J. CHEM. SOC. FARADAY TRANS., 1994, 90(21), 3281-3285 Mean Activity Coefficients of NaCl in Glucose-Water and Sucrose-Water Mixtures at 298.15 K Jianji Wang,* Wenbin Liu, Jing Fan and Jinsuo Lu Department of Chemistry, Henan Normal University, Xinxiang, Henan 453002, People's Republic of China The mean activity coefficients of NaCl in aqueous solutions of 10, 20 and 30 mass% sugar (glucose and sucrose) have been determined at 298.15 K from emf measurements in the molality range 0.006-2.0 rnol kg-'. The results have been analysed by using the Debye-Huckel extended equation and the Pitzer equation. There is good agreement between the results obtained from these theoretical models. It has been shown that two parameters of the Pitzer equation, fl(O) and ,!?('), increase linearly with the increasing reciprocal of the relative permittivity for the mixed solvents as well as the mole fraction of sugar in the mixed solvents.A similar linear relationship was also found for the ion-interaction parameter, C, of the Debye-Huckel extended equation. There is a growing interest in the determination of activity coefficients of electrolytes in mixed solvents, particularly at high electrolyte molalities. This interest is, in part, because of applications in such areas as the quantitative determination of Gibbs energies of dilution,' calculation of thermodynamic solubility products (together with solubility) and transfer Gibbs energies of electrolyte into mixed solvents,2 and pre- diction of vapour-liquid equilibrium data of ternary systems containing salt,3 where it is essential to have accurate activity coefficient values for electrolyte in mixed solvents.There have been many studies on the determination of activity coefficients for electrolytes in mixed However, most of these are the 'by-products' of measure- ments of other thermodynamic properties, such as Gibbs energies. These data are usually limited to very low electro- lyte molalities. Relatively few studies on the activity coeffi- cients at high electrolyte molalities in mixed solvents have been rep~rted.~.~-' Recently, we have investigated the solvation of some elec- trolytes in glucose-water and sucrose-water mixtures as well as the interactions of the electrolytes with glucose and sucrose in water.' '*I2 As part of the continuing study of ther- modynamic properties of water-sugar-electrolyte systems, we now report the mean activity coefficients of NaCl in aqueous solutions of 10,20 and 30 mass% sugar (glucose and sucrose) in the electrolyte molality range ca.0.006-2.0 mol kg-'. Based on these activity coefficient data, Pitzer parameters, 8'') and /I(')and the Debye-Hiickel ion-interaction param- eter, C, for NaCl were determined in different aqueous sugar solutions and are discussed in terms of the properties of the mixed solvents It was expected that this investigation would provide additional information on ion-ion interactions in these ternary systems. Experimental Reagents Anhydrous glucose (analytical reagent, Shanghai Chem.Co.) and sucrose (analytical reagent, Beijing Chem. Co.) were dried under vacuum at 343 K to constant weight and stored over P20, in a desiccator before use. NaCl (analytical reagent, Shanghai Chem. Co.) was recrystallized and dried under vacuum. Conductivity water with a conductivity of 1.2 pQ-' cm-' was prepared by distilling the deionized water from basic KMnO, in an all-Pyrex still. In order to minimise the experimental error, stock aqueous NaCl solutions were used to prepare sugar-NaC1-water ternary solutions when the concentrations