J. Chem. Thermodynamics 36 (2004) 957–964 www.elsevier.com/locate/jct
Activity coefficients of NaF in (glucose + water) and (sucrose + water) mixtures at 298.15 K Felipe Herna´ndez-Luis
a,*
, He´ctor R. Galleguillos b, Mario V. Va´zquez
c
a
Departamento de Quı´mica Fı´sica, Universidad de La Laguna, Tenerife, Spain Departamento de Ingenierı´a Quı´mica, Universidad de Antofagasta, Antofagasta, Chile Instituto de Quı´mica, Facultad de Ciencias Exactas y Naturales, Universidad de Antioquia, Medellı´n, Colombia b
c
Received 22 December 2003; received in revised form 4 May 2004; accepted 2 July 2004
Abstract The activity coefficients of NaF in (glucose + water) and (sucrose + water) mixtures were experimentally determined at 298.15 K from electromotive force measurements of the following electrochemical cell containing two ion selective electrodes (ISEs): Na ISEjNaFðmÞ; sugarðY Þ; H2 Oð100 Y ÞjF ISE The molality (m) varied between ca. 0.01 mol Æ kg1 and saturation, while the mass fractions of sugar in the mixture (Y) were 0, 0.10, 0.20, 0.30 and 0.40. The values for electromotive force were analyzed using different models for describing the variations of the activity coefficients with concentration, including an extended Debye–Hu¨ckel, the Pitzer and the Scatchard equations. Results obtained with the different models were in good agreement. Once E was determined, the mean coefficients of ionic activity for NaF, the free energy of transference from the water to the (sugar + water) mixture, and the primary NaF hydration number were calculated. The variation of these magnitudes with the composition of the mixture is comparative discussed in terms of the ion–solvent and ion–ion interactions with results from the literature for NaCl in (glucose + water) and (sucrose + water) systems. 2004 Published by Elsevier Ltd. Keywords: emf; Activity coefficients; Electrolytes; NaF; Glucose; Sucrose; Ionic interaction
1. Introduction It is well known that in recent decades there has been a marked increase in interest in the understanding of thermodynamic properties of multicomponent electrolytic systems, particularly for those which, due to their composition, are important in industrial, biological or environmental terms. Both activity coefficients and other related magnitudes such as osmotic coefficients, solvent activity,
*
Corresponding author. Fax: +34 922 318514. E-mail address: ff
[email protected] (F. Herna´ndez-Luis).
0021-9614/$ - see front matter 2004 Published by Elsevier Ltd. doi:10.1016/j.jct.2004.07.002
Gibbs free energy of the mixture (or of transfer) allow us to analyse the ion–solvent and ion–ion interactions occurring in the medium, as well as the structural implications played by the different components. Within multicomponent systems those of the (electrolyte + sugar + water) type are especially important for understanding the behaviour of sugars in living organisms. Many sugars carry out important functions in physiological processes. Such sugars are not only primary energy sources but also play key roles in the formation of macromolecules essential in many essential biochemical processes. Relatively few studies have been made, however, which contribute thermodynamic data on these multicomponent systems, especially at high
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concentrations. Among these the more notable are the studies of Morel et al. [1–3] and Wang et al. [4–12]. In two previous studies [13,14], we have undertaken the study of some thermodynamic processes in (NaCl + sugar + water) systems. The present closely related study includes the determination of mean ionic activity coefficients in aqueous NaF solutions containing both glucose and sucrose in an attempt to provide fundamental knowledge on ionic interactions in (electrolyte + sugar + water) solutions in relation to the structure and properties of the medium. The concentration of NaF varied between 0.01 mol Æ kg1 and saturation, while the mass fractions of sugar studied were 0, 0.10, 0.20, 0.30 and 0.40. The temperature was kept constant at 298.15 for all the studies. These studies were carried out using potentiometric techniques which have advanced markedly in recent decades due mainly to the development and improvement of new ion-selective electrodes (ISEs) [13–21]. Now, these electrodes are not only valuable for analytical use, but also may be employed in determining thermodynamic and transport magnitudes. The electrodes used in the present study are among those which have undergone recent development, in which a glass membrane is used for the Na+ and the solid state for the F. These electrodes have been shown to function accurately both in water and in organic–water solutions.
