Mean activity coefficients of NaCl in (sodium chloride  +  sodium bicarbonate +  water) fromT =  (293.15 to 308.15) K

J. Chem. Thermodynamics 2001, 33, 1107–1119 doi:10.1006/jcht.2000.0827 Available online at http://www.idealibrary.com on

Mean activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water) from T = (293.15 to 308.15) K Xiaoyan Ji, Xiaohua Lu,a Weilu Lin, Luzheng Zhang, Yanru Wang, Jun Shi, Nanjing University of Chemical Technology, Nanjing 210009, P.R.C.

and Benjamin C.-Y. Lu Department of Chemical Engineering, University of Ottawa, Ontario, Canada K1N 6N5

The mean activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water) were determined experimentally in the temperature range 293.15 K to 308.15 K at four NaHCO3 molality fractions (0.1, 0.3, 0.5, and 0.7). The measurements were made with an electrochemical cell, using a Na+ glass ion-selective electrode and a Cl− solid-state ionselective electrode. The experimental values reported by Butler and Huston are found to be higher than those calculated from the Pitzer equation using the existing parameters while the experimental results of this work are close to the calculated values, up to an NaHCO3 molality fraction of 0.5. At the NaHCO3 molality fraction of 0.7, the experimental data are + much lower than the calculated values, implying that the interference of HCO− 3 on the Na glass ion-selective electrode can only be neglected up to a molality fraction of NaHCO3 of c 2001 Academic Press 0.5, an observation which is consistent with that of Butler and Huston. KEYWORDS: activity coefficients; ion selective electrode; mixture; aqueous solutions; electrolyte

1. Introduction Aqueous solutions of weak electrolytes play an important role in chemical, biological, and environmental engineering. The thermodynamic properties of such solutions cannot be interpreted in the same way as those of aqueous solutions of strong electrolytes. It was noted by Peiper and Pitzer (1) that in the presence of chemical equilibrium even stoichiometric single-solute solutions should be treated as mixed electrolytes. The thermodynamic studies of aqueous solutions generally involve measurements of mean activity coefficients of electrolytes and osmotic coefficients of solvents. The a To whom correspondence should be addressed (E-mail: [email protected]).

0021–9614/01/091107 + 13 $35.00/0

c 2001 Academic Press

1108

X. Ji et al.

determination of the activity coefficients of electrolytes is usually carried out by the electromotive force (e.m.f.) method, which allows the determination of the activity of an electrolyte by measurement of the electrochemical potential of ions in an electrochemical cell. The introduction of ion-selective electrodes (i.s.e.s) has remarkably broadened the range of electrolytes, and many experimental data for binary and ternary aqueous electrolyte solutions have been determined with i.s.e.s. (2) Using such a cell with a Na (Hg) and a (silver + silver chloride) electrodes, Butler and Huston (3) measured the activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water) at T = 298.15 K. The ionic strengths were about (0.5 and 1.0) mol · kg−1 . On the other hand, they observed systematic errors in the experimental results at higher molality fractions of NaHCO3 (>0.5). E.m.f. data on this system have been determined (4–7) using cells containing standard hydrogen and (silver + silver chloride) electrodes. The equilibrium constants of: − − CO2− 3 (aq) + H2 O(l) = HCO3 (aq) + OH (aq),

(1)

CO2− 3 (aq) + CO2 (g) + H2 O(l),

(2)

2HCO− 3 (aq)

=

and the activity coefficients of NaHCO3 can be determined from these experimental values. Peiper and Pitzer (1) determined the parameters of the Pitzer equation (8) from these e.m.f. data. The activity coefficients of NaCl can be calculated using these parameters. However, the calculated values are found to be lower than the experimental values reported by Butler and Huston. In this work, the activity coefficients of NaCl were measured using a Na+ glass ionselective electrode and a Cl− solid state ion-selective electrode at four temperatures from 293.15 K to 308.15 K at 5 K intervals. The aim is: to investigate the suitability of the i.s.e. cell for measuring the activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water); to verfify the results reported by Butler anrd Huston; and to study the interference of interfering ions on the Na+ glass i.s.e. in the determination.

