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Measurement and correlation of solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose
Fluid Phase Equilibria,
97 ( 1994) 201-209
Measurement and correlation of solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose Hideyuki Eya a, Kenji Mishima a, Masanori Nagatani Yasuhiko Arai b
a, Yoshio Iwai b,*,
a Department
of Chemical Engineering, Faculty of Engineering, Fukuoka University, Jonan-ku, Fukuoka 814-01, Japan b Department of Chemical Engineering, Faculty of Engineering, Kyushu University, Higashi-ku, Fukuoka 812, Japan (Received July 20, 1993; accepted in final form December 29, 1993)
Abstract Eya, H., Mishima, K., Nagatani, M., Iwai, Y. and Arai, Y., 1994. Measurement and correlation of solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose. Fluid Phase Equilibria, 97: 201-209. The solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose were measured by a saturation method. These sugars are key components of fermentation media. The measurements were carried out at 298.15, 303.15 and 310.15 K, as these temperatures are close to the fermentation conditions. The extended scaled-particle theory proposed by Hu et al. (1985) was used to correlate the solubilities of oxygen in the solutions measured in this work, and glucose or sucrose solutions appearing in the literature. By determining the potential parameters for sugars, the experimental solubilities can be correlated with good agreement. Keywords: Experiments;
Solubility
of gas in liquid; Oxygen; Aqueous
solution;
Scaled particle theory; Glucose;
Sucrose; Maltose
1. Introduction Because of the importance of oxygen solubilities in aerobic fermentations, some workers (Popovic et al., 1979; Quicker et al., 1981) have carried out measurements of oxygen solubilities in aqueous solutions containing sugars, electrolytes or fermentation products and also correlated the solubilities of oxygen by the Sechenov equation. The objectives of this study are to measure * Corresponding
author.
0378-3812/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZO378-3812(94)02464-C
202
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
the reliable solubilities of oxygen in aqueous solutions which contain fermentation components, and to develop a predictive model which can be easily applied to calculations at other temperatures with molecular specific parameters. Prediction of the solubilities of oxygen is very important because the composition of fermentation media changes from the initial composition during the fermentation. In a previous paper (Iwai et al., 1993), the authors measured the solubilities of oxygen in aqueous solutions containing fermentation components such as sodium chloride, ammonium sulphate, dipotassium hydrogenphosphate and potassium dihydrogenphosphate by a saturation method. Further, the molecular model of Hu et al. (1985) was used to correlate solubilities in these solutions, 2-l type electrolyte solutions and aqueous glucose solutions appearing in the literature. In this work, the solubilities of oxygen in aqueous solutions containing monosaccharide and disaccharide were measured by modifying the parts for pressure measurement of the previous apparatus (Iwai et al., 1993). Sugars were chosen because they have large saltingout effects on the dissolution of oxygen, their amounts decrease owing to consumption by microorganisms during fermentation, and they are very important as carbon sources in the fermentation media. The model of Hu et al. was used to correlated the oxygen solubilities in the present solutions. In the correlation, dispersion energies for sugars were calculated by van Krevelen’s group contribution method (van Krevelen, 1990) for the solubility parameter. It has been shown that the solubilities of oxygen in aqueous sugar solutions can be correlated successfully.
2. Experimental 2.1. Materials Glucose, sucrose and maltose were purchased from Wako Chemicals Co., Nakarai Chemicals Co. and Tokyo Kasei Chemical Co., respectively. All chemicals were analytical grade and used without further purification. Oxygen (99.995%, Seitetsu Kagaku Co.) was used without further purification. 2.2. Equipment and procedures Details of the apparatus and of measuring procedures were described in the previous work (Iwai et al., 1993). In this work, measurements were carried out by modifying the parts for pressure measurement. A digital vacuum gauge (Model VAS2076LS, Okano Works Ltd.) was used for the pressure measurement instead of a manometer. The analogue output voltage from the digital vaccum gauge was measured with a microvolt meter (Model AM-1001, Ohkura Electric Co. ) coupled with a DC voltage current standard (Type 2554, Yokogawa Electric Works Co.) The experimental data for the solubilities of oxygen in pure water and aqueous glucose solutions at 298.15 K were compared with the literature (Quicker et al., 1981). The agreement can be seen in Fig. 1. Reproducibility of solubility data was better than f 1.5%.