of NaCl were below 0.1 mol kg-'. In other cases, all test solutions were made by direct weighing of water, sugar and NaC1. Determination of Activity Coefficients The emf method for determination of the activity coefficients of NaCl in aqueous sugar solutions was chosen.The differ- ence in emf of the cell (A) relative to the reference cell (B): Na glass INaCl(m), H20( 100-Y) ,sugar(Y)I AgCl I Ag (A) Na glass I NaCl(m,), H20(100-Y) , sugar(Y) I AgCl I Ag (B) was determined over a range of electrolyte molalities. In cells (A) and (B), m is the molality of electrolyte defined per kg of (sugar-water) mixture and Y mass% the amount of sugar in the mixed solvents. The purpose of introducing the reference cell (B) is to compensate the asymmetry potential of the glass electrode. The molaity of NaCl in cell (B), m,,was kept con- stant for each given solvent. A sodium-glass electrode, model 312 (Jiangsu, China) was used in this work.The Ag/AgCl electrodes were prepared by a thermal-electrolytic method. I3 The measurements were per- formed only with Ag/AgCl electrodes whose potentials showed an internal difference of less than 0.04 mV. The Nern- stian behaviour of the sodium-glass electrode was checked by measuring the difference in emf between cells (A) and (B) when Y = 0 (pure water) with the molality of NaCl varying between 0.006 and 2.0 mol kg-' (see Table 1, later). Using activity coefficients of NaCl in water calculated by the empirical equation recommended by Hamer and Wu,14 an excellent linear relationship with a correlation coefficient of 0.999996 was obtained between AE and log(my,) [see eqn. (1) later]. From the slope of this linear equation, the Nernst slope was found to be 59.10 f0.04 mV, which is in excellent agreement with the theoretical value.The H-shaped measuring cells were made of Pyrex glass. Emf measurements on cells (A) and (B) were carried out using an Orion PH meter (model 720A) with a resolution of 0.1 mV. In all measurements, the temperature inside the cells was kept constant at 298.15 f0.02 K by using a thermostatted water bath. To provide highly accurate experimental results, the method for eliminating the asymmetry potential proposed by Feakins et al." was applied. The experimental details are similar to those described in our earlier papers.' The molality of NaCl in cell (A) varies from CQ. 0.006 to 2.0 mol kg-' for each given solvent, whereas that in reference cell (B) was always constant at CQ. 0.1 mol kg-'.The molality of NaCl in all the cell solutions was accurate to ca. 0.02%. 3282 J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 The amount of sugar in the mixed solvents was known to Table 2 Experimental AE and yk values at different molalities of within kO.005mass%. NaCl in sucrose-water mixtures at 298.15 K rn/mol kg-' AE/mV yk rn/mol kg-' AEfmV Y+ Results Y=lO According to the Nernst equation, the difference in emf, AE, 0.005983 134.7 0.92 13 0.008001 120.4 0.9099 between cells (A) and (B) in a given solvent can be expressed 0.009998 109.5 0.9003 0.01OOO 109.4 0.9018 0.02000 76.2 0.8604 0.03000 56.65 0.8391by 0.03999 43.0 0.8210 0.O4001 42.9 0.8222 (1) 0.04999 32.65 0.8034 0.05999 23.85 0.7945AE = 2kN logCmr(y*),/myf1 0.08002 10.5 0.7723 0.09995" 0.0 0.7585 where kN = 2.303RT/F is the Nernst slope, yk and (y*), are 0.1500 -19.3 0.7358 0.2998 -51.65 0.6909 the activity coefficients of NaCl at concentrations m and M,, 0.4499 -70.75 0.6677 0.6005 -84.3 0.6512 respectively.The measured AEs for different molalities of 0.7998 -98.45 0.6439 0.9999 -109.9 0.6436 NaCl