We compute VLE data for the binary mixture: Acetone - Methanol at a total pressure equal to 760 mmHg. Activity Coefficients based on NRTL model. Model parameters are taken from Aspen-HYSYS.
Component 1: Acetone
Component 2: Methanol
Component 1: Acetone
Component 2: Methanol
In[]:=
Gam[i_]:=Exp(tau[j,i]G[j,i]x[j])(G[l,i]x[l])+(G[l,j]x[l])tau[i,j]-(tau[r,j]G[r,j]x[r])(G[l,j]x[l])/.x[1]X1/.x[2]X2
2
∑
j=1
2
∑
l=1
2
∑
j=1
G[i,j]x[j]
2
∑
l=1
2
∑
r=1
2
∑
l=1
In[]:=
G[i_,j_]:=Exp[-a[i,j]tau[i,j]]
In[]:=
tau[i_,j_]:=g[i,j]/(R(T+273.15))
In[]:=
g[1,1]=0;g[2,1]=296.24310;g[1,2]=118.08020;g[2,2]=0;
In[]:=
a[1,1]=0;a[2,1]=0.30030;a[1,2]=0.30030;a[2,2]=0;
Gas Constant and Total Pressure
In[]:=
R=1.987;P=760;
Vapor Pressure based on Antoine Equation and Normal Boiling Points
In[]:=
Psat[i_]:=10^((Aa[i]-Ba[i]/(T+Ca[i])))
In[]:=
Aa[1]=7.63130;Aa[2]=8.08097;Ba[1]=1566.69;Ba[2]=1582.271;Ca[1]=273.419;Ca[2]=239.726;
In[]:=
FindRoot[Psat[1]760,{T,100}]
Out[]=
{T56.3767}
In[]:=
FindRoot[Psat[2]760,{T,100}]
Out[]=
{T64.5477}
While loop to get bubble temperature and vapor mole fraction
In[]:=
i=0;While[i<101,{xe[i]=i0.01,X1=xe[i],X2=1-xe[i],T[i]=Chop[NMinimize[(P-Psat[1]Gam[1]X1-Psat[2]Gam[2](1-X1))^2,{T}][[2,1,2]]],ye[i]=Psat[1]Gam[1]xe[i]/P/.TT[i],Print[i," ",T[i]," ",xe[i]," ",ye[i]," ",Gam[1]/.TT[i]," ",Gam[2]/.TT[i]],i++}]
0 64.5477 0. 0. 1.8375 1.
1 64.2006 0.01 0.0233809 1.81457 1.00007
2 63.8673 0.02 0.0456983 1.79213 1.00026
3 63.547 0.03 0.0670233 1.77019 1.00059
4 63.2392 0.04 0.0874211 1.74872 1.00106
5 62.9433 0.05 0.106952 1.72774 1.00165
6 62.6588 0.06 0.125672 1.70722 1.00237
7 62.3852 0.07 0.143633 1.68716 1.00323
8 62.1219 0.08 0.160882 1.66755 1.00422
9 61.8684 0.09 0.177464 1.64839 1.00533
10 61.6245 0.1 0.193421 1.62966 1.00658
11 61.3895 0.11 0.20879 1.61136 1.00796
12 61.1631 0.12 0.223607 1.59347 1.00947
13 60.9451 0.13 0.237906 1.576 1.01111
14 60.7348 0.14 0.251717 1.55893 1.01288
15 60.5322 0.15 0.265069 1.54226 1.01478
16 60.3367 0.16 0.27799 1.52597 1.01682
17 60.1481 0.17 0.290504 1.51006 1.01898
18 59.9662 0.18 0.302636 1.49452 1.02128
19 59.7906 0.19 0.314408 1.47934 1.0237
20 59.621 0.2 0.325839 1.46452 1.02626
21 59.4573 0.21 0.336951 1.45005 1.02895
22 59.2992 0.22 0.347761 1.43592 1.03178
23 59.1464 0.23 0.358286 1.42213 1.03474
24 58.9987 0.24 0.368544 1.40866 1.03783
25 58.856 0.25 0.378549 1.39552 1.04105
26 58.7181 0.26 0.388315 1.38269 1.04442
27 58.5846 0.27 0.397858 1.37016 1.04791
28 58.4556 0.28 0.407189 1.35794 1.05155
29 58.3308 0.29 0.416321 1.34601 1.05532
