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Conductivities of CuSO4 and CdSO4 in Sucrose/Trehalose-Water Systems at 298.15 K Kelei Zhuo,* Yujuan Chen, Wenhao Wang, and Jianji Wang School of Chemistry and EnVironmental Science, Henan Normal UniVersity, Xinxiang, Henan 453007, People’s Republic of China
The conductivities of CuSO4 and CdSO4 in aqueous disaccharide (sucrose and trehalose) solutions were measured together with the densities, viscosities, and relative dielectric constants of the aqueous disaccharide solutions at 298.15 K. The limiting molar conductivities (Λ0) and association constants (KA) were derived from the Lee-Wheaton conductivity equation. From the obtained conductivity data, the values of the Walden product (Λ0η0) were also calculated. The ion-ion and ion-solvent interactions are discussed. 1. Introduction Carbohydrates hold a key position in living nature and have been the focus a huge interest over the past few decades because of their abilities to preserve biosystems such as cells, vaccines, or therapeutic proteins employed in the food, pharmaceuticals, and cosmetics industries.1 Indeed, disaccharides such as sucrose and trehalose can be added to biologically active solutions to overcome the limited stability range of proteins. Carbohydrates and metal cations coexist in biological fluids, and the interactions between carbohydrates and metal cations are a subject of current interest because of the importance of carbohydrate-metal complexes in chemistry and biology. The thermodynamic and transport properties of carbohydrate-electrolyte solutions are more frequently required by chemists and engineers, including density, viscosity, conductivity, transport numbers, diffusion, activity coefficients, and electrical conductivity. Recently, ion-association constants for 2:2 electrolytes (CoSO4, NiSO4, CuSO4, ZnSO4, MgSO4, CaSO4, and CdSO4) in aqueous solutions at different temperatures were determined by means of conductivity measurements.2-4 However, information on the interactions of saccharides with 2:2 electrolytes has seldom been reported in the literature. In our previous work,5 volumetric and viscosity properties of MgSO4/ CuSO4 in sucrose + water solutions at 298.15 K were reported. With the aim of carrying out a systematic investigation, in the current work, the conductivities of CuSO4 and CdSO4 in aqueous disaccharide (sucrose and trehalose) solutions were measured at 298.15 K. The limiting molar conductivities (Λ0), association constants (KA), and Walden products (Λ0η0) were derived and are discussed. 2. Experimental Section 2.1. Chemicals. Sucrose (>99.5%, Sigma) and trehalose (>99.5%, Sigma) were dried under a vacuum at room temperature to constant weight and stored over P2O5 in desiccators. Deionized water was doubly distilled over KMnO4. Water with a conductivity of (0.8-1.0) × 10-4 S · cm-1 was used throughout the experiments under an argon atmosphere to avoid taking up carbon dioxide. CuSO4 (>99.5%, Alfa) and CdSO4 (>99%, Alfa) were dissolved in pure water, and then their molarities were determined by titration with ethylenediaminetetraacetic acid (EDTA). * To whom correspondence should be addressed. Tel.: +86 373 3326336. Fax: +86 373 3326336. E-mail:
[email protected].