in water and in different glucose-water and sucrose- 1.1995 -119.1 0.6417 1.3985 -127.2 0.6444 1.5984 -133.95 0.6429 2.0001 -146.4 0.6546water mixtures are listed in Tables 1 and 2, respectively. Although the value of (y*), remains constant for each mixed Y = 20 0.005992 134.5 0.9 124 0.007999 120.2 0.9028solvent studied, it has to be known exactly in order to calcu- 0.01 000 109.25 0.8937 0.02000 76.1 0.8518late y* values in these mixed solvents.Therefore, the Debye- 0.02998 56.7 0.8289 0.03999 43.15 0.8089 Huckel extended equation and the Pitzer equation were used 0.04996 32.4 0.7981 0.05996 23.85 0.7854 here to determine (y*), values, together with the ion-0.08000 10.5 0.7633 0.09997" 0.0 0.7493 interaction parameters of these equations. 0.1500 -19.0 0.7230 0.3000 -51.52 0.6769 0.4500 -70.5 0.6564 0.5998 -84.2 0.6429 0.7998 -98.4 0.6356 1.OOO1 -109.65 0.6327 Table 1 Experimental AE and y* values at different molalities of 1.2000 -119.25 0.6356 1.3994 -127.35 0.6381 NaCl in water and in glucose-water mixtures at 298.15 K 1.5996 -134.65 0.6435 1.9997 -147.4 0.6597 Y = 30 m/mol kg-' AEImV y* m/mol kg-' AE/mV y* 0.007995 119.5 0.9OOo 0.01197 99.85 0.8811 0.02008 75.35 0.8452 0.02996 56.35 0.8208Y=O 0.o4001 42.95 0.7977 0.04988 32.45 0.7849 0.006000 135.7 0.9222 0.008002 122.1 0.9010 0.06Ooo 23.65 0.7744 0.06003 23.75 0.7725 0.009998 111.2 0.8915 0.02000 76.5 0.8755 0.07 9 9 9 10.4 0.7518 0.09999" 0.0 0.7363 0.02999 57.0 0.8534 0.04000 43.2 0.8369 0.1201 -8.65 0.7254 0.1500 -18.8 0.7076 0.05000 32.8 0.8197 0.06001 23.95 0.8114 0.3000 -51.35 0.6666 0.4500 -70.4 0.6439 0.08002 10.5 0.7905 0.1oOo" 0.0 0.7761 0.6002 -84.2 0.6315 0.8009 -98.65 0.6269 0.1250 -10.75 0.7653 0.1500 -18.95 0.7480 0.9998 -109.9 0.6251 1.1988 -119.8 0.6321 0.3000 -51.4 0.7033 0.4502 -70.5 0.6797 1.4005 -127.95 0.6340 1.6015 -135.4 0.6410 0.6OoO -84.3 0.6671 0.8002 -98.2 0.6556 2.001 1 -148.4 0.6606 1.0003 -109.3 0.6509 1.1985 -118.6 0.6510 1.3991 -126.5 0.6504 1.5957 -133.65 0.6554 " Molality of NaCl in reference cell (B).1.9963 -145.95 0.6655 Y=lO 0.005998 134.05 0.9307 0.007994 120.45 0.9099 For a 1 :1 electrolyte, the Debye-Huckel extended 0.00999 1 109.95 0.8930 0.02000 76.2 0.8604 equation16 is given by 0.02997 56.75 0.8383 0.03999 42.95 0.8218 log y* = -Am'/'/(l +Biim'/')0.04999 32.55 0.8049 0.05991 24.25 0.7894 0.08000 10.35 0.7748 0.09999" 0.0 0.7582 +Cm -log(1 +0.002mMJ (2)0.1495 -18.9 0.7325 0.2998 -51.6 0.6903 0.4497 -70.1 0.6596 0.5994 -84.35 0.6530 where d is the ion size parameter, C the ion-interaction 0.7995 -98.4 0.6435 0.9999 -109.7 0.6411 parameter and M, the mean molar mass of the mixed solvent.1.1985 -119.05 0.6416 1.3995 -127.15 0.6433 1 S994 -134.1 0.6444 1.9983 -146.7 0.6591 A and B are the conventional Debye-Huckel constants given by the equations Y = 20 0.007993 119.25 0.9054 0.009998 108.2 0.8975 A/(mol-'/' kg1I2 K3/') = 1.8246 x 106d'/'(&,T)-3/2 (3)0.02000 75.2 0.8528 0.02998 56.0 0.8266 B/(cm-'mol-'/' kg'" K'12) = 50.29d'/'(~,T)-'/~ (4)0.03998 42.45 0.8069 0.05000 32.1 0.7891 0.05996 23.65 0.7757 0.08000 10.35 0.7531 0.09995" 0.0 0.7373 0.1500 -19.0 0.7111 where d and E, are the density and relative permittivity of the 0.2999 -51.2 0.6655 0.4498 -70.3 0.6435 solvent, respectively. For the sugar-water mixtures studied, 0.6004 -84.25 0.6325 0.7995 -98.0 0.6207 density values were calculated from the equations given by 0.9993 -109.55 0.6217 1.1997 -118.7 0.6188 Daldrup and Schonert.' Values of the relative permittivity 1.3992 -127.45 0.6291 1.5991 -134.5 0.6314 were taken from the 1.9994 -147.65 0.6522 Inserting eqn. (2)into eqn.