${6\mathrm{.}10}^b.$ Mixtures of light hydrocarbons: $m-$value correlations

Because of the complex concentration functionality of the $m-$values, VLE

calculations in general require iterative procedures suited only to computer

solutions. However, in the case of mixtures of light hydrocarbons, we may assume

as a reasonable approximation that both the liquid and the vapor phases are ideal.

This allows $m-$values for light hydrocarbons to be calculated and correlated as

functions of $T$ and $P.$ Approximate values can be determined from the monographs

prepared by DePriester $(1953).$ The DePriester charts have been fit to the following

equation $($McWilliams$,1973)$:

$lnm=\frac{a_{T1}}{T^2}+a_{T2}+a_{P1}lnP+\frac{a_{P2}}{P^2}+\frac{a_{P3}}{P}$

where $T$ is in $K$ and $P$ is in kPa. The constants $a_{T1},a_{T2},a_{P_1},a_2,$ and $a_{P_3}$ are given in

Table $6\mathrm{.}4.$ This equation is valid for temperatures from $200K$ to $473K,$ and

pressures from $101\mathrm{.}3$kPa to $6000$kPa.

Table $6\mathrm{.}4$ Constants in Equation $(6-106)$: $T$ in $K,P$ in kPa

What is the bubble point of a mixture that is $15$mol$\%$ isopentane $($A$),30$mol$\%n-$

pentane $($B$),$ and $55$mol$\%-$hexane $($C$)?$ Calculate the composition of the first

bubble of vapor. The pressure is $1\mathrm{.}0$atm.