Individual Ionic Activity Coefficients of Sodium Halides in Glucose

9430

Ind. Eng. Chem. Res. 2010, 49, 9430–9435

Individual Ionic Activity Coefficients of Sodium Halides in Glucose-Water Solutions at 298.15 K Weiyan Dong, Yang Zhao, Kelei Zhuo,* and Yujuan Chen Key laboratory of Green Chemistry Media and Reactions (Ministry of Education), School of Chemistry and EnVironmental Science, Henan Normal UniVersity, Xinxiang, Henan 453007, People’s Republic of China

The individual ionic activity coefficients of sodium halides (NaX) in the NaX-glucose-water solutions were experimentally determined at 298.15 K by using ion selective electrodes. The individual ionic activity coefficients evaluated by the use of the extended DebyesHu¨ckel equation are in agreement with those by the Pitzer equation. In addition, dependences of the individual ionic activity coefficients upon molalities, properties of cations and anions are discussed. Introduction The electrolyte solutions encountered in chemical industrial processes often appear to be concentrated mixed electrolyte solution.1 And the thermodynamic properties and phase equilibria of electrolyte solutions are important to chemical process development, water treatment, water desalination, absorption heat pump development, and other processes involving electrolytes.2 Also the activity coefficients of individual ions in electrolyte solutions play an important role in those cases. Ionic equilibrium through semipermeable membranes, a basic step in the understanding of biological processes, the design of ionexchange equipment, and geological studies are some of many fields in which the activity of individual ions is needed.3 In the past decades, the values of the activity coefficients of individual ions measured using half-cell ion selective electrodes (ISE) have been reported by Vera’s group in some publications.3-18 Recently, they used an exact equation to test the predictive ability of the novel treatment of electrolyte solutions based on the activities of individual ions.19 They also made further research on the effect of the reference solution on measurements of ion activity coefficients using cells.20 In addition, Lin and Lee proposed a two-ionic-parameter approach and defined the electrolyte-specific approaching parameter and salvation parameter for each constitute ion in an electrolyte solution.2,21 However, to the best of our knowledge, the activity coefficients of individual ions in mixed solvents have not been reported. In our previous work,22 we proposed a new method for measuring the activity coefficients of individual ions in aqueous solutions of NaF, NaCl, and NaBr at 298.15 K using ion selective electrodes. As a continuation, we have measured the activity coefficients of individual ions in mixed solvents using this method. In addition, ionic property and concentration dependences of the activity coefficients of individual ions in the mixed solvents are investigated. Experimental Section NaF (>99.0%, guaranteed reagent for analysis, Beijing Chemical Co., China), NaCl, and NaBr (>99.0%, Alfa Aesar Co., U.K.) were dried respectively under a vacuum at 373, 333, and 413 K to constant weight. D-(+)-Glucose (>99.5%, Sigma Chemical Co., U.S.A.) were dried under a vacuum to constant weight. They were all stored over P2O5 in desiccators prior to * To whom correspondence should be addressed. Tel.: +86 373 3329056. Fax: +86 373 3326336. E-mail: [email protected].

use. Doubly distilled deionized water with a conductivity of 1.0 × 10-4 S · m-1 to 1.2 × 10-4 S · m-1 at 298.15 K was used throughout this work. A sodium-glass electrode (model 102, Jiangsu Electroanal Instrument Co., China), a fluoride ion-selective electrode (model 301, Jiangsu Electroanal Instrument Co., China), a chloride ionselective electrode (model 9617BN, Orion, U.S.A.), and a bromide ion-selective electrode (model 9635BN, Orion, U.S.A.) were used as test electrodes. A Hg/HgCl electrode was used as the preference electrode (REF-E) (Jiangyan Kedi Equip. Co., Jiangsu, China). The inner filling solution in this reference electrode is saturated with KCl. A PH-ISE meter (model 920A+, Orion, U.S.A.) with a resolution of 0.1 mV was used to monitor the potential measurements with two BNC (Bayonet NeilConcelman) connectors for ion-selective electrodes and two pinpin connectors for the reference electrode. The temperature of test solutions were controlled at 298.15 ( 0.02 K using a thermostatic bath. To minimize the risk of the presence of concentration gradients in the cell, the solution were continuously stirred with a magnetic stirrer. To determine activity coefficients of individual ions in the NaX, glucose, and water systems, the following cell was set up: Na-ISE/X-ISE|NaX(m), H2O, glucose(mGlc)|REF-E