(l),it follows that Y = 30 0.009998 107.7 0.8940 0.01999 74.75 0.8490 AEd =AE +2kN log(m/rn,) -2k,[Am"2/(1 +B6m1/')] 0.02998 56.25 0.81 14 0.03999 42.6 0.7934 -2kN lOg(1 +0.002mM30.04998 32.0 0.7803 0.05996 23.8 0.7629 0.08000 10.25 0.7443 0.09999" 0.0 0.7270 0.1500 -18.7 0.6973 0.3001 -51.0 0.6535 0.4500 -70.2 0.6333 0.5997 -83.9 0.6204 It is clear from this equation that there is a linear relationship 0.7954 -97.7 0.6118 1.0003 -109.7 0.6145 between AEd and m. A least-squares analysis was used to 1.1999 -119.4 0.6187 1.4OOO -127.9 0.6256 1.6006 -135.3 0.6320 2.0011 -148.3 0.65 10 determine (y*), and the parameter C for each of the mixed solvents from the experimental AEs listed in Tables 1 and 2." Molality of NaCl in reference cell (B). The values obtained are shown in Table 3, together with their J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 Table 3 Parameters of the Debye-Huckel extended equation for Table 4 Parameters of the Pitzer equation for sugar-water mix-sugar-water mixtures at 298.15 K tures at 298.15 K glucose-water 0 0.7763 0.0011 0.0536 0.0008 3.9 0.26 -0.9984 10 0.7580 0.0012 0.0666 O.ooo9 3.6 0.28 -0.9985 20 0.7366 0.0012 0.0848 O.ooo9 3.2 0.27 -0.9991 30 0.7264 0.0013 0.0903 0.0010 3.4 0.30 -0.9991 sucrose-water 10 0.7581 O.ooo9 0.0634 0.0007 3.7 0.22 -0.9989 20 0.7489 O.OOO5 0.0730 O.OOO4 3.7 0.12 -0.9998 30 0.7354 0.0007 0.0805 O.OOO6 3.8 0.18 -0.9995 standard deviations, s, and s, ,respectively, the standard devi- ation of the fit, 6,and the correlation coefficient, R.In the regressions, h was regarded as an adjustable parameter. The optimum 4 values will be those which lead to a minimum standard deviation of the fit. Values of h are also included in Table 3. The relevant equations for the activity coefficients of 1 : 1 electrolyte derived by PitzerZ0 are In yk =f, + B,rn + C,m2 (6) where f,= -A 4JX B, = 2p'"' + 2B"'y and y = [I -exp(-arn'/2)(1 + -0.5a2rn)]/(a2rn) In the above equations, b and a are parameters, A, is the Debye-Huckel coefficient for the osmotic functions. At 298.15 K A, can be calculated from eqn.(7) A mol-'/2 kg'/2) = 272.058d'/2 E~-~/~ (7) It have been shown by Koh et d2'that the same values of b and 01 for aqueous solutions could be used for the methanol- water mixtures without greatly affecting the standard devi- ation of the fit. Therefore, the values of b = 1.2 kg'/2 mol- 'I2 and a = 2.0 kg'j2 mol-'/2 were used in the present calcu- lations. In addition, for electrolytes whose concentrations do not exceed 2 mol kg-', the term containing C,in eqn. (6), which accounts for triple ion short-range interactions, may be neglected.20 At least, this is true for the water-rich mixed solvents.8 Bearing these simplifications in mind, and intro- ducing eqn.(6) into eqn. (l), the following equation was obtained AEp = AE + (2RT/F)ln(rn/mr)+ (2RT/F)f, = (2RT/F)ln(y,), -(4RT/F)B(")rn-(RT/F)@') The experimental AEs at different electrolyte molality for each of the mixed solvents were fitted to eqn. (8) by a multi- ple regression program with the A, values calculated from the density" and relative for the different sugar-water mixtures investigated. The values of (y*),, /I(') and /?