30 58.21 0.3 0.425265 1.33437 1.05922
31 58.0932 0.31 0.434034 1.32302 1.06327
32 57.9801 0.32 0.442636 1.31194 1.06746
33 57.8706 0.33 0.451083 1.30113 1.07178
34 57.7647 0.34 0.459384 1.29059 1.07625
35 57.6621 0.35 0.467549 1.28031 1.08086
36 57.5629 0.36 0.475585 1.27028 1.08561
37 57.4668 0.37 0.483501 1.26051 1.09051
38 57.3737 0.38 0.491305 1.25098 1.09555
39 57.2836 0.39 0.499005 1.24169 1.10074
40 57.1965 0.4 0.506609 1.23263 1.10608
41 57.1121 0.41 0.514123 1.22381 1.11157
42 57.0304 0.42 0.521554 1.21521 1.11721
43 56.9514 0.43 0.528909 1.20684 1.123
44 56.875 0.44 0.536194 1.19868 1.12894
45 56.801 0.45 0.543415 1.19073 1.13504
46 56.7296 0.46 0.550579 1.183 1.1413
47 56.6605 0.47 0.557691 1.17547 1.14771
48 56.5938 0.48 0.564758 1.16814 1.15428
49 56.5294 0.49 0.571783 1.16101 1.16102
50 56.4672 0.5 0.578773 1.15408 1.16792
51 56.4072 0.51 0.585733 1.14733 1.17498
52 56.3495 0.52 0.592669 1.14078 1.18222
53 56.2939 0.53 0.599585 1.13441 1.18962
54 56.2404 0.54 0.606486 1.12821 1.19719
55 56.189 0.55 0.613377 1.1222 1.20494
56 56.1397 0.56 0.620264 1.11636 1.21286
57 56.0925 0.57 0.62715 1.11069 1.22095
58 56.0473 0.58 0.634042 1.1052 1.22923
59 56.0041 0.59 0.640942 1.09987 1.23769
60 55.963 0.6 0.647857 1.0947 1.24634
61 55.9239 0.61 0.65479 1.08969 1.25517
62 55.8868 0.62 0.661748 1.08484 1.26419
63 55.8518 0.63 0.668733 1.08015 1.2734
64 55.8188 0.64 0.675752 1.07561 1.28281
65 55.7879 0.65 0.682808 1.07123 1.29241
66 55.7591 0.66 0.689907 1.06699 1.30221
67 55.7323 0.67 0.697054 1.0629 1.31222
68 55.7076 0.68 0.704253 1.05895 1.32243
69 55.6851 0.69 0.711509 1.05515 1.33285
70 55.6647 0.7 0.718828 1.05149 1.34348
71 55.6465 0.71 0.726215 1.04797 1.35432
72 55.6305 0.72 0.733674 1.04458 1.36538
73 55.6168 0.73 0.741212 1.04134 1.37667
74 55.6054 0.74 0.748834 1.03822 1.38817
75 55.5964 0.75 0.756545 1.03524 1.3999
76 55.5897 0.76 0.764351 1.03239 1.41187
77 55.5856 0.77 0.772259 1.02966 1.42406
78 55.5839 0.78 0.780274 1.02707 1.43649
79 55.5849 0.79 0.788403 1.0246 1.44917
80 55.5884 0.8 0.796652 1.02226 1.46208
81 55.5948 0.81 0.805029 1.02004 1.47525
82 55.6039 0.82 0.813539 1.01794 1.48867
83 55.6159 0.83 0.822192 1.01597 1.50234
84 55.6309 0.84 0.830993 1.01411 1.51627
85 55.649 0.85 0.839952 1.01237 1.53046
86 55.6703 0.86 0.849077 1.01076 1.54492
87 55.6948 0.87 0.858376 1.00925 1.55965
88 55.7228 0.88 0.867858 1.00787 1.57466
89 55.7543 0.89 0.877533 1.0066 1.58994
90 55.7894 0.9 0.887412 1.00544 1.60551
91 55.8283 0.91 0.897504 1.0044 1.62136
