Titanium dioxide, which is the most common white pigment in paint, can be produced from the titanium mineral, rutile, by chlorination to TiCl4, followed by oxidation to TiO2. To purify the insoluble titanium dioxide, it is washed free of soluble impurities in a continuous, countercurrent system of thickeners with water. Two hundred thousand kg/h of 99.9 wt% titanium dioxide pigment is to be produced by washing, followed by filtering and drying. The feed contains 50 wt% TiO2, 20 wt% soluble salts, and 30 wt% water. The wash liquid is pure water at a flow rate equal to that of the feed on a mass-flow basis.

(a) Determine the number of washing stages required if the underflow from each stage is 0.4 kg solution/kg TiO2.

(b) Determine the number of washing stages required if the underflow is variable asfollows:

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Concentration of solute, Retention of solution, kg solution/kg TiO; kg/solute/kg solution 0.0 0.30 0.2 0.34 0.4 0.38 0.6 0.42