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
1.5 ’ 0
0.25
0.5
0.75
203
1.0
glucose [ mol.dmv3 ]
Fig. 1. Solubility of oxygen in aqueous glucose solution: 0, experimental data at 298.15 K; l , literature data at 298.15 K from Quicker et al. (1981); A, experimental data at 303.15 K, 0, at 310.15 K, -, calculated results.
2.3. Results Experimental solubilities of oxygen are presented in Table 1 and illustrated in Figs. l-3. The solubilities of oxygen in the present solutions decrease with an increase in concentration of sugar and a rise in temperature. Figures 2 and 3 show that sucrose and maltose, which have the same molecular weight, give the same degree of salting-out effect. The densities of the solutions containing sugars were also measured using pycnometers. The experimental results for densities are listed in Table 2.
3. Correlation 3.1. Model of Hu et al. Hu et al. (1984, 1985), and Xu and Hu (1986) proposed a molecular model for gas solubility, which is based on first-order perturbation theory. From first-order perturbation theory, the Hehnholtz energy of a real fluid mixture is expressed as follows: A real= A ref + A pert (1)
For the reference term AEf, the Boublik (1970) -Mansoori-Carnahan-Starling-Leland equation can be used. The perturbation term APen is expressed as
(1971)
(2)
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
204
0
0.25
0.5
0.75 ]
1.0
sucrose [ mol.dme3
0
0.25
05
a75
1.0
maltose [ md.dm-3 ]
Fig. 2. Solubility of oxygen in aqueous sucrose solution: l , literature data at 298.15 K from Iwai et al. (1990); A, at 303.15 K from Iwai et al. ( 1993); 0, experimental data at 3 10.15 K; n , literature data at 3 10.15 K from Zander (1976); -, calculated results. Fig. 3. Solubility of oxygen in aqueous maltose solution; 3 10.15 K; -, calculated results.
0, experimental data at 298.15 K; A, at 303.15 K;
q, at
where N, p, 4 and g are the number of molecules, the number density, the potential energy and the distribution function, respectively. Hu et al. (1984) simplified the distribution function using computer simulation data for local mole fractions. Number densities (mm3) of water or sugars were calculated as looo(d-A43c)N P2 =
18.02
A
(3)
and p3=&C
(4)
where d (kg mm3), M (kg mol-‘), NA and C (mol m-‘) are the density of aqueous sugar solution, the molar mass, the Avogadro number and the concentration of sugar, respectively. The densities obtained experimentally are interpolated as a function of sugar concentration by the quadratic equations. For molecule-molecule interactions, the Lennard-Jones potential with dipole-dipole contribution is used:
where E(J), a (m3), p (C m) are the energy parameter, the polarizability and the dipole moment, respectively. Because of large differences in sizes between oxygen and sugar, the energy
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
205
Table 1 Solubilities of oxygen in aqueous sugar solutions Temp.
