Problem $2.)$

Malaria is a life$-$threatening disease caused by microorganisms of the Plasmodium group, transmitted through the bites of

infected female Anopheles mosquitoes. In $2022,$ there were $249$ million cases of malaria worldwide, resulting in an

estimated $608,000$ deaths. A safe and effective treatment for malaria is artemisinin, which is present in the leaves of

Artemisia annua $($sweet wormwood$).$ A drug company would like to produce artemisinin from Artemisia annua by

extraction with a nonpolar solvent $($hexane$,C6H14)$ using the following continuous process at steady$-$state: The dried and

ground Artemisia annua leaves are fed to a stirred tank $($the Extractor$)$ along with a stream of pure liquid hexane, which

extracts the artemisinin from the leaves.

As shown in the figure, the solvent entering the extractor is a combination of recycled and fresh hexane. The ratio of the

total $($recycled $+$ fresh$)$ hexane solvent to the seeds entering the extractor is $2\mathrm{.}9kg$ hexane $\frac{?}{kg}$ leaves. The ground leaves

are suspended in the liquid and essentially all the artemisinin in the leaves are extracted into the hexane. The extractor

output passes to a Filter where the leaf solids are collected and form a filter cake. The filter cake is a wet solid, with $80\mathrm{.}0$

mass $\%$ leaf solids and the balance artemisinin and hexane, the latter two $($artemisinin and hexane$)$ in the same ratio in

which they are present in the filtrate solution leaving the filter. The wet filter cake is discarded, and the liquid filtrate is fed

to an evaporator in which part of the hexane is vaporized, and a liquid artemisinin solution $(8$ mass $\%$ artemisinin, $92$

mass $\%$ hexane$)$ exits the evaporator. This artemisinin solution is then sent to another process for purification. The hexane

vapor is subsequently cooled and condensed, and the hexane condensate is recycled to the extractor. For this problem,

the dried artemisinin leaves are assumed to be made up only of artemisinin and solids. The composition of the ground

leaves is $1\mathrm{.}4$ mass$\%$ artemisinin, with the rest considered as leaf solids.

$($a$)$ Draw and label a flowchart of the process. Note: Please redraw the flowchart by hand. Cutting$-$and$-$pasting the above

diagram will not be graded.

$($b$)$ Identify all the system$($s$)$ and point$($s$)$ where useful Material Balances can be made. $($Hint: There should be five$).$

$($c$)$ From the General Balance Equation, derive the Balance Equation applicable to the problem $($e$.$g$.$ Steady$-$state, so

Accumulation $=0).$ Then write all the possible Material Balance equations for each of the system$($s$)$ and point$($s$)$ you

identified in $($b$).$

$($d$)$ Do the degree$-$of$-$freedom analysis on each of the system$($s$)$ and point$($s$)$ you identified in $($b$).$ Please identify the

unknowns $($based on your flowchart labels$)$ and the equations $($e$.$g$.$ from Material Balances, from given, etc.$)$

$($e$)$ Which system will you use first to solve for some of the unknowns? Why?