396
Ind, Eng. Chem. Fundam. 1982, 27, 396-401
Gas Chromatographic Study of Limiting Activity Coefficients of Organic Solutes in Squalane Tomoshlge Nltta, Kazuhlro Morlnaga,’ and Takashl Katayama. Department of Chemical Engineering, Faculty of Engineering Science, Osaka University, Toyonaka, Osaka, Japan 560
The specific retention volumes of 20 solutes in squalane coated on a silanized diatomite have been measured at 25 and 50 OC by varying the sample size for each packed column of different liquid loadings. The values for the limiting specific retention volumes extrapolated to zero sample size are slightly dependent upon the liquid loading ratio, which is attributed to the solute-solvent coadsorption on the solid surface. Polar solutes such as alcohols, acetonitrile, ketones, acetates, and ether indicate gas-liquid interface adsorption in the region of small sample size; the extrapolation to zero sample size has been carried out from the solution dominating region of large sample size. The activity coefficients in bulk-liquid squalane have been calculated from the intercepts of the plots of the limiting specific retention volume against the reciprocal liquid loadlng ratio. The experimental activity coefficients are compared with the predictions of the UNIFAC and the ASOG methods.
Introduction Vapor-liquid equilibrium is one of the fundamental properties required in the design of separation equipment such as flash evaporators, gas absorption, and distillation columns. A method for rapid measurement of the equilibrium relations is desirable along with their correlation and prediction methods. Gas-liquid chromatography is known as a rapid method and there have been a lot of investigations concerning the retention data and the equilibrium properties; they are summarized in the textbooks of Conder and Young (1979) and Laub and Pecsok (1978). From the elution theory of gas chromatography, the retention volume is related to the equilibrium distribution coefficient of the solute between the moving (gas) phase and the stationary phase, regardless of the assumption either that local equilibrium is established instantaneously (Everett, 1965; James and Martin, 1952) or that the mass transfer rate controls the elution mechanism (Van Deemter et al., 1956) if the number of plates is sufficiently large. The retention volume is, however, affected by variation of sample size, liquid loading, and supporting material since the retention behavior is controlled by concurrent mechanisms of dissolution and adsorption. Therefore, the influence of adsorption into the stationary phase should be investigated more extensively in order to obtain the true reliable activity coefficients in the bulk liquid. The contribution to the retention data of gas-liquid interface adsorption was first suggested as a consequence of surface excess at the interface by Martin (1961) and it was later verified by means of surface tension data (Martin, 1963; Martire et al., 1965; Pecsok and Gump, 1967). The effect is negligibly small for systems of nonpolar solute and nonpolar solvent, but for polar and nonpolar systems it may be significant when sample size decreases. The contribution of adsorption on a supporting material and its suppression by coating polar liquids were shown by Urone, Takahashi, and Kennedy (1968,1970), who measured the sorption isotherm by a gravimetric method. The effect could be diminished by using an inactive support though a weak adsorptive capacity was reported even for so-called inert supports of polytetrafluoroethylene (PTFE) and silanized diatomite from gas chromatographic observations Sumitomo Heavy Ind. Ltd., Tokyo.
(Berezkin, 1972; Conder, 1971; JBquier and Robin, 1968). The first aim of the present work is to examine the gas-liquid chromatographic method critically in order to obtain activity coefficients of solutes in a bulk liquid. Squalane (2,6,10,15,19,23-hexamethyltetracosane)was chosen as a solvent because it is now available as a synthetic reagent of high purity, and many literature data giving its properties are available. The effects of sample size, liquid loading, and supporting material on the retention volume were examined carefully for many nonpolar and polar solutes. A sample-size extrapolation method of Parcher and Hussay (1973) was applied to determination of the retention volume a t infinite dilution; however, a different interpretation of the limiting value, as it includes the solid-surface adsorption effect, has been suggested in the present work. The experimental values for the limiting activity coefficients of 20 solutes in squalane are compared with the predictions by the UNIFAC method (Fredenslund et al., 1977; Skjold-Jerrgensenet al., 1979) and the ASOG method (Kojima and Tochigi, 1979).