92 55.8712 0.92 0.90782 1.00347 1.63751
93 55.9182 0.93 0.918373 1.00265 1.65395
94 55.9694 0.94 0.929175 1.00195 1.67069
95 56.025 0.95 0.940239 1.00135 1.68773
96 56.0853 0.96 0.951578 1.00086 1.70509
97 56.1504 0.97 0.963208 1.00048 1.72275
98 56.2205 0.98 0.975143 1.00021 1.74073
99 56.2959 0.99 0.987402 1.00005 1.75903
100 56.3767 1. 1. 1. 1.77766
Plotting the equilibrium curve or xy data --- compared to data from Ref. 2
dataexp=;
In[]:=
tbexp=Table[{dataexp[[i]][[1]],dataexp[[i]][[2]]},{i,1,Length[dataexp]}]
Out[]=
{{0.101,0.186},{0.126,0.222},{0.2,0.328},{0.275,0.405},{0.34,0.465},{0.429,0.522},{0.485,0.561},{0.626,0.663},{0.721,0.727},{0.776,0.77},{0.823,0.806},{0.872,0.855}}
In[]:=
tb=Table[{xe[i],ye[i]},{i,0,100}];
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plt1=Show[ListPlot[tb,PlotStyleRGBColor[1,0,0],JoinedTrue,GridLines->Automatic,AspectRatio->1,Frame->True,Epilog{RGBColor[0,1,0],Line[{{0,0},{1,1}}]},FrameLabel->{Style["liquid mole fraction of Acetone",16],Style["vapor mole fraction of Acetone",16]}],ListPlot[tbexp,PlotMarkers->Style["■",Darker@Blue],GridLines->Automatic,AspectRatio->1,Frame->True,Epilog{RGBColor[0,1,0],Line[{{0,0},{1,1}}]},FrameLabel->{Style["liquid mole fraction of Acetone",16],Style["vapor mole fraction of Acetone",16]}]]
Plotting the isobaric VLE diagram or T-xy data --- compared to data from Ref. 2
Plotting the activity coefficient at 50 °C
Comparison with digitized data from Fig. 13.4 (b) of Ref. 1, which is based on experimental measurements for six binary systems at 50°C.
Comparison with digitized data from Fig. 13.4 (b) of Ref. 1, which is based on experimental measurements for six binary systems at 50°C.
References
References
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[1] J.M. Smith, Hendrick Van Ness, Michael Abbott and Mark Swihart, Introduction to Chemical Engineering Thermodynamics, 9th Edition, NY: McGraw Hill, 2022.
◼
[2] Verhoeye, L. and De Schepper, H. (1973), The vapour—liquid equilibria of the binary, ternary and quaternary systems formed by acetone, methanol, propan-2-ol, and water. J. Appl. Chem., 23: 607-619. https://doi.org/10.1002/jctb.5020230807
CITE THIS NOTEBOOK
CITE THIS NOTEBOOK
Vapor-liquid data of acetone-methanol mixture at 760 mmHg
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, March 20, 2025
https://community.wolfram.com/groups/-/m/t/3420440
by Housam Binous and Ahmed Bellagi
Wolfram Community, STAFF PICKS, March 20, 2025
https://community.wolfram.com/groups/-/m/t/3420440