2. Determination of mean activity coefficients of NaCl APPARATUS AND CHEMICALS

The apparatus and method used in this study have been described in a previous paper. (9) A concentrated electrolyte solution of known composition was added continuously to vary the ionic strength of a solution in the cell, and the variable ionic strength of the solution was determined and recorded with a computer. A Schott-Ger¨ate pH-meter (Model CG0841, >1013 , F.R.G.) was used to monitor the potential of the cell. The maximum electric potential deviation was about 0.1 mV. A Schott-Ger¨ate resistance thermometer (Model W5791 NN, F.R.G.) with a resolution of 0.1 K was used to measure the temperature. A Schott-Ger¨ate multifunctional piston burette (Model Titronic T200, F.R.G.) connected to a personal computer was used to change the ionic strength of the solution using the flow e.m.f. method. (10) The maximum dosing deviation was estimated to be ±0.15 per cent. The Na+ glass i.s.e. (Model 102C, <1.5 · 108 , P.R.C.) and the Cl− solid-state i.s.e. (Model 301, <1.5·105 , P.R.C.) were used to determine the ion activities of Na+ and Cl+

Mean activity of NaCl

1109

in the determined solution. In order to improve the stability of the electrodes, pretreatments of the i.s.e.s were necessary. Before measuring the potential of ions, the Na+ glass i.s.e. was conditioned in a NaCl solution (about 0.1 mol · kg−1 ) for 24 h, and the Cl− solid-state i.s.e. was inserted in the same solution for 30 min. Sodium chloride (Guaranteed grade, mass fraction purity > 0.998, Beijing Chemical Plant, Beijing) was dried in a low-pressure dryer until constant mass was reached. The purity of sodium bicarbonate (Guaranteed grade, mass fraction purity > 0.998, Beijing Chemical Plant, Beijing) was verified by volume titration with an aqueous NaOH solution, whose concentration was standardized with reagent grade potassium hydrogenphthalate (Reagent grade, mass fraction purity > 0.995, Beijing Chemical Plant, Beijing, P.R.C.). The de-ionized water was prepared by re-distilling water in the presence of KMnO4 and its electrical conductivity was less than 1.2 · 10−6 S · cm−1 . The concentrated stock mixed-electrolyte solution (sodium chloride + sodium bicarbonate + water) with a constant molality fraction of NaHCO3 [y2 = m(NaHCO3 )/{m(NaCl) + m(NaHCO3 )}], was prepared by dosing with the Schott-Ger¨ate multifunctional piston burette. CALIBRATION OF THE I.S.E.s

In order to test the behaviour of the electrodes, the i.s.e.s used in the ternary system were calibrated in (sodium chloride + water), using the cell: Na+ glass i.s.e. |NaCl (m), H2 O| Cl− solid-state i.s.e.

(I)

The corresponding e.m.f. values of the cell E can be expressed as: (11) E = E 0 + 2S ln(mγ± ),

(3)

E0

where E is the potential of the cell, the standard e.m.f. of the cell, S the slope of the cell, and γ± and m the mean activity coefficient and molality of NaCl, respectively. When the i.s.e.s were used to determine the activity coefficient of electrolytes in binary systems, Bates et al. (12) suggested that using the theoretical value of the reversible slope (Nernstian slope) as the slope (S) would not be justified. For this reason, both E 0 and S were treated as adjustable parameters in the present study. A Simplex optimization method was used to determine the values of the parameters E 0 and S by minimizing the following objective function: F(x) =

N X {E i (expt) − E i (calc)}2 ,

(4)

i=1

where N is the number of experimental data points and E i (calc) is obtained from equation (3). The values of γ± were calculated using the Pitzer equation. (8) The ionic interaction parameters of pure NaCl were taken from Peiper and Pitzer. (1) The calculated values of E 0 and S of the i.s.e.s in (sodium chloride + water) at the four temperatures are presented in table 1. The standard deviations of the fits at these temperatures are all less than 0.25 mV, and are less than the allowed deviation suggested by Bates et al. (12) The relative deviations of the experimental slopes from the Nernstian slope are less than 1.0 per cent, indicating that the response of the Na+ glass i.s.e. and the Cl− solid state i.s.e. to the ionic activity in solutions nearly obeys Nernst behaviour.