Sugar
(K)
Cont. (mol dme3)
Bunsen coefficient
Glucose
298.15
303.15
310.15
(%)
fpC
K-P ( Z
Dev. a
lo-* m3 02(m3 soln.) ‘I)
0.252 0.504 1.010 0.253 0.508 0.762 1.014 0.256 0.509 1.021
2.60 2.43 2.14 2.39 2.25 2.10 2.00 2.16 2.01 1.81
2.65 2.46 2.11 2.43 2.26 2.11 1.99 2.22 2.07 1.80
1.9 1.2 1.4 1.7 0.0 0.5 0.5 2.8 3.0 0.6
Sucrose
310.15
0.255 0.514 1.080
2.14 1.89 1.59
2.14 1.92 1.49
0.0 1.6 6.3
Maltose
298.15
0.240 0.505 0.960 0.242 0.509 0.965 0.245 0.513 0.979
2.53 2.21 1.77 2.31 2.05 1.69 2.09 1.86 1.56
2.54 2.23 1.74 2.33 2.07 1.72 2.13 1.90 1.57
0.4 0.9 1.7 0.9 1.0 1.8 1.9 2.2 0.6
303.15
310.15
a Dev.(%)
=
IKFp - E=‘=I x 1oo Ke”P a
Table 2 Densities of aqueous sugar solutions Sugar
Cont. (mol dmm3)
Density (kg me3) 298.15 K
303.15 K
310.15 K 1010.2 1027.3 -
Glucose
0.250 0.500 0.750 1.ooo
1014.3 1031.4 1065.4
1012.8 1029.8 1050.3 1064.1
Sucrose
0.250 0.500 1.000
_
-
1026.0 1057.9 1122.4
0.238 0.500 0.950
1028.8 1063.5 1122.5
1027.3 1061.6 1119.2
1024.9 1058.9 1116.9
Maltose
1060.8
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
206
parameter between them is calculated as follows (Saito, 1983): ‘13
=
(cl
+
,3)6
Combining Eqs. (l), (2) and (5), and using the thermodynamic relation, the Henry’s constant KH (Pa) can be derived (Hu et al., 1985). Further, the Henry’s constant can be converted to the Bunsen absorption coefficient K, (Iwai et al., 1993). 3.2. Parameters For sugars, no information about size parameters, dipole moments, polarizabilities and energy parameters can be obtained. The energy parameters for the sugars were calculated from the cohesive energies. The interaction energy between like molecules can be calculated from cohesive energy by assuming the coordination number z = 12: c3 = -2E,IzN,
(7)
where E, (J) is the cohesive energy. The solubility parameter for the dispersion forces & can be predicted from a group contribution method (van Krevelen, 1990). As the cohesive energy density to the one-half power equals to the solubility parameter &, the cohesive energy can be calculated as follows:
(8) where Fdi is the group contribution to the dispersion component and Vi is the Fedors’ (1974) molar volume of group i. The values of Fdi and Vi are listed in Table 3. The calculated cohesive energies of glucose, sucrose and maltose were 4.213 x 104, 8.301 x lo4 and 8.0729 x lo4 J mol-*, respectively. It is difhcult to determine the dipole moments for sucrose and maltose. Further, it Table 3 Solubility parameter group contributions Structual group
-CH,-CH:
>c: -o-OH Ring a van Krevelen (1990). b Fedors ( 1974).
&
cm312mol-‘)
270 80 -70 100 210 190
Vb x 103 ( m3 mol- ‘) 16.1 -1.0 - 19.2 3.8 13.0 16
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
207
Table 4 Parameters for sugars Component
u x 1O’O(m)
a/k (K)
Glucose Sucrose Maltose
6.23 7.87 7.82
844.9 1664 1618
is considered that the contribution of dispersion energies between oxygen and sugars is much larger than that of polar energies; hence, the dipole moments of sucrose and maltose are assumed to be zero. The size parameters of the sugars were determined from the oxygen solubility data in their aqueous solutions at 298.15, 303.15 and 310.15 K, including previous data for sucrose at 298.15 and 303.15 K (Iwai et al., 1990, 1993). The parameters for water were interpolated from the values proposed by Hu et al. ( 1985). All the parameters for the sugars used in this work are listed in Table 4. Size parameters obtained for monosaccharide and disaccharides are considered to be reasonable, because c3 for the former is nearly one half of that for the latter. 3.3. Results Figures l-3 show that the oxygen solubilities in aqueous glucose, sucrose and maltose solutions can be correlated successfully using the model proposed by Hu et al. with the parameters determined from the group contribution method for dispersion energies of sugars. The calculated solubilities are listed in Table 1 and also shown in Figs. l-3, together with experimental solubilities of oxygen.
4. Conclusions The solubilities of oxygen in aqueous solutions containing fermentation components such as glucose, sucrose and maltose were measured by using a saturation method. To predict solubilities of oxygen in their solutions, the model of Hu et al. was adopted. The energy parameters for sugars were estimated from the group contribution method of cohesive energy. Using these parameters, good correlation results were obtained. 5. Acknowledgements We thank Mr. Mitsuhiro Kondo and Mr. Hideyuki Shima for their helpful assistance in this work. We gratefully acknowledge the financial support provided by Hattori Houkoukai Engineering Research Scholarship Foundation (1988) and the Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Japan (C-03650775, 1991-1992).
