A municipal drinking water treatment plant discovers that it has an unacceptably high level of the pesticide carbofuran and must develop a treatment technique to reduce the concentration to satisfy the relevant water quality standard. The treatment method of choice is sorption on activated carbon. Your firm gets the design job and you are assigned to do the preliminary calculations. Research has revealed that the sorption of carbofuran onto activated carbon from water follows this isotherm:
qe=266 ( Ce) ^0.41
where Ce (mg/L) is the equilibrium concentration of the species in water and qe(mg/g) is the mass of sorbed carbofuran per mass of activated carbon. The carbofuran concentration in untreated water is 0.9 mg/L. The drinking water standard is 0.04 mg/L. You must design to treat a steady water flow rate of 0.32 m^3/s. One possible approach is to mix powdered activated carbon (PAC) with the water, wait for equilibrium to be attained, then remove the PAC. At what rate must PAC be added (g/s) to meet the proposed standard?