The system of water$(1)/$n$-$pentane$(2)/$n$-$hexane$(3)$ exists as a vapor at $101\mathrm{.}325$kPa,

$100C$ with mole fraction $z_1=0\mathrm{.}45,z_2=0\mathrm{.}25,z_3=0\mathrm{.}30.$ The system is slowly

cooled at constant pressure until it is completely condensed into a water phase and a

hydrocarbon phase. Assuming that $(1)$ the two liquid phases are immiscible, $(2)$ the

vapor phase is an ideal gas, and $(3)$ the hydrocarbons obey Raoult's law, determine

the following:

$($a$)($i$)$ The dew point temperature of the mixture and $($ii$)$ the composition of the

first condensate.

$($b$)($i$)$ The temperature at which the second liquid phase first appears. $($ii$)$ Also

find its initial composition.

$($c$)($i$)$ The bubble point temperature and $($ii$)$ the composition of the last bubble

of vapor.

Vapor pressure of hydrocarbons are given as:

$ln{P}_2^{\text{s}\text{a}\text{t}}(kPa)=13\mathrm{.}8183-\frac{2477\mathrm{.}07}{T(C)+233\mathrm{.}21}$

$ln{P}_3^{\text{s}\text{a}\text{t}}(kPa)=13\mathrm{.}8216-\frac{2697\mathrm{.}55}{T(C)+224\mathrm{.}37}$