2.2. Measurement of Densities. Solution densities (F) were measured using a vibrating-tube digital densimeter (model DMA 60/602, Anton Paar, Graz, Austria), which has been described elsewhere.6-8 The temperature around the densimeter cell was controlled by circulating water from a constant-temperature bath (Schott, Mainz, Germany). A CT-1450 temperature controller and a CK-100 ultracryostat were employed to maintain the bath temperature at 298.15 ( 0.005 K. The densimeter was calibrated with pure water (the value of density was taken to be 0.997046 g · cm-3 at 298.15 K9,10) and dry air. The uncertainty in the molalities of the saccharides and electrolytes was evaluated to be about 0.2%. The uncertainty in density was estimated to be 3 × 10-6 g · cm-3. 2.3. Measurement of Viscosities. Solution viscosities (η) were measured by a suspended level Ubbelohde viscometer, which was placed in a water thermostat (Schott, Mainz, Germany), with a flow time of about 200 s for water at 298.15 K. The temperature of the water thermostat was controlled to be as precise as for the density measurements. The viscometer was calibrated at 298.15 and 308.15 K with water. Viscosities for water at different temperatures were taken from the literature.11 Flow-time measurements were performed on a Schott AVS310 photoelectric time unit with a resolution of 0.01 s. The estimated uncertainty in the experimental viscosity was less than 0.2%. Solution viscosity (η) is given by the equation η/F ) Ct - K/t0
(1)
where C and K are the cell constants and t0 is the flow time. The details of the experimental procedure were given elsewhere.12 2.4. Measurement of Relative Dielectric Constants. Solution relative dielectric constants (D) were measured using a dielectric constant meter (model Bl-870, Brookhaven Instrument Corp., Holtsville, NY), which was described elsewhere.13 The temperature was controlled at 298.15 ( 0.02 K by using a lowtemperature thermostat (model DC-2006, Shanghai Hengping Instrument Factory). The dielectric constant meter was calibrated with pure water (the relative dielectric constant of water was taken to be 78.54 at 298.15 K14). The uncertainty in the saccharide molalities was evaluated to be about 0.2%. The uncertainty in the dielectric constant was estimated to be 0.1. 2.5. Measurement of Conductivities. A conductivity meter (model 145A+, Thermo Orion) with an accuracy of ( 0.5% and a conductivity cell (model 013016D, Thermo Orion) were
10.1021/ie900041w CCC: $40.75 2009 American Chemical Society Published on Web 06/03/2009
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1
Table 1. Values of Limiting Molar Conductivity (Λ0), Association Constant (KA), and Walden Product (Λ0η0) Obtained for /2CuSO4 and 1 /2CdSO4 in Water and Saccharide + Water Mixtures at 298.15 K mS (mol · kg-1)
Λ0 (S · cm2 · mol-1)
Λ0η0 (S · cm2 · mol-1 · mPa · s)
KA
Λ0 (S · cm2 · mol-1)
Sucrose + /2CuSO4 0.0000
0.0500 0.1000 0.1500 0.2000 0.2500 0.3000
135.03 ( 0.17 135.90a 136.06a 135.08c 129.86 ( 0.13 124.94 ( 0.11 120.21 ( 0.11 115.67 ( 0.11 111.55 ( 0.11 107.30 ( 0.14
260.9 217.5 249 237 267.9 269.4 271.2 271.6 293.1 296.7
1
120.23
135.81 ( 0.06 133.15b
254.7 212 239d
120.92
120.80 121.68 122.26 123.09 124.27 125.07
130.94 ( 0.09 126.45 ( 0.03 120.73 ( 0.11 116.59 ( 0.06 111.99 ( 0.12 107.97 ( 0.10
267.3 283.1 277.6 285.9 283.9 301.5
121.80 123.14 122.79 124.07 124.77 125.85
Trehalose + 1/2CuSO4 0.0500 0.1000 0.1500 0.2000 0.2500 0.3000 a
129.77 ( 0.31 123.89 ( 0.16 117.19 ( 0.23 113.23 ( 0.22 107.95 ( 0.13 103.59 ( 0.19
284.5 283.5 287.6 290.6 285.3 294.2
Λ0η0 (S · cm2 · mol-1 · mPa · s)
KA
Sucrose + /2CdSO4
1
Trehalose + 1/2CdSO4 129.96 ( 0.13 124.29 ( 0.11 119.37 ( 0.16 114.44 ( 0.13 109.53 ( 0.07 104.67 ( 0.13
121.33 121.64 120.89 122.69 122.96 124.02
278.9 278.2 290.2 302.1 302.5 307.4
121.51 122.03 123.14 124.00 124.76 125.32
Taken from ref 5. b Taken from ref 6. c Taken from ref 22. d Taken from ref 21.