Experimental Section Apparatus and Procedures. A gas-liquid chromatograph, shown schematically in Figure 1,was constructed by use of available commercial parts. A gaseous solute with air was injected by means of a l-cm3 gas sampler and a 220-cm3vaporizer. The concentration of the solute was reduced sequentially;helium, carrier gas, was charged until the total pressure in the vaporizer rose to the inlet pressure of the column. Carrier gas lines were finally fixed as shown in Figure 1 to reduce the instantaneous disturbances of flow rate due to the injection of gas samples. The line pressure before the gas sampler was measured by a mercury manometer. Pressure drops of each part of the lines were observed; therefore, they were measured and correlated against flow rates, from which necessary corrections were made to determine the inlet and outlet pressures of the column. A digital analyzer obtained from Shimadzu, Chromatopac ElA, provided the retention time data (1/100 min as one digit) and peak area (pV-s as one digit). A uniform packing of each new column was checked by changing the inlet and outlet sides so as to give the same retention data. Materials. Squalane was the synthetic reagent provided by Kuraray Co., Ltd., the purity of which was
0196-4313/82/1021-0396$01.25/00 1982 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982
397
AIR
Figure 1. Schematic diagram of apparatus: (1)helium cylinder; (2) pressure regulator; (3) mass flow controller; (4) vaporizer; (5) Bourdon gage; (6) mercury manometer; (7) water bath; (8) six-way valve; (9) sample tube; (10) packed column; (11) resistance column; (12) TC detector; (13) water vapor saturator; (14) soap-film flowmeter; (15) digital analyzer; (16) recorder. 472
r
I 468
t
T
R
0
?
6
5
452 0
04
0.8
6 /crn3.
1.2
1.6
s-'
Figure 2. Flow rate check of the specific retention volume of 1hexane in squalane on Uniport HP (20 w t %) at 25 "C (0.2 pmol 1-hexane).
specified as 99.9%. Most of the solute substances were spectrograde reagents from Merck, J. T. Baker, or Wako Pure Chemical Co. Methylcyclohexane, 2-butanone, ethanol, 2-methyl-1-propanol, and cyclopentane were reagent grade from Nakarai Chemical Co. AU of the materials were used without further purification, but no significant impurities were detected from the gas chromatograms. Uniport H P is the acid-washed, DMCS-treated white diatomite support prepared by Gasukuro Kogyo Inc. The surface area is reported as 1 m2 8'. A particle size of 80-100 mesh was used. Specific Retention Volume Data Reduction. The retention data were expressed by means of the specific retention volume at the column temperature VgT VgT= VN/ WL where VNis the net retention volume and WL is the mass of liquid loaded on a support. Definition and calculation procedure for VNare conventional as in standard textbooks (cf. Chapter 2 of Laub and Pecsok, 1978). A check of the flow-rate independence of VgTwas made to see that both the whole assembly of gas chromatograph and correction procedures used in the calculation were proper. Figure 2 shows the experimental values for VgT of 1-hexane in squalane on Uniport H P (20 w t %) at 25 "C against flow rate. The sample amount injected in the column was fiied at about 0.2 pmol. Data points are within f0.8% deviation. Almost the same results were obtained for other two solutes, acetone and methyl acetate. Sample Size. The sample size injected in a column was varied by decreasing the solute concentration introduced in a l-cm3 gas sampler, in which the partial pressure of 10 kPa (75 mmHg) corresponds to the amount of 4.0 pmol of the solute. The initial concentration was usually close to that corresponding to the vapor pressure of the solute. Since only the relative value of sample amount is needed,
0.2
0.4
0.6
0.8
1.0
e Figure 3. Specific retention volumes of solutes in squalane on Uniport HP at 25 "C against reduced sample sizes. Maximum sample sizes are 4.5, 5.0 and 4.9 wmol for 1-hexane, ethyl acetate, and 1-propanol, respectively. Each symbol shows different liquid load10.00 wt %; ( 0 )18.24 w t %, and (A)44.52 w t %, respecings: (0) tively.
