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Consider a binary mixture composed of acetone and water. We computes and plots the isobaric vapor-liquid equilibrium diagram, the equilibrium curve, the relative volatility, the

-value, the gas-phase fugacity coefficients and the Poynting correction factor for a pressure equal to 34.01 atm. We take into account deviation from ideal behavior in the gas phase by including gas phase fugacity coefficients obtained from pure gas Virial coefficients,

. Thus high-pressure VLE data can be obtained. The code allows for the Poynting factor correction. VLE data is computed using the following formula (the gamma-phi-poy equation) given in Ref. 2 :

sat

exp

P-

sat



, where

and

are the vapor and liquid mole fractions of component

is the total pressure,

sat

is the saturation vapor pressure of component

=exp

P-

sat



is the vapor-phase fugacity coefficient, and

is the liquid-phase activity coefficient, where

and

are determined using the Virial coefficient and the Wilson model, respectively;

is the liquid molar volume of molecule

determined using the Rackett equation.Our generated VLE data are benchmarked against the experimental data from Othmer et el. (1952).

Generating our VLE data @ P = 34.01 atm

Clear[x1,x2,y1,y2];

Total pressure is 34.01 atm

P=101.325×34.01;

Reduced temperature

Tre[i_]:=T/Tc[i];

Second virial coefficients

B0V[i_]:=0.083-0.422Tre[i]^(-1.6)

B1V[i_]:=0.139-0.172Tre[i]^(-4.2)

B[i_]:=8314Tc[i]/Pc[i](B0V[i]+ω[i]B1V[i])

Critical pressure and temperature and acentric factor

Pc[1]=4701;Tc[1]=508.2;ω[1]=0.3070;(*ACETONE*)

Pc[2]=22055;Tc[2]=647.1;ω[2]=0.345;(*WATER*)

R=1.987;(*universalgasconstantincal/gmol*K*)

Modified Antoine Equation for vapor pressures

A1=71.3031;B1=-5952.;C1=0.;D1=-8.53128;E1=7.82393/10^6;F1=2.;

A2=65.9278;B2=-7227.53;C2=0.;D2=-7.17695;E2=4.0313/10^6;F2=2.;

Psat1=Exp[A1+B1/(C1+T)+D1Log[T]+E1T^F1];

Psat2=Exp[A2+B2/(C2+T)+D2Log[T]+E2T^F2];

Wilson model for activity coefficients

l12=489.3727;l21=1422.849;V1=7.44767773150726;V2=1.78833825504182;A12=V2/V1Exp[-l12/(R*(T))];A21=V1/V2Exp[-l21/(R*(T))];Gam1=Exp[-Log[x1+x2*A12]+1-(x1/(x1+x2*A12)+x2*A21/(x1*A21+x2))];Gam2=Exp[-Log[x1*A21+x2]+1-(x1*A12/(x1+x2*A12)+x2/(x1*A21+x2))];

Rackett Equation for pure component liquid molar volumes

v11=2090.233^((1-Tre[1])^(2/7));v22=55.90.229^((1-Tre[2])^(2/7));

Boiling temperatures in Kelvin at 34.01 atm

T1=T/.FindRoot[Psat1P,{T,400}];T2=T/.FindRoot[Psat2P,{T,400}];

Summation rule

y2=1-y1;

In[]:=

{T1,T2}(*inKelvin*)

Out[]=

{487.123,514.777}

In[]:=

Clear[x1,x2];i=0;While[i<51,{x=(i)0.02,x1=x,x2=1-x1,sol=Chop@FindRoot[{Psat1x1Gam1Exp[(v11-B[1])(P-Psat1)/(8314.472T)]+Psat2(1-x1)Gam2Exp[(v22-B[2])(P-Psat2)/(8314.472T)]P,y1Psat1x1Gam1Exp[(v11-B[1])(P-Psat1)/(8314.472T)]/(P)},{y1,0.05,0.07},{T,430,510},MaxIterations1000],xe[i]=x1,ye[i]=Psat1x1Gam1Exp[(v11-B[1])(P-Psat1)/(8314.472T)]/(P)/.sol,Te[i]=T/.sol,α[i]=Psat1Gam1Exp[(v11-B[1])(P-Psat1)/(8314.472T)]/(Psat2Gam2Exp[(v22-B[2])(P-Psat2)/(8314.472T)])/.sol,poy1[i]=Exp[v11(P-Psat1)/(8314.472T)]/.sol,poy2[i]=Exp[v22(P-Psat2)/(8314.472T)]/.sol,ϕ[1][i]=Exp[B[1](P-Psat1)/(8314.472T)]/.sol,ϕ[2][i]=Exp[B[2](P-Psat2)/(8314.472T)]/.sol,i++}];

