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The measurement of activity coefficients for solutes at infinite dilution with mixed solvents formamide + glucose, or + fructose, or + sucrose using a gas liquid chromatography at 298.15 K
Fluid Phase Equilibria 202 (2002) 277–287
The measurement of activity coefficients for solutes at infinite dilution with mixed solvents formamide + glucose, or + fructose, or + sucrose using a gas liquid chromatography at 298.15 K Tong-Chun Bai a,∗ , Qing-Hu Tang b a
Department of Chemistry and Chemical Engineering, Suzhou University, Suzhou 215006, China b Department of Chemistry, Henan Normal University, Xinxiang 453002, China Received 1 February 2002; accepted 1 May 2002
Abstract Using gas liquid chromatography, activity coefficients for nine solutes at infinite dilution (γi∞ ) in stationary solvent of formamide + glucose, + fructose and + sucrose at 298.15 K have been measured. Linear dependence of ln γi∞ on the mole fraction of sugar was observed. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Activity coefficient; Gas liquid chromatography; Formamide; Glucose; Fructose; Sucrose
1. Introduction Water has been considered to possess particular solvent properties giving rise to the so-called hydrophobic effect which is regarded to act as an organizing force in the aggregation of amphiphilic molecules to give micelles and liquid crystalline phases as well as lipid bilayers and biological membranes [1]. However, it is now well established that the aggregation of amphiphilic molecules is not unique to aqueous systems but can take place also in other solvents with strong cohesive forces such as hydrazine [2,3], formamide [4,5], ethylene glycol [6,7], and glycerol [8,9]. Thus, the hydrophobic effect can be seen as a special case of a more general solvophobic effect. Extensive experimental information is available about the solvation of small organic molecules in water, and the thermodynamic properties of solute–solvent and solute–solute interactions in aqueous solution are well characterized [10]. But less information is available about the thermodynamics of solvation in other strongly associated solvents [11,12]. The activity coefficient at infinite dilution (γi∞ ) represents an important property, which is used in particular for the selection of selective solvents (e.g. for extraction and extractive distillation) and for the reliable design of thermal separation processes. The data give a good insight into solute–solvent molecular ∗
Corresponding author. E-mail address: [email protected] (T.-C. Bai). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 2 ) 0 0 1 2 5 - 5
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interactions. The measurement of γi∞ by gas–liquid chromatography (GLC) is an adequate technique [12]. Most measurements use non-polar or moderate polar solvents as stationary solvents [14–17]. Much less measurement uses polar solvent and its mixture with polar organic compound as stationary solvent. Of the solvents that can be conveniently worked with, formamide is the one that most closely resembling water. It can behave either as donor or acceptor of protons, forms, in liquid state, puckered planes of dimmer rings connected by chains of hydrogen bonded formamide molecules [11]. Spectroscopic and diffraction studies [18,19] confirm the presence of a three-dimensional state. However, compared to water the void space in the plane structure is considerably reduced. In order to get more information on the effect of a third component on the activity coefficient, the activity coefficients at infinite dilution for some organic compounds in formamide + sugar (glucose, fructose and sucrose) mixed solvents have been measured by GLC at 298.15 K. Ethyl acetate, methyl formate, acetone, 2-butone, diethylether, tetrahydrofurane, benzene, chloroform and tetrachloromethane were used as solutes. 2. Experimental The infinite dilution activity coefficients γi∞ were measured by gas–liquid chromatography (GLC). The calculation of γi∞ requires the measurement of following variables: (a) net retention time (ti − t0 ) of solute, that is, the difference between the retention times of solute (i) and inert gas (0); (b) column temperature T; (c) column inlet pressure PI and outlet pressure Po ; (d) carrier gas flow rate F measured at temperature Tf and pressure Pf ; (e) mass ws of solvent contained within the column. From these experimental data, the retention volume Vg and infinite dilution activity coefficient γi∞ were calculated. The James–Martin correction factor J32 for the pressure gradient and gas compressibility inside the column was applied in the calculation of Vg [13]. The gas phase nonideality was taken into account by means of the virial equation of state. Vg =
F (273.15/Tf )(ti − t0 )((Pf − Pws )/P0 )J32 ws
(1)
ln(273.15R/Ms Pis Vg ) − (Bii − Vi )Pis (2Bij − Vi∞ )J32 P0 + (2) RT RT In these equations, Pws and Pis are, respectively, the vapor pressure of water at temperature Tf and that of organic solute i at column temperature T; Ms the molecular weight of the stationary solvent; R the universal gas constant; Bii and Vi are second virial coefficient and the liquid molar volume of solute i at temperature T; for polar solutes the values of Bii and Bij are calculated by Tsonopoulos [20] method. The required critical data are taken from literature. The required acentric factors are calculated by Pitzer and Curl [21] method. A Shimadzu GC-9A gas chromatography with a thermal conductivity detector was used in the measurements. The carrier gas was hydrogen flowing at about 30 cm3 /min. The flow rates were measured with a soap-film meter, and temperatures with a mercury thermometer. The column outlet pressure was determined with a barometer. The pressure drop inside the column was read with a cathetometer from a U tube mercury manometer. The column was taken out of the column box, and its temperature was controlled by a water bath, with an accuracy of ±0.05 K. The mixed solvents of formamide + glucose, or + fructose, or + sucrose, are prepared by mass, and used as stationary solvents. Silanized 101 white solid support, 60/80 mesh, was used as the solid support. ln γi∞ =