the peak area printed out from the data analyzer is divided by the maximum peak area in successive runs, which is designated as the reduced sample size 9 in this work. Figure 3 shows typical examples of sample-size dependence of the specific retention volume. In the case of 1-hexane as shown in Figure 3a, the values of in VgT decrease monotonically with decreasing sample size and the slope is steeper as the liquid loading is smaller. The same behavior is observed for nonpolar hydrocarbons investigated: 1-hexane, 1-heptane, cyclopentane, cyclohexane, methylcyclohexane, benzene, carbon tetrachloride, and toluene, though the last is weakly polar. The retention equation with all three mechanisms has been generalized as (Chapter 11 of Conder and Young, 1979) V N = KLVL KIAI + KsAs (2) where K s are the distribution coefficients of a solute defined as K = (solute concn in stationary phase)/ (solute concn in gas phase) (3)
+
The major factor contributing to the experimental VgTin the case of Figure 3a is the first term of KLVL in eq 2; the third term is minor and the second may be negligible. An anti-Langmuir isotherm for the solution, which means the increase of KL with increasing solute concentration, accounts for the increase of VgTwith increasing sample size. The interpretation is compatible with the experimental results that the smaller the liquid loading, the steeper the slope of In V z against 8. The distribution coefficient KL defined by eq 3 is inversely proportional to a product of the activity coefficient of a solute y1and the molar volume of a solution dissolving the solute u. Therefore, KL follows an anti-Langmuir isotherm for systems of nonpolar solutes and squalane though y1is less than unity. This is because the decreasing rate of u with increasing solute concentration is greater than the increasing rate of y1in the solution of squalane, a large molecule. The limiting value extrapolated to zero sample size is designated as ( VgT)-,which corresponds to infinite dilution
398 Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982
Table I. Column Characteristics Used in Determining the Specific Retention Volumes for 2 0 Organic Solutes in Squalane tubing: 4 mm i.d. stainless steel supporting material: Uniport HP 8 0 - 1 0 0 mesh liquid loading ratio (wt/wt), % 10.00 mass of liquid, g 0.2957 void fraction of the packing 0.86 columna phase volume ratio (V,/V,)" 22.1 tube length, cm 75
KI decreases sharply as the solute concentration increases. The surface tension data of Pecsok and Gump (1967) encourage a view of the behavior of K I given here. It should be noted that for alcohols and acetonitrile several times more of the solute was charged in a heated vaporizer than the amount corresponding to the vapor pressure of the solute at the column temperature. This is because the interfacial adsorption is so strong that the solution dominating region often disappears if the initial amount of solute is restricted. For example, the initial amount of 4.9 pmol injected for 1-propanol is 4.6 times greater than that corresponding to the saturated vapor pressure at 25 "C. Experimental curves of VgTin this case are shown,in Figure 3c, which resemble those obtained for ethyl acetate, a less adsorptive solute. Liquid Loading. Preliminary experiments for several packed columns of different liquid loadings on Shimalite F (Teflon support) and Uniport HP (silanized diatomite support) showed that the Teflon support had a larger adsorption of solid surface than the silanized diatomite. Therefore, Uniport HP was chosen as a suitable supporting material to obtain activity coefficients in the liquid, and special care was taken to prepare the packing material. Three columns of 10.00, 18.24, and 44.5290 liquid loadings were used in the experiments. The column characteristics are shown in Table I. The experimental limiting value of VgT contains two terms of bulk-liquid solution and solid surface adsorption as shown in the preceding paragraph. The expression for (VpT)min terms of the distribution coefficients is obtained from eq 1 and 2 by neglecting the contribution of KIAI.
