Isovolatility Lines for Ternary Systems
​Case of Acetone - Chloroform - Benzene Mixture
​Authors: Housam Binous and Ahmed Bellagi

We compute the isovolatility lines for a mixture of acetone - chloroform - benzene . Activity coefficients are obtained using Wilson' s model . In addition, we use this calculations of relative volatilities to easily determine the unique azeotrope of this ternary mixture (i . e . the binary azeotrope between chloroform and acetone) .

Acetone = component 1
Chloroform = component 2
Benzene = component 3

In[]:=
Off[General::"spell1"]
Gas Constant and Total Pressure
In[]:=
R=1.987;P=760;
Vapor Pressure Using Antoine Equation
In[]:=
A1=7.11714;B1=1210.595;C1=229.664;​​A2=6.95465;B2=1170.966;C2=226.232;​​A3=6.87987;B3=1196.760;C3=219.161;​​
In[]:=
PS1=10^(A1-B1/(C1+T));​​PS2=10^(A2-B2/(C2+T));​​PS3=10^(A3-B3/(C3+T));
Binary interaction Parameters and Activities for Wilson Model
In[]:=
l12=116.1171;l21=-506.8519;l13=682.40610;​​l31=-243.96510;l23=-71.81089;l32=-11.82310;​​V1=74.05;V2=80.67;V3=89.41;​​
In[]:=
A12=V2/V1Exp[-l12/(R*(273.15+T))];​​A13=V3/V1Exp[-l13/(R*(273.15+T))];​​A32=V2/V3Exp[-l32/(R*(273.15+T))];​​A21=V1/V2Exp[-l21/(R*(273.15+T))];​​A31=V1/V3Exp[-l31/(R*(273.15+T))];​​A23=V3/V2Exp[-l23/(R*(273.15+T))];
In[]:=
GAM1=Exp[-Log[x1+x2*A12+x3*A13]+1-(x1/(x1+x2*A12+x3*A13)+x2*A21/(x1*A21+x2+x3*A23)+x3*A31/(x1*A31+x2*A32+x3))];​​GAM2=Exp[-Log[x1*A21+x2+x3*A23]+1-(x1*A12/(x1+x2*A12+x3*A13)+x2/(x1*A21+x2+x3*A23)+x3*A32/(x1*A31+x2*A32+x3))];​​GAM3=Exp[-Log[x1*A31+x2*A32+x3]+1-(x1*A13/(x1+x2*A12+x3*A13)+x2*A23/(x1*A21+x2+x3*A23)+x3/(x1*A31+x2*A32+x3))];
Calculation of Isovolatility Curves
In[]:=
y1=GAM1x1PS1/P;​​y2=GAM2x2PS2/P;​​y3=GAM3x3PS3/P;
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sol[a_,b_,c_]:=FindRoot[PGAM1PS1x1+GAM2PS2x2+GAM3PS2x3/.x1a/.x2b/.x3c,{T,100}]
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α
13
[x_,y_]:=If0≤x+y≤1,
y1y
xy3
/.sol[x,1-x-y,y]/.x1x/.x2(1-x-y)/.x3y,0
In[]:=
tb13=Table[
α
13
[x,y],{x,0.001,1,0.01},{y,0.001,1,0.01}];
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ListContourPlot[tb13,Contours20,ContourStyleRGBColor[1,1,0]]
Out[]=
In[]:=
Table[
α
13
[x,y],{x,0.001,1,0.1},{y,0.001,1,0.1}]
Out[]=
{{1.06662,1.21542,1.38363,1.57479,1.79342,2.04542,2.33859,2.68336,3.09407,3.59096},{1.16826,1.31163,1.47219,1.65302,1.85798,2.09199,2.36138,2.67445,3.04226,0},{1.25074,1.38777,1.54018,1.71051,1.90188,2.11814,2.36403,2.64549,0,0},{1.31697,1.44753,1.59174,1.75158,1.92937,2.12781,2.35009,0,0,0},{1.36997,1.49409,1.63008,1.77931,1.9433,2.12372,0,0,0,0},{1.41227,1.52988,1.65745,1.7958,1.94574,0,0,0,0,0},{1.44572,1.55659,1.67545,1.80262,0,0,0,0,0,0},{1.4716,1.5754,1.68523,0,0,0,0,0,0,0},{1.4908,1.5872,0,0,0,0,0,0,0,0},{1.50399,0,0,0,0,0,0,0,0,0}}
In[]:=
α
12
[x_,y_]:=If0≤x+y≤1,
y1y
xy2
/.sol[x,y,1-x-y]/.x1x/.x2y/.x3(1-x-y),0
In[]:=
tb12=Table[
α
12
[x,y],{x,0.001,1,0.01},{y,0.001,1,0.01}];
In[]:=
ListContourPlot[tb12,Contours20,ContourStyleRGBColor[0,1,1]]
Out[]=
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Table[
α
12
[x,y],{x,0.001,1,0.1},{y,0.001,1,0.1}]
Out[]=
{{2.5629,2.14201,1.80367,1.52692,1.29737,1.10481,0.941786,0.802764,0.683538,0.580864},{2.44757,2.07977,1.77827,1.52746,1.31628,1.13667,0.982628,0.849592,0.734051,0},{2.36136,2.03598,1.76414,1.53436,1.33822,1.16937,1.02294,0.895179,0,0},{2.29801,2.0062,1.75832,1.54581,1.36219,1.20243,1.06258,0,0,0},{2.25185,1.98694,1.75865,1.56051,1.38746,1.23549,0,0,0,0},{2.21861,1.97557,1.76352,1.57747,1.41343,0,0,0,0,0},{2.19514,1.97014,1.7717,1.59592,0,0,0,0,0,0},{2.17911,1.96918,1.78225,0,0,0,0,0,0,0},{2.16875,1.9715,0,0,0,0,0,0,0,0},{2.16266,0,0,0,0,0,0,0,0,0}}
In[]:=
α
23
[x_,y_]:=If0≤x+y≤1,
y2y
xy3
/.sol[1-x-y,x,y]/.x2x/.x3y/.x1(1-x-y),0
In[]:=
tb23=Table[
α
23
[x,y],{x,0.001,1,0.01},{y,0.001,1,0.01}];
In[]:=
ListContourPlot[tb23,Contours20,ContourStyleRGBColor[1,0,1]]
Out[]=
In[]:=
Table[
α
23
[x,y],{x,0.001,1,0.1},{y,0.001,1,0.1}]
Out[]=
{{0.699852,0.736384,0.778145,0.826419,0.882933,0.95007,1.0312,1.13126,1.25761,1.42154},{0.760962,0.804984,0.855721,0.914888,0.984817,1.06875,1.1713,1.29923,1.46258,0},{0.830735,0.883854,0.945586,1.01823,1.10491,1.21004,1.33993,1.50379,0,0},{0.911,0.975277,1.05063,1.14014,1.24805,1.38038,1.54583,0,0,0},{1.00418,1.08233,1.17481,1.2858,1.42115,1.58924,0,0,0,0},{1.11359,1.20929,1.32374,1.46275,1.63456,0,0,0,0,0},{1.2439,1.36229,1.50566,1.68228,0,0,0,0,0,0},{1.40184,1.55034,1.7329,0,0,0,0,0,0,0},{1.59729,1.78696,0,0,0,0,0,0,0,0},{1.84501,0,0,0,0,0,0,0,0,0}}
We find an azeotrope between Acetone and Chloroform