Q$5)$ Draw a diagram and set up a total mass and component balance equation for a crystallizer where $100kg$ of a concentrated sugar solution containing $85\%$ sucrose and $1\%$ inert, watersoluble impurities enters. Upon cooling, the sugar crystallizes from solution. A centrifuge then separates the crystals from a liquid fraction, called the mother liquor. The crystal slurry fraction has, for $20\%$ of its weight, a liquid having the same composition as the mother liquor. The mother liquor contains $60\%$ sucrose by weight. $($Mother Liquor$=21\mathrm{.}9$ kg & Crystals$=78\mathrm{.}1$ kg$)$