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The stationary phase for each column was prepared by mixing with ethanol with known masses of solvents and inert solid support. The relative loading of the stationary phase (mass of the solvents / mass of the solid support) for the columns used in the measurements is about 1/4. Ethanol was then slowly evaporated from the mixture, in a rotary evaporator at low temperature (308.15 K) and under reduced pressure. Stainless steel column (length = 200 mm, i.d. = 4.1 mm) was carefully filled with the coated solid support. The amount of stationary phase inside the column was determined gravimetrically. The accuracy data of ws were checked by extraction before and after measurement. The average data of ws was used. To check if solvent losses occurred during the measurements, the liquid loading was determined before and after the measurement gravimetrically. With the use of pre-saturation column the loss of solvent was kept to a minimum. The experimental condition, (gas flow, solvent loss, etc.), was checked by measuring the retention time and retention volume Vg of a reference substance (ethyl acetate) in regular intervals. The relative error of Vg values was within ±2%. Hamilton gastight syringes, 1 l capacity, were used to inject the solutes into the carrier gas stream. Air was used as the inert gas to obtain the reference retention time t0 . For most of solutes, good peaks were obtained by injecting 0.2 l liquid solute together with similar amount of air. Formamide, chemical reagent grade, was dried by CaO, and then purified by vacuum distillation. Glucose, fructose and sucrose were of analytical grade. Glucose and sucrose were dried at 373.15 K for 10 h under vacuum before use. Fructose was dried at 343.15 K for 24 h under vacuum. Silanized 101 white solid support was washed by ethanol and then dried at 393.15 K. All other chemicals used as solutes were of reagent grade, without further purification. Since GLC is itself a separation technique, the experimental results are not influenced by small amount of impurities. All chemicals were from Shanghai Chemical Co.
3. Results and discussion 3.1. The data of γi∞ in formamide + sugar solvents Ancillary data of vapor pressures (Pis ), virial coefficients (Bii and Bij ), liquid molar volume at temperature 298.15 K (Vi ) and acentric factors (ω) of solute are provided in Table 1, Table 1 Vapor pressures (Pis ), virial coefficients (Bii and Bij ), liquid mole volumes (Vi ) and acentric factors (ω) of solute at temperature 298.15 K Solute
Pis (kPa)
Vi (cm3 mol−1 )
ω
Bii (cm3 mol−1 )
Bij (cm3 mol−1 )
Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
14.76 26.22 12.68 48.25 12.52 12.05 23.46 77.71 32.07
97.08 80.67 89.41 104.7 98.55 90.17 81.76 62.35 73.99
0.190 0.221 0.211 0.282 0.362 0.327 0.371 0.257 0.312
−1532 −1166 −1537 −1129 −1800 −1759 −1554 −777.4 −1231
−17.29 −14.18 −17.13 −9.018 −14.59 −15.09 −14.04 −8.203 −10.98
Vi was from literature [23]; Pis was calculated by Antoine equation; Bii and Bij are calculated by Tsonopoulos [20] method; the required acentric factors are calculated by Pitzer and Curl [21] method.
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Table 2 The retention volumes Vg and infinite dilution activity coefficients γi∞ for solutes in glucose + formamide mixed solvent at 298.15 K x (%) 0.0
0.2599
0.8267
1.3020
1.8097
2.433
3.011
3.542
4.158
Vg (cm3 g−1 ) Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
32.1 111 77.0 26.6 385 701 394 146 488
30.9 109 74.3 26.0 376 686 389 142 477
29.7 103 71.6 24.8 356 650 373 137 455
28.6 99.8 69.4 23.7 338 626 363 131 438
27.4 96.4 66.8 22.8 328 604 354 128 427
26.1 91.0 63.0 21.6 308 569 339 121 405
25.3 89.0 61.6 20.9 299 557 331 117 396
24.2 85.3 59.0 19.9 285 534 320 113 381
22.6 80.6 55.7 18.7 266 501 306 108 360
γi∞ Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
107 17.4 51.8 40.0 10.5 5.99 5.51 4.56 3.27
110. 17.6 53.2 40.6 10.7 6.08 5.55 4.63 3.31
113 18.3 54.4 42.0 11.1 6.30 5.68 4.74 3.41
115 18.7 55.3 43.3 11.5 6.45 5.77 4.86 3.49
119 19.1 56.6 44.4 11.7 6.59 5.83 4.93 3.54
122 19.9 59.0 46.0 12.2 6.88 5.98 5.11 3.66
124 20.0 59.4 46.7 12.4 6.91 6.03 5.19 3.69
128 20.6 61.1 48.5 12.8 7.11 6.13 5.30 3.78
135 21.4 63.6 50.5 13.5 7.45 6.30 5.48 3.93
Experimental data of the retention volume (Vg ) and the activity coefficients at infinite dilution (γi∞ ) are provided in Tables 2–4. All experimental data of Vg were reproducible within ±2%. For solutes containing oxygen atom, the values of γi∞ increase in the sequence: acetone < methyl formate < tetrahydrofurane < 2-butanone < ethylacetate < diethylether. For solutes of chlorohydrocarbons, the values of γi∞ increase in the sequence: chloroform < tetrachloromethane. Benzene is a non-polar compound. Its value of γi∞ is higher than diethylether, but lower than tetrachloromethane. 3.2. The effect of composition in stationary solvents on γi∞ The activity coefficients of a nonelectrolyte solute in a sugar + formamide solution, at low sugar mole fraction, is given by the Setschenow equation [22] ln γi∞ = ln γi∞,0 + kx
(3)
where, γi∞,0 is the activity coefficient at infinite dilution of solute i in pure solvent, γi∞ the activity coefficient in a sugar solution at mole fraction x. The physical meaning of k is similar to the salting out effect parameter in electrolyte solution [22]. It has a characteristic value for a given sugar–nonelectrolyte solute pair. It represents the effect of sugar on γi∞ .
