Barium carbonate, which is essentially water insoluble, is to be made by precipitation from an aqueous solution containing 120,000 kg/day of water and 40,000 kg/day of barium sulfide, with the stoichiometric amount of solid sodium carbonate. The reaction also produces a by-product of water-soluble sodium sulfide. The process will be carried out in a continuous, countercurrent system of five thickeners. The reaction will take place completely in the first thickener to which will be fed the solid sodium carbonate, the aqueous solution of barium sulfide, and the overflow from the second thickener. Sufficient fresh water will enter the last thickener so that the overflow from the first thickener will be 10 wt% sodium sulfide assuming that the underflow from each thickener contains two parts of water per one part of barium carbonate by weight.

(a) Draw a schematic diagram of the process and label it with all the given information.

(b) Determine the kg/day of sodium carbonate required and the kg/day of barium carbonate and sodium sulfide produced by the reaction.

(c) Determine the kg/day of fresh water needed, the wt% of sodium sulfide in the liquid portion of the underflow that leaves each thickener, and the kg/day of sodium sulfide that will remain with the barium carbonate product after it is dried.