Effect of Dimerization on Vapor Liquid Equilibrium 
for the Binary Systems: 
Acetic Acid - Water and Formic Acid - water
Author's Data: Housam BINOUS
Department of Chemical Engineering
National Institute of Applied Sciences and Technology
Tunis, TUNISIA
Email: binoushousam@yahoo.com

Binary system: Acetic Acid - Water

Activity coefficients using Wilson Model
Component 1= Acetic Acid
Component 2= Water

A12=v2/v1 Exp[-d12/(R (273.15+T))];A21=v1/v2 Exp[-d21/(R (273.15+T))];

d12=-180.83700;d21=813.09710;v1=57.54;v2=18.07;

G1=Exp[-Log[x1+A12 x2]+x2 (A12/(x1+A12 x2)-A21/(A21 x1+x2))];
G2=Exp[-Log[x2+A21 x1]-x1 (A12/(x1+A12 x2)-A21/(A21 x1+x2))];

Vapor Pressure using Antoine Equation

A1=8.02100;B1=1936.010;C1=258.451;
A2=8.07131;B2=1730.630;C2=233.426;

PS1=1.01325 10^5/76010^(A1-B1/(C1+T));
PS2=1.01325 10^5/76010^(A2-B2/(C2+T));

FindRoot[PS1== 1.01325 10^5,{T,300}]

FindRoot[PS2== 1.01325 10^5,{T,300}]

Gas Constant and Pressure

P=1.01325  10^5;R=1.987;

Dimerization constant for Acetic Acid obtained from Venimadhavan, Malone and Doherty, AIChE Journal, Vol. 45, No 3, pp. 546-556

K=10^(-12.5454+3166/(273.15+T))

K/.T-> 24.85

Taking into account dimerization of acetic acid in the gaz phase gives correct Vapor Liquid Equilibrium behavior. In particular, there is no azeotrope.

i=0;h=0.01;x1=.;x2=.;T=.;Eq=.

While[i<101,{x1[i]=Evaluate[h i],Eq1=G1(PS1 x1)== P y1 (1+Sqrt[(1+4 K PS1)])/(1+Sqrt[(1+4 K P y1 (2-y1))])/.x1->x1[i]/.x2->(1-x1[i]),
Eq2=G2(PS2 x2)== P (1-y1)(2 (1-y1+Sqrt[(1+4 K P y1 (2-y1))]))/((2-y1) (1+Sqrt[(1+4 K P y1 (2-y1))]))/.x1->x1[i]/.x2->(1-x1[i]),
T[i]=FindRoot[{Eq1,Eq2},{T,90,140},{y1,0.001,0.8}][[1,2]],y1[i]=FindRoot[{Eq1,Eq2},{T,90,140},{y1,0.001,0.8}][[2,2]],
,i++}];

tbl4=Chop[Table[{x1[i],y1[i]},{i,0,100}]];

plt4=ListPlot[tbl4,Joined->True,PlotStyle->RGBColor[0,0,1],Epilog->{RGBColor[1,0,0],Line[{{0,0},{1,1}}]}]

tbl5=Chop[Table[{x1[i],T[i]},{i,0,100}]];

tbl6=Chop[Table[{y1[i],T[i]},{i,0,100}]];

plt5=ListPlot[tbl5,Joined->True,PlotStyle->RGBColor[1,0,0]];

plt6=ListPlot[tbl6,Joined->True,PlotStyle->RGBColor[0,0,1]];

Show[plt5,plt6,PlotRange->{95,120}]

Comparing with the Vapor Liquid results from Wikepedia or Alpert, N. and P.J. Elving, I&EC, 41, 2864 (1949).

tbl7={{114.6,0.123,0.0545},{110.6,0.298,0.189},{104.4,0.649,0.522},{100.5,0.944,0.923}};

plt7=ListPlot[Table[{1-tbl7[[i,2]],tbl7[[i,1]]},{i,1,4}],PlotStyle->RGBColor[0,0,1]];

plt8=ListPlot[Table[{1-tbl7[[i,3]],tbl7[[i,1]]},{i,1,4}],PlotStyle->RGBColor[1,0,0]];

plt9=ListPlot[Table[{1-tbl7[[i,3]],1-tbl7[[i,2]]},{i,1,4}],PlotStyle->RGBColor[0,1,0]];