(I)

One point of the run measured with the above cell was considered as a reference cell for reducing the data. Thus, we write Na-ISE/X-ISE|NaX(mR), H2O, glucose(mGlc)|REF-E

(II) where m and mR are the molalities of NaX in the working and reference solutions, respectively, defined as the number of moles of solutes per kilogram of the mixed solvents (glucose and water), and mGlc is the molality of glucose in pure water. All the electrodes were treated according to the manufacturer procedure prior to the measurement. The experimental procedure has been elaborated in previous work.22 The cell potentials measured are listed in the supplementary data (Tables S1-3, Supporting Information). The repeatability of cell potentials measured is (0.2 mV. Results and Discussion For a cell composed of an ISE and a reference electrode, the cell potential E can be expressed as4,23

10.1021/ie1008103  2010 American Chemical Society Published on Web 08/20/2010

B (Å-1 · mol-1/2 · kg1/2) ) 50.2901 × [d (g · cm-3)]1/2 /(εrT/K)1/2 (6) where d is the density (g · cm-3) of the mixed solvent, and εr is the relative permittivity of the mixed solvents. The values of density and relative permittivity for the (glucose and water) mixtures were taken from Zhuo et al.25 and Chen et al.,26 respectively. T is the thermodynamic temperature. And the values of A and B at different molalities of the mixed solvents (glucose and water) at 298.15 K are listed in the supplementary data (seen in Table S4, Supporting Information). The range of validity of the eq 4 is up to about 1 mol · kg-1, which was stated in the literature.27 By inserting eq 4 into eq 3, we used a least-squares fit to obtain values of γi,R and C for each mixed solvent. It should be pointed out that the values of å obtained by a least-squares fit for the electrolyte NaX were used to obtain the individual ionic activity coefficients. The resulting values are listed in the supplementary data (Tables S5-7), as well as the standard deviations of the fit. According to γi,R and ∆E′, the activity coefficients of individual ions were calculated from eq 3 at various concentrations of NaX and different mixed solvents (glucose and water). These values are shown in Tables 1-3.

0.02067 0.04043 0.06023 0.08082 0.1009c 0.2062 0.4053 0.6081 0.7095 0.7932

mGlc ) 0.6000 mol · kg-1(w ) 9.76%) 0.901 0.860 0.880 0.880 0.862 0.853 0.856 0.858 0.807 0.827 0.818 0.817 0.779 0.786 0.782 0.783 0.759 0.754 0.757 0.756 0.728 0.743 0.735 0.735 0.662 0.692 0.675 0.677 0.611 0.641 0.626 0.626 0.584 0.612 0.598 0.598 0.569 0.590 0.580 0.580 -1 mGlc ) 1.2000 mol · kg (w ) 17.78%) 0.861 0.863 0.863 0.862 0.821 0.795 0.807 0.808 0.782 0.781 0.781 0.782 0.754 0.761 0.760 0.757 0.739 0.738 0.738 0.739 0.679 0.686 0.682 0.683 0.637 0.631 0.635 0.634 0.610 0.595 0.604 0.602 0.592 0.589 0.591 0.590 0.581 0.558 0.569 0.570 0.01065 0.02057 0.04033 0.06071 0.08157 0.1005c 0.1996 0.3984 0.5992 0.8007

γ(b γ(a γFγNa+

9431 a The mean ionic activity coefficients of NaF determined from the chemical potentials of the cells: Na-ISE vs F-ISE as reference electrodes. b The mean ionic activity coefficients of NaF calculated from the individual ionic activity coefficients of Na+ and F-. c Reference point molalities: w, the mass fraction of glucose in the mixed solvents (glucose and water).

A (mol-1/2 · kg1/2) ) 1.8247 × 106[d (g · cm-3)]1/2 /(εrT/K)3/2 (5)

0.01049 0.02051 0.04067 0.06084 0.08036 0.1004c 0.1994 0.3988 0.5994 0.8001

where a is the ion size parameter (Å), I is ionic strength of the electrolyte [I, at molality m scale, which is defined as the number of moles of solutes per kilogram of the mixed solvents (glucose + water), is given by I ) 1/2∑imiZ2i , (for NaX, I ) m)], C is the ion-interaction parameter, ν is the number of ions into which the electrolyte dissociates, and MS is the mean molar mass of the mixed solvent. A and B are the DebyesHu¨ckel parameters and can be calculated by

