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Vapour-liquid equilibrium of dialkylphenols in cyclohexane
173
Fluid Phase Equilibria, 57 (1990) 173-190
Elsevier Science Publishers B.V., Amsterdam -
VAPOUR-LIQUID EQUILIBRIUM IN CYCLOHEXANE ANDRZEJ KSI@CZAK,
Printed in The Netherlands
OF DIALKYLPHENOLS
JERZY JAN KOSINSKI and KRZYSZTOF
MOORTHI
Department of Physical Chemistry, Technical University of Warsaw, 00-664 Warsaw (Poland)
(Received December 22, 1988; accepted in final form August 16, 1989)
ABSTRACT Ksi@czak, A., Kosihski, J.J. and Moorthi, K., 1990. Vapour-liquid kylphenols in cyclohexane. Fluid Phase Equilibria, 57: 173-190.
equilibrium
of dial-
The vapour pressure of solutions of 4-tert-butyl-2-methylphenol, 2-tert-butyl-%methylphenol, 2-tert-butyl-6-methylphenol, 2,6-di-iso-propylphenol and 2,6-di-tert-butylphenol in cyclohexane at 298.15 and 323.15 K have been measured. The vapour pressure and activity coefficients determined on the basis of the thermodynamic properties of monosubstituted phenols have been compared with those predicted by the UNIFAC method. The influence of the steric hindrance around the hydroxyl group on the structure and thermodynamic properties of the solutions has been examined.
INTRODUCTION
Polar groups in molecules in a solution greatly influence the deviations of the properties of the solution from ideality. In the case of polar groups such as -OH, -COOH, -SH, and -NH, the departures are due to the hydrogen bonds leading to association. The geometric conditions of the reactive centre determine how easily the associates are formed. The increase of the steric hindrance around the reactive centre decreases the capability to form hydrogen bonds. Large steric hindrance precludes the formation of associates. The X-ray study of 2,6-di-tert-butyl-4-methylphenol (Maze and Rerat, 1964) proves that hydrogen bonds are not formed in the solid phase. The concept of steric hindrance is an indispensable tool for explaining the variation in the reactivity of chemical compounds (Chapman and Shorter, 1972). Steric hindrance influences thermodynamic parameters such as the association constant K, enthalpy of association AH* and heat capacity of association ACT. These parameters can be determined on the basis of an association model assumed for the description of the activity coefficients or 0378-3812/90/$03.50
0 1990 - Elsevier Science Publishers B.V.
174
thermodynamic properties of the pure compounds. In a previous paper (Ksi$czak and Moorthi, 1985) the prediction of vapour pressures of monoalkylphenols and dimethylphenols in cyclohexane on the basis of thermodynamic properties of pure liquids was presented. The athermal MeckeKempter model has enabled us to obtain a good prediction of vapour pressures of the solutions. Attempts to apply this model to solid-liquid equilibria have produced unsatisfactory results (Ksi$czak and Anderko, 1987). Analysis of solid-liquid equilibria has indicated that the associated structures in the liquid solution along the solubility curve are the same as in the solid phase (Ksi@czak, 1983). The phenols with small steric hindrance form mainly trimers. This result suggests the existence of monomer-trimer equilibrium in the solution. Phenols with considerable steric hindrance form mainly dimers, which favours monomer-dimer equilibrium. The aim of this paper is to investigate the influence of the geometric conditions prevailing around the hydroxyl group of the phenol on the associated structure and the thermodynamic properties of pure compounds and their solutions. Vapour pressures of solutions of dialkylphenols in cyclohexane at 298.15 and 323.15 K were measured. Phenols with a significantly varying steric hindrance were chosen. Phenols possessing one methyl and one tert-butyl substituent, such as 4-tert-butyl-2-methylphenol, 2-tert-butyl-5-methylpheno1 and 2-tert-butyl-6-methylphenol were taken into consideration. Phenols having two equal-sized ortho-substituents: 2,6-di-iso-propylphenol and 2,6di-tert-butylphenol were also examined. EXPERIMENTAL
Vapour pressure measurements of solutions were performed by employing the static (bubble and dew point) method (Ksi@czak and Buchowski, 1980). Cyclohexane and the solutions used for our investigations were dehydrated in the measuring device .as described in the paper mentioned above. Dehydration of the solution is possible up to concentrations of about 0.3 mole fraction of the polar component. For this reason measurements were performed only over a limited range of concentrations. MATERIALS
Spectroscopy grade cyclohexane (POCh, Gliwice) was dried over sodium and distilled through a 50 theoretical-plate distillation column. The impurities determined by means of gas chromatography were 0.1%. Phenols were
175 TABLE 1 Source and purity of phenols used Phenol
Source
4-tert-butyl-2-methylphenol 2-tert-butyl-5-methylphenol 2-tert-butyl-6-methylphenol 2,6-di-iso-propylphenol 2,6-di-tert-butylphenol
Fluka Fluka Eastman Fluka Fluka
Purity(W) (Pratt.) (Purum) (Pratt.) (Pratt.) @rum)
99.1 99.7 99.0 99.5 99.3
purified either by distillation under reduced pressure or by vacuum sublimation (see Table 1).
MODEL OF ASSOCIATION
The phenols investigated are almost involatile at the selected experimental temperatures and, consequently, the total vapour pressure ( p) is equal to the partial vapour pressure of the solvent and can be expressed by the equation P =P&Y~
exp[O% - V,)(P,” -p)/RTl
(1)
where ps* is the vapour pressure of the pure solvent, xs is the mole fraction of solvent, y, is the activity coefficient, B, is the second virial coefficient (for cyclohexane, B, = - 1919 cm3 mol-’ at 298.15 K and B, = - 1505 cm3 mol-’ at 323.15 K have been used), Vs is the molar volume of the pure solvent and R is the gas constant. In order to establish a well-defined structure of the associates, the following models were taken into consideration: monomer-dimer, monomer-trimer and the Mecke-Kempter continuous association model. These models were applied by assuming the associates to form ideal or athermal solutions. The activity coefficient of the solvent ys is assumed to consist of a contribution due to specific interactions leading to association, yr, and a contribution due to non-specific interactions, ySphY”., which involve mainly dispersion interactions
Earlier results (Ksigczak and Kosihski, 1988) indicate that an increase in the number of adjustable parameters makes the equation more flexible to give a better correlation of phase equilibrium data but, frequently, the adjusted parameters do not have the physical meaning that is attributed to them. These parameters often give unsatisfactory prediction of other phase
176
equilibria. For this reason, a model of the solution involving as few adjustable parameters as possible must be constructed. The activity coefficient of the solvent in the Mecke-Kempter model was calculated as follows (Kehiaian, 1964) ass. =
1
YS
2XA
_
1 + (1 + K,,X,X,)“2
[
I
1
(3)
xs
where xA is the mole fraction of the associated substance and K,, is the association constant for the Mecke-Kempter model. The association constant of the ideal monomer-dimer model, KMr,, is related to the thermodynamic constant K,, by the equation K m=(Km+1)Km
(4)
The activity coefficient of the solvent was calculated as follows (Kehiaian, 1963) 2
XA
ass. = 1+ 2 _ xA lUS
1
+ [l + 4K,,x,(2
- x~)]~‘~
Analogous parameters for the ideal monomer-trimer K MT
=
( KMK
+
lJ2 KMK
2XA
Ysass. = 1+ 3 _ 2xA 1+ i
where K,,
model are (6)
(a - 1)1’3 - (a + 1)1’3 [2K,,x:(3
- 2x,)]1’2
l/2 1
(7)
is the trimerization constant 4 %,X:(3
-
2X,)
(74
The activity coefficient of the solvent in the athermal Mecke-Kempter model can be calculated as follows (Kehiaian and Treszczanowicz, 1968) K@’ MK =K
MK
e
(8)
where as and aA are the volume fractions of the solvent and the associated compound, respectively, VA is the molar volume of the associated compound, e is the base of natural logarithms (e = 2.718281828.. .) and K& is the volume-fraction association constant.