1110

X. Ji et al. TABLE 1. Standard e.m.f. of the cell E o , slope of the cell S, theoretical value of the reversible slope (Nernstian slope) in (NaCl + H2 O) at four temperatures T T /K

E 0 /mV

S/mV

σ/mVa

Nernstian slope, ST /mV

102 · |S − ST |/ST

293.15

21.37

25.00

0.22

25.26

1.03

298.15

22.37

25.60

0.11

25.69

0.35

303.15

23.79

26.23

0.17

26.12

0.43

308.15

24.60

26.65

0.08

26.55

0.38

hP aσ =

N 2 i=1 {E(calc)−E(expt)}i

(N −1)

i1/2

, where N denotes the number of experimental data

points at each temperature.

25

E 0 / mV

24

23

22

21 3.2

3.4

3.3 10

3 / (T

3.5

/ K)

FIGURE 1. Temperature effect on the standard e.m.f. E 0 of (sodium chloride + water): , experimental data; —, linear fit.

The relationship between the standard e.m.f.s E 0 and the reciprocal of temperatures is depicted in figure 1. The approximate linear relationship indicates that the behaviour of the i.s.e.s obeys the Gibbs–Helmholtz equation.

Mean activity of NaCl

1111

DETERMINATION OF THE ACTIVITY COEFFICIENTS OF NACL IN THE TERNARY SYSTEM

The cell for the ternary system was arranged as: Na+ glass i.s.e. | NaCl (m 1 ), NaHCO3 (m 2 ), H2 O|Cl− solid-state i.s.e.

(II)

For a ternary system containing possible interfering ions, the electrochemical potential of an electrode would be expressed by the following equation: (2) ! M X 0 E = E + S ln a1 + kjaj , (5) j=1

where a1 is the activity of NaCl, a j is the activity of interfering species j, M is the number of interfering species, and k j is the potentiometric selectivity coefficient of the i.s.e. selective to NaCl towards other interfering species j. If interference is neglected, the corresponding e.m.f. values of the cell can be described by equation (3) in which: m = {(m 1 + m 2 ) · m}1/2 . (6) The standard e.m.f. of the cell (E 0 ) and the electrode slope (S) of equation (3) must be a priori known for the determination of mean activity coefficients of electrolytes in the ternary system from the e.m.f. data. Butler and Huston (3) adopted the Nernstian slope with the value of E 0 evaluated from the known composition and activity coefficients of the binary system. Haghtelab and Vera (13,14) adopted values of S and E 0 regressed from the binary system. Since the same i.s.e.s were used in cells (I) and (II), and the measured slopes deviated only slightly from the values of the Nernstian slope, the values of E 0 and S, regressed from the experimental data of (sodium chloride + water), were adopted in this work. These values are also presented in table 1. If the interference of the interfering ions on the Na+ glass i.s.e. was small enough to be neglected, the mean activity coefficients of NaCl could be obtained with the determined values of E 0 and S by the following equation: γ±,expt = (1/m) · exp[{E(expt) − E 0 }/2S].

(7)

In this work, the potential values of the cell were determined at the four temperatures (293.15, 298.15, 303.15, and 308.15) K in (sodium chloride + sodium bicarbonate + water). As mentioned above, experimental determinations were made at four molality factions of NaHCO3 (y2 = 0.1, 0.3, 0.5, and 0.7). The mean ionic activity coefficients of NaCl were calculated by means of equation (7).

3. Discussion During the measurements, the concentrations of (sodium chloride + sodium bicarbonate + water) may have varied due to the removal of carbon dioxide. However, Butler and Huston (3) observed that concentration changes due to the removal of carbon dioxide had a negligible effect on the measured activity coefficients. Therefore, the effect of carbon dioxide removal was neglected in this work.

1112

X. Ji et al. TABLE 2. Ionic strength I , molality fraction of NaHCO3 y2 , and mean activity coefficients of NaCl γ± in (sodium chloride + sodium bicarbonate + water) as reported by Butler and Huston, and as calculated from the Pitzer equation using literature parameters I /mol · kg−1

1 − y2

γ±,1 (expt)

γ±,2 (expt)

γ± (expt)a

γ± (calc)

b 1γ±

0.5073

0.7486

0.6621

0.6653

0.6637

0.6727

−1.36

0.5133

0.5055

0.6634

0.6614

0.6624

0.6658

−0.51

0.5215

0.1793

0.6177

0.6142

0.6160

0.6568

−6.62

0.5240

0.0761

0.6347

0.6409

0.6378

0.6540

−2.54

1.0400

0.4122

0.6163

0.6153

0.6158

0.6330

−2.79

1.0115

0.1135

0.5991

0.5979

0.5985

0.6241

−4.27

1.0049

0.0444

0.5950

0.5926

0.5938

0.6209

−4.56

a γ (expt) = 0.5 · {γ b ± ±,1 (expt) + γ±,2 (expt)}, 1γ± = {γ± (expt) − γ± (calc)}/γ± (expt) where γ±,1 (expt) and γ±,2 (expt) are experimental data reported under the same conditions of temperature, ionic strength and molality fraction.