18.24 44.52 0.3435 0.7693 0.81 0.72 11.9 50
4.7 50
a Determined from the retention volume of air by substracting the dead volume of the line other than a column.
of solute in both the stationary and the gas phases. Since the overall concentration of a peak falls during its passage along the column, the functional form of VgT(6) is somewhat ambiguous; therefore, the extrapolation to zero sample size was carried out by assuming a linear relation between In V and 6. The values of (V,')" so obtained are close to eaca other, but the differences exceed experimental errors; they decrease gradually with increasing the liquid loading for all the solutes investigated. This weak dependence on liquid loading ratio is attributed to the solid surface adsorption at infinite dilution Ks-As. Since the contribution to ( VgT)" of the term KSmAS is within several percent in most cases for Uniport HP, variation in Ks with sample size may be hidden behind the variation of the dominative factor KL. In cases of Figures 3b and 3c for ethyl acetate and 1propanol, respectively, the specific retention volumes decrease at first with decreasing sample size and then they go up rapidly through a minimum. Curves of this type have been obtained for all the polar solutes investigated. The increase of VgT in the region of small sample size is attributed to adsorption at the gas-liquid interface as compared with the curves of Figure 3a. The high concentration region, where VgT decreases gradually with decreasing sample size, is considered to be the region where the term of KLVL is dominative and KsAs is minor as in the cases of nonpolar solutes. The straight line is extrapolated from the region to give the limiting value of (V,')". This may exclude the contribution of gas-liquid interface adsorption since a surface active solute covers the whole interface at low concentration, which means that
(4)
where w is the liquid loading expressed by the weight to weight ratio as w = WJW, (5)
A linear relationship between ( VgT)" and l l w is expected for each solute since Ks"As/ Ws is a constant. Figure 4 shows the plots of ( VPT)" against the inverse of w for the three solutes demonstrated in Figure 3. The data points lie on each straight line for the three and similar results have been obtained for most of other solutes listed in Table 11. The intercept of the line gives the value of KLm/pL,
Table 11. Limiting Values for Specific Retention Volumes of Solutes in Squalane at Three Different Liquid Loadings on Uniport HP, ( VgT)-in cm3 (g of solvent)-' 25 "C
solute 1 2 3
4 5 6 7
8 9
10 11 12 13 14 15 16 17
18 19 20
1-hexane 1-heptane cyclopentane cyclohexane methylcyclohexane benzene toluene carbon tetrachloride acetone Z-butanone methyl acetate ethyl acetate tetrahydrofuran acetonitrile methanol ethanol 1-propanol 2-propanol 1-butanol 2-methyl- 1-propanol
10% 462 1466 298 8 84
1801 655 2230 708 56 201 92.9 24 9 369 33 13 31 113 60 3 74 252
18% 459 1442 295 876 1786 649 2198
700 54.0
197 91.4 24 5 36 5 31.7 11.3 29.6 107 58.8 361 24 6
5 0 "C 4 5%
10%
18%
4 5%
456 1431 293 871 1772 64 5 2175 695 53.5 194 90.6 24 2 360 30.7
190
189 50 8 133 34 8 652 270 782 288 29 90.9 44.7 106 159 18.6 7.4
188 505 133 346 6 50 269 776 288 28.8 89.7 44.3 105 158 18.1 6.9
17.7
17.0
55.0 32.0
52.6 31.2 154
10.0 29.1 104 58.3 352 244
515 130 3 50 657 272 785 290
-
160 114
110
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982 399 Table 111. Physical Properties of Pure Substances Used in the Data Reduction 25 "C substance 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
1-hexane 1-heptane cy clopentane cyclohexane methylcyclohexane benzene toluene carbon tetrachloride acetone 2-butanone methyl acetate ethyl acetate tetrahydrofuran acetonitrile methanol ethanol 1-propanol 2-propanol l-butanol 2-methyl-l-propanol
a Boublik et al. (1973). cm3 mol-', f Value at 20
50 "C
p'Wa
u blue e
BIldlue
20.169" 6.090' 42.31 8' 13.011' 6.178' 12.676" 3.793' 15.249 ' 30.661 12.055' 28.830' 12.616' 21.622' 11.775' 16.937' 7.875" 2.780 6.021 0.824' 1.363
131.61 147.47 94.719 108.75 128.34 89.407 106.86 97.087 74.045 90.17 79.836 98.493 81.09f 52.862 40.733 58.685 75.145 76.923 91.965 92.91
-1990 -3050 -1190 -1880 -2650 -1680 -2740 -1670 -1960 -2680 -1 540 -2260 -1710 -6130 -2060 -2920 -3760 -3280 -5090 -5730
'
Riddick and Bunger (1970).