177
The athermal described as K&, = K,,
= Ysass.
monomer-dimer
model (Treszczanowicz,
1968) may be
e
1 01) (10)
Qs exp 1 - 7% + 7v,
WGD
xs
S
*
1 +
2 K3DA +
(1 + 4K;r,@A)1’2
where K&, is the volume-fraction association constant. The volume-fraction association constant K& and the activity coefficient of the solvent in the athermal monomer-trimer model are expressed as K& = K,,
e2
(12)
(13) where K&
is the volume-fraction
association constant
(134 It is assumed that the contribution to the activity coefficients due to non-specific interactions can be described in terms of the HildebrandScatchard regular solution theory as PhYs.= exp Ys
V D2Q2 SRT *
where D is the difference of the solubility parameter of the solvent and the modified solubility parameter of the associated compounds, R is the gas constant and T is the equilibrium temperature. The modified solubility parameters of the associated compounds reflecting non-specific interactions in the solution were determined as presented elsewhere (Ksi@czak and Moorthi, 1985). RESULTS AND DISCUSSION
The values of vapour pressures over the solutions of phenols and the activity coefficients of cyclohexane are listed in Table 2. The solution of 4-tert-butyl-2-methylphenol which is endowed with the least steric hindrance has the largest value of the activity coefficients of cyclohexane at an identical mole fraction.- Smaller values of ys are found for 2-tert-butyl-5methylphenol. The hydroxyl group in this compound is screened by the bulky o&o tert-butyl group. The lowest values of ys for the isomeric
178 TABLE 2 Vapour pressure and activity coefficients of cyclohexane xA
T = 323.15 K
T = 298.15 K P (mm I-W
YS
P
97.75
-
271.50
-
1.0332 1.0471 1.0608 1.0832 1.1035 1.1202 1.1529
262.63 261.&I 258.42 256.22 253.09 250.05 247.50 242.96
1.0192 1.0247 1.0358 1.0486 1 SO679 1.0864 1.1010 1.1308
2-tert-butyl-5-methylphenol+ cyclohexane 0.0429 95.01 1.0158 0.0613 93.95 1.0243 0.0988 92.26 1.0479 0.1250 90.74 1.0617 0.1477 89.92 1.0802 0.1798 88.78 1.1084 0.2010 87.44 1.1208 1.1448 0.2297 86.09 ’ 0.2534 85.42 1.1720
262.74 259.62 253.53 248.95 245.68 242.41 238.22 233.29 229.55
1.0120 1.0197 1.0377 1.0498 1.0639 1.0911 1.1011 1.1189 1.1363
262.24 261.80
1.0072 1.0057
1.0162 1.0240 1.0292 1.0372 1.0407 1.0675 1.0920 1.1298
257.24 252.06 248.87 243.62 240.39 237.70 227.56 218.33 210.15
1.0093 1.0118 1.0208 1.0220 1.0306 1.0323 1.0542 1.0774 1.1077
2,6-di-iso-propylphenol + cyclohexane 0.0561 93.79 1.0170 0.0793 92.49 1.0283 0.1309 89.19 1.0508 0.1575 87.95 1.0691 0.2064 84.81 1.0948 0.2582 81.82 1.1303 0.3013 79.77 1.1703
259.79 255.33 245.64 241.59 231.73 222.27 215.73
1.0147 1.0228 1.0432 1.0587 1.0789 1.1080 1.1423
cyclohexane -
4-tert-butyl-2-methylphenol+ cyclohexane 0.0502 0.0609 0.0801 0.0989 0.1258 0.1508 0.1704 0.2068
94.81 94.12 93.39 92.51 91.54 90.77 89.31
2-tert-butyl-6-methylphenol+ cyclohexane 0.0395 94.45 1.0063 0.0403 0.0404 94.35 1.0062 0.0496 93.69 1.0089 0.0602 0.0810 0.1004 0.1200 0.1387 0.1496 0.2021 0.2504 0.2978
91.22 89.97 88.44 87.22 86.40 83.13 79.86 77.38
(mm
W
Ys
179 TABLE 2 (continued) xA
T = 298.15 K
T = 323.15 K
P (mm L-W
Ys
2,6-di-tert-butylphenol + cyclohexane 0.0324 94.80 1.0026 0.0467 93.52 1.0041 0.0693 91.53 1.0068 0.0958 88.99 1.0078 0.1170 87.17 1.0111 0.1631 83.28 1.0196 0.2080 79.49 1.0288 0.2988 71.18 1.0415 0.3984 61.97 1.0579
P (mm I-W
US
262.83 259.13 -
1.0012 1.0022
245.98 240.70 228.97 217.71 194.37 168.03
1.0040 1.0065 1.0112 1.0169 1.0273 1.0373
phenols examined are seen to occur for 2-tert-butyl-6-methylphenol. As expected, the solutions of 2,6-di-tert-butylphenol have the smallest values of the activity coefficients of cyclohexane among all the investigated dialkylphenols. It appears that, as the steric hindrance around the hydroxyl group increases, the departure of the solution from ideal behaviour decreases. Another paper (Ksi@czak and Kosihski, 1990) describes the method of prediction of thermodynamic properties of polysubstituted phenols based on the thermodynamic properties of monosubstituted phenols. The vapour pressures of pure phenols were correlated using the monomer-dimer, monomer-trimer and continuous association models to obtain practically identical standard deviations. For this reason, the properties of the pure liquid cannot be attributed to a specific model of association. The thermodynamic association constants of the Mecke-Kempter model (K,,) of the discussed
TABLE 3 Association constants, solubility parameters and molar volumes of substances used Phenol
4-tert-butyl-2-methylphenol 2-tert-butyl-5-methylphenol 2-tert-butyl-6-methylphenol 2,6-di-iso-propylphenol 2,6-di-tert-butylphenol cyclohexane
W
K(h)Mx
v,
(cal cm-3)‘/2
(cm3 1
298.15 K
323.15 K
298.15 K
323.15 K
9.495 3.812 1.214 5.912 0.319 -
6.224 2.689 0.930 3.646 0.270
9.21 9.17 9.01 8.95 8.51 8.20
169.1 170.7 169.9 186.7 220.2 108.7
174.3 174.3 173.5 190.6 224.8 112.4
cyclohexane 25.467 43194.957 6118.918 31.786 12882.076 5587.158 cyclohexane 13.957 66.838 693.325 17.164 74.450 693.594 cyclohexane 11.663 57.022 529.478 13.661 58.681 467.400 cyclohexane 6.845 25.117 149.007 10.483
4-tert-butyl-2-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer Ideal monomer-trimer Athermal Mecke-Kempter A thermal monomer-dimer AthermaI monomer-trimer
2-tert-butyl-5-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer IdeaI monomer- trimer Athermal Mecke-Kempter Athermal monomer-dimer Athermal monomer-trimer
2-tert-butyl-5-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer Ideal monomer-trimer Athermal Mecke-Kempter
K(a)
Variant I
4tert-butyl-2-methylphenol+ Ideal Mecke- Kemp ter Ideal monomer-dimer IdeaI monomer-trimer Athermal Mecke-Kempter Athermal monomer-dimer Athermal monomer-trimer
Association model SD b
0.83 0.28 0.13 0.19 0.24 0.13
0.000 1.140 0.000 0.597
T = 323.15 K
1.35 0.62 0.89 0.61
298.15 K 0.40 0.000 1.418 0.19 0.565 0.22 1.037 0.27 0.20 1.858 1.524 0.25
T=
0.000 1.527 0.594 0.795 1.940 1.528
T = 323.15 K
T= 298.15 K 0.000 0.47 1.517 0.12 0.797 0.06 0.08 0.752 1.945 0.11 1.614 0.04
D(a) a
1.566 1.490 1.230 1.156
1.676 1.688 1.346 1.325 1.883 1.456
1.577 1.632 1.042 0.823 1.879 1.260
1.642 1.894 1.286 1.049 2.127 1.611
D(a) a
variant II
Association constants, D parameters and standard deviations in the three variants
TABLE 4
0.01110 0.01700 0.00420 0.00053 0.02319 0.01043
0.01004 0.00850 0.00380 0.00263
0.01241 0.01269 0.00579 0.00541 0.01733 0.00784
0.00971 0.01087 0.00043 - 0.00227 0.01661 0.00376
&
2.22 1.01 2.03 0.90
0.90 0.37 0.65 0.33 0.19 0.25
1.91 0.37 0.68 0.18 0.30 0.78
0.18 0.30 0.04
0.40
1.00 0.46
SD b
2.689 9.919 36.588 7.309
3.812 18.344 88.271 10.362 49.864 652.243
6.224 44.959 324.777 16.918 122.212 2399.799
9.495 99.644 1045.732 25.809 270.860 7726.975
K(h)
Variant III
4.81 3.79 2.52 1.42
2.25 2.15 1.15 0.96 2.88 1.34
3.41 3.26 0.64 0.70 4.75 1.20
1.65 2.13 0.63 0.18 2.84 1.18
SDb
323.15 K 0.000 0.718 0.000 0.799 1.470 1.088
2,6-di-iso-propylphenol + cyclohexane T= Ideal Mecke-Kempter 3.783 Ideal monomer-dimer 12.687 Ideal monomer- trimer 38.498 Athermal Mecke-Kempter 6.039 Athermal monomer-dimer 10.856 Athermal monomer-trimer 83.498 1.90 0.71 1.96 1.04 0.82 1.11
0.65 0.26 0.49 0.40 0.30 0.41
T = 323.15 K 0.000 0.72 1.019 0.63 1.952 0.98 1.115 0.71 1.519 0.67 0.996 0.92 298.15 K 0.000 0.990 0.000 1.041 1.614 1.309
cyclohexane 2.199 2.484 0.000 2.403 2.298 21.876
2-tert-butyl-6-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer Ideal monomer-trimer Athermal Mecke-Kempter Athermal monomer-dimer Athermal monomer-trimer
0.59 0.64
T = 298.15 K 0.000 0.24 1.119 0.19 0.000 0.37 1.144 0.23 1.588 0.21 1.154 0.31
1.653 1.217
2,6-di-iso-propylphenol + cyclohexane T= Ideal Mecke-Kempter 5.510 Ideal monomer-dimer 18.999 Ideal monomer- trimer 97.085 Athermal Mecke-Kempter 7.179 Athermal monomer-dimer 15.837 Athermal monomer-trimer 118.207
