2816
Ind. Eng. Chem. Res. 1997, 36, 2816-2820
GENERAL RESEARCH Measurement and Modeling of Solubilities of D-Glucose in Water/Alcohol and Alcohol/Alcohol Systems Anto´ nio M. Peres and Euge´ nia A. Macedo* Laboratory of Separation and Reaction Engineering, Departamento de Engenharia Quı´mica, Faculdade de Engenharia, Rua dos Bragas, 4099 Porto Codex, Portugal
In this work, the solubilities of D-glucose in water/methanol and ethanol/methanol mixtures are measured at 40 and 60 °C, using a simple and accurate analytical method. A modified UNIQUAC model is used for the correlation of the experimental solubility data. New UNIQUAC interaction parameters for the pairs D-glucose/alcohol, water/alcohol, and alcohol/alcohol are estimated based on the ternary solubility data presented in this work together with those available in the literature for D-glucose in water/ethanol. The solubility calculations were performed using an equation based on enthalpy of fusion data for D-glucose. The model describes satisfactorily the experimental solubility data of D-glucose in water/ethanol, water/methanol, and ethanol/methanol mixtures at both temperatures. Introduction Carbohydrate solutions have a prominent and significant role in a variety of areas including biological and food industries, especially for the design and operation of crystallization processes. An increased interest in these kinds of biological molecules has shown a need for thermodynamic properties of mixtures containing sugars. Despite their importance, a literature survey has shown that there is a considerable lack of information concerning the solid-liquid equilibrium data of common sugars in water, as discussed recently by Goldberg and Tewari (1989). Nevertheless, some experimental data can be found in the literature: (i) For binary water/sugar systems: Jackson et al. (1926); Young and Jones (1949); Young et al. (1952); Young (1957); Stephen and Stephen (1963a); Vasa´tko and Smelı´k (1967); Mullin (1972). (ii) For ternary and quaternary water/mixed sugars systems: Kelly (1954a,b); Stephen and Stephen (1963b); Gabas and Lague´rie (1990); Abed et al. (1992). Unfortunately, as far as multicomponent solvent mixtures are concerned, the lack of experimental data is much more evident and only a few studies are available in the literature: sucrose/ethanol/water at 14 and 40 °C (Stephen and Stephen, 1963b); D-xylose/ water/ethanol and D-mannose/water/ethanol at 25 °C (Gabas et al., 1988); D-glucose/water/ethanol at 35 °C (Bockstanz et al., 1989); and D-glucose/water/ethanol at 40 and 60 °C (Peres and Macedo, 1997). Concerning the modeling works available in the literature for the description of these complex systems, only a few approaches have been proposed in the literature. In this way, Gabas and Lague´rie (1990, 1993), Abed et al. (1992), Catte´ et al. (1994, 1995), and more recently Peres and Macedo (1996), among others, have contributed to the progress of the representation of the solubilities of one or more sugars in water, proposing different models and approaches. For the * Corresponding author. S0888-5885(96)00458-7 CCC: $14.00
description of the solubilities of one sugar in mixed solvents only two approaches have been presented in the literature (Bockstanz et al., 1989; Peres and Macedo, 1997), which can be partly explained by the scarce number of experimental data available. Bockstanz et al. (1989) have measured the solubilities of D-glucose in water/ethanol mixtures at 35 °C and used a RedlichKister equation to describe the experimental data. In a previous work (Peres and Macedo, 1997), the solubilities of D-glucose in water/ethanol mixtures at 40 and 60 °C were measured and new UNIQUAC interaction parameters were estimated. In this work new experimental data have been measured for the ternary systems D-glucose/water/ methanol and D-glucose/ethanol/methanol also at 40 and 60 °C, using a simple and accurate analytical apparatus. These experimental data together with those measured in the previous work have been used as the data base for the development of a modified UNIQUAC model for the correlation of phase equilibria in systems containing sugars. The experimental data measured by Bockstanz et al. (1989) were not used for the evaluation of the correlation capabilities of the modified UNIQUAC model proposed. New UNIQUAC temperature-independent interaction parameters for D-glucose/ethanol, D-glucose/ methanol, water/ethanol, water/methanol, and ethanol/ methanol are presented. Experimental Section Materials. In all experiments double-deionized water was used. Anhydrous D-glucose was supplied by Sigma Chemical Co. (ACS reagent) and dried in a vacuum oven at 55 °C before being used. The ethanol and methanol used for the preparation of the solvent mixtures were supplied by Merck, with a minimum purity of 99.8 vol %. No further purification was employed. Apparatus and Procedure. The solubility of Dglucose in water/methanol and ethanol/methanol mixtures was determined using the same isothermal method described in detail in a previous work (Peres and Macedo, 1997). © 1997 American Chemical Society
