Feed of $5,000$ kg$/$h of $40$ wt$\%$ sodium acetate in water. Monoclinic crystals of the trihydrate are

formed. $20\%$ of the water in the feed is evaporated at $40$C$.$ Crystal growth rate, G$,$ is $0\mathrm{.}0002$

m$/$h$.$ Predominant crystal size, Ld$,$ is $20$ U$.$S$.$ standard mesh. Solubility of sodium acetate at $40$C

$=65\mathrm{.}5$ g$/100$ g water. Crystal density $=1\mathrm{.}45$ g$/$cm$3$

$.$ Mother liquid density $=1\mathrm{.}20$ g$/$cm$3$

$.$ Find:

$1)$ The kg$/$h of crystals in the exiting magma.

$2)$ The kg$/$h of mother liquor in the exiting magma.

$3)$ The volume in m$3$ of magma in the crystallizer.

$[15$ Marks$]$

$($b$)$ Adsorption is one of the most common separation processes being used in chemical industries.

$1)$ Classify the types of adsorption

$2)$ State the main isotherm models and the application for each model