cyclohexane 3.049 3.707 23.795 3.258 3.538 31.724
26.892 238.663
2-tert-butyl-6-methylphenol+ Ideal Mecke- Kempter Ideal monomer-dimer Ideal monomer- trimer Athermal Mecke-Kempter Athermai monomer-dimer Athermal monomer-trimer
Athermal monomer-dimer Athermal monomer-trimer
0.193 0.542 0.000 O.ooO 1.143 0.311
0.000 0.730 0.000 0.000 1.315 0.693
1.296 1.194 1.243 1.068 1.252 0.914
1.366 1.270 1.250 1.132 1.363 1.019
1.652 1.175
0.00358 0.00183 0.00383 0.00383 0.00507 - 0.00317
-
0.00383 0.00020 0.00383 0.00383 0.00794 - 0.00056
-
0.00692 0.00521 0.00601 0.00328 0.00616 0.00121
0.00819 0.00648 0.00614 0.00424 0.00814 0.00258
0.01190 0.00293
1.73 0.71 3.46 2.21 1.61 2.31
0.64 0.35 1.38 1.05 0.67 1.05
0.93 0.63 1.53 0.67 0.86 0.88
0.40 0.20 0.61 0.22 0.31 0.31
0.55 0.60
3.646 16.938 78.693 9.911 46.043 581.467
5.912 40.861 282.422 16.070 111.071 2086.828
0.930 1.794 3.443 2.528 4.878 25.588
1.214 2.686 5.947 3.299 7.302 43.940
26.961 270.347
2.70 1.28 5.48 4.07 3.37 2.85
1.32 0.32 2.17 1.68 1.93 0.97
2.91 2.17 2.82 1.46 2.59 0.96
1.32 1.02 1.12 0.69 1.28 0.50
5.13 1.39
’ (caI cm-3)1/2;
0.42 0.42 0.42 0.16 0.16 0.28
0.35 0.35 0.35 0.12 0.12 0.19
SDb
b standard deviation of vapour pressure in mm Hg.
0.838 0.838 0.838 0.897 1.055 0.492
T = 323.15 K
D(a) a
2,6-di-tert-butylphenol + cyclohexane IdeaI Mecke-Kempter 0.000 IdeaI monomer-dimer 0.000 Ideal monomer- trimer 0.000 Athermal Mecke-Kempter 0.634 AthermaI monomer-dimer 0.432 Athermal monomer-trimer 5.042
I
T = 298.15 K 1.020 1.020 1.020 0.634 0.985 0.520
K(a)
variant
2,6-di-tert-butylphenol + cyclohexane IdeaI Mecke-Kempter 0.008 IdeaI monomer-dimer 0.008 IdeaI monomer-trimer 0.000 Athermal Mecke-Kempter 1.652 Athermal monomer-dimer 1.465 Athermal monomer-trimer 10.494
Association model
TABLE 4 (continued)
0.314 0.263 0.395 0.840 0.898 0.690
0.680 0.660 0.718 0.982 1.042 0.864
D(a) a
variant
II
o.OooO2 - 0.00019 0.00043 0.00437 0.00509 0.00273
0.00263 0.00243 0.00301 0.08622 0.00709 0.00466
112
0.73 0.62 1.23 0.15 0.30 0.34
0.44 0.40 0.61 0.18 0.12 0.29
SDb
0.270 0.343 0.436 0.734 0.933 3.221
0.319 0.420 0.554 0.867 1.143 4.097
K(h)
variant
III
0.67 0.59 1.18 3.09 3.60 1.97
0.68 0.60 0.86 1.59 1.80 1.22
SDb
183
phenols predicted by the substituent contribution method employed elsewhere (Ksi@czak and Kosihski, 1990) are listed in Table 3. The van der Waals volume of the o&o-alkyl substituents can be treated as an approximate measure of the steric hindrance. As expected, the value of the association constants decreases when the volume of the ortho-substituent increases. The calculated association constants are used to predict the activity coefficients of cyclohexane y? related to specific interactions. The association constants were determined from the association constants for the MeckeKempter model according to eqns. (4), (6), (8), (10) and (12). The activity coefficients yr for the six models are predicted by employing eqns. (3), (5), (7), (9), (11) and (13). The activity coefficients relating to non-specific interactions are estimated by eqn. (14). The solubility parameters of dialkylphenols 6(h) are determined using Hoy’s correlation (Barton, 1983). The parameters 6(h) are presented in Table 3. The calculations were performed in three variants. In variant I, the association constant K(a) and parameter D(a) were obtained for the appropriate equation by adjusting it to the vapour pressure of the solution. The values of these parameters and standard deviation SD are listed in Table 4. The standard deviations were determined as
1 1’2
05)
where N is the number of measurements and N, is the number of adjusted parameters. The adjustable parameters were obtained using the following objective function F = 5 { pylc.[K(a), i=l
o(a)] -~fx~.}~
The activity coefficients of cyclohexane calculated on the basis of the adjusted parameters K(a) and O(a) are shown as solid lines in Figs. l-5. The aim of variant I was to select the association model that gives the best description of the vapour pressure of the solution. The monomer-trimer model with the athermal or the ideal assumption gave the best fit of the vapour pressure of the 4-tert-butyl-2-methylphenol solution. These results are consistent with those obtained from solid-liquid equilibrium studies (Ksi@czak, 1986; Ksi@czak and Anderko, 1987). The athermal MeckeKempter model and the monomer-trimer model correlate the vapour pressure of the solutions within the experimental error. This result is consistent with the results obtained from the liquid-vapour equilibria studied for other phenols (Ksi@czak and Moorthi, 1985). The vapour pressures of the dialkylphenols possessing a greater steric hindrance are fitted best by the
184
Fig Ib T- 323,15 K
0,o
0.1
q2
0.3
x
a,0
OJ
42
0,s
1
Fig. 1. Activity coefficient of cyclohexane ys in the (4tert-butyl-2-methylphenol+ cyclohexane) system: (a) at 298.15 K, (b) at 323.15 K; 0, experimental points; calculated in variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC:
IL
Fig 2a
1’ I‘
1.1
0,o
0,l
0.2
0.3
x
0,o
0.1
0,2
0,3
x
Fig. 2. Activity coefficient of cyclohexane ys in the (2-tert-butyM-methylphenol + cyclohexane) system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; calculated in variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC:
185
0,o
0,l
0.2
0,3
x
0,o
0)
0,2
0,3
x
Fig. 3. Activity coefficient of cyclohexane ys in the (2-tert-butyl-Gmethylphenol + cyclohexane) system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; -, calculated in variant I; .- - -. , predicted in variant III; - - - - - -, predicted using UNIFAC.
monomer-dimer model with the athermal or the ideal assumption. The association constant of 2,6-di-tert-butylphenol is equal to zero when the molecules are assumed to form an ideal solution. This result is consistent
T=323.15 K
0.2 0.3 x 0.1 0,o 0.1 0,2 0,3 x 0,o Fig. 4. Activity coefficient of cyclohexane ys in the (2,6-di-iso-propylphenol+ system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; -, variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC.
cyclohexane) calculated in
Fig 5a
Fig 5b
T=298,15K
T=323,15K
J
0,o
0,l
0,2
0,3
x
w
91
0,2
0,3
x
Fig. 5. Activity coefficient of cyclohexane ys in the (2,6-di-tert-butylphenol+ system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; -, variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC.
cyclohexane) calculated in
with the experimental data concerning a similar compound (2,6-di-tertbutyl-4-methylphenol) described elsewhere (Ksiqzczak, 1977, 1982, 1983; Ksi$czak and Kosinski, 1988). In variant II, the parameters D(a) were adjusted and the association constants K(h) were predicted using the homomorph concept; they are listed in Table 3. The aim of variant II is to verify K(h) and the binary parameters I,, which are a measure of the departure from the geometric mean assumption (Barton, 1983) D’(a) = (6, - as)* + 2
42
8,
6,
(17)
where 8, is the solubility parameter of the solvent. The values of parameters I,, are presented in Table 4. The low values of the binary parameters I,, are consistent with those obtained for other phenols in the same solvent (Ksi$czak and Moorthi, 1985; Ksi@czak and Anderko, 1987). Similar results obtained with toluene (the homomorph in relation to phenol) were presented by Funk and Prausnitz (1970). The standard deviations of the vapour pressure in variant II are slightly larger than those in variant I with two adjusted parameters (see Table 4). The model best describing the vapour pressure data in variant II is consistent with analogous results obtained in variant I. This agreement demonstrates that the association constants calculated from the properties of monoalkylphenols have the physical meaning attributed to them.