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2817 Table 1. Solid-Liquid Equilibrium Data for D-Glucose/ Water/Methanol at 40 and 60 °C 40 °C
Table 2. Solid-Liquid Equilibrium Data for D-Glucose/ Ethanol/Methanol at 40 and 60 °C
60 °C
D-glucose
40 °C
D-glucose
60 °C
D-glucose
D-glucose
w′watera
(wt %)
σb
w′watera
(wt %)
σb
w′ethanola
(wt %)
σb
w′ethanola
(wt %)
σb
0.000 9.961 20.018 29.971 38.579 49.202 58.452 79.728 79.777 100.000
3.405 7.477 15.811 27.722 37.851 47.452 53.797 62.622 62.665 67.332
0.004 0.005 0.007 0.011 0.018 0.020 0.024 0.027 0.029 0.017
0.000 10.033 10.100 20.029 29.661 40.102 49.223 59.538 78.760 100.000
6.643 15.358 15.523 31.181 45.586 56.080 62.122 66.570 71.768 75.071
0.004 0.007 0.007 0.015 0.022 0.028 0.031 0.033 0.036 0.040
0.000 9.995 19.985 30.030 39.979 49.499
3.406 2.847 2.385 1.960 1.620 1.337
0.003 0.004 0.0002 0.001 0.001 0.001
59.486 70.185 79.725 100.000
1.098 0.880 0.726 0.523
0.003 0.0004 0.001 0.002
0.000 10.018 19.962 30.007 39.998 49.751 49.873 59.906 69.922 80.080 100.000
6.643 5.526 4.635 3.864 3.219 2.640 2.672 2.244 1.850 1.502 1.056
0.001 0.001 0.003 0.005 0.004 0.003 0.0003 0.001 0.003 0.0002 0.0003
a w′ water is the water mass percentage in a sugar-free solvent mixture. b σ is the standard deviation of experimentally measured D-glucose weight percentage.
Glass-jacketed cells of about 80-100 cm3 each are charged with different mixtures of the desired mixed solvent and kept inside an insulated box, in order to maintain the temperature inside it constant. Dried D-glucose was added to the solution in a small excess over the expected solubility. The temperature in each cell is controlled by circulating thermostatic water in the jacket and can be considered to be accurate within (0.1 K. Liquid and solid phases were stirred for 48 h and allowed to stand for about 24 h at a constant temperature to enable any finely dispersed solids to settle down. From each equilibrium cell, samples of the clear supernatant liquid were carefully withdrawn using pipettes at a slightly higher temperature than the solution temperature in order to avoid any precipitation. The solubility is determined by slow evaporation of the solvent mixture from a previous weighted sample of saturated solution and by weighting the precipitated sugar regularly until a constant value is achieved. The drying procedure consists of two steps: first, the sample is allowed to dry slowly at ambient temperature to avoid loosing any solid, until the majority of the solvent mixture has been evaporated; and latter, the remaining sample is dried in a vacuum oven at approximately 55 °C. Each experimental point is an average of three different results obeying one of the following criteria: if the experimental solubility is less than 10 wt %, then the standard deviation (σ) of the three measurements should be less than 0.005; for solubilities higher than 10 wt %, then 2σ/solubility should be less than 0.001 (Pinho and Macedo, 1996). Solubility Data. The experimental data obtained for the systems D-glucose/water/methanol and D-glucose/ ethanol/methanol at 40 and 60 °C are given in Tables 1 and 2, respectively. Model Development For the successful representation of the solubilities of D-glucose in the mixed solvent systems at 40 and 60 °C and their dependence with the temperature, it is necessary to be able to represent accurately the activity coefficients of the different species in the solution. In order to describe the solid-liquid equilibria, the same semiempirical modified UNIQUAC model proposed by Peres and Macedo (1997) is used. The combinatorial contribution of the UNIQUAC model is given by the expression of the combinatorial term of the molar excess Gibbs energy proposed by Larsen et al. (1987) with the modification of Kikic et al. (1980); for the residual
a w′ ethanol is the ethanol mass percentage in a sugar-free solvent mixture. b σ is the standard deviation of experimentally measured D-glucose weight percentage.