('I are summarised in Table 4 together with their stan- dard deviations sr, so and sl, respectively, and the standard deviation of the fit, 6. As can be seen from Tables 3 and 4, within experimental error, there is a good agreement between the (y*), values glucose-water 0 0.7759 0.0015 0.0813 0.0024 0.231 0.016 0.25 10 0.7584 0.0018 0.0940 0.0030 0.232 0.020 0.30 20 0.7380 0.0018 0.1117 0.0030 0.251 0.020 0.30 30 0.7275 0.0022 0.1227 0.0034 0.294 0.023 0.33 sucrose-water 10 0.7588 0.0013 0.0899 0.0024 0.256 0.015 0.24 20 0.7496 0.0008 0.1028 0.0013 0.296 0.009 0.14 30 0.7371 0.0017 0.1142 0.0029 0.368 0.020 0.29 obtained from the two theoretical models for each of the mixed solvents.Therefore, the mean of two (y*), values for a given solvent was used to calculate the y* for NaCl in this solvent by using eqn. (1). The yk values thus obtained are also included in Tables 1 and 2. Discussion In the molality range studied, the standard deviation of the activity coefficients between our experimental values and those reported in the literat~re'~ was calculated to be k0.005 in pure water solvent.Considering the fact that the two sets of y* data were determined by different experimental tech- niques, it would appear that the agreement between our values and those from the literature is quite good. To the best of our knowledge, no activity coefficient data for NaCl in glucose--water and sucrose-water mixtures have been re-ported in the literature. Analysis of the activity coefficient data for NaCl in sugar- water mixtures shows some interesting features. As the pro- portion of the mixed solvent is fixed, the activity coefficients first decrease and then increase with increasing molality of the electrolyte. On the other hand, they decrease with increasing content of sugar in the mixed solvents when the molality of the electrolyte is fixed.Similar trends of the activ- ity coefficient have been noticed for NaBr in methanol-water rnixt~res,~for NaCl in ethanol-water mixtures' and for HCl in aqueous solutions of methan01,~ ethanol, glycerol and 1,4-dioxane.lo The Pitzer equation was based on a semiempirical theory of statistical mechanics. Although this equation has been used successfully for representing activity coefficients of elec- trolyte in mixed solvent^,^^^.^ not much effort has been devoted to understanding the nature of the Pitzer parameters in mixed solvents.2'.22 Values of pC0)and fl(') determined in this work are positive in all the solvents, indicating a net repulsive force in short- range interactions and positive second virial coefficients in sugar-water-NaC1 systems.22 This is the typical profile observed with 1 : 1 electrolytes (and most others) in aqueous solutions.23 Furthermore, it is interesting to note that both Po)and /3(') vary linearly with the reciprocal of relative per- mittivity for sugar-water mixtures (see Fig.1 and 2). Similar linear plots can also be obtained between these parameters and the mole fraction of sugar in the mixed solvents. On further analysis of the results of alkali-metal chlorides and HCl in methan~l-water~.~' and of NaCl in ethanol-water,' it is shown that B(") and /?(I) for these electrolytes in these solvent mixtures indeed increase linearly with increasing 1/~,, except for LEI, KC1, RbCl and CsCl in methanol-water sol-vents, where the values for /?(") are almost constant or decrease slightly with increasing 1/~,.An example is given in Fig. 3. 