187
In variant III calculations, the parameters (K(h) and D(h) = a,, - Ss) were predicted on the basis of the thermodynamic properties of the pure liquids listed in Table 3. The activity coefficients of cyclohexane as calculated by variant III for the model giving the best fit in variant I are shown by a dotted line in Figs. l-5. In spite of the lack of information about the solution, a useful description of the vapour pressure of the solution has been obtained. The values of the parameters K(h) and D(h) differ considerably from those adjusted in variant I. These results suggest that the objective function of the properties discussed is very flat in a certain direction on the parameter surface. A slight change of the objective function causes great changes in the adjusted parameters (K(a) and O(a)). The UNIFAC method (Fredenslund et al., 1977) was applied to predict the activity coefficients of cyclohexane and the vapour pressure of the solution. The predicted ys are shown as broken lines in Figs. 1-5. The necessary parameters were taken from a paper by Tiegs et al. (1987). The UNIFAC method gives only one relation between ys and x for phenols possessing identical substituents. This relation for the three isomeric phenols investigated lies between all the experimental points giving the best prediction for 2-tert-butyl-5-methylphenol. These results demonstrate that UNIFAC can predict low values of solvent activity coefficients for isomeric phenols with no ortho-substituents. Standard deviations of the vapour pressure SD(UNIFAC) are listed in Table 5. In our opinion the large values of SD(UNIFAC) are due to the lack of parameters determining the influence of the geometric conditions of the hydroxyl group on the energetic parameters in the UNIFAC method. It is seen from Figs. 1-5 that the predictions of the activity coefficients ( ys) obtained on the basis of the properties of pure liquids (variant III) are better than those obtained by the UNIFAC method. In variant III, the better description of the solution vapour pressure is obtained despite the lack of information about the solution and the properties of pure dialkylphenols.
TABLE 5 Vapour pressure prediction for the UNIFAC method Phenol
4-tert-butyl-2-methylphenol 2-tert-butyl-S-methylphenol 2-tert-butyl-6-methylphenol 2,6-di-iso-propylphenol 2,6-di-tert-butylphenol
SD (mm Hg) 298.15 K
323.15 K
2.44 1.35 2.21 0.87 2.82
4.39 1.38 6.54 1.52 8.65
188 CONCLUSION
The increase of steric hindrance around the hydroxyl group changes the structure of the dialkylphenol solution. The best fit of the activity coefficients of cyclohexane for the 4-tert-butyl-2-methylphenol solution is obtained for the monomer-trimer model. The other dialkylphenols with one o&o-butyl substituent associate in agreement with the monomer-dimer model. The same results have been obtained with the assumption that the associates form an athermal or an ideal solution. The phenols having two ortho-tert-butyl substituents probably do not associate. The two bulky substituent groups completely screen the hydroxyl group. The values of association constants K(h) of the dialkylphenols decrease when the volume of ortho substituents increases. A similar behaviour has been observed for the activity coefficients (ys) which decrease when the steric hindrance decreases. The thermodynamic properties of the dialkylphenol solutions predicted on the basis of pure-compound thermodynamic properties of monoalkylphenols give better results than the UNIFAC method does. In this case a far extrapolation of association constants was required, extracted from the properties of pure monoalkylphenols. LIST OF SYMBOLS
a k9 4
AC; D e 0
AH” K K MK K MD K Kg GD
Gl-
symbol in eqn. (7) (see eqn. (7a)) symbol in eqn. (13) (see eqn. (13a)) adjusted value of parameter second virial coefficient of pure solvent standard specific heat of association difference of solubility parameter of solvent and modified solubility parameter of associated solute base of natural logarithms, e = 2.718281828.. . objective function (see eqn. (16)) parameter value predicted from homomorph concept standard enthalpy of association association constant association constant in the Mecke-Kempter model association constant in the monomer-dimer model association constant in the monomer-trimer model volume-fraction association constant in the athermal MeckeKemp ter model volume-fraction association constant in the athermal monomerdimer model volume-fraction _association constant in the athermal monomertrimer model
189 1
1;’ xi P pica'=. p,““.
PC R
SD v, Yn v, XA XS
binary parameter (see eqn. (17)) number of data points number of adjusted parameters vapour pressure of solution calculated vapour pressure experimental vapour pressure vapour pressure of pure solvent gas constant R = 8.31431 J mol-’ K-l standard deviation of calculated vapour pressures from experimental values (see eqn. (15)) molar volume of solute molar volume of liquid solute or solvent molar volume of solvent mole fraction of solute mole fraction of solvent
Greek letters
activity coefficient of solvent contribution to activity coefficient of solvent due to specific interacYY tions phys. contribution to activity coefficient of solvent due to non-specific US interactions (see eqn. (14)) modified solubility parameter of solute ‘h solubility parameter of solvent 8s volume fraction of solute @A volume fraction of solvent Q’s US
ACKNOWLEDGMENTS
The authors thank Professor A. Bylicki for suggestions and discussions. The work reported herein was sponsored by the Polish Academy of Sciences within the framework of Project 1.16. REFERENCES Barton, A.F.M., 1983. CRC Handbook of Solubility Parameters and Other Cohesion Parameters, CRC Press, Boca Raton, FL. Chapman, N.B. and Shorter, J., 1972. Advances in linear free energy relationship, Plenum, London. Fredenslund, A., Gmehling, J. and Rasmussen, P., 1977. Vapor-liquid equilibria using UNIFAC, Elsevier, Amsterdam.
190 Funk, E.W. and Prausnitz, J.M., 1970. Thermodynamic properties of liquid mixtures: aromatic-saturated hydrocarbon systems. Ind. Eng. Chem., 62: 8-15. Kehiaian, H., 1963. Thermodynamics of chemically reacting mixtures. VI. Excess enthalpy and excess entropy of ideal associated mixtures of the type A+ B+ A,. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 11: 591-596. Kehiaian, H., 1964. Thermodynamics of chemically reacting mixtures. XIII. Thermodynamic excess functions of ideal associated mixtures of the Mecke-Kempter type. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 12: 567-573. Kehiaian, H. and Trsezczanowicz, A., 1968. Excess free enthalpy of athermal associated mixtures of the Mecke-Kempter type. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 16: 445-452. Ksi@czak, A., 1977. Sterically hindered association of alkylphenols. Rocz. Chem., 51: 185-187. Ksi$czak, A., 1982. Substituent effect on the excess Gibbs energy of saturated solution of phenols. Fluid Phase Equilibria, 9: 287-293. Ksi@czak, A., 1983. Solid-liquid equilibrium and the hydrogen bond in crystals. Fluid Phase Equilibria, 15: 1-9. Ksi@czak, A., 1986. The effect of auto-association on solid-liquid equilibrium. Fluid Phase Equilibria, 28: 39-56. Ksi$czak, A. and Anderko, A., 1987. Prediction of solid-liquid equilibria on the basis of pure compound properties. Fluid Phase Equilibria, 35: 127-151. Ksi@czak, A. and Buchowski, H., 1980. Determination of traces of water in a solvent. I. Method using vapor pressure differences. Fluid Phase Equilibria, 5: 131-140. Ksigczak, A. and Kosihski, J.J., 1988. Vapour pressure of binary, three-phase (S-L-V) systems and solubility. Fluid Phase Equilibria, 44: 211-236. Ksi$czak, A. and Kosihski, J.J., 1990. Vapour pressure and association of phenols. Fluid Phase Equilibria, 55: 17-37. Ksigczak, A. and Moorthi, K., 1985. Prediction of thermodynamic properties of alkylphenol + hydrocarbon binary systems on the basis of pure liquids properties. Fluid Phase Equilibria, 23: 153-164. Maze, M. and Rerat, C., 1964. Etude de la structure du bromo4 ditertiobutyl-2,6 phenol et du methyl-4 ditertiobutyl-2,6 phenol. C. R. Acad. Sci., 259: 4612-4615. Tiegs, D., Gmehling, J., Rasmussen, P. and Fredenslund, A., 1987. Vapour-liquid equilibria by UNIFAC group contribution 4. Revision and extension. Ind. Eng. Chem. Res., 26: 159-161. Treszczanowicz, A., 1968. Excess free enthalpy of athermal associated mixtures of the type A+A, +B. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 16: 71-75.
