch reactor, and in the other, the water flows through four sequential reactors, each receiving a dose of 1.25mgAC per liter. Assume that the water equilibrates with AC in each reactor and that no AC transfers from one reactor to the next