H. Eya et al. / Fluid Phase Equilibria 97 (1994) 201-209
6. List of symbols A
c d E” Fdi k JL &I A4 N NA r vi Z
Hehnholtz energy concentration of sugar density of aqueous solution cohesive energy dispersion forces of group i Boltzmann constant Bunsen absorption coefficient Henry’s constant molar mass number of molecules Avogadro number distance molar volume of group i coordination number
6.1. Greek letters
id
E P P 0 C#J
polar&ability solubility parameter contributed energy parameter dipole moment number density size parameter potential function
by dispersion forces
6.2. Subscripts 1 2 3
oxygen water sugar
6.3. Superscripts talc exp pert real ref
calculated value experimental value perturbation term real fluid mixture term reference term
References Boublik, T., 1970. Hard-sphere equation of state. J. Chem. Phys., 53: 471-472.
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
209
Fedors, R.F., 1974. A method for estimating both the solubility parameters and molar volumes of liquids. Polym. Eng. Sci., 14: 147-154. Hu, Y., Ludecke, D. and Prausnitz, J.M., 1984. Molecular thermodynamics of fluid mixtures containing molecules differing in size and potential energy. Fluid Phase Equilibria, 17: 217-241. Hu, Y., Xu, Y.N. and Prausnitz, J.M., 1985. Molecular thermodynamics of gas solubility. Fluid Phase Equilibria, 23: 15-40. Iwai, Y., Kohashi, K., Eya, H., Honda, K. and Arai, Y., 1990. Measurement and correlation of oxygen solubilities in aqueous solutions containing salts and sugar. Kagaku Kogaku Ronbunshu, 16: 1247-1251. Iwai, Y., Eya, H., Itho, Y., Arai, Y. and Takeuchi, K., 1993. Measurement and correlation of solubilities of oxygen in aqueous solutions containing salts and sucrose. Fluid Phase Equilibria, 83:271-278. Mansoori, G.A., Camahan, N.F., Starling, K.E. and Leland, T.W., 1971. Equilibrium thermodynamic properties of the mixture of hard spheres. J. Chem. Phys., 54: 1523-1525. Popovic, M., Niebelschtitz, H. and ReuS, M., 1979. Oxygen solubilities in fermentation fluids. Eur. J. Appl. Microbial. Biotechnol., 8: 1- 15. Quicker, G., Schumpe, A., Kiinig, B. and Deckwer, W.-D., 1981. Comparison of measured and calculated oxygen solubilities in fermentation media. Biotechnol. Bioeng., 23: 635-650. Saito, S., 1983. Heikoubussei suisan no kiso. Baifukan, Tokyo. van Krevelen, D.W., 1990. Properties of polymers, 3rd. edn. Elsevier, New York. Xu, Y.N. and Hu, Y., 1986. Prediction of Henry’s constants of gases in electrolyte solutions. Fluid Phase Equilibria, 30: 221-228. Zander, R., 1976. The distribution space of physically dissolved oxygen in aqueous solutions of organic substance. Z. Naturforsch, Teil C, 31: 339-352.
97 ( 1994) 201-209
Measurement and correlation of solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose Hideyuki Eya a, Kenji Mishima a, Masanori Nagatani Yasuhiko Arai b
a, Yoshio Iwai b,*,
a Department
of Chemical Engineering, Faculty of Engineering, Fukuoka University, Jonan-ku, Fukuoka 814-01, Japan b Department of Chemical Engineering, Faculty of Engineering, Kyushu University, Higashi-ku, Fukuoka 812, Japan (Received July 20, 1993; accepted in final form December 29, 1993)
Abstract Eya, H., Mishima, K., Nagatani, M., Iwai, Y. and Arai, Y., 1994. Measurement and correlation of solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose. Fluid Phase Equilibria, 97: 201-209. The solubilities of oxygen in aqueous solutions containing glucose, sucrose and maltose were measured by a saturation method. These sugars are key components of fermentation media. The measurements were carried out at 298.15, 303.15 and 310.15 K, as these temperatures are close to the fermentation conditions. The extended scaled-particle theory proposed by Hu et al. (1985) was used to correlate the solubilities of oxygen in the solutions measured in this work, and glucose or sucrose solutions appearing in the literature. By determining the potential parameters for sugars, the experimental solubilities can be correlated with good agreement. Keywords: Experiments;
Solubility
of gas in liquid; Oxygen; Aqueous
solution;
Scaled particle theory; Glucose;
Sucrose; Maltose
1. Introduction Because of the importance of oxygen solubilities in aerobic fermentations, some workers (Popovic et al., 1979; Quicker et al., 1981) have carried out measurements of oxygen solubilities in aqueous solutions containing sugars, electrolytes or fermentation products and also correlated the solubilities of oxygen by the Sechenov equation. The objectives of this study are to measure * Corresponding
author.