contribution, the original UNIQUAC equation (Abrams and Prausnitz, 1975), with linear temperature dependency for the interaction parameters introduced by Hansen et al. (1991), is used for the D-glucose/water pair; for the other interaction parameters no temperature dependency was considered. The solubility of D-glucose in the mixed solvent mixtures is calculated from an equation based on the symmetric convention for the calculation of the activity coefficients; i.e., the pure liquid at the solution temperature is the standard state for the sugar, together with the fusion enthalpy and the melting temperature data for D-glucose (Raemy and Schweizer, 1983; Gabas and Lague´rie, 1992; Roos, 1993). For a general case, this equation can be derived from an idealized thermodynamic cycle between the solid and liquid sugar phase states. Some assumptions are made: (i) The solvent does not appear in the solid phase. (ii) The difference between the heat capacities of the pure liquid and the pure solid sugars (∆Cp) is a linear function of temperature in the temperature range T (temperature of the mixture) and Tm (melting point of the sugar):
∆Cp ) ∆A + ∆B(T - T°)
(1)
where ∆A and ∆B are temperature-independent parameters, and T° is an arbitrary reference temperature, which was, in this work, set equal to 298.15 K. The resulting expression is
ln(γglucosexglucose) )
[
-
](
)
∆Hf ∆A - ∆BT° 1 ∆B 2 1 + Tm + Tm + R R 2R T Tm
( )
∆B ∆A - ∆BT° T ln (T - Tm) (2) + R Tm 2R where the solubility of D-glucose in the mixed solvent (xglucose) is related to some thermodynamic properties of D-glucose, such as the mole fraction symmetric activity coefficient (γglucose), the melting point (Tm), the enthalpy of fusion (∆Hf) at Tm, and the difference of heat capacities (∆Cp). Results and Discussion The calculation of the mole fraction symmetric activity coefficient of D-glucose by means of the modified UNIQUAC model requires the knowledge of the volume
2818 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 Table 3. Structural Parameters (Ri and Qi) for D-Glucose, Water, Ethanol, and Methanol Ri Qi
D-glucose
water
ethanol
methanol
8.1528 7.920
0.9200 1.400
2.5755 2.588
1.9011 2.048
Table 4. UNIQUAC-10p Interaction Parameters: First t t Row, a°ij; Second Row, aij (K); aij ) a°ij + aij (T - T°)
where superscripts calc and exp mean calculated values according to the model and experimental data, respectively, n is the number of experimental data points, and S represents the solubility of D-glucose in the mixed solvent mixtures at 40 and 60 °C. The RMSD and AAD values were calculated using the following equations:
j i
D-glucose
water
ethanol
methanol
D-glucose
0 0 96.5267c 0.2770c 119.8019b 0a 35.9896b 0a
-68.6157c -0.0690c 0 0 187.2511b 0a 24.7242b 0a
72.4890b 0a -49.6976b 0a 0 0 -164.9502b 0a
123.4104b 0a 70.7893b 0a 164.6254b 0a 0 0
water ethanol methanol a
b
c
Set in this work equal to zero. Estimated Parameters. Peres and Macedo (1996).