"c.
IkPa 54.037' 18.874 ' 103.81a 36.234a 18.441' 36.162' 12.280' 41.618a 81.368' 35.536' 79.117 ' 3 7.953 ' 58.604a 33.796' 55.539' 29.460a 12.1626 23.930 4.430 7.097 PO
' Brown and Smith (1954).
B,, dlv* -1560 -2310 -950 -1460 -2010 -1290 -2030 -1300 -1420 -1930 -1160 -1680 -1 280 -4030 -1190 -1690 -2170 -1930 -2870 -3 2 20
Tsonopoulos (1974).
u*= 1
e
Table IV. Experimental Values for K L - I P L , yom,and 7,- in Squalane at 25 and 50 '(2' 25 "C
50 "C (K L ~ I L P1
(KL-IPL)
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 a
solute 1-hexane l-heptane cyclopentane cyclohexane methylcyclohexane benzene toluene carbon tetrachloride acetone 2-butanone methyl acetate ethyl acetate tetrahydrofuran acetonitrile methanol ethanol 1-propanol 2-propanol l-butanol 2-meth yl-l-propanol
V'
yP-
455 1422 29 2 86 7 1764 64 2 2160 691 52.9 192 90.0 240 3 58 30.0 9.1 28.7 101 57.9 34 5 24 2
0.639 0.677 0.474 0.520 0.538 0.720 0.715 0.556 3.61 2.53 2.26 1.94 0.754 16.6 38 25.9 20.9 16.8 20.7 17.8
71-
0.650 0.682 0.484 0.525 0.542 0.727 0.718 0.562 3.70 2.56 2.30 1.96 0.766 17.1 39 26.1 21.0 16.9 20.7 17.9
V' 187 501 133 345 64 8 268 772 287 28.6 89.0 44.1 104 157 17.8 6.6 16.5 51.0 30.6 150 107
7P-
0.627 0.672 0.460 0.508 0.53 2 0.656 0.670 0.53 2 2.73 2.01 1.82 1.60 0.691 10.6 17.3 13.1 10.2 8.68 9.56 8.37
71-
0.648 0.683 0.478 0.519 0.540 0.668 0.677 0.544 2.85 2.06 1.89 1.64 0.712 11.1 18 13.3 10.3 8.84 9.61 8.45 ~~
V*= 1 cm3 g - l .
which is related to the limiting activity coefficient of solute in bulk-liquid squalane. Table I1 summarizes the experimental limiting values for the specific retention volumes of organic solutes in squalane loaded in three different loading ratios on Uniport HP. The retention data at 25 "C are complete, but some of those at 50 "C are lacking for the low liquidloading column, mainly because the elution rates were too fast.