2. Experimental D -(+)-glucose (C6H12O6) and sucrose (C12H22O11) (Fluka, BioChemika 99.5%) was dried in vacuo at 330 K for 5 days before use. NaF (Merck, pro analysi 99.5%), was also dried in vacuo at 373 K for 5 days. Both were stored over silica gel in a desiccator and used without further purification. For each set of experiments (corresponding to a mass fraction of sugar) working solutions were obtained by adding successive known masses of solid NaF to a solution previously prepared of sugar and double-distilled water (k = 5 Æ 107 S Æ cm1). The precision of the molality was estimated to be about ±0.0001. The solutions were continually stirred with a magnetic stirrer. Na-ISE (mod. 6.0501.100) and F-ISE (mod. 6.0520.150) were obtained from Metrohm Corp. A double wall vessel Metrohm cell was used to hold the electrodes and the solution. The temperature in the cell was maintained constant at 25.00 ± 0.02 C using a Hetofrig model 04 PT thermoregulator and a platinum resistance thermometer (Guildline model 9540) was used to record the temperature. The emf measurements were carried out with a 614 Keithley Electrometer having an inner impedance greater than 5 Æ 1013 X with a resolution of ±0.1 mV. To obtain more precise emf readings, the 2 V analog
output of the electrometer was connected to a Keithley model 197A Microvolt DMM with an input greater than 1012 X and resolution of ±0.01 mV. Depending on the concentration of the NaF studied, and independently of the mass fractions of sugar in the mixture, it was observed that after approximately 45 min, the variation of the potential with time was very small [around (0.10 to 0.15) mV per (10 to 15) min]. The reading at this moment was considered to represent the cell in equilibrium.
3. Results Ionic mean activity coefficient values for NaF in (sugar + water) mixtures were determined from the emf measurements of the following galvanic cells without transference: Na ISEjNaFðmÞ; sugarðY Þ; H2 Oð100 Y ÞjF ISE ð1Þ In these cells, m is the molality of NaF (moles NaF/kg mixed-solvent) in the working solution in the mixed solvent and Y the mass fraction of sugar in the mixture. Applying the Nernst equation, the following expression is obtained: E ¼ E 2k lg mc;
ð2Þ
where E is the emf of the cell, k = (ln 10)RT/F is the Nernst slope and m and c are the molality and stoichiometric ionic mean activity coefficients of NaF. E* is the apparent standard potential (molal scale) of the cell and contains the potential of asymmetry of both selective electrodes [14–16]. In this study, these asymmetry potentials were always small and independent of the solvent composition. E values for different (sugar + water) mixtures as a function of the NaF molalities are shown in tables 1 and 2. Since the activity coefficients of the NaF in pure water are well known [22], the values of E that appear in table 1 for sugar mass fraction 0, allow carrying out a calibration of the electrode system, using equation (2). A very good linear relationship is obtained when E vs. lg mc is plotted. The value obtained when applying a least-squares regression analysis to the previous representation gives k = 60.46 ± 0.07 mV, with a correlation coefficient of 0.99999 and a standard deviation of 0.24 mV. This value of k differs only by about 2%, of the theoretical value. This exceeds acceptable levels for a system containing two ion selective electrodes. In this calculation it has been assumed that kNa @ kF @ k @ (kNa + kF)/2. The most important and decisive point in this type of study is determination of the apparent standard potential in the cell, E* with the greatest possible precision for each mixture studied, since this affects the accuracy