used for measurement of conductivity. The conductance cell was equipped with a water-circulating jacket, and the temperature was controlled at 298.15 ( 0.02 K with a low-temperature thermostat (model DC-2006, Shanghai Hengping Instrument Factory). The cell was calibrated by adding potassium chloride solutions consecutively.15 All data were corrected at 298.15 K with the conductivity of the corresponding solvent. At the beginning of every measuring cycle, the cell was filled with a weighed amount of solvent. After measurement of the solvent conductivity, the stepwise concentration was carried out by successive additions, using a gastight syringe, of weighed amounts of electrolytic solution (with or without disaccharide). The uncertainty in conductivity was estimated to be less than 0.5%. All of the instruments were calibrated using at least three samples before they were used, and every sample was measured at least three times. The uncertainty in the measurements for each apparatus was estimated and collected. 3. Results and Discussion The densities, viscosities, and dielectric constants of water and water + disaccharide mixtures are reported in Table S1 (Supporting Information), and the densities and molar conductivities of 1/2CuSO4 (one-half formula unit of copper sulfate) and 1/2CdSO4 (one-half formula unit of cadmium sulfate) in water + disaccharide mixtures are collected in Tables S2 and S3 (Supporting Information), respectively. The experimental data were analyzed using the Lee-Wheaton16-18 conductivity equation in the form suggested by Pethybridge and Taba.19,20 Three-parameter fits were used to obtain the limiting molar conductivity Λ0, the association constant KA, and the distance parameter R by nonlinear leastsquares iterations. The input data for the calculation of the coefficients were the solvent properties given in Table S1 (Supporting Information). The lower limit, a, of the association integral is the distance of closest approach of cation and anion (contact distance) a ) a + + a-
(2)
calculated from the ionic radii of the metal ions (a+ ) 0.330 nm for Cu2+ and a+ ) 0.103 nm for Cd2+) and SO42- (a- ) 0.258 nm).21 From extended investigations on electrolyte
solutions in amphiprotic hydroxylic solvents (water, alcohols), it is known that the upper limit of association is given by an expression of the type R ) a + ns
(3)
where s is the length of an oriented solvent molecule and n is an integer, n ) 0, 1, 2,... Here, s is the length of an OH group, dOH, and s ) dOH) 0.28 nm. The limiting molar conductivity, Λ0, and the association constant, KA, which were obtained by fitting at R ) a + 1s are summarized in Table 1, together with values given in the literature.22 All of the divalent metal sulfates investigated are strongly hydrated salts and exhibit very similar properties in dilute aqueous solutions.23 As shown in Table 1, the Λ0 values for 1 /2CuSO4 and 1/2CdSO4 decrease with increasing mS. This behavior can be ascribed to the facts that (i) with the decrease in dielectric constant of the mixtures, the electrostatic attraction between the ions increases, and hence, the number of ions in the free state decrease; (ii) the possible association of cation and disaccharide reduces the ionic mobility; and (iii) with the increase in microscopic viscosity of the mixed solutions, the mobility of ions decreases. For a given electrolyte, the limiting molar conductivities in aqueous sucrose solutions are higher than those in aqueous trehalose solutions (see Figure 1). Based on the conclusions of Galema et al.24 and Barone et al.,25,26 sucrose fits better into the structure of water than does trehalose, and the hydrogen bonds of the former with water are stronger than those of the latter. Consequently, the viscosities of trehalose + water solutions are higher, and the ionic mobilities in trehalose + water solutions are lower. For a given disaccharide + water solution, the limiting molar conductivities are in the order CdSO4 > CuSO4, indicating that the hydrated radii are in the order Cu2+ > Cd2+. Both Cu2+ and Cd2+ have two net positive charges, but they have different ionic radii (see Table 2).21 The smaller Cu2+ ions, with a higher surface charge density, could associate a greater number of solvent molecules to form a larger entity with lower mobility. Therefore, the hydrating capacity of Cu2+ is stronger. This is confirmed by the hydration number of Cu2+/Cd2+ (see Table 2).27 Figure 2 shows that the association constants (KA) increase with increasing disaccharide molality, and for given electrolyte,
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Figure 1. Variation with saccharide molality of the limiting molar conductivities of 1/2CuSO4 and 1/2CdSO4: 9, sucrose + CuSO4; b, sucrose + CdSO4; 2, trehalose + CuSO4; 3, trehalose + CdSO4.