Isobaric VLE diagram @ 34.01 atm

In[]:=

Tbl1=Table[{xe[i],Te[i]-273.15},{i,0,50}];Tbl2=Table[{ye[i],Te[i]-273.15},{i,0,50}];

In[]:=

plt1=ListPlot[Tbl1,PlotStyle{Thickness[.005],RGBColor[1,.47,0]},PlotRange{{0,1},{205,245}},JoinedTrue];plt2=ListPlot[Tbl2,PlotStyle{Thickness[.005],ColorData["HTML","Green"]},PlotRange{{0,1},{205,245}},JoinedTrue];

experimental data from Ref. 1

DATA={{93.9,92.1,211.1},{88.4,85.3,209.2},{78.9,75.0,208.5},{66.9,66.3,206.0},{54.7,58.5,207.5},{41.2,52.7,208.6},{29.1,46.5,210.6},{18.5,40.8,212.7},{9.2,31.8,218.9},{2.3,14.0,230.}};

In[]:=

plt1exp=ListPlot[Table[{DATA[[i]][[1]]/100,DATA[[i]][[3]]},{i,1,10}],PlotStyle{Thickness[.005],RGBColor[0.6,.47,0]},PlotRange{{0,1},{205,245}}];plt2exp=ListPlot[Table[{DATA[[i]][[2]]/100,DATA[[i]][[3]]},{i,1,10}],PlotStyle{Thickness[.005],RGBColor[0.1,.47,0]},PlotRange{{0,1},{205,245}}];

In[]:=

Show[plt2,plt1,plt1exp,plt2exp,FrameTrue,ImageSize{400,400},FrameLabel{Style["mole fractions of ACETONE",14],Style["Temperature in °C",14]},GridLinesAutomatic,AspectRatio1]

Out[]=

VL Equilibrium Curve @ 34.01 atm

In[]:=

Tbl3=Table[{xe[i],ye[i]},{i,0,50}];

In[]:=

plt3=ListPlot[Tbl3,PlotStyle{Thickness[.005],RGBColor[.7,.08,.64]},JoinedTrue];

plt3exp=ListPlot[Table[{DATA[[i]][[1]]/100,DATA[[i]][[2]]/100},{i,1,10}],PlotStyle{Thickness[.005],RGBColor[.07,.08,.64]}];(*experimentaldatafromRef.1*)

In[]:=

Show[plt3,plt3exp,EpilogLine[{{0,0},{1,1}}],FrameTrue,AxesOrigin{0,0},ImageSize{400,400},GridLinesAutomatic,AspectRatio1,FrameLabel{Style["liquid mole fractions of ACETONE",14],Style["vapor mole fractions of ACETONE",14]},PlotRangeAll]

Out[]=

Relative volatility @ 34.01 atm

In[]:=

Tbl6=Table[{xe[i],α[i]},{i,0,50}];

In[]:=

plt6=ListPlot[Tbl6,PlotStyle{Thickness[.005],ColorData["HTML","Green"]},JoinedTrue];

In[]:=

Showplt6,GraphicsTextStyle"

sat

exp



P-

sat



sat

exp



P-

sat



",RGBColor[0.2,0.24,0.02],16,{0.5,5.8},FrameTrue,AxesOrigin{0,0},PlotRange{0,10},FrameTrue,ImageSize{400,400},GridLinesAutomatic,AspectRatio1,FrameLabel{Style["mole fractions of ACETONE",14],Style["relative volatility",14]}

Equilibrium constants @ 34.01 atm

Poynting correction factors @ 34.01 atm

Fugacity coefficients @ 34.01 atm

References

◼

[1] Othmer, D. F., Chudgar, M. M., & Levy, S. L. (1952). Binary and Ternary Systems of Acetone, Methyl Ethyl Ketone, and Water. Industrial & Engineering Chemistry, 44(8), 1872–1881. https://doi.org/10.1021/ie50512a042

◼

[2] M.F. Doherty and M.F. Malone, Conceptual Design of Distillation Systems, Boston : McGraw - Hill, 2001.

CITE THIS NOTEBOOK

High-pressure vapor-liquid equilibrium data for binary mixture : acetone-water
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, June 6, 2025
https://community.wolfram.com/groups/-/m/t/3475277