Problem $2(25$ PTS$).$ In a single$-$stage liquid$-$liquid extraction, a feed $($A$)$ containing $50wt\%$ of solute $($B$)$ enters a single stage extractor at a total flow rate of $1,000k\frac{g}{h}$ and is contacted with $1,500k\frac{g}{h}$ solvent $($C$).$ Using the ternary phase diagram on the next page, answer the following questions $($show all calculations for partial credit and label the diagram$).$

i$.$ On the phase diagram $($next page$),$ label the mixture $($M$),$ feed $($F$),$ solvent $($S$),$ extract $($E$),$ and raffinate $(R)$ compositions directly on the graph.

ii$.$ What is the mass fraction of solute in the raffinate?

iii. What is the mass fraction of solute in the extract?

iv$.$ What is the total mass flow rate of extract, E$?$

v$.$ What is the partition coefficient, $K_D,$ of solute $($mass basis$)?$