0378-3812/94/$07.00 0 1994 - Elsevier Science B.V. All rights reserved SSDZO378-3812(94)02464-C
202
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
the reliable solubilities of oxygen in aqueous solutions which contain fermentation components, and to develop a predictive model which can be easily applied to calculations at other temperatures with molecular specific parameters. Prediction of the solubilities of oxygen is very important because the composition of fermentation media changes from the initial composition during the fermentation. In a previous paper (Iwai et al., 1993), the authors measured the solubilities of oxygen in aqueous solutions containing fermentation components such as sodium chloride, ammonium sulphate, dipotassium hydrogenphosphate and potassium dihydrogenphosphate by a saturation method. Further, the molecular model of Hu et al. (1985) was used to correlate solubilities in these solutions, 2-l type electrolyte solutions and aqueous glucose solutions appearing in the literature. In this work, the solubilities of oxygen in aqueous solutions containing monosaccharide and disaccharide were measured by modifying the parts for pressure measurement of the previous apparatus (Iwai et al., 1993). Sugars were chosen because they have large saltingout effects on the dissolution of oxygen, their amounts decrease owing to consumption by microorganisms during fermentation, and they are very important as carbon sources in the fermentation media. The model of Hu et al. was used to correlated the oxygen solubilities in the present solutions. In the correlation, dispersion energies for sugars were calculated by van Krevelen’s group contribution method (van Krevelen, 1990) for the solubility parameter. It has been shown that the solubilities of oxygen in aqueous sugar solutions can be correlated successfully.
2. Experimental 2.1. Materials Glucose, sucrose and maltose were purchased from Wako Chemicals Co., Nakarai Chemicals Co. and Tokyo Kasei Chemical Co., respectively. All chemicals were analytical grade and used without further purification. Oxygen (99.995%, Seitetsu Kagaku Co.) was used without further purification. 2.2. Equipment and procedures Details of the apparatus and of measuring procedures were described in the previous work (Iwai et al., 1993). In this work, measurements were carried out by modifying the parts for pressure measurement. A digital vacuum gauge (Model VAS2076LS, Okano Works Ltd.) was used for the pressure measurement instead of a manometer. The analogue output voltage from the digital vaccum gauge was measured with a microvolt meter (Model AM-1001, Ohkura Electric Co. ) coupled with a DC voltage current standard (Type 2554, Yokogawa Electric Works Co.) The experimental data for the solubilities of oxygen in pure water and aqueous glucose solutions at 298.15 K were compared with the literature (Quicker et al., 1981). The agreement can be seen in Fig. 1. Reproducibility of solubility data was better than f 1.5%.
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
1.5 ’ 0
0.25
0.5
0.75
203
1.0
glucose [ mol.dmv3 ]
Fig. 1. Solubility of oxygen in aqueous glucose solution: 0, experimental data at 298.15 K; l , literature data at 298.15 K from Quicker et al. (1981); A, experimental data at 303.15 K, 0, at 310.15 K, -, calculated results.
2.3. Results Experimental solubilities of oxygen are presented in Table 1 and illustrated in Figs. l-3. The solubilities of oxygen in the present solutions decrease with an increase in concentration of sugar and a rise in temperature. Figures 2 and 3 show that sucrose and maltose, which have the same molecular weight, give the same degree of salting-out effect. The densities of the solutions containing sugars were also measured using pycnometers. The experimental results for densities are listed in Table 2.