Fluid Phase Equilibria, 57 (1990) 173-190
Elsevier Science Publishers B.V., Amsterdam -
VAPOUR-LIQUID EQUILIBRIUM IN CYCLOHEXANE ANDRZEJ KSI@CZAK,
Printed in The Netherlands
OF DIALKYLPHENOLS
JERZY JAN KOSINSKI and KRZYSZTOF
MOORTHI
Department of Physical Chemistry, Technical University of Warsaw, 00-664 Warsaw (Poland)
(Received December 22, 1988; accepted in final form August 16, 1989)
ABSTRACT Ksi@czak, A., Kosihski, J.J. and Moorthi, K., 1990. Vapour-liquid kylphenols in cyclohexane. Fluid Phase Equilibria, 57: 173-190.
equilibrium
of dial-
The vapour pressure of solutions of 4-tert-butyl-2-methylphenol, 2-tert-butyl-%methylphenol, 2-tert-butyl-6-methylphenol, 2,6-di-iso-propylphenol and 2,6-di-tert-butylphenol in cyclohexane at 298.15 and 323.15 K have been measured. The vapour pressure and activity coefficients determined on the basis of the thermodynamic properties of monosubstituted phenols have been compared with those predicted by the UNIFAC method. The influence of the steric hindrance around the hydroxyl group on the structure and thermodynamic properties of the solutions has been examined.
INTRODUCTION
Polar groups in molecules in a solution greatly influence the deviations of the properties of the solution from ideality. In the case of polar groups such as -OH, -COOH, -SH, and -NH, the departures are due to the hydrogen bonds leading to association. The geometric conditions of the reactive centre determine how easily the associates are formed. The increase of the steric hindrance around the reactive centre decreases the capability to form hydrogen bonds. Large steric hindrance precludes the formation of associates. The X-ray study of 2,6-di-tert-butyl-4-methylphenol (Maze and Rerat, 1964) proves that hydrogen bonds are not formed in the solid phase. The concept of steric hindrance is an indispensable tool for explaining the variation in the reactivity of chemical compounds (Chapman and Shorter, 1972). Steric hindrance influences thermodynamic parameters such as the association constant K, enthalpy of association AH* and heat capacity of association ACT. These parameters can be determined on the basis of an association model assumed for the description of the activity coefficients or 0378-3812/90/$03.50
0 1990 - Elsevier Science Publishers B.V.
174
thermodynamic properties of the pure compounds. In a previous paper (Ksi$czak and Moorthi, 1985) the prediction of vapour pressures of monoalkylphenols and dimethylphenols in cyclohexane on the basis of thermodynamic properties of pure liquids was presented. The athermal MeckeKempter model has enabled us to obtain a good prediction of vapour pressures of the solutions. Attempts to apply this model to solid-liquid equilibria have produced unsatisfactory results (Ksi$czak and Anderko, 1987). Analysis of solid-liquid equilibria has indicated that the associated structures in the liquid solution along the solubility curve are the same as in the solid phase (Ksi@czak, 1983). The phenols with small steric hindrance form mainly trimers. This result suggests the existence of monomer-trimer equilibrium in the solution. Phenols with considerable steric hindrance form mainly dimers, which favours monomer-dimer equilibrium. The aim of this paper is to investigate the influence of the geometric conditions prevailing around the hydroxyl group of the phenol on the associated structure and the thermodynamic properties of pure compounds and their solutions. Vapour pressures of solutions of dialkylphenols in cyclohexane at 298.15 and 323.15 K were measured. Phenols with a significantly varying steric hindrance were chosen. Phenols possessing one methyl and one tert-butyl substituent, such as 4-tert-butyl-2-methylphenol, 2-tert-butyl-5-methylpheno1 and 2-tert-butyl-6-methylphenol were taken into consideration. Phenols having two equal-sized ortho-substituents: 2,6-di-iso-propylphenol and 2,6di-tert-butylphenol were also examined. EXPERIMENTAL
Vapour pressure measurements of solutions were performed by employing the static (bubble and dew point) method (Ksi@czak and Buchowski, 1980). Cyclohexane and the solutions used for our investigations were dehydrated in the measuring device .as described in the paper mentioned above. Dehydration of the solution is possible up to concentrations of about 0.3 mole fraction of the polar component. For this reason measurements were performed only over a limited range of concentrations. MATERIALS
Spectroscopy grade cyclohexane (POCh, Gliwice) was dried over sodium and distilled through a 50 theoretical-plate distillation column. The impurities determined by means of gas chromatography were 0.1%. Phenols were
175 TABLE 1 Source and purity of phenols used Phenol
Source
4-tert-butyl-2-methylphenol 2-tert-butyl-5-methylphenol 2-tert-butyl-6-methylphenol 2,6-di-iso-propylphenol 2,6-di-tert-butylphenol
Fluka Fluka Eastman Fluka Fluka
Purity(W) (Pratt.) (Purum) (Pratt.) (Pratt.) @rum)
99.1 99.7 99.0 99.5 99.3
purified either by distillation under reduced pressure or by vacuum sublimation (see Table 1).
MODEL OF ASSOCIATION
The phenols investigated are almost involatile at the selected experimental temperatures and, consequently, the total vapour pressure ( p) is equal to the partial vapour pressure of the solvent and can be expressed by the equation P =P&Y~
exp[O% - V,)(P,” -p)/RTl
(1)
where ps* is the vapour pressure of the pure solvent, xs is the mole fraction of solvent, y, is the activity coefficient, B, is the second virial coefficient (for cyclohexane, B, = - 1919 cm3 mol-’ at 298.15 K and B, = - 1505 cm3 mol-’ at 323.15 K have been used), Vs is the molar volume of the pure solvent and R is the gas constant. In order to establish a well-defined structure of the associates, the following models were taken into consideration: monomer-dimer, monomer-trimer and the Mecke-Kempter continuous association model. These models were applied by assuming the associates to form ideal or athermal solutions. The activity coefficient of the solvent ys is assumed to consist of a contribution due to specific interactions leading to association, yr, and a contribution due to non-specific interactions, ySphY”., which involve mainly dispersion interactions
Earlier results (Ksigczak and Kosihski, 1988) indicate that an increase in the number of adjustable parameters makes the equation more flexible to give a better correlation of phase equilibrium data but, frequently, the adjusted parameters do not have the physical meaning that is attributed to them. These parameters often give unsatisfactory prediction of other phase
176
equilibria. For this reason, a model of the solution involving as few adjustable parameters as possible must be constructed. The activity coefficient of the solvent in the Mecke-Kempter model was calculated as follows (Kehiaian, 1964) ass. =
1
YS
2XA
_
1 + (1 + K,,X,X,)“2
[
I
1
(3)
xs
where xA is the mole fraction of the associated substance and K,, is the association constant for the Mecke-Kempter model. The association constant of the ideal monomer-dimer model, KMr,, is related to the thermodynamic constant K,, by the equation K m=(Km+1)Km
(4)
The activity coefficient of the solvent was calculated as follows (Kehiaian, 1963) 2
XA
ass. = 1+ 2 _ xA lUS
1
+ [l + 4K,,x,(2
- x~)]~‘~
Analogous parameters for the ideal monomer-trimer K MT
=
( KMK
+
lJ2 KMK
2XA
Ysass. = 1+ 3 _ 2xA 1+ i
where K,,
model are (6)
(a - 1)1’3 - (a + 1)1’3 [2K,,x:(3
- 2x,)]1’2
l/2 1
(7)
is the trimerization constant 4 %,X:(3
-
2X,)
(74
The activity coefficient of the solvent in the athermal Mecke-Kempter model can be calculated as follows (Kehiaian and Treszczanowicz, 1968) K@’ MK =K
MK
e
(8)
where as and aA are the volume fractions of the solvent and the associated compound, respectively, VA is the molar volume of the associated compound, e is the base of natural logarithms (e = 2.718281828.. .) and K& is the volume-fraction association constant.