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TABLE 1 Experimental E and c values calculated for the NaF in the mixtures of (glucose + water) at 298.15 K Y=0
Y = 0.10
Y = 0.20
Y = 0.30
Y = 0.40
m
E
c
m
E
c
m
E
c
m
E
c
m
E
c
0.02710 0.05380 0.06928 0.08685 0.1248 0.1677 0.2315 0.2806 0.3506 0.4188 0.5047 0.6012 0.6683 0.7315 0.8183 0.8780 0.9492 0.9830
218.83 252.19 264.50 275.55 292.57 306.34 321.20 330.01 340.21 348.31 357.01 364.91 369.76 373.92 379.07 382.26 385.18 386.35
0.850 0.808 0.793 0.781 0.752 0.727 0.699 0.682 0.663 0.647 0.634 0.618 0.610 0.603 0.595 0.589 0.576 0.569
0.02858 0.05608 0.08176 0.1337 0.1656 0.2452 0.2875 0.3240 0.4096 0.4875 0.5799 0.6730 0.7692 0.8274 0.8467
223.46 256.54 274.58 297.74 307.81 325.89 333.23 338.52 349.33 357.25 364.84 370.31 376.89 380.03 381.29
0.840 0.804 0.777 0.739 0.723 0.688 0.675 0.663 0.644 0.629 0.611 0.584 0.580 0.572 0.573
0.02815 0.07149 0.1121 0.1573 0.2075 0.2791 0.3342 0.3817 0.4538 0.5493 0.6152 0.7010
227.05 272.88 293.65 309.03 321.55 334.72 342.65 348.68 356.71 365.34 370.53 376.65
0.813 0.767 0.726 0.694 0.667 0.638 0.619 0.608 0.596 0.580 0.572 0.564
0.00804 0.02128 0.05062 0.1115 0.1724 0.2213 0.2917 0.3329 0.3917 0.4428 0.5052 0.5360 0.5691 0.6075
170.67 219.76 261.47 298.42 318.80 330.24 343.14 349.34 357.00 362.68 368.84 371.60 374.47 377.56
0.879 0.846 0.787 0.722 0.689 0.667 0.647 0.638 0.627 0.618 0.609 0.605 0.602 0.598
0.05557 0.07516 0.08980 0.1171 0.1597 0.1957 0.2237 0.2573 0.2832 0.3216 0.3610 0.4056 0.4525 0.4859
272.97 287.40 295.93 308.16 322.46 331.22 337.50 343.99 348.30 354.05 359.33 364.70 369.80 373.08
0.747 0.727 0.716 0.693 0.667 0.643 0.634 0.624 0.616 0.605 0.596 0.587 0.580 0.575
Units: moles NaF/kg mixed-solvent for m; mV for E. TABLE 2 Experimental E and c values calculated for the NaF in the mixtures of (sucrose + water) at 298.15 K Y = 0.10
Y = 0.20
Y = 0.30
Y = 0.40
m
E
c
m
E
c
m
E
c
m
E
c
0.07745 0.1113 0.1836 0.2570 0.3300 0.4085 0.4859 0.5679 0.6571 0.7370 0.7990
274.35 291.76 315.27 330.71 342.08 351.70 359.77 367.00 373.73 378.93 382.14
0.771 0.748 0.709 0.680 0.657 0.638 0.625 0.614 0.603 0.594 0.582
0.02187 0.04784 0.07369 0.1112 0.1408 0.1974 0.2656 0.3400 0.3972 0.4618 0.5630 0.6289 0.6746 0.7207 0.7353
218.20 257.05 277.53 296.53 307.58 323.22 336.96 348.38 355.55 362.47 371.68 376.89 380.11 382.90 383.55
0.839 0.804 0.771 0.734 0.715 0.687 0.663 0.644 0.632 0.620 0.606 0.599 0.594 0.586 0.582
0.03707 0.05509 0.08452 0.1097 0.1562 0.1968 0.2413 0.2692 0.3022 0.3341 0.3672 0.4448 0.5295 0.5909 0.6086
250.03 269.52 289.59 301.98 318.61 329.38 338.82 343.94 349.30 353.28 357.83 366.55 375.13 380.19 381.54
0.801 0.781 0.746 0.727 0.701 0.683 0.667 0.659 0.650 0.634 0.630 0.613 0.607 0.599 0.597
0.03342 0.06648 0.09785 0.1366 0.1647 0.2261 0.2683 0.3370 0.3967 0.4804
251.52 285.25 303.70 319.36 328.14 342.92 350.87 361.49 369.10 377.92
0.807 0.771 0.744 0.718 0.704 0.680 0.666 0.649 0.638 0.623
Units: moles NaF/kg mixed-solvent for m; mV for E.
