QUESTION FIVE

A plant produces $100$ Tonnes$/$day of TiO$2$ pigment which must be $99\mathrm{.}9\%($pure when dried. The pigment is produces by precipitation and the material as prepared is contaminated with $1$ ton of salt solution containing $0\mathrm{.}55$ ton of salt $/$ ton of pigment. The material is washed counter currently with water in a number of thickeners arranged in series. How many thickeners will be required if water is added at the rate of $200$ tons $/$ day and the solid discharged from each thickener removed $0\mathrm{.}5$ ton of solvent $/$ ton of pigment. What will be the number of thickeners if the amount of solution removed in association with pigment varies in the following way with the concentration of the solution in the thickeners $[10$ Marks$]$