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Table 3 The retention volumes Vg and infinite dilution activity coefficients γi∞ for solutes in fructose + formamide mixed solvent at 298.15 K x (%) 0.2552
0.7646
1.3039
1.8340
2.4221
2.9900
3.5704
4.2045
Vg (cm3 g−1 ) Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
31.7 110 76.2 26.3 382 694 394 144 482
30.7 106 74.0 25.2 365 668 383 140 466
29.5 102 71.1 24.3 347 637 369 134 449
28.4 98.7 68.5 23.1 334 615 357 130 431
27.3 93.8 65.4 22.1 316 582 343 124 411
26.2 90.9 63.2 21.0 303 561 333 120 398
25.1 88.0 61.1 20.1 291 542 325 116 385
24.0 84.0 57.9 19.1 275 512 310 110 367
γi∞ Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
108 17.5 51.9 40.2 10.5 6.00 5.48 4.57 3.27
109 17.9 52.7 41.3 10.8 6.14 5.54 4.64 3.34
112 18.3 54.0 42.2 11.2 6.34 5.67 4.77 3.41
114 18.6 55.2 43.7 11.5 6.48 5.76 4.85 3.50
117 19.3 56.8 44.9 12.0 6.72 5.90 4.98 3.61
120 19.6 57.9 46.5 12.3 6.87 5.99 5.08 3.67
123 19.9 58.9 47.8 12.6 7.00 6.04 5.16 3.73
127 20.5 61.2 49.4 13.1 7.28 6.23 5.34 3.85
In Fig. 1, the curves of ln γi∞ versus the sugar mole fraction x, for system of glucose + formamide + some solutes, (ethyl acetate, methyl formate, acetone, 2-butanone, tetrahydrofurane and diethylether), are presented. All the curves show linear relationship between ln γi∞ with x, and with a positive k value. The values of k and the standard deviation of linear fitting, S.D., by a least square method, are listed in Table 5. These results indicate that the values of S.D. are <1%. The values of k increase in the order: THF < methyl formate ∼ acetone < 2-butanone < diethylether < ethyl acetate. In the case of acetone and methyl formate, there are nearly same k values. The k value for ethyl acetate is the greatest, even higher than diethylether and non-polar solute benzene and tetrachloromethane. In Fig. 2, the curves of ln γi∞ and x for other three solutes, benzene, tetrachloromethane and chloroform in glucose + formamide are presented. The values of k are listed in Table 5, together with the values of S.D. Linear relationship can be observed for these systems. The values of k increase in the order: chloroform ∼ benzene < tetrachloromethane. Figs. 3–6 show the curves of ln γi∞ and x for solutes in fructose + formamide and sucrose + formamide mixed solvents. Similar to the curves in Figs. 1 and 2, good linear curves are observed for these systems. The values of k and S.D. are listed in Table 5. By comparing the k values for these three sugar +formamide mixtures, it can be found that there is a nearly same increase sequence for these systems. That is THF < methyl formate < acetone < 2-butanone < diethylether < ethyl acetate, and chloroform < benzene < tetrachloromethane.
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Table 4 The retention volumes Vg and infinite dilution activity coefficients γi∞ for solutes in sucrose + formamide mixed solvent at 298.15 K x (%)
Vg (cm3 g−1 ) Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone γi∞ Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
0.1365
0.2534
0.4004
0.6868
0.9661
1.1380
1.2836
1.5931
31.7 109 75.7 26.2 380 691 390 144 478
31.3 107 75.1 25.7 373 682 386 141 474
30.8 106 73.8 25.1 366 671 381 139 465
29.6 103 71.6 24.2 354 647 371 135 454
28.5 99.6 69.0 23.5 338 625 361 131 436
28.0 96.9 67.3 22.7 331 611 354 129 429
27.1 94.8 65.4 22.3 321 595 348 126 419
26.5 92.3 63.5 21.3 311 573 338 122 407
107 17.7 52.2 40.3 10.6 6.02 5.52 4.57 3.30
108 17.8 52.3 40.8 10.7 6.06 5.54 4.62 3.30
109 17.9 52.7 41.4 10.8 6.10 5.55 4.65 3.33
111 18.1 53.3 42.0 10.9 6.21 5.61 4.69 3.36
113 18.3 54.3 42.7 11.2 6.32 5.66 4.76 3.43
114 18.6 55.1 43.4 11.4 6.39 5.71 4.80 3.45
117 18.9 56.2 44.1 11.6 6.51 5.75 4.85 3.50
117 19.0 56.8 45.2 11.8 6.64 5.82 4.93 3.54
Fig. 1. The values of ln γi∞ for solutes in glucose + formamide as a function of the glucose mole fraction x: acetone (䊐), 2-butanone (), methyl formate (䊊), THF ( ), ethyl acetate (䉫), and diethylether (+).