of the activity coefficients and the other thermodynamic functions subsequently calculated. The determination of E* was carried out following the method of Hitchcock [23] and using the extended equations of Debye–Hu¨ckel [24,25] for showing the dependency of lg c with concentration. For 1:1 electrolytes, this equations may be written as lgc ¼ Am1=2 =ð1þBam1=2 Þþcmlgð1þ0:002 mMÞþExt; ð3Þ with a the ion size parameter, c the ion-interaction parameter, M the average molecular mass of mixed solvent and Ext the contribution of the extended terms. A and B are the Debye–Hu¨ckel constants given by
A ¼ 1:8247 106 d 1=2 =ðer T Þ 3=2
3=2
kg1=2 mol1=2 ;
ð3aÞ
ð3bÞ B ¼ 502:901d 1=2 =ðer T Þ kg1=2 mol1=2 nm; where d, er and T stands for the density, relative permittivity (static dielectric constant) of the solvent and the temperature, respectively. For the (sugar + water) mixtures studied, density and relative permittivity were taken from the literature [26,27] and appear together with the constant A and B and the average molecular mass, M, in table 3. By combining equations (2) and (3), the values of E* can be optimised, as well as the interaction parameters characteristic of model. In table 4, these values are presented as well as the standard deviation of the fit.
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TABLE 3 Values of average molecular mass, relative permittivity, densities, Debye–Hu¨ckel and Pitzer constant as a function of the mass fraction of sugar in the (glucose + water) and (sucrose + water) mixtures at 298.15 K Y
M
er
d
A
B
A/
0
18.015
78.38
0.9971
0.5100
0.3285
0.3915
0.10 0.20 0.30 0.40
19.797 21.970 24.678 28.148
75.97 73.28 70.28 66.94
(Glucose + water) 1.0364 1.0781 1.1224 1.1699
0.5449 0.5866 0.6373 0.6999
0.3402 0.3533 0.3681 0.3850
0.4183 0.4503 0.4892 0.5373
0.10 0.20 0.30 0.40
19.900 22.226 25.168 29.007
76.04 73.50 70.70 67.56
(Sucrose + water) 1.0368 1.0794 1.1252 1.1745
0.5443 0.5844 0.6324 0.6917
0.3401 0.3529 0.3674 0.3840
0.4178 0.4486 0.4855 0.5310
In order to obtain a good estimation of E*, two further equations were employed. Thus, for 1:1 electrolyte, the Pitzer equation [28,29] can be written as ln c ¼ f c þ Bc m þ C c m2 ;
ð4Þ
where 1=2
c
f ¼ A/ m c
0
1
1=2
1 þ bm 2
B ¼ 2b þ 2b a m
þ ð2=bÞ ln 1 þ bm
1 1 þ am
1=2
2
1=2
A/ ¼ 1:4006 106 d 1=2 =ðer T Þ3=2 kg1=2 mol1=2 ; ;
a m=2 exp am
ð4aÞ 1=2
:
ð4bÞ
TABLE 4 Summary of the values obtained for the parameters of the Debye– Hu¨ckel equation in the different (sugar + water) mixture at 298.15 K Y
E*/mV
a/nm
c/(kg Æ mol1)
r/mV
0
416.86 ± 0.21 417.04 ± 0.13
0.41 ± 0.02 0.38 ± 0.01
0.008 ± 0.007
0.24 0.24
0.10
419.26 ± 0.30 420.16 ± 0.25
0.20
425.38 ± 0.49 424.98 ± 0.31
0.31 ± 0.05 0.36 ± 0.01
0.025 ± 0.027
0.44 0.44
0.30
430.71 ± 0.22 430.31 ± 0.20
0.40 ± 0.03 0.48 ± 0.01
0.034 ± 0.014
0.27 0.33
0.40
440.01 ± 0.29 439.37 ± 0.16
0.36 ± 0.03 0.43 ± 0.01
0.040 ± 0.017
0.19 0.22
0.10
422.32 ± 0.33 422.27 ± 0.16
0.002 ± 0.010
0.19 0.18
0.20
428.14 ± 0.25 427.86 ± 0.16
0.39 ± 0.03 0.43 ± 0.01
0.015 ± 0.011
0.26 0.27
0.30
434.70 ± 0.31 434.41 ± 0.16
0.43 ± 0.03 0.46 ± 0.01