(Ri) and the surface area (Qi) parameters of D-glucose, water, ethanol, and methanol and the interaction parameters between the different molecules. The Ri and Qi parameters for all the components were calculated using the size parameters of the groups involved in each molecule and are given in Table 3. The size parameters of the groups were taken from the UNIFAC Parameter Tables (Fredenslund et al., 1977; Skjold-Jørgensen et al., 1979). The thermodynamic data and the temperatureindependent coefficients of eq 1, needed for the calculation of the solubility of D-glucose in the water/ethanol, water/methanol, and ethanol/methanol mixtures, are the same as those used or estimated by Peres and Macedo (1996): Tm ) 423.15 K; ∆Hf ) 32 432 J mol-1; ∆A ) 139.5766 J mol-1 K-1; and ∆B ) 0 J mol-1 K-2. Concerning the modeling of the solid-liquid equilibrium data, the modified UNIQUAC model proposed by Peres and Macedo (1997) is used to describe the experimental solubility data of D-glucose in the three mixed solvent systems at 40 and 60 °C. In total 51 experimental data points were used: 16 from Peres and Macedo (1997) and 35 presented in this work. The data measured by Bockstanz et al. (1989) for D-glucose/water/ ethanol at 35 °C were not included in the data base since neither of the above-mentioned reproducibility criteria, recommended and used here, are respected. In this work, 10 new interaction parameters are estimated simultaneously (UNIQUAC-10p): D-glucose/ ethanol, D-glucose/methanol, water/ethanol, water/ methanol, and ethanol/methanol. The D-glucose/water UNIQUAC parameters used in this study were estimated previously from different thermodynamic properties of binary aqueous solutions of D-glucose (Peres and Macedo, 1996). The correlation results obtained are very satisfactory (AAD ) 1.2%), showing that the model is able to describe the experimental data accurately. It should be emphasized that for each D-glucose/mixed solvent system studied only four interaction parameters are estimated and that at least two of them are always common to another D-glucose/mixed solvent system. A IMSL routine was used to estimate the new model parameters. It uses a finite difference LevenbergMarquardt algorithm to minimize the following objective function:
Fobj )
∑n
(
)
2
exp calc Sglucose - Sglucose exp Sglucose
n
(3)
x| | | | ∑n
RMSD )
Sexp n
NDE
∑n
AAD )
calc Sexp n - Sn
2
× 100
(4)
calc Sexp n - Sn
Sexp n
NDE
× 100
(5)
where NDE is the total number of experimental data points. The UNIQUAC interaction parameters estimated in this work together with those given by Peres and Macedo (1996) for D-glucose/water are listed in Table 4. These parameters were used in the calculations of the solubility of D-glucose in water/ethanol, water/ methanol, and ethanol/methanol mixtures with eq 2. In order to reduce the number of fitted parameters from 10 to 4 (D-glucose/ethanol; D-glucose/methanol), the solvent/solvent UNIQUAC interaction parameters were set equal to those published by Gmehling et al. (ab 1977). However, this procedure (UNIQUAC-4p) introduces two major disadvantages: (i) In the above-mentioned compilation it is possible to find a significant number of quite different values for the same solvent/solvent UNIQUAC interaction parameters: water/ethanol, 55; water/methanol, 53; ethanol/methanol, 9. Therefore, the number of possible combinations of the three pairs of parameters is enormous (55 × 53 × 9), which results in a very timeconsuming task, since all these possibilities for the solvent/solvent UNIQUAC interaction parameters should be considered in order to find the combination that minimizes eq 3. Moreover, it turns out to be very difficult to extrapolate to other sugars, since all of this procedure should be repeated. (ii) None of the available parameters presented by Gmehling et al. (ab 1977) was obtained for the same experimental conditions of the measurements performed in this work: atmospheric pressure and temperatures from 40 to 60 °C. Nevertheless, after a significant number of optimizations for each individual D-glucose/mixed solvent system, it was possible to choose one pair of parameters for each solvent/solvent pair that minimizes eq 3. These are listed in Table 5. The pressure and temperature ranges of the vapor-liquid equilibrium data used by Gmehling et al. (ab 1977) to estimate these specific parameters are as follows:
water/ethanol: P ) 250 mmHg, 53.30 °C e T e 69.65 °C water/methanol: P ) 760 mmHg, 65.71 °C e T e 97.44 °C ethanol/methanol: P ) 760 mmHg, T ) 25, 100, and 140 °C
Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997 2819 Table 5. UNIQUAC-4p Interaction Parameters: First t t Row, a°ij; Second Row, aij (K); aij ) a°ij + aij (T - T°) j i
D-glucose
water
ethanol
methanol
D-glucose
0 0 96.5267c 0.2770c 94.4178b 0a 85.5076b 0a
-68.6157c -0.0690c 0 0 194.9110d 0a 100.3102d 0a
108.7735b 0a -39.2880d 0a 0 0 48.9896d 0a
61.4844b 0a -54.9014d 0a -38.5170d 0a 0 0
water ethanol methanol
a Set in this work equal to zero. b Estimated parameters. c Peres and Macedo (1996). d Gmehling et al. (ab 1977).
Figure 3. Correlated and experimental results for ethanol/methanol at 40 and 60 °C.