Figure 3. Variation with saccharide molality of the Walden products of 1 /2CuSO4 and 1/2CdSO4: 9, sucrose + CuSO4; b, sucrose + CdSO4; 2, trehalose + CuSO4; 3, trehalose + CdSO4.
Table 2. Values of Ionic Radii (r) and Hydration Number (n) for Cu2+ and Cd2+
remains unchanged. As shown in Figure 3, the absolute values of the Walden product (Λ0η0) increase slowly with increasing mS. According to the uncertainties in the experimental viscosity and conductivity, it can be reasonably expected that some experimental points will deviate from the linear relation, but this does not influence the increasing tendency. This suggests that these ions do not have the same effective radius in different solvent compositions and consequently provides evidence for the solvation of the ions in solution. Similar phenomena have been observed in other mixtures of water with organic cosolvents.30,31 This behavior seems to be caused by the preferential solvation of ions by water molecules that, in turn, verifies that the change in the microscopic viscosity related to the addition of saccharide is smaller than the change in the macroscopic viscosity (the so-called “sorting effect”32). Furthermore, with mS increasing, the interactions of ions with saccharides are stronger, leading to larger radii of the solvated ions and thus decreasing ion mobility. In addition, the deviation of the Walden product in disaccharide + water systems from that in water is in the order sucrose >trehalose. This indicates that the interactions of sucrose with the electrolytes are stronger than those of trehalose.
a
rp (Å) 2+
Cd Cu2+ a
0.97 0.72
r
a G
(Å)
1.03 0.72
n
b theory
12.4 13.4
b average
n
12 12.2
Taken from ref 21. b Taken from ref 27.
Figure 2. Variation with saccharide molality of the association constants (KA) of CuSO4 and CdSO4: 9, sucrose + CuSO4; b, sucrose + CdSO4; 2, trehalose + CuSO4; 3, trehalose + CdSO4.
the values of KA are larger in trehalose + water solutions. With decreasing dielectric constant of the mixed solvent, the electrostatic attraction between cations and anions increases, and the association degree enhances; consequently, the values of KA increase with increasing saccharide molality. The association degree is stronger in trehalose + water solutions, confirming that the interactions of sucrose with the electrolytes are stronger than those of trehalose. To eliminate the influence of macroscopic viscosity on the ionic mobility, the viscosities of the mixtures were determined using the method reported in the literature.28 The values of the Walden product (Λ0η0) were calculated and are also included in Table 1. An increase in viscosity leads to a decrease in conductivity. This effect was formulated quantitatively by the Walden rule,29 which states that the product Λ0η0 should be approximately constant for a given electrolyte, irrespective of the nature of the solvent, provided that the radius of the ion
4. Conclusions The conductivities of CuSO4 and CdSO4 in aqueous disaccharide (sucrose and trehalose) solutions were measured. The limiting molar conductivities (Λ0), association constants (KA), and Walden products (Λ0η0) were calculated. The Λ0 values were found to decrease with increasing mS, and KA was found to increase with increasing saccharide molality. The Λ0η0 values increased with increasing saccharide molality for both disaccharides, which is ascribed to the preferential solvation of the ions by water molecules. The deviations of the Walden product in disaccharide + water systems from those in water is in the order sucrose > trehalose, indicating that the interactions of sucrose with the electrolytes are stronger than those of trehalose. Acknowledgment Financial support from the Innovation Foundation of Colleges and Universities of Henan Province and the National Natural Science Foundation of China (No. 20673033) is gratefully acknowledged.
