BaCO₃, which is water insoluble, is to be made by precipitation from a solution containing 120,000 kg/day of water and 40,000 kg/day of BaS, with a stoichiometric amount of solid Na₂CO₃. The reaction, which produces a byproduct of watersoluble Na₂S, will be carried out in a continuous, countercurrent system of five thickeners. Complete reaction will take place in the first thickener, which will be fed solid Na₂CO₃, an aqueous solution of BaS, and overflow from the second thickener. Sufficient fresh water will enter the last thickener so that overflow from the first thickener will be 10 wt% Na2S, assuming the underflow from each thickener contains two parts of water per one part of BaCO₃ by weight. 

(a) Draw a process flow diagram and label it with all given information. 

(b) Determine the kg/day of Na₂CO₃ required and kg/day of BaCO₃ and Na₂S produced. 

(c) Determine the kg/day of fresh water needed, wt% of Na₂S in the liquid portion of the underflow that leaves each thickener, and kg/day of Na₂S that will remain with the BaCO₃ product after it is dried.