0.01047 0.02075 0.03977 0.06009 0.08069 0.1008c 0.1960 0.3986 0.5977 0.7988

(4)

0

mGlc ) 0.4000 mol · kg-1(w ) 6.72%) 0.859 0.871 0.865 0.865 0.815 0.839 0.825 0.827 0.801 0.775 0.789 0.788 0.782 0.757 0.771 0.770 0.758 0.745 0.751 0.752 0.705 0.701 0.702 0.703 0.661 0.650 0.655 0.656 0.644 0.623 0.632 0.634 0.635 0.610 0.623 0.622 0.626 0.589 0.607 0.607 -1 mGlc ) 1.0000 mol · kg (w ) 15.27%) 0.903 0.912 0.906 0.908 0.881 0.830 0.855 0.855 0.822 0.808 0.817 0.815 0.783 0.794 0.789 0.789 0.754 0.784 0.767 0.769 0.748 0.765 0.758 0.756 0.699 0.726 0.713 0.713 0.642 0.677 0.658 0.659 0.618 0.637 0.628 0.627 0.583 0.617 0.600 0.600

- log(1 + 0.001VmiMs) + CI

0.02077 0.04083 0.05993 0.07931 0.09905c 0.1992 0.4007 0.5017 0.6017 0.6861

1 + Ba0√I

mGlc ) 0.2000 mol · kg-1(w ) 3.48%) 0.876 0.876 0.876 0.876 0.823 0.839 0.831 0.831 0.812 0.803 0.807 0.807 0.785 0.785 0.786 0.785 0.770 0.761 0.764 0.765 0.718 0.716 0.717 0.717 0.672 0.674 0.672 0.673 0.642 0.649 0.647 0.646 0.614 0.624 0.619 0.619 0.608 0.599 0.603 0.603 -1 mGlc ) 0.8000 mol · kg (w ) 12.60%) 0.878 0.916 0.896 0.897 0.862 0.852 0.858 0.857 0.822 0.809 0.815 0.816 0.787 0.787 0.785 0.787 0.764 0.749 0.758 0.757 0.740 0.746 0.741 0.743 0.696 0.683 0.687 0.689 0.650 0.643 0.646 0.647 0.613 0.621 0.615 0.617 0.596 0.577 0.585 0.586

A|Zi | 2√I

0.01991 0.04060 0.06050 0.08093 0.1010c 0.2018 0.4054 0.6070 0.8045 0.8923

log γi ) -

mNaF (mol · kg-1)

where ∆E ) EI - EII, ∆EJ ) EIJ - EIIJ , and EI and EII are cell potentials of cells I and II, respectively. The difference in the junction potentials between the reference point and the test point, ∆EJ, appearing in eq 3 were neglected.22 And the slope of the electrodes was set to S ) RT/F (25.69 mV at 298.15K). Ionic activity coefficients can be calculated from the extended DebyesHu¨ckel equation24

γ(b

(3)

γ(a

)

γF-

miγi mi,Rγi,R

γNa+

(

∆E' ) ∆E - ∆EJ ) (S ln

mNaF mol · kg-1

0 where EISE is the standard potential of the ISE, and ERE is the electrochemical potential of the reference electrode. Obviously, E0′ is a function of the molality m of electrolyte through the term EJ,K. E0 is a constant for given ISE and REF-E. We took a specific point of the same run as a reference point [cell (II)]. Then, for cells I and II, we have

γ(b

(2)

γ(a

0 E0′ ) (EISE - ERE) + EJ,K ) E0 + EJ,K

γF-

where Si refers to the slope of the electrode responsive to ion i (Na+ or X-), Zi is the charge number of ion i, ai is the activity of ion i (ai ) γimi), and γi is the activity coefficient of ion i. The term E0′ can be expressed as22

γNa+

(1)

mNaF (mol · kg-1)

E ) E + (Si /Zi) ln ai

Table 1. Individual Ionic Activity Coefficients of Na+ and F- Calculated by the Extended DebyesHu¨ckel Equation in Different Mixed Solvents (glucose and water) mGlc at Various Concentrations mNaF at 298.15 K