Direct determination of the mean ionic activity coefficients of NaCl by means of i.s.e.s is a rapid method. However, the interference of interfering ions must be taken into consideration. Only when such interference is small enough to be neglected, would the results obtained by equation (7) be reliable. For (sodium chloride + sodium bicarbonate + water), Butler and Huston (3) measured the activity coefficients at T = 298.15 K by using a cell with a Na+ glass and (silver + silver chloride) electrodes. It was found that the interference of interfering ions could be neglected up to a molality fraction of 0.5. On the other hand, for the same system, Peiper and Pitzer (1) correlated the literature data (4–7) using the Pitzer equation, (8) and the resulting parameters of the Pitzer equation are found to be adequate for predicting the activity coefficients of NaCl in this system. A comparison of the experimental data of Bulter and Huston (3) obtained at T = 298.15 K with the calculation results obtained from the Pitzer equation is shown in table 2, indicating large deviations between the two sets of values. A further comparison of the experimental values obtained in this work with the literature data of Bulter and Huston (3) and the calculated values obtained from Pitzer equation at T = 298.15 K with an ionic strength of 1.0 mol · kg−1 is depicted in figure 2. It is clearly shown that the experimental results of this work are very close to those obtained from the Pitzer equation up to a molality fraction of NaHCO3 of 0.5. On the other hand, at the high molality fraction of NaHCO3 (y2 = 0.7), the experimental value obtained in this work is much lower than that calculated from the Pitzer equation. In other words, the interference of interfering ions cannot be neglected at high molality fractions of NaHCO3 (y2 > 0.5). This observation is consistent with the conclusion of Bulter and Huston. (3) In addition, the measured activity coefficients of NaCl obtained in this work are compared with those calculated from the Pitzer equation in the whole ionic strength at

Mean activity of NaCl

1113

0.24

0.23

– lgγ±

0.22

0.21

0.20

0.19

0.18 0.0

0.2

0.4

0.6

0.8

1.0

1 – y2

FIGURE 2. A comparison of the NaCl activity coefficients in (sodium chloride + sodium bicarbonate + water) at T = 298.15 K (the ionic strength of NaCl is 1.0 mol · kg−1 ); , experimental data of this work; —, calculated values using the Pitzer equation; N, experimental data of Butler and Huston.

molality fractions of NaHCO3 of 0.1, 0.3, and 0.5 at T = 298.15 K. The deviations between ln γ± (expt) and ln γ± (calc) are depicted in figure 3, and are less than 6 · 10−3 . Since chemical reactions occur, the real composition would deviate from the apparent composition. An example at a total ionic strength of 0.8 mol · kg−1 is presented in table 3. The parameters of the Pitzer equation and chemical reaction equilibrium constants were all taken from the work of Peiper and Pitzer. (1) Although the real compositions are different from the apparent compositions as shown in the table, the real molality fractions y ∗ are nearly identical to the apparent molality fraction y2 . This agreement indicates that the pair of i.s.e.s selected in this work could be used to determine the activity coefficients of NaCl in this system up to a molality fraction of NaHCO3 of 0.5, the activity coefficients of NaCl can be calculated by equation (5), and the experimental activity coefficients (γ±,expt ) of NaCl up to a molality fraction of NaHCO3 of 0.5 as listed in table 4 are reliable. The activity coefficients obtained at the molality fraction of NaHCO3 of 0.7 are not reported in the table, as they appeared to be not reliable.