D-glucose/
Table 6. Comparison between the AAD and RMSD Values Calculated for the Two Approaches Used in This Work: UNIQUAC-4p and UNIQUAC-10p
system D-glucose/water/
ethanol D-glucose/water/ methanol D-glucose/ethanol/ methanol total
Figure 1. Correlated and experimental results for water/ethanol at 40 and 60 °C.
D-glucose/
Figure 2. Correlated and experimental results for water/methanol at 40 and 60 °C.
D-glucose/
These parameters were then set equal to those presented in Table 5 and used in the estimation of the D-glucose/ethanol and D-glucose/methanol UNIQUAC interaction parameters, using the same 51 experimental data points as before, by means of the same IMSL routine. Table 5 also presents the D-glucose/alcohol UNIQUAC interaction parameters estimated when the solvent/ solvent parameters were fixed. Figures 1-3 show a comparison between the experimental data and the correlation results obtained with both modeling procedures adopted in this work: UNIQUAC-10p and UNIQUAC-4p. From the above-mentioned figures it is interesting to remark that both models are able to describe very satisfactorily the “S”shaped curves of the solubilities of D-glucose in water/ ethanol or methanol mixtures as well as the monotonous
UNIQUAC-4p
UNIQUAC-10p
T (°C)
NDE
ADD (%)
RMSD (%)
AAD (%)
RMSD (%)
40 60 40 60 40 60 40, 60
8 8 9 9 8 9 51
2.4 1.9 1.6 1.8 2.6 1.6 2.0
5.5 4.8 4.2 4.5 5.7 4.3 2.0
1.6 1.2 0.9 1.2 1.2 0.9 1.2
4.4 3.8 3.1 3.6 3.9 3.2 1.5
decreasing behavior of the solubility of this sugar in the mixed ethanol/methanol solvents and that both procedures accurately describe the experimental data at both 40 and 60 °C. However, the UNIQUAC-10p gives slightly better results than the UNIQUAC-4p, as expected. This conclusion can also be drawn when comparing the AAD values calculated per temperature and per system studied for both procedures, which are presented in Table 6. It is important to remember once again that, for each D-glucose/mixed solvent system, the UNIQUAC-10p procedure estimates only two additional interaction parameters compared to the UNIQUAC-4p procedure. Although the low number of reliable experimental data points available for the solubilities of D-glucose in the mixed solvents studied is a disadvantage for the estimation of the 10 UNIQUAC interaction parameters, this approach is recommended since this disadvantage can be easily overcome with future experimental work on phase equilibria of sugars in mixed solvents. However, the inconveniences pointed out for the UNIQUAC4p cannot be so easily overcome. Conclusions The very satisfactory and accurate results obtained for the description of the experimental solubilities of D-glucose in water/ethanol, water/methanol, and ethanol/methanol mixtures at 40 and 60 °C show that the modified UNIQUAC model used is adequate for the description of these highly complex systems, even if the model does not take into account the difference in D-glucose crystals present in solution or the role that hydrogen bonding plays in the solute-solvent interaction. From the results obtained and in view of future work with other sugars, it is recommended to adopt the approach where all the parameters are estimated since it will be more flexible and easy to extrapolate.
2820 Ind. Eng. Chem. Res., Vol. 36, No. 7, 1997
