Q$5$: We are given the pressure $P$ and the vapor composition $x.$ We want to find the dew point temperature and the liquid composition. Assume that the system is ideal: Raoult's and Dalton's laws apply. The system total pressure is $18$atm.

Partial pressure $=P_i=y_{i}P=x_i{P}_i^{**}$

$y_i=(\frac{P_i^{**}}{P})x_i=K_i{x}_i$

Antoine Coefficients:

$\backslash$table$[[,$Ethylene,Ethane,Propane,n$-$Butane$],[$A$,3\mathrm{.}86690,3\mathrm{.}93264,3\mathrm{.}97721,3\mathrm{.}84431],[$B$,584\mathrm{.}146,659\mathrm{.}739,819\mathrm{.}296,909\mathrm{.}65],[$C$,-18\mathrm{.}307,-16\mathrm{.}719,-24\mathrm{.}417,-36\mathrm{.}146],[$y$,0\mathrm{.}10,0\mathrm{.}30,0\mathrm{.}40,0\mathrm{.}20]]$

$log{P}_i^{**}=A-\frac{B}{C+T}$

$P=$ Total pressure $(atm)$

$P_i^{**}=$ vapor pressure of component $i(atm)$

$T=$ Temperature $(K)$