0.015 ± 0.014
0.26 0.26
0.40
441.09 ± 0.32 441.61 ± 0.16
0.63 ± 0.05 0.54 ± 0.01
0.028 ± 0.014
0.17 0.21
(Glucose + water) 0.49 ± 0.04 0.038 ± 0.009 0.36 ± 0.01
(Sucrose + water) 0.40 ± 0.03 0.40 ± 0.01
In these equations a and b are assumed fixed parameters with values of 2.0 and 1.2, respectively [28–30]; b0, b1 and Cc are solute-specific interaction parameters and A/ is the Debye–Hu¨ckel constant for the osmotic coefficients defined by
0.29 0.42
ð4cÞ
all symbols having their usual meaning. A/ values appear in table 3. Also, for 1:1 electrolyte, the Scatchard equation [31,32] can be written as ln c ¼ 2Sm1=2 1 þ am1=2 þ 2að1Þ m þ ð3=2Það2Þ m2 þ ð4=3Það3Þ m3 þ ð5=4Það4Þ m4 2; ð5Þ where S = 3A/ and a, a(1), a(2), a(3) and a(4) are the characteristic interaction parameters of the model. By combining equations (2) and (4) or (2) and (5), the values of E* can be optimized, as well as the interaction parameters characteristic of each model. Table 5 shows the values obtained using the Pitzer equation. Values obtained using the Scatchard equation have not been tabulated as they did not present any substantive additional information.
4. Discussion Table 4 shows that it was not necessary to consider parameter c from the linear term in the Debye–Hu¨ckel equation in order to obtain good fits. Appreciable changes in the deviation are not detected when we consider this parameter, nor when we take into account the contribution of the extended terms, Ext. The values obtained for the ion size parameter, a, of the NaF remain almost constant at 0.40 ± 0.06 nm for the (glucose + water) mixture and 0.45 ± 0.08 nm for that of (sucrose + water). These values are similar to those obtained for the NaCl in (glucose + water) (0.35 ± 0.01 nm) [6], (sucrose + water) (0.38 ± 0.01 nm) [6], (fruc-
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TABLE 5 Summary of the values obtained for the parameters of the Pitzer equation in the different (sugar + water) mixture at 298.15 K Y
E*/mV
b0
b1 1
Cc 1
kg Æ mol
2
kg Æ mol
kg Æ mol
0.1139 ± 0.1176 0.2505 ± 0.0331
0.0608 ± 0.05032
0.24 0.25
0.1182 ± 0.0928
0.29 0.29
1.0028 ± 0.2835 0.1585 ± 0.0983
0.5367 ± 0.1746
0.31 0.43
0.0793 ± 0.1177 0.0691 ± 0.0163
0.6634 ± 0.2316 0.3776 ± 0.0573
0.2294 ± 0.1804
0.27 0.28
0.3660 ± 0.1581 0.0738 ± 0.0193
1.2564 ± 0.3224 0.3590 ± 0.0667
0.7137 ± 0.2526
0.16 0.19
0.0046 ± 0.1144
0.20 0.19
0.3213 ± 0.2029 0.3034 ± 0.0487
0.0109 ± 0.1198
0.27 0.26
0.3064 ± 0.1133 0.0476 ± 0.0164
1.1593 ± 0.2394 0.4217 ± 0.0625
0.5118 ± 0.1628
0.20 0.26
0.4438 ± 0.1398 0.0202 ± 0.0260
1.6603 ± 0.2713 0.8507 ± 0.0855
0.7232 ± 0.2368
0.15 0.22
0
417.14 ± 0.28 416.88 ± 0.19
0.10
419.03 ± 0.39 419.41 ± 0.26
(Glucose + water) 0.1158 ± 0.0786 0.6274 ± 0.1843 0.0165 ± 0.0103 0.4001 ± 0.0477
0.20
424.20 ± 0.51 425.39 ± 0.46
0.3438 ± 0.1297 0.0513 ± 0.0244
0.30
430.56 ± 0.26 430.77 ± 0.21
0.40
438.84 ± 0.49 440.09 ± 0.25
0.10
422.33 ± 0.65 422.36 ± 0.30
(Sucrose + water) 0.0228 ± 0.0993 0.2796 ± 0.2484 0.0268 ± 0.0103 0.2699 ± 0.0493
0.20
428.16 ± 0.36 428.18 ± 0.23
0.0352 ± 0.0920 0.0435 ± 0.0116
0.30