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Table 5 Setschenow parameter k in Eq. (3) and S.D. for the linear fitting, S.D. Solute
Glucose (k)
S.D.
Fructose (k)
S.D.
Sucrose (k)
S.D.
Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Tetrahydrofurane Methyl formate Acetone
5.1 4.7 4.6 5.4 5.7 5.0 3.1 4.2 4.2
0.008 0.007 0.007 0.006 0.008 0.008 0.004 0.004 0.007
4.2 3.9 4.0 5.2 5.5 4.7 3.0 3.8 4.0
0.004 0.004 0.005 0.004 0.006 0.005 0.006 0.004 0.005
6.1 5.3 5.9 7.4 7.4 6.5 3.5 4.9 5.1
0.002 0.003 0.004 0.003 0.004 0.004 0.002 0.002 0.003
In order to observe the effect of sugar on k, the relative k value is used for analysis. In Fig. 7, the k values of solute in fructose + formamide are taken as the x-axis, the k values of solute in glucose and sucrose + formamide are taken as the y-axis respectively. Approximately linear curves are obtained, and all the curves are in the area up the diagonal. For solutes containing oxygen atom in glucose solvents, the linear curve is near to the diagonal, its value of slope is 1.01. This results indicate that the replacement of fructose by glucose, cause a slight increase in k values. In the case of these solutes in sucrose solvent, the linear curve is on a more upside area, and its slope is 1.65. This result indicates that the replacement of fructose by sucrose, cause an increase in k values is observable. Another two linear curves in Fig. 7 are the cases of benzene, chloroform and tetrachloromethane in glucose and sucrose + formamide solvent. The values of slopes are 1.5 and 3.5, respectively. This is an indication that sucrose and glucose cause
Fig. 2. The values of ln γi∞ for solutes in glucose + formamide as a function of the glucose mole fraction x: benzene ( ), chloroform (䊊), and tetrachloromethane (䊐).
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Fig. 3. The values of ln γi∞ for solutes in fructose + formamide as a function of the fructose mole fraction x: acetone (䊐), 2-butanone (), methyl formate (䊊), THF ( ), ethyl acetate (䉫), and diethylether (+).
Fig. 4. The values of ln γi∞ for solutes in fructose + formamide as a function of the fructose mole fraction x: benzene ( ), chloroform (䊊), and tetrachloromethane (䊐).
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285
Fig. 5. The values of ln γi∞ for solutes in sucrose + formamide as a function of the sucrose mole fraction x: acetone (䊐), 2-butanone (), methyl formate (䊊), THF ( ), ethyl acetate (䉫), and diethylether (+).
Fig. 6. The values of ln γi∞ for solutes in sucrose + formamide as a function of the sucrose mole fraction x: benzene ( ), chloroform (䊊), and tetrachloromethane (䊐).
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Fig. 7. The relative k values for systems of (solute + glucose and sucrose + formamide) to the system (solute + fructose + formamide). Here, (䊐): solutes containing oxygen atom in glucose + formamide; (䊊): solutes containing oxygen atom in sucrose + formamide; ( ): benzene, chloroform and tetrachloromethane in glucose + formamide; (): benzene, chloroform and tetrachloromethane in sucrose + formamide.
the k value of these solutes increase more rapidly than the case oxygen containing solutes. The effect of sucrose on k is lager than that of glucose.
4. Conclusion Using gas liquid chromatography, activity coefficients for nine solutes at infinite dilution (γi∞ ) in stationary solvent of formamide + glucose, + fructose and + sucrose at 298.15 K have been measured. Linear dependence of ln γi∞ on the mole fraction of sugar was observed, with the fitting S.D. <1%. By comparing the values of Setschenow’s equation coefficients (k) for these three sugar + formamide mixtures, it can be found that there is a nearly same increase sequence for these systems. That is THF < methylformate < acetone < 2-butanone < diethylether < ethyl acetate, and chloroform < benzene < tetrachloromethane. The replacement of fructose and glucose by sucrose, cause an observable increase in the values of k. List of symbols Bii the second virial coefficient of molecule i at temperature T Bij the cross second virial coefficient of molecule i and j at temperature T F carrier gas flow rate James–Martin correction factor for the pressure gradient and gas compressibility J32 inside the column
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k Ms Pf Pis PI Po Pws R S.D. t0 ti T Tf Vg Vi ws x γi∞ ω
287
Setschenow’s equation coefficients in Eq. (3) the molecular mass of stationary solvent pressure of carrier gas in a soap-film meter the vapor pressure of organic solute i at column temperature T column inlet pressure column outlet pressure the vapor pressure of water at temperature Tf the universal gas constant the standard deviation retention time of inert gas (0), air retention time of solute (i) column temperature temperature of carrier gas in a soap-film meter retention volume the liquid molar volume of solute i at temperature T mass of solvent contained within the column mole fraction of a sugar in solution infinite dilution activity coefficients of solute i acentric factors
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The measurement of activity coefficients for solutes at infinite dilution with mixed solvents formamide + glucose, or + fructose, or + sucrose using a gas liquid chromatography at 298.15 K Tong-Chun Bai a,∗ , Qing-Hu Tang b a
Department of Chemistry and Chemical Engineering, Suzhou University, Suzhou 215006, China b Department of Chemistry, Henan Normal University, Xinxiang 453002, China Received 1 February 2002; accepted 1 May 2002