Ind. Eng. Chem. Res., Vol. 49, No. 19, 2010 0′

0.910 0.823 0.795 0.776 0.772 0.752 0.748 0.755 0.773 0.800 0.01052 0.03054 0.05087 0.08089 0.1007c 0.2003 0.4011 0.6007 0.8007 1.0008 0.01014 0.03022 0.04968 0.07921 0.1003c 0.2004 0.4005 0.6011 0.8004 1.0003 0.01020 0.03025 0.05058 0.07990 0.1003c 0.2003 0.3997 0.6006 0.7989 0.9985

a The mean ionic activity coefficients of NaCl determined from the chemical potentials of the cells: Na-ISE vs Cl-ISE as reference electrodes. b The mean ionic activity coefficients of NaCl calculated from the individual ionic activity coefficients of Na+ and Cl-. c Reference point molalities: w, the mass fraction of glucose in the mixed solvents (glucose and water). d Calculated from eq 2 in ref 28 by the use of the parameters given in ref 28 for NaCl in aqueous solutions of glucose, w ) 10% and 20%, respectively.

mGlc ) 0.6000 mol · kg (w ) 9.76%) 0.900 0.896 0.896 0.894d 0.844 0.839 0.842 0.840d 0.807 0.815 0.815 0.810d 0.777 0.787 0.788 0.779d 0.758 0.773 0.774 0.764d 0.694 0.729 0.728 0.710d 0.629 0.688 0.687 0.673d 0.597 0.671 0.673 0.654d 0.563 0.662 0.662 0.645d 0.546 0.658 0.660 0.641d mGlc ) 1.2000 mol · kg-1(w ) 17.78%) 0.890 0.898 0.900 0.889d 0.831 0.827 0.827 0.830d 0.796 0.797 0.795 0.797d 0.756 0.766 0.766 0.764d 0.738 0.755 0.755 0.748d 0.668 0.710 0.709 0.698d 0.600 0.669 0.670 0.653d 0.565 0.652 0.653 0.635d 0.535 0.645 0.643 0.627d 0.514 0.641 0.641 0.625d 0.891 0.839 0.824 0.798 0.790 0.764 0.751 0.759 0.777 0.798 0.01072 0.03121 0.05011 0.07977 0.09939c 0.1999 0.4003 0.6008 0.8016 0.9977

mGlc ) 0.4000 mol · kg (w ) 6.72%) 0.951 0.859 0.903 0.904 0.835 0.855 0.844 0.845 0.814 0.817 0.817 0.816 0.793 0.784 0.790 0.789 0.777 0.777 0.778 0.777 0.759 0.708 0.736 0.733 0.749 0.641 0.694 0.693 0.761 0.600 0.677 0.676 0.775 0.572 0.668 0.666 0.790 0.552 0.660 0.660 -1 mGlc ) 1.0000 mol · kg (w ) 15.27%) 0.950 0.858 0.901 0.903 0.837 0.823 0.831 0.830 0.796 0.802 0.798 0.799 0.761 0.775 0.768 0.768 0.747 0.758 0.753 0.752 0.722 0.691 0.707 0.706 0.719 0.620 0.668 0.668 0.721 0.586 0.651 0.650 0.731 0.560 0.643 0.640 0.747 0.545 0.640 0.638 0.01029 0.03064 0.05111 0.08082 0.1014c 0.2019 0.4028 0.6036 0.8036 1.0034

mGlc ) 0.2000 mol · kg (w ) 3.48%) 0.946 0.868 0.904 0.906 0.876 0.846 0.860 0.861 0.811 0.827 0.818 0.819 0.783 0.795 0.789 0.789 0.770 0.776 0.773 0.773 0.745 0.720 0.731 0.732 0.737 0.640 0.687 0.687 0.735 0.605 0.665 0.667 0.746 0.579 0.657 0.657 0.760 0.563 0.653 0.654 -1 mGlc ) 0.8000 mol · kg (w ) 12.60%) 0.917 0.881 0.898 0.899 0.834 0.833 0.835 0.834 0.812 0.807 0.807 0.810 0.779 0.772 0.775 0.776 0.766 0.759 0.762 0.762 0.749 0.687 0.718 0.717 0.733 0.632 0.679 0.681 0.740 0.585 0.656 0.658 0.751 0.569 0.652 0.654 0.774 0.547 0.649 0.650 0.01029 0.02054 0.05065 0.08025 0.09947c 0.1984 0.3982 0.5984 0.7989 0.9980

γ (a γClγNa+ γ (a γClγNa+

-1

γ (b

mNaCl (mol · kg-1)

-1

γ (b

mNaCl (mol · kg-1)

