QUESTION $1[29$ Marks$]$

You are tasked with evaluating a liquid$-$liquid extraction system for extracting natural products

$($isopropyl ether$)$ from plant extracts $($acetic acid$)$ in a botanical extraction facility. The facility

specializes in extracting bioactive compounds from botanical sources for use in cosmetics$.$ A

mixture containing isopropyl $(0\mathrm{.}1$kmol$)$ and acetic acid $(0\mathrm{.}45$kmol$)$ is equilibrated in a co$-$current

single$-$stage extractor using water $(1\mathrm{.}499$kmol to leach isopropyl ether. The composition of

water at the mixing point is $46\%.$ To ensure that the extraction system achieves a high extraction

efficiency, $0\mathrm{.}013$kmol of isopropyl ether enters with water; estimate the following:

$1\mathrm{.}1.$ The composition of isopropyl at the mixing point $(x_M).$ Hint; use mass balance!

$1\mathrm{.}2.$ The composition of isopropyl in the extract, if its composition is $6\%$ in the raffinate

stream $(x_R).$ Hint; use lever$-$arm rule $(mm)!$