Show[plt4,plt9]

Show[plt5,plt6,plt7,plt8,PlotRange->{95,120}]

Binary system: Formic Acid - Water

Activity coefficients using Wilson Model
Component 1= Formic Acid
Component 2= Water

d21=-310.1060;d12=1180.8040;v1=37.91;v2=18.07;

A12=v2/v1 Exp[-d12/(R (273.15+T))];A21=v1/v2 Exp[-d21/(R (273.15+T))];

G1=Exp[-Log[x1+A12 x2]+x2 (A12/(x1+A12 x2)-A21/(A21 x1+x2))];
G2=Exp[-Log[x2+A21 x1]-x1 (A12/(x1+A12 x2)-A21/(A21 x1+x2))];

Vapor Pressure using Antoine Equation

A1=6.94459;B1=1295.260;C1=218.00;
A2=8.07131;B2=1730.630;C2=233.426;

PS1=1.01325 /760 10^(A1-B1/(C1+T));
PS2=1.01325 /760 10^(A2-B2/(C2+T));

FindRoot[PS1== 1.01325 ,{T,300}]

FindRoot[PS2== 1.01325 ,{T,300}]

Gas Constant and Pressure

P=1.01325 ;R=1.987;

Dimerization constant for Acetic Acid from Bessling et al., Design of Processes with Reactive Distillation Line Diagrams,  Ind. Eng. Chem. Res. 1997, 36, 3032-3042

K=Exp[-18.22+7099/(273.15+T)]

K/.T-> 24.85

Taking into account dimerization of acetic acid in the gaz phase gives correct Vapor Liquid Equilibrium behavior. In particular, there is a negative azeotrope or maximum boiling azeotrope.

i=0;h=0.01;x1=.;x2=.;T=.;Eq=.

While[i<101,{x1[i]=Evaluate[h i],Eq1=G1(PS1 x1)== P y1 (1+Sqrt[(1+4 K PS1)])/(1+Sqrt[(1+4 K P y1 (2-y1))])/.x1->x1[i]/.x2->(1-x1[i]),
Eq2=G2(PS2 x2)== P (1-y1)(2 (1-y1+Sqrt[(1+4 K P y1 (2-y1))]))/((2-y1) (1+Sqrt[(1+4 K P y1 (2-y1))]))/.x1->x1[i]/.x2->(1-x1[i]),
T[i]=FindRoot[{Eq1,Eq2},{T,90,110},{y1,0.001,0.9}][[1,2]],y1[i]=FindRoot[{Eq1,Eq2},{T,90,110},{y1,0.001,0.9}][[2,2]],
,i++}];

tbl4=Chop[Table[{x1[i],y1[i]},{i,0,100}]];

plt4=ListPlot[tbl4,Joined->True,PlotStyle->RGBColor[0,0,1],Epilog->{RGBColor[1,0,0],Line[{{0,0},{1,1}}]}]

tbl5=Chop[Table[{x1[i],T[i]},{i,0,100}]];

tbl6=Chop[Table[{y1[i],T[i]},{i,0,100}]];

plt5=ListPlot[tbl5,Joined->True,PlotStyle->RGBColor[1,0,0]];

plt6=ListPlot[tbl6,Joined->True,PlotStyle->RGBColor[0,0,1]];

Show[plt5,plt6,PlotRange->{98,109}]

Comparing with the Vapor Liquid results from Wikipedia or ITO, T. and F. YOSHIDA, J. Chem. Eng. Data, 8, 315 (1963) .

tbl7={{102.3,0.0245,0.0405},{105.9,0.162,0.218 },{107.6,0.482,0.464},{101.8, 0.951,0.90}};

plt7=ListPlot[Table[{1-tbl7[[i,2]],tbl7[[i,1]]},{i,1,4}],PlotStyle->RGBColor[0,0,1]];

plt8=ListPlot[Table[{1-tbl7[[i,3]],tbl7[[i,1]]},{i,1,4}],PlotStyle->RGBColor[1,0,0]];

plt9=ListPlot[Table[{1-tbl7[[i,3]],1-tbl7[[i,2]]},{i,1,4}],PlotStyle->RGBColor[0,1,0]];

Show[plt4,plt9]

Show[plt5,plt6,plt7,plt8,PlotRange->{98,110}]