γNa+

γCl-

γ (a

-1

γ (b

γ (d

Ind. Eng. Chem. Res., Vol. 49, No. 19, 2010

mNaCl (mol · kg-1)

Table 2. Individual Ionic Activity Coefficients of Na+ and Cl- Calculated by the Extended DebyesHu¨ckel Equation in Different Mixed Solvents (Glucose and Water) mGlc at Various Concentrations mNaCl at 298.15 K

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The uncertainties are evaluated to be (0.02. The mean ionic activity coefficients of NaX computed by γ( ) (γν++ γν--)1/ν and determined from the chemical potentials of the cell: Na-ISE vs X-ISE as reference electrodes are also listed in these tables. It can be seen that the mean ionic activity coefficients of NaX obtained from the two methods are in good agreement with each other. Wang et al.28 measured the mean activity coefficients for NaCl in glucose-water mixed solvents. Values calculated from eq 2 in ref 28 by the use of the parameters given in ref 28 are also listed in Table 2. Results show that the agreement is also reasonable. For 1:1 electrolyte, the Pitzer equation is given by29 ln γ ) fγ + Bγm + Cγm2

(7)

fγ ) -AΦx

(8)

Bγ ) 2β0 + 2β1y

(9)

x ) m1/2 /(1 + bm1/2) + (2/b)ln(1 + bm1/2)

(10)

where

y ) [1 - exp(-Rm1/2)(1 + Rm1/2 - 0.5R2m)]/(R2m)

(11) In the equations above, a and b are empirical parameters with values of 2.0 and 1.2 (in kg1/2 · mol-1/2),30 respectively, and AΦ is the DebyesHu¨ckel constant for the osmotic coefficients defined by AΦ (mol-1/2 · kg1/2) ) 1.4006 × 106[d (g · cm-3)]1/2 /(εrT/K)3/2 (12) The values of AΦ are listed in the Supporting Information (seen in Table S4). By inserting eq 7 to eq 3, the values of γR, β0, β1, and Cγ are optimized for each system studied. Their values were summarized in the Supporting Information (Tables S8-10), together with the standard deviations of the fit. Because the standard deviations of all parameters from the fit without Cγ (i.e., with Cγ ) 0) is smaller than the fit with Cγ, the results obtained by the fit without Cγ are considered as experimental values. And then by inserting γR into eq 3, activity coefficients of ion i and mean activity coefficients of NaX were computed at various concentrations and are given in the Supporting Information (Tables S11-13). It can be seen from these tables that the individual ionic activity coefficients obtained by these two equations are in good agreement with each other. So both equations could be used to evaluate the individual ionic activity coefficients for the mixed solvents. Here, it is necessary to state the reasons why we neglected the junction potential. To investigate the effect of the concentration of the reference solution (e.g., KCl, KNO3) on the junction potential, we have calculated the values of the junction potential EJ for the NaBr + water system at 298.15 K using the Henderson equation modified by Bates.31 The results show that the higher the concentration of the reference solution is, the smaller the junction potential becomes. Moreover, the junction potential increases with increasing the molality of NaBr. This shows that the type and concentration of the reference solution have a significant effect on the junction potential. Therefore, to decrease the junction potential, the reference solution should be selected based on the following points: (i) the transference number of the cation is close to that of anion of the electrolyte and (ii) the concentration of the reference solution is as high as

0.01006 0.03024 0.04980 0.08001 0.09978c 0.1999 0.3998 0.5999 0.7999 1.0002 0.01023 0.03033 0.05027 0.08018 0.1007c 0.2004 0.4006 0.6005 0.8007 1.0005

a The mean ionic activity coefficients of NaBr determined from the chemical potentials of the cells: Na-ISE vs Br-ISE as reference electrodes. b The mean ionic activity coefficients of NaBr calculated from the individual ionic activity coefficients of Na+ and Br-. c Reference point molalities: w, the mass fraction of glucose in the mixed solvents (glucose and water).