177
The athermal described as K&, = K,,
= Ysass.
monomer-dimer
model (Treszczanowicz,
1968) may be
e
1 01) (10)
Qs exp 1 - 7% + 7v,
WGD
xs
S
*
1 +
2 K3DA +
(1 + 4K;r,@A)1’2
where K&, is the volume-fraction association constant. The volume-fraction association constant K& and the activity coefficient of the solvent in the athermal monomer-trimer model are expressed as K& = K,,
e2
(12)
(13) where K&
is the volume-fraction
association constant
(134 It is assumed that the contribution to the activity coefficients due to non-specific interactions can be described in terms of the HildebrandScatchard regular solution theory as PhYs.= exp Ys
V D2Q2 SRT *
where D is the difference of the solubility parameter of the solvent and the modified solubility parameter of the associated compounds, R is the gas constant and T is the equilibrium temperature. The modified solubility parameters of the associated compounds reflecting non-specific interactions in the solution were determined as presented elsewhere (Ksi@czak and Moorthi, 1985). RESULTS AND DISCUSSION
The values of vapour pressures over the solutions of phenols and the activity coefficients of cyclohexane are listed in Table 2. The solution of 4-tert-butyl-2-methylphenol which is endowed with the least steric hindrance has the largest value of the activity coefficients of cyclohexane at an identical mole fraction.- Smaller values of ys are found for 2-tert-butyl-5methylphenol. The hydroxyl group in this compound is screened by the bulky o&o tert-butyl group. The lowest values of ys for the isomeric
178 TABLE 2 Vapour pressure and activity coefficients of cyclohexane xA
T = 323.15 K
T = 298.15 K P (mm I-W
YS
P
97.75
-
271.50
-
1.0332 1.0471 1.0608 1.0832 1.1035 1.1202 1.1529
262.63 261.&I 258.42 256.22 253.09 250.05 247.50 242.96
1.0192 1.0247 1.0358 1.0486 1 SO679 1.0864 1.1010 1.1308
2-tert-butyl-5-methylphenol+ cyclohexane 0.0429 95.01 1.0158 0.0613 93.95 1.0243 0.0988 92.26 1.0479 0.1250 90.74 1.0617 0.1477 89.92 1.0802 0.1798 88.78 1.1084 0.2010 87.44 1.1208 1.1448 0.2297 86.09 ’ 0.2534 85.42 1.1720
262.74 259.62 253.53 248.95 245.68 242.41 238.22 233.29 229.55
1.0120 1.0197 1.0377 1.0498 1.0639 1.0911 1.1011 1.1189 1.1363
262.24 261.80
1.0072 1.0057
1.0162 1.0240 1.0292 1.0372 1.0407 1.0675 1.0920 1.1298
257.24 252.06 248.87 243.62 240.39 237.70 227.56 218.33 210.15
1.0093 1.0118 1.0208 1.0220 1.0306 1.0323 1.0542 1.0774 1.1077
2,6-di-iso-propylphenol + cyclohexane 0.0561 93.79 1.0170 0.0793 92.49 1.0283 0.1309 89.19 1.0508 0.1575 87.95 1.0691 0.2064 84.81 1.0948 0.2582 81.82 1.1303 0.3013 79.77 1.1703
259.79 255.33 245.64 241.59 231.73 222.27 215.73
1.0147 1.0228 1.0432 1.0587 1.0789 1.1080 1.1423
cyclohexane -
4-tert-butyl-2-methylphenol+ cyclohexane 0.0502 0.0609 0.0801 0.0989 0.1258 0.1508 0.1704 0.2068
94.81 94.12 93.39 92.51 91.54 90.77 89.31
2-tert-butyl-6-methylphenol+ cyclohexane 0.0395 94.45 1.0063 0.0403 0.0404 94.35 1.0062 0.0496 93.69 1.0089 0.0602 0.0810 0.1004 0.1200 0.1387 0.1496 0.2021 0.2504 0.2978
91.22 89.97 88.44 87.22 86.40 83.13 79.86 77.38
(mm
W
Ys
179 TABLE 2 (continued) xA
T = 298.15 K
T = 323.15 K
P (mm L-W
Ys
2,6-di-tert-butylphenol + cyclohexane 0.0324 94.80 1.0026 0.0467 93.52 1.0041 0.0693 91.53 1.0068 0.0958 88.99 1.0078 0.1170 87.17 1.0111 0.1631 83.28 1.0196 0.2080 79.49 1.0288 0.2988 71.18 1.0415 0.3984 61.97 1.0579
P (mm I-W
US
262.83 259.13 -
1.0012 1.0022
245.98 240.70 228.97 217.71 194.37 168.03
1.0040 1.0065 1.0112 1.0169 1.0273 1.0373
phenols examined are seen to occur for 2-tert-butyl-6-methylphenol. As expected, the solutions of 2,6-di-tert-butylphenol have the smallest values of the activity coefficients of cyclohexane among all the investigated dialkylphenols. It appears that, as the steric hindrance around the hydroxyl group increases, the departure of the solution from ideal behaviour decreases. Another paper (Ksi@czak and Kosihski, 1990) describes the method of prediction of thermodynamic properties of polysubstituted phenols based on the thermodynamic properties of monosubstituted phenols. The vapour pressures of pure phenols were correlated using the monomer-dimer, monomer-trimer and continuous association models to obtain practically identical standard deviations. For this reason, the properties of the pure liquid cannot be attributed to a specific model of association. The thermodynamic association constants of the Mecke-Kempter model (K,,) of the discussed
TABLE 3 Association constants, solubility parameters and molar volumes of substances used Phenol
4-tert-butyl-2-methylphenol 2-tert-butyl-5-methylphenol 2-tert-butyl-6-methylphenol 2,6-di-iso-propylphenol 2,6-di-tert-butylphenol cyclohexane
W
K(h)Mx
v,
(cal cm-3)‘/2
(cm3 1
298.15 K
323.15 K
298.15 K
323.15 K
9.495 3.812 1.214 5.912 0.319 -
6.224 2.689 0.930 3.646 0.270
9.21 9.17 9.01 8.95 8.51 8.20
169.1 170.7 169.9 186.7 220.2 108.7
174.3 174.3 173.5 190.6 224.8 112.4
cyclohexane 25.467 43194.957 6118.918 31.786 12882.076 5587.158 cyclohexane 13.957 66.838 693.325 17.164 74.450 693.594 cyclohexane 11.663 57.022 529.478 13.661 58.681 467.400 cyclohexane 6.845 25.117 149.007 10.483
4-tert-butyl-2-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer Ideal monomer-trimer Athermal Mecke-Kempter A thermal monomer-dimer AthermaI monomer-trimer
2-tert-butyl-5-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer IdeaI monomer- trimer Athermal Mecke-Kempter Athermal monomer-dimer Athermal monomer-trimer
2-tert-butyl-5-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer Ideal monomer-trimer Athermal Mecke-Kempter
K(a)
Variant I
4tert-butyl-2-methylphenol+ Ideal Mecke- Kemp ter Ideal monomer-dimer IdeaI monomer-trimer Athermal Mecke-Kempter Athermal monomer-dimer Athermal monomer-trimer
Association model SD b
0.83 0.28 0.13 0.19 0.24 0.13
0.000 1.140 0.000 0.597
T = 323.15 K
1.35 0.62 0.89 0.61
298.15 K 0.40 0.000 1.418 0.19 0.565 0.22 1.037 0.27 0.20 1.858 1.524 0.25
T=
0.000 1.527 0.594 0.795 1.940 1.528
T = 323.15 K
T= 298.15 K 0.000 0.47 1.517 0.12 0.797 0.06 0.08 0.752 1.945 0.11 1.614 0.04
D(a) a
1.566 1.490 1.230 1.156
1.676 1.688 1.346 1.325 1.883 1.456
1.577 1.632 1.042 0.823 1.879 1.260
1.642 1.894 1.286 1.049 2.127 1.611
D(a) a
variant II
Association constants, D parameters and standard deviations in the three variants
TABLE 4
0.01110 0.01700 0.00420 0.00053 0.02319 0.01043
0.01004 0.00850 0.00380 0.00263
0.01241 0.01269 0.00579 0.00541 0.01733 0.00784
0.00971 0.01087 0.00043 - 0.00227 0.01661 0.00376
&
2.22 1.01 2.03 0.90
0.90 0.37 0.65 0.33 0.19 0.25
1.91 0.37 0.68 0.18 0.30 0.78
0.18 0.30 0.04
0.40
1.00 0.46
SD b
2.689 9.919 36.588 7.309
3.812 18.344 88.271 10.362 49.864 652.243
6.224 44.959 324.777 16.918 122.212 2399.799
9.495 99.644 1045.732 25.809 270.860 7726.975
K(h)
Variant III
4.81 3.79 2.52 1.42
2.25 2.15 1.15 0.96 2.88 1.34
3.41 3.26 0.64 0.70 4.75 1.20
1.65 2.13 0.63 0.18 2.84 1.18
SDb
323.15 K 0.000 0.718 0.000 0.799 1.470 1.088
2,6-di-iso-propylphenol + cyclohexane T= Ideal Mecke-Kempter 3.783 Ideal monomer-dimer 12.687 Ideal monomer- trimer 38.498 Athermal Mecke-Kempter 6.039 Athermal monomer-dimer 10.856 Athermal monomer-trimer 83.498 1.90 0.71 1.96 1.04 0.82 1.11
0.65 0.26 0.49 0.40 0.30 0.41
T = 323.15 K 0.000 0.72 1.019 0.63 1.952 0.98 1.115 0.71 1.519 0.67 0.996 0.92 298.15 K 0.000 0.990 0.000 1.041 1.614 1.309
cyclohexane 2.199 2.484 0.000 2.403 2.298 21.876
2-tert-butyl-6-methylphenol+ Ideal Mecke-Kempter Ideal monomer-dimer Ideal monomer-trimer Athermal Mecke-Kempter Athermal monomer-dimer Athermal monomer-trimer
0.59 0.64
T = 298.15 K 0.000 0.24 1.119 0.19 0.000 0.37 1.144 0.23 1.588 0.21 1.154 0.31
1.653 1.217
2,6-di-iso-propylphenol + cyclohexane T= Ideal Mecke-Kempter 5.510 Ideal monomer-dimer 18.999 Ideal monomer- trimer 97.085 Athermal Mecke-Kempter 7.179 Athermal monomer-dimer 15.837 Athermal monomer-trimer 118.207
cyclohexane 3.049 3.707 23.795 3.258 3.538 31.724
26.892 238.663
2-tert-butyl-6-methylphenol+ Ideal Mecke- Kempter Ideal monomer-dimer Ideal monomer- trimer Athermal Mecke-Kempter Athermai monomer-dimer Athermal monomer-trimer
Athermal monomer-dimer Athermal monomer-trimer
0.193 0.542 0.000 O.ooO 1.143 0.311
0.000 0.730 0.000 0.000 1.315 0.693
1.296 1.194 1.243 1.068 1.252 0.914
1.366 1.270 1.250 1.132 1.363 1.019
1.652 1.175
0.00358 0.00183 0.00383 0.00383 0.00507 - 0.00317
-
0.00383 0.00020 0.00383 0.00383 0.00794 - 0.00056
-
0.00692 0.00521 0.00601 0.00328 0.00616 0.00121
0.00819 0.00648 0.00614 0.00424 0.00814 0.00258
0.01190 0.00293
1.73 0.71 3.46 2.21 1.61 2.31
0.64 0.35 1.38 1.05 0.67 1.05
0.93 0.63 1.53 0.67 0.86 0.88
0.40 0.20 0.61 0.22 0.31 0.31
0.55 0.60
3.646 16.938 78.693 9.911 46.043 581.467
5.912 40.861 282.422 16.070 111.071 2086.828
0.930 1.794 3.443 2.528 4.878 25.588
1.214 2.686 5.947 3.299 7.302 43.940
26.961 270.347
2.70 1.28 5.48 4.07 3.37 2.85
1.32 0.32 2.17 1.68 1.93 0.97
2.91 2.17 2.82 1.46 2.59 0.96
1.32 1.02 1.12 0.69 1.28 0.50
5.13 1.39
’ (caI cm-3)1/2;
0.42 0.42 0.42 0.16 0.16 0.28
0.35 0.35 0.35 0.12 0.12 0.19
SDb
b standard deviation of vapour pressure in mm Hg.
