The overall system of $2$ mole mixture of $n-$pentane$(1)/$nhexane$(2)/$n$-$heptane$(4)$ at $92\mathrm{.}9C$ and $2$ bar has the overall composition $=0\mathrm{.}25,=0\mathrm{.}45,=0\mathrm{.}30.$ Assuming that Raoult's law is appropriate to this system, calculate:

a$.$ The pressure range $($bubble point pressure and dew point pressure$)$ for the existence of two phases.

b$.$ The fraction of obtained vapor $(V)$ and the mole fraction of each species in the vapor and liquid phase.

c$.$ The molar ratio of vapor $($V$)$ to liquid$($L$)$ Phase

NB: use the Antoine equation in the textbook.