01-07-2017, 10:28 AM
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:
The results are shown in the tables below,
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
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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 |