Answer:
(a) [tex]x_1=0.34\\x_2=0.66\\y_1=0.74\\y_2=0.24[/tex]
(b) [tex]95.24^0C[/tex]
Explanation:
Hello,
The Rachford-Rice equation should be used in this case:
[tex]\frac{z_1(K_1-1)}{1+V/F(K_1-1)} +\frac{z_2(K_2-1)}{1+V/F(K_2-1)} =0\\\frac{0.5(\frac{P_{1,sat}}{P}-1)}{1+V/F(\frac{P_{1,sat}}{P}-1)} +\frac{z_2(\frac{P_{2,sat}}{P}-1)}{1+V/F(\frac{P_{2,sat}}{P}-1)} =0[/tex]
The distribution coefficients could be approximated via Raoult's law and the Antoine equation for the vapor pressure:
[tex]K_i=\frac{P_{i,sat}}{P}=\frac{10^{A-\frac{B}{C+T} }}{P}[/tex]
For n-hexane: A=6,9895, B=1216,92 and C=227,451
For n-octane: A=7,14462, B=1498,96 and C=225,874
*Those values and the Antoine law are used in °C and mmHg.
Replacing each value in the Rachford-Rice equation and solving for T, one gets the flash drum temperature as 95.24°C (attached picture), thus, the compositions in both the liquid and the vapor phases are:
[tex]x_1=\frac{z_1}{1+V/F(K_1-1)}=\frac{0.5}{1+0.4*(2.175-1)} =0.34\\x_2=1-x_1=0.66\\y1=K_1*x_1=2.175*0.34=0.74\\y_2=1-y_1=0.24[/tex]
Best regards.