Abstract Using gas liquid chromatography, activity coefficients for nine solutes at infinite dilution (γi∞ ) in stationary solvent of formamide + glucose, + fructose and + sucrose at 298.15 K have been measured. Linear dependence of ln γi∞ on the mole fraction of sugar was observed. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Activity coefficient; Gas liquid chromatography; Formamide; Glucose; Fructose; Sucrose
1. Introduction Water has been considered to possess particular solvent properties giving rise to the so-called hydrophobic effect which is regarded to act as an organizing force in the aggregation of amphiphilic molecules to give micelles and liquid crystalline phases as well as lipid bilayers and biological membranes [1]. However, it is now well established that the aggregation of amphiphilic molecules is not unique to aqueous systems but can take place also in other solvents with strong cohesive forces such as hydrazine [2,3], formamide [4,5], ethylene glycol [6,7], and glycerol [8,9]. Thus, the hydrophobic effect can be seen as a special case of a more general solvophobic effect. Extensive experimental information is available about the solvation of small organic molecules in water, and the thermodynamic properties of solute–solvent and solute–solute interactions in aqueous solution are well characterized [10]. But less information is available about the thermodynamics of solvation in other strongly associated solvents [11,12]. The activity coefficient at infinite dilution (γi∞ ) represents an important property, which is used in particular for the selection of selective solvents (e.g. for extraction and extractive distillation) and for the reliable design of thermal separation processes. The data give a good insight into solute–solvent molecular ∗
Corresponding author. E-mail address: [email protected] (T.-C. Bai). 0378-3812/02/$ – see front matter © 2002 Elsevier Science B.V. All rights reserved. PII: S 0 3 7 8 - 3 8 1 2 ( 0 2 ) 0 0 1 2 5 - 5
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interactions. The measurement of γi∞ by gas–liquid chromatography (GLC) is an adequate technique [12]. Most measurements use non-polar or moderate polar solvents as stationary solvents [14–17]. Much less measurement uses polar solvent and its mixture with polar organic compound as stationary solvent. Of the solvents that can be conveniently worked with, formamide is the one that most closely resembling water. It can behave either as donor or acceptor of protons, forms, in liquid state, puckered planes of dimmer rings connected by chains of hydrogen bonded formamide molecules [11]. Spectroscopic and diffraction studies [18,19] confirm the presence of a three-dimensional state. However, compared to water the void space in the plane structure is considerably reduced. In order to get more information on the effect of a third component on the activity coefficient, the activity coefficients at infinite dilution for some organic compounds in formamide + sugar (glucose, fructose and sucrose) mixed solvents have been measured by GLC at 298.15 K. Ethyl acetate, methyl formate, acetone, 2-butone, diethylether, tetrahydrofurane, benzene, chloroform and tetrachloromethane were used as solutes. 2. Experimental The infinite dilution activity coefficients γi∞ were measured by gas–liquid chromatography (GLC). The calculation of γi∞ requires the measurement of following variables: (a) net retention time (ti − t0 ) of solute, that is, the difference between the retention times of solute (i) and inert gas (0); (b) column temperature T; (c) column inlet pressure PI and outlet pressure Po ; (d) carrier gas flow rate F measured at temperature Tf and pressure Pf ; (e) mass ws of solvent contained within the column. From these experimental data, the retention volume Vg and infinite dilution activity coefficient γi∞ were calculated. The James–Martin correction factor J32 for the pressure gradient and gas compressibility inside the column was applied in the calculation of Vg [13]. The gas phase nonideality was taken into account by means of the virial equation of state. Vg =
F (273.15/Tf )(ti − t0 )((Pf − Pws )/P0 )J32 ws
(1)
ln(273.15R/Ms Pis Vg ) − (Bii − Vi )Pis (2Bij − Vi∞ )J32 P0 + (2) RT RT In these equations, Pws and Pis are, respectively, the vapor pressure of water at temperature Tf and that of organic solute i at column temperature T; Ms the molecular weight of the stationary solvent; R the universal gas constant; Bii and Vi are second virial coefficient and the liquid molar volume of solute i at temperature T; for polar solutes the values of Bii and Bij are calculated by Tsonopoulos [20] method. The required critical data are taken from literature. The required acentric factors are calculated by Pitzer and Curl [21] method. A Shimadzu GC-9A gas chromatography with a thermal conductivity detector was used in the measurements. The carrier gas was hydrogen flowing at about 30 cm3 /min. The flow rates were measured with a soap-film meter, and temperatures with a mercury thermometer. The column outlet pressure was determined with a barometer. The pressure drop inside the column was read with a cathetometer from a U tube mercury manometer. The column was taken out of the column box, and its temperature was controlled by a water bath, with an accuracy of ±0.05 K. The mixed solvents of formamide + glucose, or + fructose, or + sucrose, are prepared by mass, and used as stationary solvents. Silanized 101 white solid support, 60/80 mesh, was used as the solid support. ln γi∞ =