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List of Symbols c ) concentration C ) cell constant D ) relative dielectric constant K ) cell constant KA ) association constant mS ) molality of saccharide n ) hydration number r ) ionic radii R ) distance parameter t0 ) flow time Greek Letters η ) viscosity F ) density Λ ) molar conductivity Λ0 ) limiting molar conductivity
Supporting Information Available: Densities, viscosities, and dielectric constants of water and water + disaccharide mixtures (Table S1). Solution densities and molar conductivities of 1/2CuSO4 (Table S2) and 1/2CdSO4 (Table S3) in water + disaccharide mixtures. This material is available free of charge via the Internet at http://pubs.acs.org. Literature Cited (1) Lerbret, A.; Bordat, P.; Affouard, F.; Descamps, M.; Migliardo, F. How Homogeneous Are the Trehalose, Maltose, and Sucrose Water Solutions? An Insight from Molecular Dynamics Simulations. J. Phys. Chem. B 2005, 109, 11046–11057. (2) Tomsˇicˇ, M.; Besˇter-Rogacˇ, M.; Jamnik, A.; Neueder, R.; Barthel, J. Conductivity of Magnesium Sulfate in Water from 5 to 35°C and from Infinite Dilution to Saturation. J. Solution Chem. 2002, 31 (1), 19–31. (3) Besˇter Rogacˇ, M.; Babicˇ, V.; Perger, T. M. Conductometric study of ion association of divalent symmetric electrolytes: I. CoSO4, NiSO4, CuSO4 and ZnSO4 in water. J. Mol. Liq. 2005, 118, 111–118. (4) Katayama, S. Conductimetric determination of ion-association constants for calcium, cobalt, zinc, and cadmium sulfates in aqueous solutions at various temperatures between 0°C and 45°C. J. Solution Chem. 1976, 5, 241–248. (5) Zhuo, K. L.; Chen, Y. J.; Wang, W. H.; Wang, J. J. Volumetric and Viscosity Properties of MgSO4/CuSO4 in Sucrose + Water Solutions at 298.15 K. J. Chem. Eng. Data 2008, 53, 2022–2028. (6) Zhuo, K. L.; Wang, J. J.; Yue, Y. K.; Wang, H. Q. Volumetric properties for the monosaccharide (D-xylose, D-arabinose, D-glucose, D-galactose)-NaCl-water systems at 298.15 K. Carbohydr. Res. 2000, 328, 383–391. (7) Zhuo, K. L.; Wang, J. J.; Wang, H. Q.; Yue, Y. K. Densities, apparent molar volumes, and interaction parameters for the monosaccharide (D-xylose, D-arabinose, D-glucose, D-galactose)-NaBr-water systems at 298.15 K. Z. Phys. Chem. 2001, 215, 561–573. (8) Zhuo, K. L.; Wang, J. J.; Zheng, H. H.; Xuan, X. P.; Zhao, Y. Volumetric parameters of interaction of monosaccharides (D-xylose, Darabinose, D-glucose, D-galactose) with NaI in water at 298.15 K. J. Solution Chem. 2005, 34, 155–170. (9) Kell, G. S. Density, Thermal Expansivity, and Compressibility of Liquid Water from 0° to 150°C: Correlations and Tables for Atmospheric Pressure and Saturation Reviewed and Expressed on 1968 Temperature Scale. J. Chem. Eng. Data 1975, 20, 97–105. (10) Weir, R. D. On the conversion of thermodynamic properties to the basis of the International Temperature Scale of 1990. J. Chem. Thermodyn. 1996, 28, 261–276. (11) James, C. J.; Mulcahy, D. E.; Steel, B. J. Viscometer calibration standards: Viscosities of water between 0 and 60 °C and of selected aqueous
