Certain solid substances, known as hydrated compounds, have well$-$defined molecular ratios of water to some other species, which often is a salt. For example, calcium sulfate dihydrate $($commonly known as gypsum, $CaS{O}_{4}2H_{2}O),$ has $2$ moles of water per mole of calcium sulfate; alternatively, it may be said that $1$ mole of gypsum consists of $1$ mole of calcium sulfate and $2$ moles of water. The water in such substances is called water of hydration. Solid gypsum is formed in a crystallizer and leaves that unit as a slurry $($a suspension of solid particles in a liquid$)$ of solid gypsum particles suspended in an aqueous $CaS{O}_4$ solution. The slurry flows from the crystallizer to a filter in which the particles are collected as a filter cake. The filter cake, which is $95\mathrm{.}0wt\%$ solid gypsum and the remainder $CaS{O}_4$ solution, is fed to a dryer in which all water $($including the water of hydration in the crystals$)$ is driven off to yield anhydrous $($water$-$free$)CaS{O}_4$ as product. A flowchart and relevant process data are given below.

Solids content of slurry leaving crystallizer: $0\mathrm{.}35kgCaS{O}_4*2H_2\frac{O}{L}$ slurry

$CaS{O}_4$ content of slurry liquid: $0\mathrm{.}209$gCaS$\frac{O_4}{100}g{H}_{2}O$

Specific gravities: $CaS{O}_4*2H_{2}O($s$),2\mathrm{.}32$; liquid solutions, $1\mathrm{.}05$

$($a$)$ Briefly explain in your own words the functions of the three units $($crystallizer$,$ filter, and dryer$).$

$($b$)$ Take a basis of one liter of solution leaving the crystallizer and calculate the mass $(kg)$ and volume $($L$)$ of solid gypsum, the mass of $CaS{O}_4$ in the gypsum, and the mass of $CaS{O}_4$ in the

liquid solution.

$($c$)$ Calculate the percentage recovery of $CaS{O}_4-$ that is$,$ the percentage of the total $CaS{O}_4($precipitated plus dissolved$)$ leaving the crystallizer recovered as solid anhydrous $CaS{O}_4.$