0.00977 0.02995 0.05017 0.07995 0.1002c 0.2001 0.4003 0.6000 0.8006 1.0006

mGlc ) 0.6000 mol · kg-1(w ) 9.76%) 0.935 0.876 0.905 0.905 0.851 0.836 0.845 0.843 0.807 0.825 0.816 0.816 0.790 0.789 0.791 0.790 0.788 0.774 0.781 0.781 0.760 0.721 0.740 0.740 0.756 0.666 0.712 0.710 0.764 0.635 0.697 0.697 0.789 0.611 0.697 0.694 0.813 0.596 0.698 0.696 -1 mGlc ) 1.2000 mol · kg (w ) 17.78%) 0.930 0.859 0.895 0.894 0.834 0.843 0.839 0.839 0.810 0.815 0.811 0.813 0.786 0.779 0.784 0.783 0.777 0.767 0.772 0.772 0.754 0.710 0.731 0.732 0.751 0.654 0.701 0.701 0.769 0.622 0.690 0.691 0.790 0.605 0.690 0.691 0.817 0.591 0.695 0.694 0.01009 0.03024 0.04948 0.07970 0.09981c 0.1998 0.4000 0.6000 0.7999 0.9999



γ(b γ(a γBrγNa+ mNaBr (mol · kg-1) γ(b γ(a γBrγNa+ mNaBr (mol · kg-1) γ(b γ(a γBrγNa+ mNaBr (mol · kg-1)

Table 3. Individual Ionic Activity Coefficients of Na+ and Br- Calculated by the Extended DebyesHu¨ckel Equation in Different Mixed Solvents (Glucose and Water) mGlc at Various Concentrations mNaBr at 298.15 K


9433

Figure 1. Individual ionic activity coefficients of Na+ for NaBr (2) in pure water22 and at different molalities of the mixed solvents (glucose and water) at 298.15 K: (9) 0.2000 and (O) 1.2000 mol · kg-1 and (s) from the extended DebyesHu¨ckel equation.

possible. In this work, we used a Hg/HgCl electrode as the preference electrode, and its inner filling solution is saturated with KCl. So it produces a very small junction potential. This is the first reason why we neglected the junction potential EJ and ∆EJ in our work. Second, we have noticed Vera’s work. Their results showed that even a change of sign in the junction potential had a small effect on the values of the activity of ions below 1 mol kg-1 solution.15 In this work, the concentrations of sodium halides ranged from 0 to about 1 mol kg-1. Thus, the neglecting of the effect of the junction potential should not produce a significant error to the activity coefficients. Third, to the best of our knowledge, the values of the limiting equivalent ionic conductance λi and the transference numbers of the cation and anion in the mixed saccharide + water solvents have not been reported in the literature. The experimental measurements of them are a relative complex work. However, they are needed for evaluating the junction potentials based on the modified Henderson equation. Therefore, we neglected the effect of the junction potential in data treatments. In addition, we have tested the values of individual ionic activity coefficients by taking different reference points in the reduction of data for each run. It was found that the differences in activity coefficients based on different reference points are less than 0.001. This shows also that it is reasonable to neglect the junction potential. The individual ionic activity coefficients calculated by the extended DebyesHu¨ckel equation were represented in Figure 1 for Na+ and Figure 2 for Br-, respectively. To compare the effect of glucose on the results, the activity coefficients of individual ions for NaBr in the pure water have also been represented in Figures 1 and 2. It can be seen from these figures that the activity coefficients of Na+ first decrease and then increase with increasing the molality of NaBr. However, those of Br- decrease with increasing the molality of NaBr. Similar trends can be observed for Na+ and F- or Cl- in NaF and NaCl solutions at the studied composition of glucose. Figures 1 and 2 show also that the change of the activity coefficients of individual ions with the increasing composition of glucose in the mixed solvents is not marked. The weak effect of glucose on the ionic activity coefficients can not be represented accurately by the results obtained in this work within experimental error. This indicates that the interactions of glucose

9434


Figure 2. Individual ionic activity coefficients of Br- for NaBr (2) in pure water22 and at different molalities of the mixed solvents (glucose and water) at 298.15 K: (9) 0.2000 and (O) 1.2000 mol · kg and (s) from the extended DebyesHu¨ckel equation.