3284 -r6 s 's 0.0 1.2 1.3 1.4 1.5 102/E, Fig. (0)P(') and (0)B(')for NaCl in glucose-water mix ires as a function of relative permittivity In the discussion of hard-core effects on osmotic and activ- ity coefficients in terms of the extended form of the Debye- Huckel theory, Pitzer2' has pointed out that B(')would be a function of rc2. Because ic2 involves the reciprocal of the rela- tive permittivity as shown in eqn. (9), it is expected that /3(') would be a function of 1/~,.rc2 = 2e2~, E~ kT) (9)rnd/(~, 0.4 0.3 6 o^60.2 0.1 0.0 1.2 1.3 1.4 1.5 102/&, Fig. 2 (0)B(O) and (0)8"' for NaCl in sucrose-water mixtures as a function of relative permittivity 2.0 1.5 -r -P 1.0 s 's 0.5 v0.0 ' -1.o 1.5 2.0 2.5 3.0 102/&, Fig. 3 (0)B'O) and (0)B(') for NaCl in methanol-water mixtures as a function of relative permittivity J. CHEM. SOC. FARADAY TRANS., 1994, VOL. 90 where k is the Boltzmann constant and other symbols have their usual meanings. According to Pitzer,20 the main contribution to /?(') comes from the short-range interactions of unlike charged ions, while B(O) is determined by the short-range interactions of both like and unlike charged ions.The radial distribution functions at hard-core contact, g+ -, g+ + , g--, therefore, contribute in weighted proportion to #I(')whereas only g+ -contribute to /3('). In Pizter's thermodynamic treatment of electrolyte solutions, there is no explicit dependence of /?(') on relative permittivity. However, the radial distribution func- tions at hard-core contact were found to be a function of the relative permittivity of the solvents.22 Thus the dependence of pCo)on E, observed in the present investigation is understand- able. The radial distribution functions, g+ -,g+ + and g--,for methanol-water mixtures have been calculated by Gupta22 from an exponential form of the Debye-Huckel theory, which has been proven by Monte Carlo calculations to give identi- cal results for aqueous 1 : 1 electrolyte up to 0.4 mol kg-'.24 It has been shown that g+ -increases whereas g+ + and g--decrease with increasing content of methanol in the mixed solvents. Using the same equations, we have calculated these radial distribution functions at hard-core contact for glucose- water, sucrose-water and ethanol-water mixtures.The same trends of g+ -, g+ + and g--with the composition of the organic component in these mixed solvents as in methanol- water mixtures were observed. Since the relative permittivity of the solvents studied decreases with increasing content of the organic component in the mixed s~lvents,~*'~*'~~~~ it is expected that /3(') would increase with 1/~,.This is consistent with the results discussed above. Moreover, as 8'') values for NaCl in aqueous solutions of glucose, sucrose, methanol and ethanol, and for HCI in aqueous methanol solutions are found to increase with increasing l/~,,it would appear that they are influenced more by the interactions of unlike-charged ions than by those of like-charged ions in these systems. On the contrary, /3(") values decrease with increasing 1/~,for the other alkali-metal chlorides in methanol-water mixtures, indicating that in these cases the parameters are influenced more by the interactions of like-charged ions. Finally, it is interesting to note that the Debye-Huckel ion- interaction parameter, C, is numerically close to @') for each of the sugar-water mixtures. Also, it increases linearly with 1/~,and the mole fraction of sugar in the mixed solvents studied.Financial support from the Natural Science Foundation of China and the Natural Science Foundation of Henan Prov- ince is gratefully acknowledged. References 1 J. A. Rard, J. Solution Chem., 1990, 19, 525. 2 J. W. Lorimer, Pure Appl. Chem., 1993,65, 183. 3 H. Pan, S. Han and Y. Yao, J. Chem. Znd. Eng. (China), 1992,43, 360. 4 A. K. Covington and T. Dickinson, Physical Chemistry of Organic Soloent Systems, Plenum Press, New York, 1973. 5 Y.Macpherson and R. Palepu, Can. J. Chem., 1993,71,2038; D. Chu, Q. 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