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The stationary phase for each column was prepared by mixing with ethanol with known masses of solvents and inert solid support. The relative loading of the stationary phase (mass of the solvents / mass of the solid support) for the columns used in the measurements is about 1/4. Ethanol was then slowly evaporated from the mixture, in a rotary evaporator at low temperature (308.15 K) and under reduced pressure. Stainless steel column (length = 200 mm, i.d. = 4.1 mm) was carefully filled with the coated solid support. The amount of stationary phase inside the column was determined gravimetrically. The accuracy data of ws were checked by extraction before and after measurement. The average data of ws was used. To check if solvent losses occurred during the measurements, the liquid loading was determined before and after the measurement gravimetrically. With the use of pre-saturation column the loss of solvent was kept to a minimum. The experimental condition, (gas flow, solvent loss, etc.), was checked by measuring the retention time and retention volume Vg of a reference substance (ethyl acetate) in regular intervals. The relative error of Vg values was within ±2%. Hamilton gastight syringes, 1 l capacity, were used to inject the solutes into the carrier gas stream. Air was used as the inert gas to obtain the reference retention time t0 . For most of solutes, good peaks were obtained by injecting 0.2 l liquid solute together with similar amount of air. Formamide, chemical reagent grade, was dried by CaO, and then purified by vacuum distillation. Glucose, fructose and sucrose were of analytical grade. Glucose and sucrose were dried at 373.15 K for 10 h under vacuum before use. Fructose was dried at 343.15 K for 24 h under vacuum. Silanized 101 white solid support was washed by ethanol and then dried at 393.15 K. All other chemicals used as solutes were of reagent grade, without further purification. Since GLC is itself a separation technique, the experimental results are not influenced by small amount of impurities. All chemicals were from Shanghai Chemical Co.
3. Results and discussion 3.1. The data of γi∞ in formamide + sugar solvents Ancillary data of vapor pressures (Pis ), virial coefficients (Bii and Bij ), liquid molar volume at temperature 298.15 K (Vi ) and acentric factors (ω) of solute are provided in Table 1, Table 1 Vapor pressures (Pis ), virial coefficients (Bii and Bij ), liquid mole volumes (Vi ) and acentric factors (ω) of solute at temperature 298.15 K Solute
Pis (kPa)
Vi (cm3 mol−1 )
ω
Bii (cm3 mol−1 )
Bij (cm3 mol−1 )
Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
14.76 26.22 12.68 48.25 12.52 12.05 23.46 77.71 32.07
97.08 80.67 89.41 104.7 98.55 90.17 81.76 62.35 73.99
0.190 0.221 0.211 0.282 0.362 0.327 0.371 0.257 0.312
−1532 −1166 −1537 −1129 −1800 −1759 −1554 −777.4 −1231
−17.29 −14.18 −17.13 −9.018 −14.59 −15.09 −14.04 −8.203 −10.98
Vi was from literature [23]; Pis was calculated by Antoine equation; Bii and Bij are calculated by Tsonopoulos [20] method; the required acentric factors are calculated by Pitzer and Curl [21] method.
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Table 2 The retention volumes Vg and infinite dilution activity coefficients γi∞ for solutes in glucose + formamide mixed solvent at 298.15 K x (%) 0.0
0.2599
0.8267
1.3020
1.8097
2.433
3.011
3.542
4.158
Vg (cm3 g−1 ) Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
32.1 111 77.0 26.6 385 701 394 146 488
30.9 109 74.3 26.0 376 686 389 142 477
29.7 103 71.6 24.8 356 650 373 137 455
28.6 99.8 69.4 23.7 338 626 363 131 438
27.4 96.4 66.8 22.8 328 604 354 128 427
26.1 91.0 63.0 21.6 308 569 339 121 405
25.3 89.0 61.6 20.9 299 557 331 117 396
24.2 85.3 59.0 19.9 285 534 320 113 381
22.6 80.6 55.7 18.7 266 501 306 108 360
γi∞ Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
107 17.4 51.8 40.0 10.5 5.99 5.51 4.56 3.27
110. 17.6 53.2 40.6 10.7 6.08 5.55 4.63 3.31
113 18.3 54.4 42.0 11.1 6.30 5.68 4.74 3.41
115 18.7 55.3 43.3 11.5 6.45 5.77 4.86 3.49
119 19.1 56.6 44.4 11.7 6.59 5.83 4.93 3.54
122 19.9 59.0 46.0 12.2 6.88 5.98 5.11 3.66
124 20.0 59.4 46.7 12.4 6.91 6.03 5.19 3.69
128 20.6 61.1 48.5 12.8 7.11 6.13 5.30 3.78
135 21.4 63.6 50.5 13.5 7.45 6.30 5.48 3.93
Experimental data of the retention volume (Vg ) and the activity coefficients at infinite dilution (γi∞ ) are provided in Tables 2–4. All experimental data of Vg were reproducible within ±2%. For solutes containing oxygen atom, the values of γi∞ increase in the sequence: acetone < methyl formate < tetrahydrofurane < 2-butanone < ethylacetate < diethylether. For solutes of chlorohydrocarbons, the values of γi∞ increase in the sequence: chloroform < tetrachloromethane. Benzene is a non-polar compound. Its value of γi∞ is higher than diethylether, but lower than tetrachloromethane. 3.2. The effect of composition in stationary solvents on γi∞ The activity coefficients of a nonelectrolyte solute in a sugar + formamide solution, at low sugar mole fraction, is given by the Setschenow equation [22] ln γi∞ = ln γi∞,0 + kx
(3)
where, γi∞,0 is the activity coefficient at infinite dilution of solute i in pure solvent, γi∞ the activity coefficient in a sugar solution at mole fraction x. The physical meaning of k is similar to the salting out effect parameter in electrolyte solution [22]. It has a characteristic value for a given sugar–nonelectrolyte solute pair. It represents the effect of sugar on γi∞ .
