A feed $($flow rate $=1000$ kg$/$hr$)$ containing $50$ wt$\%$ acetic acid $($component A$)$ and

$50$ wt$\%$ water $($component D$)$ is extracted in a countercurrent column using pure diisopropyl ether

$($component S$,$ flow rate $=2000$ kg$/$hr$)$ as solvent to remove acetic acid in the solution. When examining

the raffinate stream leaving the column, we observe that its flow rate is $650$ kg$/$hr and its acetic acid

composition is $7\mathrm{.}6923$ w t$\%.$ The extraction takes place at $1$ atm.

a$.)$ Show the ternary diagram $($composition unit: mass fraction$)$ for liquid$-$liquid

equilibria. When selecting the thermodynamic package, choose the NRTL activity

coefficient model. To select the right compounds in Aspen Properties, type

$$ACETIC$-$ACID$,$WATER$,$ and $$DIISOPROPYL$-$ETHER$$ under the

$$compound name$$ column. By exploring the options on the right of the ternary

map window in Aspen Properties.

b$.)$ Determine the midpoint composition Xm and locate it on the ternary diagram.

c$.)$ What is the recovery of acetic acid in the raffinate stream leaving the column?

The recovery of component $($i$)$ in a stream is defined as the ratio of molar flow rate

of component $($i$)$ in that stream over the molar flow rate of component $($i$)$ in the feed stream.

d$.)$ Determine acetic acid, diisopropyl ether, and water compositions $($in wt$\%)$ in

the extract and raffinate streams leaving the column

e$.)$ Calculate X$($D$)$ for all three components and locate it on the ternary diagram graph. Note that you may

get negative values for X$($D$).$ This may require extrapolation of the ternary map

f$.)$ Using the graphical method, draw X$($R$,$N$)$

$ compositions for the top five equilibrium stages $($i$.$e$.,$ n$=$

$1,...,5).$ You may need to reasonably estimate or extrapolate the tie lines. You must show your graphical

steps and label the compositions on the ternary diagram