Problem $4.$ The boiling temperatures of a binary mixture are $220C$ and $250C$ for

component $1$ and component $2$ respectively. At a temperature $T^{**}$ of $180C$ there

is a triple phase coexistence of a liquid $($rich in component $2),$ a liquid $($rich in

component $1)$ and a vapor phase. The mole fractions at the three phase line are

$x_1^{}=0\mathrm{.}88,x_1^{}=0\mathrm{.}12,y_1^{**}=0\mathrm{.}33.$ LLE exists below $T^{**}.$ At $T=150C,$ the coexistent

liquid phases have mole fractions $x_1^{}=0\mathrm{.}06,x_1^{}=0\mathrm{.}92.$

a$)$ With the data given, graph the T$-$x$1-$y$1$ diagram showing where in the

diagram we find VLE, LLE, three phase, and one phase. Label all phases.

b$)$ At overall composition of $z_1=0\mathrm{.}28,$ describe what phases$/$compositions do

you encounter as temperature is reduced from $T=230C$ at constant overall

mole fraction until $T=170C.$

c$)$ If the saturation pressures at a given temperature $T$ are Psat $1=70$ bar and

Psat $2=50$ bar, and the $3-$phase pressure $P^{**}=100$ bar, with $y^{**}=0\mathrm{.}25,$

$x_1^{}=0\mathrm{.}15,x_1^{}=0\mathrm{.}78.$ sketch the $P-x_1-y_1$ diagram and show where the VLE,

LLE, VLLE, and single phases are found. Label them. If there are tie$-$lines

show them.

d$)$ Assume that the two liquids are completely immiscible with each other.

How do the diagrams in parts a and c change?