Activity Coefficients at Infinite Dilution Experimental Activity Coefficient. The approximate value for the activity coefficient of the solue at infinite dilution ypmis calculated from
where M is the molar mass of solvent. The accurate lim-
iting activity coefficient ylmis calculated as (Chapter 5 of Conder and Young, 1979)
The values for the second virial coefficients Bll and B12 were evaluated by means of the Tsonopoulos correlation (1974). Since the values of twice the cross term B12are positive and close t o those of the molar volumes of each solute, the last term in eq 7 was neglected in the calculation. The vapor pressures were calculated from the Antoine constants taken from literatures (Boublik et al., 1973; Brown and Smith, 1954; Riddick and Bunger, 1970). The physical properties used in the data reduction are summarized in Table 111. Table IV is the list of experimental values for KL"/PL, yp", and ylmobtained in this work. Although the reproducibilities of retention data in successive runs at a
400
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982 465t
50
1
1:
201
I
1
/
"
I "
'
"
'
ESTERS
KETOtiES,
g
ETHER
l c 5k
I
t
t,
96
0
2
4
6
6
10
12
1lW
Figure 4. Limiting specific retention volume (VET)-against reciprocal of liquid loadings. Table V. Comparison of Experimental Limiting Activity Coefficients in Squalane with Literature Values lit. this work
Y
Y L 0.2
1
, I , ,
0.5
I
I
1
2
I
,
I
I
5
# I 8 1
10
1
20
,
I
I
la2
50
J-GP
Figure 5. Experimental limiting activity coefficients of various solutes in squalane and those predicted by the UNIFAC method. 0
SATURATED I Y D Q O C A R B O N S
71
solute 1-hexane 1-heptane cyclohexane methylcyclohexane benzene toluene
TI-
30 30 30 30
0.649 0.682 0.524 0.541
0.636 0.668 0.517 0.531
0.642 0.669 0.515 0.529
30 30
0.714 0.709
0.700 0.686
0.699 0.689
solute 2-propanol 1-butanol 2-methyl-1-propanol a
r i m ( 1 0 (7-10 wt %) wt % ) a
temp, "C
Harbison et al. (1979).
-
temp, -flm 71 "C (this work) (lit.)b 50 50 50
8.84 9.61 8.45
8.39 7.46 6.37
Cadogan et al. (1969).
specified flow rate were within 0.5%, the accuracy of the activity coefficients may be worse mainly because of the two extrapolation procedures, It is estimated to be within & l % for nonpolar solutes and f3% for most of polar solutes. Exceptions are methanol, the least reliable up to & E % , ethanol, and acetonitrile to rt8% since these solutes are less soluble in squalane and highly adsorptive at the interface. Experiments with longer columns would be preferable for the three substances. Comparison with Literature Values. The experimental values of limiting activity coefficients have been compared with those in the literature. Two examples are shown in Table V. The values of ylmreported by Harbison et al. (1979) were obtained by use of the columns of 7-10 wt/wt % liquid loadings on Chromosorb G (60/80 mesh, acid-washed, and silanized with DMCS). The values of ylmat 30 "C in this work, which are interpolated from the data of 25 and 50 "C, are about 2% greater than those of Harbison et al.; however, if the values for (VgT)"obtained from the 10 w t / w t % liquid loading column in this work ~ , are shown are used in the data reduction for T ~which as ylm(10 w t %) in Table V, the agreement with their data is within k0.003 except for 1-hexane. The activity coefficients of alcohols were reported by Cadogan et al. (19691, who reduced the retention data by plotting (VN/VL)against (1/VL). According to their report
Figure 6. Experimental limiting activity coefficients of various solutes in squalane and those predicted by the ASOG method.