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Table 3 The retention volumes Vg and infinite dilution activity coefficients γi∞ for solutes in fructose + formamide mixed solvent at 298.15 K x (%) 0.2552
0.7646
1.3039
1.8340
2.4221
2.9900
3.5704
4.2045
Vg (cm3 g−1 ) Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
31.7 110 76.2 26.3 382 694 394 144 482
30.7 106 74.0 25.2 365 668 383 140 466
29.5 102 71.1 24.3 347 637 369 134 449
28.4 98.7 68.5 23.1 334 615 357 130 431
27.3 93.8 65.4 22.1 316 582 343 124 411
26.2 90.9 63.2 21.0 303 561 333 120 398
25.1 88.0 61.1 20.1 291 542 325 116 385
24.0 84.0 57.9 19.1 275 512 310 110 367
γi∞ Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
108 17.5 51.9 40.2 10.5 6.00 5.48 4.57 3.27
109 17.9 52.7 41.3 10.8 6.14 5.54 4.64 3.34
112 18.3 54.0 42.2 11.2 6.34 5.67 4.77 3.41
114 18.6 55.2 43.7 11.5 6.48 5.76 4.85 3.50
117 19.3 56.8 44.9 12.0 6.72 5.90 4.98 3.61
120 19.6 57.9 46.5 12.3 6.87 5.99 5.08 3.67
123 19.9 58.9 47.8 12.6 7.00 6.04 5.16 3.73
127 20.5 61.2 49.4 13.1 7.28 6.23 5.34 3.85
In Fig. 1, the curves of ln γi∞ versus the sugar mole fraction x, for system of glucose + formamide + some solutes, (ethyl acetate, methyl formate, acetone, 2-butanone, tetrahydrofurane and diethylether), are presented. All the curves show linear relationship between ln γi∞ with x, and with a positive k value. The values of k and the standard deviation of linear fitting, S.D., by a least square method, are listed in Table 5. These results indicate that the values of S.D. are <1%. The values of k increase in the order: THF < methyl formate ∼ acetone < 2-butanone < diethylether < ethyl acetate. In the case of acetone and methyl formate, there are nearly same k values. The k value for ethyl acetate is the greatest, even higher than diethylether and non-polar solute benzene and tetrachloromethane. In Fig. 2, the curves of ln γi∞ and x for other three solutes, benzene, tetrachloromethane and chloroform in glucose + formamide are presented. The values of k are listed in Table 5, together with the values of S.D. Linear relationship can be observed for these systems. The values of k increase in the order: chloroform ∼ benzene < tetrachloromethane. Figs. 3–6 show the curves of ln γi∞ and x for solutes in fructose + formamide and sucrose + formamide mixed solvents. Similar to the curves in Figs. 1 and 2, good linear curves are observed for these systems. The values of k and S.D. are listed in Table 5. By comparing the k values for these three sugar +formamide mixtures, it can be found that there is a nearly same increase sequence for these systems. That is THF < methyl formate < acetone < 2-butanone < diethylether < ethyl acetate, and chloroform < benzene < tetrachloromethane.
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Table 4 The retention volumes Vg and infinite dilution activity coefficients γi∞ for solutes in sucrose + formamide mixed solvent at 298.15 K x (%)
Vg (cm3 g−1 ) Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone γi∞ Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Terahydrofurane Methyl formate Acetone
0.1365
0.2534
0.4004
0.6868
0.9661
1.1380
1.2836
1.5931
31.7 109 75.7 26.2 380 691 390 144 478
31.3 107 75.1 25.7 373 682 386 141 474
30.8 106 73.8 25.1 366 671 381 139 465
29.6 103 71.6 24.2 354 647 371 135 454
28.5 99.6 69.0 23.5 338 625 361 131 436
28.0 96.9 67.3 22.7 331 611 354 129 429
27.1 94.8 65.4 22.3 321 595 348 126 419
26.5 92.3 63.5 21.3 311 573 338 122 407
107 17.7 52.2 40.3 10.6 6.02 5.52 4.57 3.30
108 17.8 52.3 40.8 10.7 6.06 5.54 4.62 3.30
109 17.9 52.7 41.4 10.8 6.10 5.55 4.65 3.33
111 18.1 53.3 42.0 10.9 6.21 5.61 4.69 3.36
113 18.3 54.3 42.7 11.2 6.32 5.66 4.76 3.43
114 18.6 55.1 43.4 11.4 6.39 5.71 4.80 3.45
117 18.9 56.2 44.1 11.6 6.51 5.75 4.85 3.50
117 19.0 56.8 45.2 11.8 6.64 5.82 4.93 3.54
Fig. 1. The values of ln γi∞ for solutes in glucose + formamide as a function of the glucose mole fraction x: acetone (䊐), 2-butanone (), methyl formate (䊊), THF ( ), ethyl acetate (䉫), and diethylether (+).