0.838 0.838 0.838 0.897 1.055 0.492
T = 323.15 K
D(a) a
2,6-di-tert-butylphenol + cyclohexane IdeaI Mecke-Kempter 0.000 IdeaI monomer-dimer 0.000 Ideal monomer- trimer 0.000 Athermal Mecke-Kempter 0.634 AthermaI monomer-dimer 0.432 Athermal monomer-trimer 5.042
I
T = 298.15 K 1.020 1.020 1.020 0.634 0.985 0.520
K(a)
variant
2,6-di-tert-butylphenol + cyclohexane IdeaI Mecke-Kempter 0.008 IdeaI monomer-dimer 0.008 IdeaI monomer-trimer 0.000 Athermal Mecke-Kempter 1.652 Athermal monomer-dimer 1.465 Athermal monomer-trimer 10.494
Association model
TABLE 4 (continued)
0.314 0.263 0.395 0.840 0.898 0.690
0.680 0.660 0.718 0.982 1.042 0.864
D(a) a
variant
II
o.OooO2 - 0.00019 0.00043 0.00437 0.00509 0.00273
0.00263 0.00243 0.00301 0.08622 0.00709 0.00466
112
0.73 0.62 1.23 0.15 0.30 0.34
0.44 0.40 0.61 0.18 0.12 0.29
SDb
0.270 0.343 0.436 0.734 0.933 3.221
0.319 0.420 0.554 0.867 1.143 4.097
K(h)
variant
III
0.67 0.59 1.18 3.09 3.60 1.97
0.68 0.60 0.86 1.59 1.80 1.22
SDb
183
phenols predicted by the substituent contribution method employed elsewhere (Ksi@czak and Kosihski, 1990) are listed in Table 3. The van der Waals volume of the o&o-alkyl substituents can be treated as an approximate measure of the steric hindrance. As expected, the value of the association constants decreases when the volume of the ortho-substituent increases. The calculated association constants are used to predict the activity coefficients of cyclohexane y? related to specific interactions. The association constants were determined from the association constants for the MeckeKempter model according to eqns. (4), (6), (8), (10) and (12). The activity coefficients yr for the six models are predicted by employing eqns. (3), (5), (7), (9), (11) and (13). The activity coefficients relating to non-specific interactions are estimated by eqn. (14). The solubility parameters of dialkylphenols 6(h) are determined using Hoy’s correlation (Barton, 1983). The parameters 6(h) are presented in Table 3. The calculations were performed in three variants. In variant I, the association constant K(a) and parameter D(a) were obtained for the appropriate equation by adjusting it to the vapour pressure of the solution. The values of these parameters and standard deviation SD are listed in Table 4. The standard deviations were determined as
1 1’2
05)
where N is the number of measurements and N, is the number of adjusted parameters. The adjustable parameters were obtained using the following objective function F = 5 { pylc.[K(a), i=l
o(a)] -~fx~.}~
The activity coefficients of cyclohexane calculated on the basis of the adjusted parameters K(a) and O(a) are shown as solid lines in Figs. l-5. The aim of variant I was to select the association model that gives the best description of the vapour pressure of the solution. The monomer-trimer model with the athermal or the ideal assumption gave the best fit of the vapour pressure of the 4-tert-butyl-2-methylphenol solution. These results are consistent with those obtained from solid-liquid equilibrium studies (Ksi@czak, 1986; Ksi@czak and Anderko, 1987). The athermal MeckeKempter model and the monomer-trimer model correlate the vapour pressure of the solutions within the experimental error. This result is consistent with the results obtained from the liquid-vapour equilibria studied for other phenols (Ksi@czak and Moorthi, 1985). The vapour pressures of the dialkylphenols possessing a greater steric hindrance are fitted best by the
184
Fig Ib T- 323,15 K
0,o
0.1
q2
0.3
x
a,0
OJ
42
0,s
1
Fig. 1. Activity coefficient of cyclohexane ys in the (4tert-butyl-2-methylphenol+ cyclohexane) system: (a) at 298.15 K, (b) at 323.15 K; 0, experimental points; calculated in variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC:
IL
Fig 2a
1’ I‘
1.1
0,o
0,l
0.2
0.3
x
0,o
0.1
0,2
0,3
x
Fig. 2. Activity coefficient of cyclohexane ys in the (2-tert-butyM-methylphenol + cyclohexane) system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; calculated in variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC:
185
0,o
0,l
0.2
0,3
x
0,o
0)
0,2
0,3
x
Fig. 3. Activity coefficient of cyclohexane ys in the (2-tert-butyl-Gmethylphenol + cyclohexane) system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; -, calculated in variant I; .- - -. , predicted in variant III; - - - - - -, predicted using UNIFAC.
monomer-dimer model with the athermal or the ideal assumption. The association constant of 2,6-di-tert-butylphenol is equal to zero when the molecules are assumed to form an ideal solution. This result is consistent
T=323.15 K
0.2 0.3 x 0.1 0,o 0.1 0,2 0,3 x 0,o Fig. 4. Activity coefficient of cyclohexane ys in the (2,6-di-iso-propylphenol+ system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; -, variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC.
cyclohexane) calculated in
Fig 5a
Fig 5b
T=298,15K
T=323,15K
J
0,o
0,l
0,2
0,3
x
w
91
0,2
0,3
x
Fig. 5. Activity coefficient of cyclohexane ys in the (2,6-di-tert-butylphenol+ system: (a) at 298.15 K; (b) at 323.15 K; 0, experimental points; -, variant I; . -. -. , predicted in variant III; - - - - - -, predicted using UNIFAC.
cyclohexane) calculated in
with the experimental data concerning a similar compound (2,6-di-tertbutyl-4-methylphenol) described elsewhere (Ksiqzczak, 1977, 1982, 1983; Ksi$czak and Kosinski, 1988). In variant II, the parameters D(a) were adjusted and the association constants K(h) were predicted using the homomorph concept; they are listed in Table 3. The aim of variant II is to verify K(h) and the binary parameters I,, which are a measure of the departure from the geometric mean assumption (Barton, 1983) D’(a) = (6, - as)* + 2
42
8,
6,
(17)
where 8, is the solubility parameter of the solvent. The values of parameters I,, are presented in Table 4. The low values of the binary parameters I,, are consistent with those obtained for other phenols in the same solvent (Ksi$czak and Moorthi, 1985; Ksi@czak and Anderko, 1987). Similar results obtained with toluene (the homomorph in relation to phenol) were presented by Funk and Prausnitz (1970). The standard deviations of the vapour pressure in variant II are slightly larger than those in variant I with two adjusted parameters (see Table 4). The model best describing the vapour pressure data in variant II is consistent with analogous results obtained in variant I. This agreement demonstrates that the association constants calculated from the properties of monoalkylphenols have the physical meaning attributed to them.
