For a system composed of: n$-$pentane & n$-$heptane

Antoine's Equation with pressure, $P$ in kPa, Temperature, $T$ in degrees Kelvin.

$P(kPa)=\frac{101\mathrm{.}325}{760\mathrm{.}0}$exp$[(A-\frac{B}{T(K)+C})]$

Constants and Other Information:

$\backslash$table$[[$Component$,$n$-$pentane,n$-$heptane$],[,$Antoine Vapor Pressure Constants,$],[$B$,15\mathrm{.}8333,15\mathrm{.}8737],[$C$,2477\mathrm{.}07,2911\mathrm{.}32],[$Minimum K$,-39\mathrm{.}94,-56\mathrm{.}51],[$Maximum K$,220,270],[$Boiling Pt K$,330,400],[$Boiling Pt C$,309\mathrm{.}2,371\mathrm{.}6],[$Boiling Pt F$,36\mathrm{.}1,98\mathrm{.}5],[,97\mathrm{.}0,209\mathrm{.}3]]$

a$)$ Using Antoine's Equation determine vapor pressures $-$ at relevant temperatures $($at temperatures between the boiling points of the two pure species$)$

b$)$ Using Raoult's Law calculate and plot the $Txy$ diagram at a total pressure of $101\mathrm{.}325$kPa.

c$)$ Plot the $xy$ data for this system at a total pressure of $101\mathrm{.}325$kPa.

n$-$Pentane $/$ n$-$Heptane System.

A rectification column is fed $600$kgmol$\frac{e}{h}r$ of a mixture that is $46$ mole$\%$ n$-$pentane $-54$ mole$\%$ n$-$heptane at $101\mathrm{.}325$kPa $($abs$)$ pressure. The distillate is to contain $94$ mole $\%$ n$-$pentane and the bottoms $90$ mole $\%$ nheptane. The reflux ratio is $3\mathrm{.}0$:$1\mathrm{.}0$ or $R=3\mathrm{.}0.$

a$)$ Calculate the flowrates $(mo\frac{l}{h}r)$ of the distillate, $D$ and bottoms, $B.$

Assuming that the feed mixture is a saturated liquid, e$.$g$.$ vertical $q-$line $...$

b$)$ Determine the theoretical number of trays and the feed tray number for the specified operation.

c$)$ Determine the minimum reflux ratio, Rmin and the minimum number of theoretical trays at total reflux. Assuming that the feed mixture is saturated vapor, e$.$g$.$ horizontal $q-$line $...$

d$)$ Determine the theoretical number of trays and the feed tray number for the specified operation.

e$)$ Determine the minimum reflux ratio, RMIN and the minimum number of theoretical trays at total reflux.