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283
Table 5 Setschenow parameter k in Eq. (3) and S.D. for the linear fitting, S.D. Solute
Glucose (k)
S.D.
Fructose (k)
S.D.
Sucrose (k)
S.D.
Tetrachloromethane Chloroform Benzene Diethylether Ethyl acetate 2-Butanone Tetrahydrofurane Methyl formate Acetone
5.1 4.7 4.6 5.4 5.7 5.0 3.1 4.2 4.2
0.008 0.007 0.007 0.006 0.008 0.008 0.004 0.004 0.007
4.2 3.9 4.0 5.2 5.5 4.7 3.0 3.8 4.0
0.004 0.004 0.005 0.004 0.006 0.005 0.006 0.004 0.005
6.1 5.3 5.9 7.4 7.4 6.5 3.5 4.9 5.1
0.002 0.003 0.004 0.003 0.004 0.004 0.002 0.002 0.003
In order to observe the effect of sugar on k, the relative k value is used for analysis. In Fig. 7, the k values of solute in fructose + formamide are taken as the x-axis, the k values of solute in glucose and sucrose + formamide are taken as the y-axis respectively. Approximately linear curves are obtained, and all the curves are in the area up the diagonal. For solutes containing oxygen atom in glucose solvents, the linear curve is near to the diagonal, its value of slope is 1.01. This results indicate that the replacement of fructose by glucose, cause a slight increase in k values. In the case of these solutes in sucrose solvent, the linear curve is on a more upside area, and its slope is 1.65. This result indicates that the replacement of fructose by sucrose, cause an increase in k values is observable. Another two linear curves in Fig. 7 are the cases of benzene, chloroform and tetrachloromethane in glucose and sucrose + formamide solvent. The values of slopes are 1.5 and 3.5, respectively. This is an indication that sucrose and glucose cause
Fig. 2. The values of ln γi∞ for solutes in glucose + formamide as a function of the glucose mole fraction x: benzene ( ), chloroform (䊊), and tetrachloromethane (䊐).
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Fig. 3. The values of ln γi∞ for solutes in fructose + formamide as a function of the fructose mole fraction x: acetone (䊐), 2-butanone (), methyl formate (䊊), THF ( ), ethyl acetate (䉫), and diethylether (+).
Fig. 4. The values of ln γi∞ for solutes in fructose + formamide as a function of the fructose mole fraction x: benzene ( ), chloroform (䊊), and tetrachloromethane (䊐).
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285
Fig. 5. The values of ln γi∞ for solutes in sucrose + formamide as a function of the sucrose mole fraction x: acetone (䊐), 2-butanone (), methyl formate (䊊), THF ( ), ethyl acetate (䉫), and diethylether (+).
Fig. 6. The values of ln γi∞ for solutes in sucrose + formamide as a function of the sucrose mole fraction x: benzene ( ), chloroform (䊊), and tetrachloromethane (䊐).
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Fig. 7. The relative k values for systems of (solute + glucose and sucrose + formamide) to the system (solute + fructose + formamide). Here, (䊐): solutes containing oxygen atom in glucose + formamide; (䊊): solutes containing oxygen atom in sucrose + formamide; ( ): benzene, chloroform and tetrachloromethane in glucose + formamide; (): benzene, chloroform and tetrachloromethane in sucrose + formamide.
the k value of these solutes increase more rapidly than the case oxygen containing solutes. The effect of sucrose on k is lager than that of glucose.
4. Conclusion Using gas liquid chromatography, activity coefficients for nine solutes at infinite dilution (γi∞ ) in stationary solvent of formamide + glucose, + fructose and + sucrose at 298.15 K have been measured. Linear dependence of ln γi∞ on the mole fraction of sugar was observed, with the fitting S.D. <1%. By comparing the values of Setschenow’s equation coefficients (k) for these three sugar + formamide mixtures, it can be found that there is a nearly same increase sequence for these systems. That is THF < methylformate < acetone < 2-butanone < diethylether < ethyl acetate, and chloroform < benzene < tetrachloromethane. The replacement of fructose and glucose by sucrose, cause an observable increase in the values of k. List of symbols Bii the second virial coefficient of molecule i at temperature T Bij the cross second virial coefficient of molecule i and j at temperature T F carrier gas flow rate James–Martin correction factor for the pressure gradient and gas compressibility J32 inside the column
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k Ms Pf Pis PI Po Pws R S.D. t0 ti T Tf Vg Vi ws x γi∞ ω
287
Setschenow’s equation coefficients in Eq. (3) the molecular mass of stationary solvent pressure of carrier gas in a soap-film meter the vapor pressure of organic solute i at column temperature T column inlet pressure column outlet pressure the vapor pressure of water at temperature Tf the universal gas constant the standard deviation retention time of inert gas (0), air retention time of solute (i) column temperature temperature of carrier gas in a soap-film meter retention volume the liquid molar volume of solute i at temperature T mass of solvent contained within the column mole fraction of a sugar in solution infinite dilution activity coefficients of solute i acentric factors
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