187
In variant III calculations, the parameters (K(h) and D(h) = a,, - Ss) were predicted on the basis of the thermodynamic properties of the pure liquids listed in Table 3. The activity coefficients of cyclohexane as calculated by variant III for the model giving the best fit in variant I are shown by a dotted line in Figs. l-5. In spite of the lack of information about the solution, a useful description of the vapour pressure of the solution has been obtained. The values of the parameters K(h) and D(h) differ considerably from those adjusted in variant I. These results suggest that the objective function of the properties discussed is very flat in a certain direction on the parameter surface. A slight change of the objective function causes great changes in the adjusted parameters (K(a) and O(a)). The UNIFAC method (Fredenslund et al., 1977) was applied to predict the activity coefficients of cyclohexane and the vapour pressure of the solution. The predicted ys are shown as broken lines in Figs. 1-5. The necessary parameters were taken from a paper by Tiegs et al. (1987). The UNIFAC method gives only one relation between ys and x for phenols possessing identical substituents. This relation for the three isomeric phenols investigated lies between all the experimental points giving the best prediction for 2-tert-butyl-5-methylphenol. These results demonstrate that UNIFAC can predict low values of solvent activity coefficients for isomeric phenols with no ortho-substituents. Standard deviations of the vapour pressure SD(UNIFAC) are listed in Table 5. In our opinion the large values of SD(UNIFAC) are due to the lack of parameters determining the influence of the geometric conditions of the hydroxyl group on the energetic parameters in the UNIFAC method. It is seen from Figs. 1-5 that the predictions of the activity coefficients ( ys) obtained on the basis of the properties of pure liquids (variant III) are better than those obtained by the UNIFAC method. In variant III, the better description of the solution vapour pressure is obtained despite the lack of information about the solution and the properties of pure dialkylphenols.
TABLE 5 Vapour pressure prediction for the UNIFAC method Phenol
4-tert-butyl-2-methylphenol 2-tert-butyl-S-methylphenol 2-tert-butyl-6-methylphenol 2,6-di-iso-propylphenol 2,6-di-tert-butylphenol
SD (mm Hg) 298.15 K
323.15 K
2.44 1.35 2.21 0.87 2.82
4.39 1.38 6.54 1.52 8.65
188 CONCLUSION
The increase of steric hindrance around the hydroxyl group changes the structure of the dialkylphenol solution. The best fit of the activity coefficients of cyclohexane for the 4-tert-butyl-2-methylphenol solution is obtained for the monomer-trimer model. The other dialkylphenols with one o&o-butyl substituent associate in agreement with the monomer-dimer model. The same results have been obtained with the assumption that the associates form an athermal or an ideal solution. The phenols having two ortho-tert-butyl substituents probably do not associate. The two bulky substituent groups completely screen the hydroxyl group. The values of association constants K(h) of the dialkylphenols decrease when the volume of ortho substituents increases. A similar behaviour has been observed for the activity coefficients (ys) which decrease when the steric hindrance decreases. The thermodynamic properties of the dialkylphenol solutions predicted on the basis of pure-compound thermodynamic properties of monoalkylphenols give better results than the UNIFAC method does. In this case a far extrapolation of association constants was required, extracted from the properties of pure monoalkylphenols. LIST OF SYMBOLS
a k9 4
AC; D e 0
AH” K K MK K MD K Kg GD
Gl-
symbol in eqn. (7) (see eqn. (7a)) symbol in eqn. (13) (see eqn. (13a)) adjusted value of parameter second virial coefficient of pure solvent standard specific heat of association difference of solubility parameter of solvent and modified solubility parameter of associated solute base of natural logarithms, e = 2.718281828.. . objective function (see eqn. (16)) parameter value predicted from homomorph concept standard enthalpy of association association constant association constant in the Mecke-Kempter model association constant in the monomer-dimer model association constant in the monomer-trimer model volume-fraction association constant in the athermal MeckeKemp ter model volume-fraction association constant in the athermal monomerdimer model volume-fraction _association constant in the athermal monomertrimer model
189 1
1;’ xi P pica'=. p,““.
PC R
SD v, Yn v, XA XS
binary parameter (see eqn. (17)) number of data points number of adjusted parameters vapour pressure of solution calculated vapour pressure experimental vapour pressure vapour pressure of pure solvent gas constant R = 8.31431 J mol-’ K-l standard deviation of calculated vapour pressures from experimental values (see eqn. (15)) molar volume of solute molar volume of liquid solute or solvent molar volume of solvent mole fraction of solute mole fraction of solvent
Greek letters
activity coefficient of solvent contribution to activity coefficient of solvent due to specific interacYY tions phys. contribution to activity coefficient of solvent due to non-specific US interactions (see eqn. (14)) modified solubility parameter of solute ‘h solubility parameter of solvent 8s volume fraction of solute @A volume fraction of solvent Q’s US
ACKNOWLEDGMENTS
The authors thank Professor A. Bylicki for suggestions and discussions. The work reported herein was sponsored by the Polish Academy of Sciences within the framework of Project 1.16. REFERENCES Barton, A.F.M., 1983. CRC Handbook of Solubility Parameters and Other Cohesion Parameters, CRC Press, Boca Raton, FL. Chapman, N.B. and Shorter, J., 1972. Advances in linear free energy relationship, Plenum, London. Fredenslund, A., Gmehling, J. and Rasmussen, P., 1977. Vapor-liquid equilibria using UNIFAC, Elsevier, Amsterdam.
190 Funk, E.W. and Prausnitz, J.M., 1970. Thermodynamic properties of liquid mixtures: aromatic-saturated hydrocarbon systems. Ind. Eng. Chem., 62: 8-15. Kehiaian, H., 1963. Thermodynamics of chemically reacting mixtures. VI. Excess enthalpy and excess entropy of ideal associated mixtures of the type A+ B+ A,. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 11: 591-596. Kehiaian, H., 1964. Thermodynamics of chemically reacting mixtures. XIII. Thermodynamic excess functions of ideal associated mixtures of the Mecke-Kempter type. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 12: 567-573. Kehiaian, H. and Trsezczanowicz, A., 1968. Excess free enthalpy of athermal associated mixtures of the Mecke-Kempter type. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 16: 445-452. Ksi@czak, A., 1977. Sterically hindered association of alkylphenols. Rocz. Chem., 51: 185-187. Ksi$czak, A., 1982. Substituent effect on the excess Gibbs energy of saturated solution of phenols. Fluid Phase Equilibria, 9: 287-293. Ksi@czak, A., 1983. Solid-liquid equilibrium and the hydrogen bond in crystals. Fluid Phase Equilibria, 15: 1-9. Ksi@czak, A., 1986. The effect of auto-association on solid-liquid equilibrium. Fluid Phase Equilibria, 28: 39-56. Ksi$czak, A. and Anderko, A., 1987. Prediction of solid-liquid equilibria on the basis of pure compound properties. Fluid Phase Equilibria, 35: 127-151. Ksi@czak, A. and Buchowski, H., 1980. Determination of traces of water in a solvent. I. Method using vapor pressure differences. Fluid Phase Equilibria, 5: 131-140. Ksigczak, A. and Kosihski, J.J., 1988. Vapour pressure of binary, three-phase (S-L-V) systems and solubility. Fluid Phase Equilibria, 44: 211-236. Ksi$czak, A. and Kosihski, J.J., 1990. Vapour pressure and association of phenols. Fluid Phase Equilibria, 55: 17-37. Ksigczak, A. and Moorthi, K., 1985. Prediction of thermodynamic properties of alkylphenol + hydrocarbon binary systems on the basis of pure liquids properties. Fluid Phase Equilibria, 23: 153-164. Maze, M. and Rerat, C., 1964. Etude de la structure du bromo4 ditertiobutyl-2,6 phenol et du methyl-4 ditertiobutyl-2,6 phenol. C. R. Acad. Sci., 259: 4612-4615. Tiegs, D., Gmehling, J., Rasmussen, P. and Fredenslund, A., 1987. Vapour-liquid equilibria by UNIFAC group contribution 4. Revision and extension. Ind. Eng. Chem. Res., 26: 159-161. Treszczanowicz, A., 1968. Excess free enthalpy of athermal associated mixtures of the type A+A, +B. Bull. Acad. Pol. Sci., Ser. Sci. Chim., 16: 71-75.