A stream containing 5.15wt% chromium Cr is contained in the wastewater from a metal finishing plant. The wastewater stream is fed to a treatment unit that removes 95% of the chromium in the feed and recycles it to the plant. The residual liquid stream leaving the treatment unit is sent to a waste lagoon. The treatment unit has a maximum capacity of 4500 kg wastewater/h. If wastewater leaves the finishing plant at a rate higher than the capacity of the treatment unit, the excess (anything above 4500 kg/h) bypasses the unit and combines with the residual Liquid leaving the unit, and the combined stream goes to the waste lagoon.

(a) Without assuming a basis of calculation, draw and label a flow chart of the process.

(b) Wastewater leaves the finishing plant at a rate m₁ = 6000 kg/h. Calculate the flow rate of liquid to the waste lagoon m₆ (kg/h), and the mass fraction of Cr in this liquid x₆ (kg Cr/kg).

(c) Calculate the flow rate of liquid to the waste lagoon and the mass fraction of Cr in this liquid for m₁ varying from 1000 kg/h to 10,000 kg/h in 1000 kg/h increments. Generate a plot of x₆ versus m₁. (Suggestion: Use a spreadsheet for these calculations.)

(d) The company has hired you as a consultant to help them determine whether or not to add capacity to the treatment unit to increase the recovery of chromium. What would you need to know to make this determination?

Wastewater m(kg/h) 0.0515 kg Cr/kg m(kg/h) s 4500 kg/h m3(kg/h) ma(kg Cr/h) (no water] 95% of Cr in feed to unit m5(kg/h) mg(kg/h) To waste lagoon