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sucrose solutions at 25 °C from measurements with a flared capillary viscometer. J. Phys. D: Appl. Phys. 1984, 17, 225–230. (12) Yan, Z. N.; Wang, J. J.; Lu, J. S. Viscosity behavior of some R-amino acids and their groups in water-sodium acetate mixtures. Biophys. Chem. 2002, 99, 199–207. (13) Chen, Y. J.; Zhuo, K. L.; Kang, L.; Xun, S. J.; Wang, J. J. Dielectric Constants for Binary Saccharide-Water Solutions at 278.15∼313.15 K. Acta Phys.-Chim. Sin. 2008, 24 (1), 91–96. (14) Harned, H. S.; Owen, B. B. The Physical Chemistry of Electrolytic Solutions, 3rd ed.; Reinhold: New York, 1958; pp 158-193. (15) Barthel, J.; Feuerlein, F.; Neueder, R.; Wachter, R. Calibration of conductance cells at various temperatures. J. Solution Chem. 1980, 9, 209– 219. (16) Lee, W. H.; Wheaton, R. J. Conductance of Symmetrical, Unsymmetrical and Mixed Electrolytes. J. Chem. Soc., Faraday Trans. 2 1978, 74, 743–766. (17) Lee, W. H.; Wheaton, R. J. Conductance of Symmetrical, Unsymmetrical and Mixed Electrolytes. J. Chem. Soc., Faraday Trans. 2 1978, 74, 1456–1482. (18) Lee, W. H.; Wheaton, R. J. Conductance of Symmetrical, Unsymmetrical and Mixed Electrolytes. J. Chem. Soc., Faraday Trans. 1 1979, 75, 1128–1145. (19) Pethybridge, A. D.; Taba, S. S. Precise Conductometric Studies on Aqueous Solutions of 2:2 Electrolytes. J. Chem. Soc., Faraday Trans. 1 1982, 78, 1331–1344. (20) Pethybridge, A. D.; Taba, S. S. Precise Conductometric Studies on Aqueous Solutions of 2:2 Electrolytes. J. Chem. Soc., Faraday Trans. 1 1980, 76, 368–376. (21) Barthel, J. M. G.; Krienke, H.; Kunz, W. Physical Chemistry of Electrolyte Solutions: Modern Aspects; Springer: New York, 1998. (22) Acevedo, V. H.; DeMoran, J. A.; Sales, L. A. Conductimetric studies on aqueous solutions of electrolytes. 2. Conductivities of zinc sulfate. J. Chem. Eng. Data 1989, 34 (1), 101–102. (23) Bestˇer-Rogacˇ, M. Determination of the Limiting Conductances and the Ion-Association Constants of Calcium and Manganese Sulfates in Water from Electrical Conductivity Measurements. Acta Chim. SloV. 2008, 55, 201–208. (24) Galema, S. A. Stereochemical Aspects of Hydration of Carbohydrates in Aqueous Solutions. 3. Density and Ultrasound Measurements. J. Phys. Chem. 1991, 95, 5321–5326. (25) Barone, G. Physical of Aqueous Solutions of Oligosaccharides. Thermochim. Acta 1990, 162, 17–30. (26) Barone, G.; Castronuovo, G.; Doucas, D.; Elia, V. A.; Mattia, C. Excess Enthalpies of Aqueous Solutions of Monosaccharides at 298.15 K.: Pentoses and 2-Deoxy Sugars. J. Phys. Chem. 1983, 87, 1931–1937. (27) Conway, B. E. Ionic Hydration In Chemistry and Biophysics; Elsevier: New York, 1981; pp 582-606. (28) Zhao, C. W.; Ma, P. S.; Li, J. D. Partial molar volumes and viscosity B-coefficients of arginine in aqueous glucose, sucrose and L-ascorbic acid solutions at T ) 298.15K. J. Chem. Thermodyn. 2005, 37, 37–42. (29) Robinson, R. H.; Stokes, R. H. Electrolyte Solutions; Butterworth: London, 1955; p 125. (30) Gregorowicz, J.; Bald, A.; Szejgis, A.; Chmielewska, A. Gibbs Energy of Transfer and Conductivity Properties of NaI Solutions in Mixtures of Water with Butan-1-ol at 298.15 K, and Some Physicochemical Properties of Mixed Solvent. J. Mol. Liq. 2000, 84, 149–160. (31) Gregorowicz, J.; Bald, A.; Szejgis, A.; Zurada, M. Gibbs Energy of Transfer and Conductivity Properties of NaBr Solutions in Mixtures of Water with Propan-1-ol at 298.15 K. J. Mol. Liq. 1999, 79, 167–176. (32) Kay, R. L.; Broadw, T. L. Mixtures. 3. Ionic Conductances in Ethanol-Water Mixtures at 10 and 25 °C. J. Solution Chem. 1976, 5, 57– 76.
ReceiVed for reView January 10, 2009 ReVised manuscript receiVed April 29, 2009 Accepted May 22, 2009 IE900041W
