$10\mathrm{.}27.$ For the system methane$(1)/$ethane$(2)/$propane$(3)$ as a gas, estimate hat$(f{)}_1,$hat$(f{)}_2,$hat$(f{)}_3,$hat$({)}_1,$hat$({)}_2,$ and hat$({)}_3$ at $t=100C,P=35$ bar, $y_1=0\mathrm{.}21,$

and $y_2=0\mathrm{.}43$ :

$($a$)$ Through application of Eq$.(10\mathrm{.}64).$ Eq $10\mathrm{.}64$

ln$\_$k$=$P$/$RT $($B$\_$kk$+1/2\_$i$\_$j$$y$\_$i y$\_$j $(2\backslash$delta $\_$ik$-\backslash$delta $\_$ij $))$

$($b$)$ Assuming that the mixture is an ideal solution.