433.83 ± 0.38 434.85 ± 0.27
0.40
440.75 ± 0.34 441.61 ± 0.29
0.0698 ± 0.0469 0.0136 ± 0.0066
tose + water) (0.37 ± 0.01 nm) [14], (trehalose + water) (0.34 ± 0.07 nm) [13] and (maltose + water) (0.42 ± 0.05 nm) [13]. It should be noted in all the previously cited cases it is verified that a > q with q being the Bjerrum interionic distance parameter defined as q ¼ jzþ z je2 2er kT ;
r/mV 2
ð6Þ
where the symbols retain their habitual meanings. It is well known that, according to the Bjerrum [33] theory, the formation of ionic pairs requires that the interionic distances must be less than the critical distance q. Thus, it does not appear that NaF is more highly associated in these (sugar + water) mixtures than it is in pure water. In other mixtures such as (methanol + water) and (ethanol + water) [15], it was verified that a < q, producing a strong ionic association which increased with the molar fraction of the co-disolvent. Also, for the (water + ethylene carbonate) mixture [34] where a 6 q, a slight increase is observed in the ionic association with increase in the presence of EC. Regarding the Pitzer equation, table 5 shows that the consideration of parameterCc does not cause a notable improvement of the standard deviations of the fit. This is because the NaF concentration was always less that 1 molal and the C/ parameter which
takes into account the triple ion short-range interactions can be neglected [28,29]. As is well known in Pitzer thermodynamic treatments of electrolyte solutions, the electrostatic term is a constant for all electrolytes of the same valence type and does not take into consideration the differences in the solvation of the ions, ionic sizes, and the distance of closest approach. The second virial coefficient is a complicated function of many interactions and b0 and b1 parameters, which govern the coefficient, absorbed the effect of these factors. In figure 1 the b0 and b1 values obtained of the fit are plotted against the reciprocal of relative permittivity of the two (sugar + water) mixtures. For comparative purposes, the NaCl in these mixtures also shows similar values. It is interesting to note that both b0 (which can be identified with the total binary ionic interactions) and b1 (which can be identified with the interactions between unlike-charged ions) become linear with 1/er. This is the typical profile observed with 1:1 electrolytes [6,13,29,35] both in water as mixed solvents as amply documented by Gupta [35]. The average values for E* which appear in the second column of table 6 were calculated considering the three studied models: Debye–Hu¨ckel, Pitzer and Scatchard. These average values were used to calculate the mean ionic activity coefficients c which are listed in
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962
1.0
1.0
sucrose-water
glucose-water 0.8
β i / kg mol-1
β i / kg mol-1
0.8 0.6 0.4
0.6 0.4
0.2
0.2
0.0
0.0 0.013
0.014 1 / εr
0.015
0.013
0.014 1 / εr
0.015
FIGURE 1. (s) b0 and (h) b1 for NaF in (sugar + water) mixtures at 298.15 K as a function of inverse of relative permittivity.