the injected sample sizes were corresponding to the region where the gas-liquid interface adsorption was significant. The discrepancies between the values of Cadogan et al. and those of this work cannot be explained by experimental errors but by the different method of the retention-data reduction. Comparison with UNIFAC and ASOG Methods. Among many methods proposed for predicting the activity coefficients in liquid solution, the UNIFAC and the ASOG methods are chosen to test their applicability and limitation using the experimental data in this work. The application of such systems to substances having vastly different boiling temperatures may be questionable since both methods neglect density effects on the free energy and since most of the interaction parameters were determined from binary systems of substances having relatively close boiling temperatures. The deviations from the experimental data in this work, however, may magnify the inadequacy of both methods. The revised parameters (Skjold-Jrargensenet al., 1979) were used for the UNIFAC method. Figures 5 and 6 show
Ind. Eng. Chem. Fundarn., Vol. 21, No. 4, 1982 401
the log-log plots of the predicted and the experimental activity coefficients with f50% deviation lines. Here are some comments on the two results. (1) The UNIFAC method always predicts smaller values and the deviation is rather stable against temperature variation, except for alcohols. (2) The predictions of the ASOG method are sorted into a fair group such as alcohols and a questionable group such as acetonitrile. The temperature dependence of the interaction parameters should be revised for some groups. (3) The free-volume effect suggested by Oishi and Prausnitz (1978) gives 5 2 0 % greater values than those of the UNIFAC method, which improves the prediction. For alcohols, new constants concerning the temperature dependence of interaction parameters with OH group should be introduced because the hydrogen bonding is much stronger than the other group interactions. Conclusions The specific retention volumes of 20 organic solutes in squalane on Uniport H P (silanized diatomite) were measured at 25 and 50 “C by varying the sample size for each packed column of different liquid loadings. The specific retention volume decreased gradually with decreasing sample size, owing to the concentration effects on the distribution coefficient of the bulk liquid. For polar solutes, gas-liquid interface adsorption was observed in the region of small sample size. Solid surface adsorption was observed for all solutes, both polar and nonpolar, even on silanized diatomite and much more on Teflon supports. The limiting activity coefficients were calculated from the limiting specific retention volumes by plotting them against the inverse of the liquid loading ratio. Comparison of the UNIFAC and the ASOG methods with the experimental limiting activity coefficients indicated that the former gave stable predictions though all were smaller than the experimental values. In the latter method the temperature dependence of the interaction parameters needs improvement for several groups. Gas chromatographic retention data can give a reproducible limiting activity coefficient in a bulk liquid. However, if the gas-liquid interface adsorption is significant, the reliability of the activity coefficients is lost by several percent because of the exprapolation procedure. Solid surface adsorption also interferes with the activity coefficient measurements, but experiments with a column of high liquid loading on silanized diatomite will be adequate if one wishes to obtain the activity coefficientswithin several percent accuracy. Acknowledgment The authors are grateful to Hirotsugu Kubo, Minoru Akiyama, and Akihito Watanabe for their experimental assistance and to Kuraray Co. Ltd. for presenting the high-purity squalane. This work was partially supported by Grant-in-Aid for Scientific Research No. 343022 from the Ministry of Education, Science, and Culture, Japan. Nomenclature AI, As = surface areas of gas-liquid interface and supporting material, respectively, m2 B = second virial coefficient, m3 mol-’ Fo = volumetric flowrate at 0 O C and 1 atm, m3 s-l
J34= correction factor for gas compressibility = distribution coefficient of solute for bulk liquid phase K,, KS = distribution coefficients of solute for gas-liquid interface and support surface, respectively, m M = molar mass, kg mol-’ P - pressure at the column outlet, Pa p8 vapor pressure, Pa R = gas constant, J mol-’ K-’ T = absolute temperature, K V, = volume of gas phase in a column, m3 VL = volume of bulk liquid in a column, m3 V - net retention volume, m3 V): specific retention volume at the column temperature, m3 g-’ u = molar volume of liquid, m3 mol-’ uo = molar volume of pure liquid, m3 mol-’ W,, Ws = masses of liquid and support in a column, re_. ipectively, g w = weight ratio of liquid loading to support (= WL/ W,) Greek Letters y = activity coefficient in liquid phase yp = approximate activity coefficient calculated from eq 6 8 = sample size reduced to the maximum amount of solute injection pL = density of liquid, kg m-3 Subscripts 1 = solute 2 = carrier gas, helium Superscript m = limiting value at infinite dilution Literature Cited KL
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Received for review July 2, 1981 Accepted August 9, 1982