3. Correlation 3.1. Model of Hu et al. Hu et al. (1984, 1985), and Xu and Hu (1986) proposed a molecular model for gas solubility, which is based on first-order perturbation theory. From first-order perturbation theory, the Hehnholtz energy of a real fluid mixture is expressed as follows: A real= A ref + A pert (1)
For the reference term AEf, the Boublik (1970) -Mansoori-Carnahan-Starling-Leland equation can be used. The perturbation term APen is expressed as
(1971)
(2)
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
204
0
0.25
0.5
0.75 ]
1.0
sucrose [ mol.dme3
0
0.25
05
a75
1.0
maltose [ md.dm-3 ]
Fig. 2. Solubility of oxygen in aqueous sucrose solution: l , literature data at 298.15 K from Iwai et al. (1990); A, at 303.15 K from Iwai et al. ( 1993); 0, experimental data at 3 10.15 K; n , literature data at 3 10.15 K from Zander (1976); -, calculated results. Fig. 3. Solubility of oxygen in aqueous maltose solution; 3 10.15 K; -, calculated results.
0, experimental data at 298.15 K; A, at 303.15 K;
q, at
where N, p, 4 and g are the number of molecules, the number density, the potential energy and the distribution function, respectively. Hu et al. (1984) simplified the distribution function using computer simulation data for local mole fractions. Number densities (mm3) of water or sugars were calculated as looo(d-A43c)N P2 =
18.02
A
(3)
and p3=&C
(4)
where d (kg mm3), M (kg mol-‘), NA and C (mol m-‘) are the density of aqueous sugar solution, the molar mass, the Avogadro number and the concentration of sugar, respectively. The densities obtained experimentally are interpolated as a function of sugar concentration by the quadratic equations. For molecule-molecule interactions, the Lennard-Jones potential with dipole-dipole contribution is used:
where E(J), a (m3), p (C m) are the energy parameter, the polarizability and the dipole moment, respectively. Because of large differences in sizes between oxygen and sugar, the energy
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
205
Table 1 Solubilities of oxygen in aqueous sugar solutions Temp.
Sugar
(K)
Cont. (mol dme3)
Bunsen coefficient
Glucose
298.15
303.15
310.15
(%)
fpC
K-P ( Z
Dev. a
lo-* m3 02(m3 soln.) ‘I)
0.252 0.504 1.010 0.253 0.508 0.762 1.014 0.256 0.509 1.021
2.60 2.43 2.14 2.39 2.25 2.10 2.00 2.16 2.01 1.81
2.65 2.46 2.11 2.43 2.26 2.11 1.99 2.22 2.07 1.80
1.9 1.2 1.4 1.7 0.0 0.5 0.5 2.8 3.0 0.6
Sucrose
310.15
0.255 0.514 1.080
2.14 1.89 1.59
2.14 1.92 1.49
0.0 1.6 6.3
Maltose
298.15
0.240 0.505 0.960 0.242 0.509 0.965 0.245 0.513 0.979
2.53 2.21 1.77 2.31 2.05 1.69 2.09 1.86 1.56
2.54 2.23 1.74 2.33 2.07 1.72 2.13 1.90 1.57
0.4 0.9 1.7 0.9 1.0 1.8 1.9 2.2 0.6
303.15
310.15
a Dev.(%)
=
IKFp - E=‘=I x 1oo Ke”P a
Table 2 Densities of aqueous sugar solutions Sugar
Cont. (mol dmm3)
Density (kg me3) 298.15 K
303.15 K
310.15 K 1010.2 1027.3 -
Glucose
0.250 0.500 0.750 1.ooo
1014.3 1031.4 1065.4
1012.8 1029.8 1050.3 1064.1
Sucrose
0.250 0.500 1.000
_
-
1026.0 1057.9 1122.4
0.238 0.500 0.950
1028.8 1063.5 1122.5
1027.3 1061.6 1119.2
1024.9 1058.9 1116.9
Maltose
1060.8
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
206
parameter between them is calculated as follows (Saito, 1983): ‘13
=
(cl
+
,3)6
Combining Eqs. (l), (2) and (5), and using the thermodynamic relation, the Henry’s constant KH (Pa) can be derived (Hu et al., 1985). Further, the Henry’s constant can be converted to the Bunsen absorption coefficient K, (Iwai et al., 1993). 3.2. Parameters For sugars, no information about size parameters, dipole moments, polarizabilities and energy parameters can be obtained. The energy parameters for the sugars were calculated from the cohesive energies. The interaction energy between like molecules can be calculated from cohesive energy by assuming the coordination number z = 12: c3 = -2E,IzN,
(7)
where E, (J) is the cohesive energy. The solubility parameter for the dispersion forces & can be predicted from a group contribution method (van Krevelen, 1990). As the cohesive energy density to the one-half power equals to the solubility parameter &, the cohesive energy can be calculated as follows:
(8) where Fdi is the group contribution to the dispersion component and Vi is the Fedors’ (1974) molar volume of group i. The values of Fdi and Vi are listed in Table 3. The calculated cohesive energies of glucose, sucrose and maltose were 4.213 x 104, 8.301 x lo4 and 8.0729 x lo4 J mol-*, respectively. It is difhcult to determine the dipole moments for sucrose and maltose. Further, it Table 3 Solubility parameter group contributions Structual group
-CH,-CH:
>c: -o-OH Ring a van Krevelen (1990). b Fedors ( 1974).