Acknowledgment A.M.P. acknowledges Junta Nacional de Investigac¸ a˜o Cientı´fica e Tecnolo´gicasPRAXIS XXI (Portugal) for the financial support. Nomenclature AAD ) absolute average deviation aij, a°ij, aijt ) UNIQUAC interaction parameters calc ) calculated values according to the model exp ) experimental data Fobj ) objective function i, j ) molecules in solution n ) number of experimental data points NDE ) total number of experimental data points, eqs 4 and 5 Qi ) surface area parameter Ri ) volume parameter RMSD ) root mean square deviation S ) solubility of D-glucose (wt %) T ) temperature (K) T° ) arbitrary reference temperature, set equal to 298.15 K Tm ) melting point of the sugar (K) xglucose ) mole fraction of glucose γglucose ) mole fraction symmetric activity coefficient ∆A ) temperature-independent parameter in eq 1 (J mol-1 K-1) ∆B ) temperature-independent parameter in eq 1 (J mol-1 K-2) ∆Cp ) difference between the heat capacities of the pure liquid and the pure solid sugars (J mol-1 K-1) ∆Hf ) enthalpy of fusion (J mol-1)
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Water-Sucrose-Fructose and Water-Xylose-Mannose. J. Cryst. Growth 1993, 128, 1245-1249. Gabas, N.; Carillon, T.; Hiquily, N. Solubilities of D-Xylose and D-Mannose in Water-Ethanol at 25 °C. J. Chem. Eng. Data 1988, 33, 128-130. Gmehling, J.; Onken, U. Vapor-Liquid Equilibrium Data Collection; DECHEMA Chemistry Data Series; DECHEMA: Frankfurt, Germany, ab 1977. Goldberg, R. N.; Tewari, Y. B. Thermodynamic and Transport Properties of Carbohydrates and their Monophosphates: The Pentoses and Hexoses. J. Phys. Chem. Ref. Data 1989, 18, 809880. Hansen, H. K.; Rasmussen, P.; Fredenslund, Aa.; Schiller, M.; Gmehling, J. Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension 5. Ind. Eng. Chem. Res. 1991, 30, 2352-2355. Jackson, R. F.; Silsbee, C. G.; Profitt, M. J. Sci. Pap. Bur. Stand. 1926, 57, 588. Kelly, F. H. Phase Equilibria in Sugar Solutions. I. Ternary System of Water-Glucose-Sucrose. J. Appl. Chem. 1954a, 4, 405-407. Kelly, F. H. Phase Equilibria in Sugar Solutions. II. Ternary System of Water-Glucose-Fructose. J. Appl. Chem. 1954b, 4, 409-411. Kikic, I.; Alessi, P.; Rasmussen, P.; Fredenslund, Aa. On the Combinatorial Part of the UNIQUAC Models. Can. J. Chem. Eng. 1980, 58, 253-258. Larsen, B. L.; Rasmussen, P.; Fredenslund, Aa. A Modified GroupContribution Model for Prediction of Phase Equilibria and Heats of Mixing. Ind. Eng. Chem. Res. 1987, 26, 2274-2286. Mullin, J. W. Crystallization, 2nd ed.; Butterworths: London, 1972. Peres, A. M.; Macedo, E. A. Thermodynamic Properties of Sugars in Aqueous Solutions: Correlation and Prediction Using a Modified UNIQUAC Model. Fluid Phase Equilib. 1996, 123, 71-95. Peres, A. M.; Macedo, E. A. Solid-Liquid Equilibrium of Sugars in Mixed Solvents. Entropie 1997, 202/203, 1-5. Pinho, S. P.; Macedo, E. A. Representation of Salt Solubility in Mixed Solvents: A Comparison of Thermodynamic Models. Fluid Phase Equilib. 1996, 116, 209-216. Raemy, A.; Schweizer, T. F. Thermal Behavior of Carbohydrates Studied by Heat Flow Calorimetry. J. Therm. Anal. 1983, 28, 95-108. Roos, Y. Melting and Glass Transitions of Low Molecular Weight Carbohydrates. Carbohydr. Res. 1993, 238, 39-48. Skjold-Jørgensen, S.; Kolbe, B.; Gmehling, J.; Rasmussen, P. Vapor-Liquid Equilibria by UNIFAC Group Contribution. Revision and Extension. Ind. Eng. Chem. Process Des. Dev. 1979, 18, 714-722. Stephen, H.; Stephen, T. Solubility of Inorganic and Organic Compounds. Binary Systems; Pergamon Press: Oxford, 1963a; Vol. I, Parts 1 and 2. Stephen, H.; Stephen, T. Solubility of Inorganic and Organic Compounds. Ternary Systems; Pergamon Press: Oxford, 1963b; Vol. II, Parts 1 and 2. Vasa´tko, J.; Smelı´k, A. Solubility of Anhydrous β-D-Fructose in Water. Chem. Zvesti 1967, 21, 736-738. Young, F. E. D-Glucose-Water Phase Diagram. J. Phys. Chem. 1957, 61, 616-619. Young, F. E.; Jones, F. T. Sucrose Hydrates: The Sucrose-Water Phase Diagram. J. Phys. Chem. 1949, 53, 1334-1350. Young, F. E.; Jones, F. T.; Lewis, H. J. D-Fructose-Water Phase Diagram. J. Phys. Chem. 1952, 56, 1093-1096.
Received for review July 26, 1996 Revised manuscript received April 8, 1997 Accepted April 15, 1997X IE9604583 X Abstract published in Advance ACS Abstracts, June 1, 1997.
