Temperature-Composition for Binary Mixtures
01-07-2017, 10:28 AM (This post was last modified: 01-07-2017 10:43 AM by Ángel Martin.)
Post: #1
 Ángel Martin Senior Member Posts: 1,068 Joined: Dec 2013
Temperature-Composition for Binary Mixtures
Temperature-Composition for binary mixtures. [ WILSON, VANLAAR ]
From the author’s Engineering Collection, included in the ETSII3 module

This program obtains tabular representations of the composition-boiling point temperature diagram of a binary mixture in non-ideal conditions (where Raoult’s law won’t apply), under constant pressure conditions. The Antoine constants for each component must be known. Two models are available, using either Van-Laar or Wilson dissolution constants and equations. The program also calculates the vapor-liquid composition diagram. The tabulations can also be plotted as graphic curves on the thermal printer if available.

The expressions used for the calculations are shown below. Note that in both cases the solution requires solving the equation for the value of the temperature “T” for each value of the liquid fractions (x1,x2) of both components.

Let {A1, B1, C1} and {A2, B2, C2} the Antoine constants for each component as per the corresponding sub-index. The main equations are written as follows:

x1 exp [ Z1 ] = P – x2 exp [ Z2 ] ; where x1 + x2 =1
y1 = (x1/P) exp[ Z1] ; molar fraction of vapor,: y1 = y1(T, x1)

Let {a,b} the Van-Laar constants for the dissolution; then we have:

Z1 = A1 – B1/(T+C1) + a / (1+ a.x1/b.x2)^2; and
Z2 = A2 – B2/(T+C2) + a / (1+ a.x1/b.x2)^2

Let {G12, G21} the Wilson constants for the dissolution; then we have:

Z1 = A1 – B1/(T+C1) – Ln(x1+G12.x2) + x2 [(G12/(x1+G12.x2) – G21/(x2+G21.x1)]
Z2 = A2 – B2/(T+C2) – Ln(x2+G12.x1) + x1 [(G12/(x1+G12.x2) – G21/(x2+G21.x1)]

The pressure remains constant. The program assumes an atmospheric pressure of 760 mm Hg. This can be changed by modifying the value in program lines .151, .300, and .366

Example.

Tabulate and represent the ‘Temperature-Composition” and “vapor-liquid” diagrams for a non-ideal mixture of methanol and acetone, with the following data known:

Code:
Methanol        Acetone         Disso - Van-Laar   Disso -Wilson ---------------------------------------------------------------- A1 = 18.5875    A1 = 16.6513    a = 0.5076         G12 =1.2847 B1 = 3,626.55   B1 = 2,940.46   b = 0.962536       G21 = 0.3661 C1 = -34.29     C1 = -35.93

The results are shown in the tables below,
Code:
      |      Van-Laar     |      Wilson       ||       |      Van-Laar       |     Wilson ================================================================================​============== x1   |    y1      T      |    y1      T      ||   x1  |     y1      T       |    y1      T ---------------------------------------------------------------------------------------------- 0.05 |  0,0574  329,1995 |  0,0514  329,3898 ||  0.55 |   0,4771  329,5147  |  0,4761  330,6398 0.10 |  0,1107  329,0104 |  0,1004  329,366  ||  0.60 |   0,5115  329,8039  |  0,5151  330,9648 0.15 |  0,1606  328,8766 |  0,1475  329,3758 ||  0.65 |   0,5463  330,1511  |  0,5548  331,3404 0.20 |  0,2074  328,7946 |  0,1927  329,4184 ||  0.70 |   0,5823  330,5686  |  0,596   331,7767 0.25 |  0,2515  328,7616 |  0,2362  329,4931 ||  0.75 |   0,6208  331,0765  |  0,6398  332,2893 0.30 |  0,2932  328,7754 |  0,2784  329,5998 ||  0.80 |   0,6637  331,7091  |  0,6876  332,982 0.35 |  0,3328  328,8343 |  0,3194  329,7387 ||  0.85 |   0,7143  332,5254  |  0,7418  333,6535 0.40 |  0,3707  328,9374 |  0,3594  329,9105 ||  0.90 |   0,778   333,6293  |  0,8063  334,6074 0.45 |  0,4072  329,0845 |  0,3987  330,1165 ||  0.95 |   0,8656  335,2137  |  0,8879  335,8748 0.50 |  0,4425  329,2762 |  0,4375  330,3585 ||  1.00 |
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