&
cm312mol-‘)
270 80 -70 100 210 190
Vb x 103 ( m3 mol- ‘) 16.1 -1.0 - 19.2 3.8 13.0 16
H. Eya et al. 1 Fluid Phase Equilibria 97 (1994) 201-209
207
Table 4 Parameters for sugars Component
u x 1O’O(m)
a/k (K)
Glucose Sucrose Maltose
6.23 7.87 7.82
844.9 1664 1618
is considered that the contribution of dispersion energies between oxygen and sugars is much larger than that of polar energies; hence, the dipole moments of sucrose and maltose are assumed to be zero. The size parameters of the sugars were determined from the oxygen solubility data in their aqueous solutions at 298.15, 303.15 and 310.15 K, including previous data for sucrose at 298.15 and 303.15 K (Iwai et al., 1990, 1993). The parameters for water were interpolated from the values proposed by Hu et al. ( 1985). All the parameters for the sugars used in this work are listed in Table 4. Size parameters obtained for monosaccharide and disaccharides are considered to be reasonable, because c3 for the former is nearly one half of that for the latter. 3.3. Results Figures l-3 show that the oxygen solubilities in aqueous glucose, sucrose and maltose solutions can be correlated successfully using the model proposed by Hu et al. with the parameters determined from the group contribution method for dispersion energies of sugars. The calculated solubilities are listed in Table 1 and also shown in Figs. l-3, together with experimental solubilities of oxygen.
4. Conclusions The solubilities of oxygen in aqueous solutions containing fermentation components such as glucose, sucrose and maltose were measured by using a saturation method. To predict solubilities of oxygen in their solutions, the model of Hu et al. was adopted. The energy parameters for sugars were estimated from the group contribution method of cohesive energy. Using these parameters, good correlation results were obtained. 5. Acknowledgements We thank Mr. Mitsuhiro Kondo and Mr. Hideyuki Shima for their helpful assistance in this work. We gratefully acknowledge the financial support provided by Hattori Houkoukai Engineering Research Scholarship Foundation (1988) and the Grant-in-Aid for Scientific Research of the Ministry of Education, Science and Culture, Japan (C-03650775, 1991-1992).
H. Eya et al. / Fluid Phase Equilibria 97 (1994) 201-209
6. List of symbols A
c d E” Fdi k JL &I A4 N NA r vi Z
Hehnholtz energy concentration of sugar density of aqueous solution cohesive energy dispersion forces of group i Boltzmann constant Bunsen absorption coefficient Henry’s constant molar mass number of molecules Avogadro number distance molar volume of group i coordination number
6.1. Greek letters
id
E P P 0 C#J
polar&ability solubility parameter contributed energy parameter dipole moment number density size parameter potential function
by dispersion forces
6.2. Subscripts 1 2 3
oxygen water sugar
6.3. Superscripts talc exp pert real ref
calculated value experimental value perturbation term real fluid mixture term reference term
References Boublik, T., 1970. Hard-sphere equation of state. J. Chem. Phys., 53: 471-472.
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