Figure 4. Individual ionic activity coefficients of X- for NaX (mGlc ) 0.8000 mol · kg-1) at 298.15 K: (9) F-, (•) Cl-, and (2) Br- and (s) from the extended DebyesHu¨ckel equation.

and then increases ionic activity coefficients. Results show that the order γNa+(NaBr) > γNa+(NaCl) > γNa+(NaF) are controlled by the attraction between Na+ and X-. The smaller the ions are, the stronger the interionic attractions are. For X- in NaX solutions, the differences in activity coefficients of X- are mainly dependent on those in Na+-Xattractions. At the same time, the X--X- repulsions contribute a positive value to γX-, and the repulsions are dependent on the radii of X-. The trend γF- > γCl- arises from the F--Frepulsion being slightly stronger than that of Cl--Cl-. The dehydration of F- caused by the F--F- interactions gives a more positive free energy and has a larger contribution to the activity coefficient of F- than that of Cl-. This is also a reason why γF- > γCl-. Conclusions +

Figure 3. Individual ionic activity coefficients of Na for NaX (mGlc ) 0.8000 mol · kg-1) at 298.15 K: (9) Na+ for NaF, (•) Na+ for NaCl, (2) Na+ for NaBr, and (s) from the extended DebyesHu¨ckel equation.

molecule with cation, anion and water molecule influence slightly the activity coefficients of individual ions of NaX. Figures 3 and 4 show the variation of the activity coefficients of Na+ and X-, respectively, in aqueous NaX + glucose solutions with molalities of ions at 0.8 mol · kg-1 of glucose. As shown in Figure 3, at given mE and mGlc, the activity coefficients of Na+ are in the order: γNa+(NaBr) > γNa+(NaCl) > γNa+(NaF). However, the activity coefficients of X- in aqueous NaX and glucose solutions are in the order: γBr- > γF- > γCl(see Figure 4). The ionic activity coefficients represent interionic interactions: Na+-Na+, Na+-X-, and X--X-. For Na+ in different NaX solutions, the differences in activity coefficients are attributed to those in Na+-X- interactions since the self-interaction of Na+ are identical in three NaX solutions. The order γNa+(NaBr) > γNa+(NaCl) > γNa+(NaF) is the same as that of the Pauling radii in Å [Br-(1.95) > Cl-(1.81) > F-(1.36)]. However, this does not keep relationship with neither the hydration free energies in kJ mol-1 [Br-(-309.8) > Cl-(-336.0) > F-(-468.2)]32 nor the hydrated ionic radii in Å [Br-(3.30) > Cl-(3.32) > F-(3.52)].33 The dehydration of the ions contributes a positive free energy,

The individual ionic activity coefficients of NaX in aqueous glucose solutions were determined with the extended DebyeHu¨ckel and the Pitzer equation, respectively. The results from these two equations are in quite agreement with each other. So both two equations could be used to evaluate the individual ionic activity coefficients in the mixed solvents. At the same molalities of glucose and NaX, the activity coefficients of Na+ are in the order γNa+(NaBr) > γNa+(NaCl) > γNa+(NaF). This can be attributed to the differences in Na+-X- interactions which are dependent on the Pauling radii of X-. However, the activity coefficients of X- in different NaX, glucose, and water solutions are in the order γBr- > γF- > γCl-. The exception γF- > γCl- is possibly due to a larger repulsion between F- ions, which causes a larger dehydration of F- than that between Cl- ions. In addition, the increase in composition of glucose influences slightly on the individual ionic activity coefficients of NaX. Acknowledgment Financial supports from the National Natural Science Foundation of China (No. 20673033, 20937055) and the Innovator Foundation of Colleges and Universities of Henan Province are gratefully acknowledged. Supporting Information Available: Experimental cell potentials (E) for NaX in the mixed solvents (Tables S1-3), values


of A, B, and AΦ at different molalities of mixed solvents (Table S4), values of all parameters of the extended DebyesHu¨ckel equation for NaX (Tables S5-7), parameters of the Pitzer equation for NaX (Tables S8-10), and individual ionic activity coefficients of Na+ and X- calculated form the Pitzer equation at various concentrations (Tables S11-13). This material is available free of charge via the Internet at http://pubs.acs.org. Nomenclature m ) molality E ) potential, mV S ) the Nernst slope of the ISE F ) Faraday constant R ) gas constant A, B ) Debye-Hu¨ckel parameters Zi ) charge of ion i I ) ionic strength of the electrolyte a0 ) ion size parameter MS ) mean molar mass of the mixed solvent C ) ion-interaction parameter AΦ ) DebyesHu¨ckel constant for the osmotic coefficient T ) temperature, K Greek Letters γ ) activity coefficient β0, β1, Cγ ) solute specific interaction parameters λi ) limiting equivalent ionic conductance

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ReceiVed for reView April 3, 2010 ReVised manuscript receiVed August 4, 2010 Accepted August 5, 2010 IE1008103

Individual Ionic Activity Coefficients of Sodium Halides in Glucose

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