TABLE 6 Values of average standard emf, DE and DGt (molal scale) in (NaF + glucose + water) and (NaF + sucrose + water) system at 298.15 K Y
ÆE*æ/mV
DE/mV
DGt /(kJ Æ mol1)
0 0.10 0.20 0.30 0.40
(Glucose + water) 416.87 ± 0.01 0.00 ± 0.01 419.31 ± 0.07 2.45 ± 0.07 425.38 ± 0.01 8.52 ± 0.01 430.73 ± 0.03 13.86 ± 0.03 440.04 ± 0.04 23.17 ± 0.04
0.00 ± 0.01 0.24 ± 0.01 0.82 ± 0.00 1.34 ± 0.00 2.24 ± 0.01
0 0.10 0.20 0.30 0.40
(Sucrose + water) 416.87 ± 0.01 0.00 ± 0.01 422.34 ± 0.02 5.47 ± 0.03 428.15 ± 0.02 11.28 ± 0.03 434.75 ± 0.07 17.88 ± 0.08 441.27 ± 0.24 24.40 ± 0.25
0.00 ± 0.01 0.53 ± 0.00 1.09 ± 0.00 1.73 ± 0.01 2.35 ± 0.02
tables 1 and 2 for each molality of NaF and each mass fraction of sugar. For the range of molality studied, the standard deviations of the activity coefficients among
our values and those reported in the literature were calculated to be less than ±0.003 in pure water, showing good agreement between both groups of data. Figure 2 shows lg c vs. m1/2 for two mass fractions in the two systems being compared, as well as for pure water. These curves demonstrate typical profiles of variation, governed by the ion–ion and ion–solvent interactions, with a decrease (compared with the value in pure water) greater in the (glucose + water) mixture than in the (sucrose + water) mixture. The standard free energy of transference, DGt , is probably one of the most useful parameters available for understanding the different behaviours of a solute in both pure and mixed solvent. It is defined as the difference between the standard free energy per mole of electrolyte in a pure solvent, usually water, and that in another pure or mixed solvent. It is a measure of the change in the total solvation energy of the solute when it is transferred from one solvent to another at infinite
0.00
0.00
Y=0.40
-0.04
-0.04
-0.08
-0.08
log γ
log γ
Y=0.20
-0.12
-0.12
-0.16
-0.16
-0.20
-0.20
-0.24
-0.24
0.0
0.2
0.4
0.6
0.8
m1/2 / mol1/2kg-1/2
1.0
0.0
0.2
0.4
0.6
0.8
1.0
m1/2 / mol1/2kg-1/2
FIGURE 2. Plot of lg c vs. m1/2 for NaF in (sugar + water) mixtures at 298.15 K. (- - -) pure water; (s) glucose; (h) sucrose.
