Notebook converts the mass-fraction tie-line data to mole fractions using molar masses M(phenol) = 94.11 g/mol, M(DIPE) = 102.17 g/mol, M(water) = 18.015 g/mol.​To do so, one can use:​​
​​Notebook also computes distribution (D) and separation coefficients (S). Note S comes out essentially identical to the mass - fraction values in the original table (the ratio is basis - invariant to good approximation), while D is larger on a mole basis because the DIPE - rich organic phase has a much lower average molar mass, which inflates phenol' s mole fraction there relative to its mass fraction .​​
​​​
LLE data conversion: mass fraction -> mole fraction
System: Phenol (1)+DIPE (2)+Water (3) at T=298.15 K and P=101.3 kPa
Molar masses, g/mol
M1=94.11;(*Phenol*)​​M2=102.17;(*DIPE*)​​M3=18.015;(*Water*)
Raw mass-fraction tie-line data: {w1w,w2w,w3w,w1o,w2o,w3o} for each tie line
massData={{0.0002,0.0173,0.9825,0.0050,0.9770,0.0180},{0.0056,0.0176,0.9768,0.0900,0.8908,0.0192},{0.0069,0.0177,0.9753,0.1010,0.8796,0.0194},{0.0105,0.0178,0.9717,0.1320,0.8486,0.0194},{0.0155,0.0188,0.9657,0.1740,0.8065,0.0195},{0.0162,0.0189,0.9649,0.1786,0.8016,0.0198},{0.0192,0.0192,0.9616,0.2074,0.7722,0.0204},{0.0246,0.0203,0.9551,0.2549,0.7244,0.0207}};
Convert a mass-fraction triplet {w1,w2,w3} to mole fractions
massToMole[{w1_,w2_,w3_}]:=Module[{n1,n2,n3,nTot},n1=w1/M1;​​n2=w2/M2;​​n3=w3/M3;​​nTot=n1+n2+n3;​​{n1,n2,n3}/nTot];
Apply conversion to aqueous phase (1-3) and organic phase (4-6) of each row
moleData=Map[Function[row,Join[massToMole[row[[1;;3]]],massToMole[row[[4;;6]]]]],massData];
In[]:=
Join[{{Style["Aqueous phase",Darker@Blue],"","",Style["Organic phase",Darker@Red],"",""}},{{"Phenol","DIPE","water","Phenol","DIPE","water"}},moleData]//TableForm
Out[]//TableForm=
Aqueous phase
Organic phase
Phenol
DIPE
water
Phenol
DIPE
water
0.0000388448
0.003095
0.996866
0.00500522
0.900865
0.0941297
0.00109277
0.00316348
0.995744
0.089036
0.811738
0.0992261
0.00134814
0.00318546
0.995466
0.0997476
0.800164
0.100089
0.0020576
0.00321295
0.994729
0.130049
0.770103
0.0998474
0.00305261
0.00341044
0.993537
0.170798
0.729208
0.0999933
0.0031926
0.00343087
0.993377
0.17503
0.723603
0.101367
0.00379427
0.00349495
0.992711
0.202292
0.693764
0.103944
0.00488801
0.0037154
0.991397
0.247406
0.647637
0.104957
Distribution coefficient (phenol),mole-fraction basis:D=x1^o/x1^w
massDcoeff=Map[#[[4]]/#[[1]]&,massData];
In[]:=
massDcoeff//TableForm
Out[]//TableForm=
25.
16.0714
14.6377
12.5714
11.2258
11.0247
10.8021
10.3618
Separation coefficient (phenol relative to water), mole-fraction basis: S=(x1^o/x1^w)/(x3^o/x3^w)
massScoeff=Map[(#[[4]]/#[[1]])/(#[[6]]/#[[3]])&,massData];
In[]:=
massScoeff//TableForm
Out[]//TableForm=
1364.58
817.634
735.883
629.673
555.936
537.259
509.181
478.094
Assemble full results table: {x1w,x2w,x3w,x1o,x2o,x3o,D,S}
results=MapThread[Append[#1,#2]&,{MapThread[Append,{massData,massDcoeff}],massScoeff}];
Pretty-print as a table
TableForm[results,TableHeadings->{None,{"x1_w","x2_w","x3_w","x1_o","x2_o","x3_o","D","S"}}]
Export to CSV if desired
Export["LLE_MoleFraction_Results.csv",Prepend[results,{"x1_w","x2_w","x3_w","x1_o","x2_o","x3_o","D","S"}]];
Out[]//TableForm=
Distribution coefficient (phenol), mole-fraction basis: D=x1^o/x1^w
moleDcoeff=Map[#[[4]]/#[[1]]&,moleData];
In[]:=
moleDcoeff//TableForm
Out[]//TableForm=
128.852
81.4774
73.9889
63.2044
55.9515
54.8235
53.3151
50.6149
Separation coefficient (phenol relative to water), mole-fraction basis: S=(x1^o/x1^w)/(x3^o/x3^w)
moleScoeff=Map[(#[[4]]/#[[1]])/(#[[6]]/#[[3]])&,moleData];
In[]:=
moleScoeff//TableForm
Out[]//TableForm=
1364.58
817.634
735.883
629.673
555.936
537.259
509.181
478.094
Assemble full results table:{x1w,x2w,x3w,x1o,x2o,x3o,D,S}
results=MapThread[Append[#1,#2]&,{MapThread[Append,{moleData,moleDcoeff}],moleScoeff}];
Pretty-print as a table
TableForm[results,TableHeadings->{None,{"x1_w","x2_w","x3_w","x1_o","x2_o","x3_o","D","S"}}]
Export to CSV if desired
Export["LLE_MoleFraction_Results.csv",Prepend[results,{"x1_w","x2_w","x3_w","x1_o","x2_o","x3_o","D","S"}]];
Out[]//TableForm=
Let us reproduce the ternary diagram given below for the Phenol - DIPE - water system

References

[1] https://pubs.acs.org/jceaax/article-abstract/65/11/5210/874007/Liquid-Liquid-Equilibria-for-the-Quaternary-System?redirectedFrom=fulltext

CITE THIS NOTEBOOK

Extraction of phenol from aqueous solution with diisopropyl ether (DIPE)​
by Housam Binous​
Wolfram Community, STAFF PICKS, August 2, 2026
https://community.wolfram.com/groups/-/m/t/3771875