F. Herna´ndez-Luis et al. / J. Chem. Thermodynamics 36 (2004) 957–964
dilution, and it can be easily calculated from the values of E* according to the following expression [13,15,36]:
3 NaF-S
asym DGt ¼ nF ðEs Ew Þ ¼ nF ðE Easym Þ ; s Ew Þ ðE s w
where E, E* and Easym stand for the standard potential, the apparent standard potential and the asymmetry asym potential ðeasym Þ, respectively. Subscript s refers Na þ eF to mixed solvent and w to water. All the other symbols have their habitual meanings. As we mentioned previously, in our case, Easym is a small value and independent of the composition of the solvent, which allows us to affirm that ðEasym Easym Þ is negligible compared to s w ðEs Ew Þ, and thus equation (7) may be used without problems. Prior to calculation of DGt , the Born condition for the functional dependency of DE ¼ ðEs Ew Þ with 1/ er was demonstrated. A linear variation of the standard emf with the reciprocal of the dielectric constant is presented in figure 3 for the (glucose + water) (cor = 0.997, r = 0.40 mV) and (sucrose + water) (cor = 0.999, r = 0.27 mV) mixtures. Table 6 shows the values for DGt calculated for each system. It is notable in all cases that the values of DGt become more positive with increasing mass fraction of sugar, which shows that the transference of NaF from water to the (sugar + water) mixtures studied here is a not a spontaneous process. Figure 4 shows the variation of DGt with the mole fraction of sugar, Xs, for the systems studied, as well as for systems containing NaCl. In all cases an increase in the standard free energy of transference is observed with increase in sugar in the mixture, which indicates an decrease in hydration of the electrolyte in the (sugar + water) system as a probable consequence of the increase in the hydration of the sugar. It is also observed that for a given electrolyte, DGt increases more in the presence of sucrose than of glucose, which may be in agreement with the fact that
10
∆ E 0 / mV
0
glucose-water
-10 -20 -30
sucrose-water
-40 0.013
0.014
0.015
0.016
1 / εr FIGURE 3. Test of the Born condition for the variation of DE, on the inverse of relative permittivity for the (sugar + water) mixtures.
NaCl-G
NaCl-S
∆ G t0 / kJ mol-1
ð7Þ
963
NaF-G
2
1
0 0.00
0.02
0.04
0.06
Xs FIGURE 4. Variation of DGt for the NaF and NaCl as a function of mole fraction of sugar in (sugar + water) mixtures. S, sucrose; G, glucose.
the sucrose is somewhat more hydrated than the glucose [37,38]. Finally, since DGt is fundamentally related to the changes in solvation undergone by the electrolyte in the presence of the sugar, it is of interest to estimate the hydration number of the NaF in each case. For this we used the equation of Feakins and French [39,40] which allows calculation of the primary hydration number of the electrolyte based on the dependency which exists between the standard potential of the cell and the logarithm of the mass fraction of water in the mixture according to DE ¼ nhydr k lg w:
ð8Þ
Figure 5 shows a plot of DE vs. k lg w where an excellent correlation is observed, and is linear in all cases. The values found for nhydr were almost the same: 1.6 (cor = 0.995) for the (glucose + water) mixture and 1.9 (cor = 0.999) for (sucrose + water) mixture. It should be noted that the derivation of equation (8) implies an ideal model for the solutions and that therefore the values of nhydr obtained should not be considered entirely reliable as considered by their authors [39,40]. These values for nhydr are lower than those obtained by our group for NaF in (methanol + water) and (ethanol + water) mixtures [15], that is, 6.0 and 7.0, respectively. This same effect is observed for the NaCl, with nhydr values of 2.5 and 2.5 for the (glucose + water) and (sucrose + water) systems [14] and 4.5 and 5.5 for the (methanol + water) and (ethanol + water) systems [15], respectively. Although the relation between the hydration and the stereochemistry of the sugars is very complicated, especially when there are electrolytes present [8], the low hydration undergone by both the NaF and the NaCl in the presence of the sugars may be due to the
F. Herna´ndez-Luis et al. / J. Chem. Thermodynamics 36 (2004) 957–964
964
0.01
0.01
0.00
0.00
glucose-water
-0.01
∆E0 / V
∆E0 / V
-0.01 -0.02 -0.03 -0.04
sucrose-water
-0.03
nhydr = 1.6 cor = 0.995
-0.05 0.000
0.006
-0.02
-0.04 0.012
0.018
nhydr = 1.9 cor = 0.999
-0.05 0.000
0.006
- k logw
0.012
0.018
- k logw
FIGURE 5. Variation of DE with mass fraction of water in (sugar + water) mixtures at 298.15 K.
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JCT 03-186