1114

X. Ji et al. 0.006

0.004

t

0.002

0.000

– 0.002

– 0.004

– 0.006 0.0

1.0

0.5

1.5

2.0

I/

FIGURE 3. Deviations between ln γ± (expt) and ln γ± (calc) of NaCl in (sodium chloride + sodium bicarbonate + water) system as a function of the ionic strength I at T = 298.15 K. TABLE 3. The equilibrium compositions of real species (I = 0.8 mol · kg−1 ) at T = 298.15 K and molality fraction of NaHCO3 y2 y2 = 0.1 m(Na+ )/mol · kg−1

y2 = 0.3

y2 = 0.5

y2 = 0.7

0.80

0.80

0.80

0.80

−1 m(CO2− 3 )/mol · kg

1.2 · 10−3

3.6 · 10−3

5.9 · 10−3

8.2 · 10−3

−1 m(HCO− 3 )/mol · kg

0.078

0.233

0.388

0.544

1.0 · 10−6

1.0 · 10−6

1.0 · 10−6

1.0 · 10−6

m(OH− )/mol · kg−1 m(CI− )/mol · kg−1

0.72

0.56

0.40

0.24

ya

0.098

0.29

0.49

0.69

a y = m(HCO− )/{m(Cl− ) + m(HCO− )}. 3 3

γ±,1

0.8308 0.7987 0.7806 0.7537 0.7349 0.7211 0.7110

0.8120 0.7806 0.7660 0.7396 0.7225

0.8176 0.7907 0.7743 0.7462 0.7260 0.7110

0.8197 0.7904

I /mol · kg−1

0.05 0.08 0.10 0.15 0.20 0.25 0.30

0.05 0.08 0.10 0.15 0.20

0.05 0.08 0.10 0.15 0.20 0.25

0.05 0.08 −143.9 −121.7

−155.6 −133.8 −123.7 −105.3 −92.3 −82.2

−147.5 −126.0 −115.8 −97.3 −84.1

−140.1 −118.6 −108.6 −90.1 −77.0 −68.8 −58.4

E/mV

0.35 0.40

0.30 0.35 0.40 0.45 0.50 0.55

0.25 0.30 0.35 0.40 0.45

0.35 0.40 0.45 0.50 0.55 0.60 0.65

I /mol · kg−1

0.6967 0.6881

0.6997 0.6886 0.6808 0.6743 0.6681 0.6633

0.7076 0.6977 0.6866 0.6802 0.6737

0.7011 0.6918 0.6852 0.6789 0.6753 0.6707 0.6667

γ±,1

I /mol · kg−1

0.6587 0.6522 0.6483 0.6464 0.6435 0.6406

0.6624 0.658

0.50 0.55 0.60 0.70 0.80 0.60 0.65 0.70 0.75 0.80 0.85

y2 = 0.3 −74.0 −65.6 −58.7 −52.5 −47.1 y2 = 0.5 −73.9 −67.0 −60.9 −55.5 −50.7 −46.3 T = 298.15 K y2 = 0.1 −52.6 0.70 −46.4 0.80

0.6675 0.6640 0.6595 0.6529 0.6468

0.70 0.80 0.90 1.00 1.10 1.20 1.30

0.6627 0.6592 0.6541 0.6507 0.6486 0.6468 0.6455

γ±,1

−51.4 −45.4 −40.0 −35.2 −30.7 −26.7 −23.0

T = 293.15 K y2 = 0.1

E/mV

−19.7 −13.2

−42.3 −38.8 −35.4 −32.1 −29.1 −26.3

−42.3 −37.8 −38.8 −26.6 −20.4

−19.6 −13.2 −7.7 −2.7 1.9 6.1 10.0

E/mV

1.50 1.60

0.90 0.95 1.00 1.05

0.90 1.00 1.10 1.20 1.30

1.40 1.50 1.60 1.70 1.80

I /mol · kg−1

0.6506 0.6518

0.6386 0.6348 0.6353 0.6336

0.6432 0.6398 0.6378 0.6385 0.6385

0.6468 0.6462 0.6472 0.6507 0.6513

γ±,1

18.4 21.8

−23.6 −21.2 −18.6 −16.3

−14.8 −9.8 −5.2 −0.8 3.2

13.8 17.2 20.5 23.8 26.7

E/mV

TABLE 4. Ionic strength I , mean ionic activity coefficients of NaCl γ±1 in (sodium chloride + sodium bicarbonate + water), potential of the cell E, molality fraction of NaHCO3 y2 at temperature T

Mean activity of NaCl 1115

γ±,1

0.7778 0.7486 0.7308 0.7164 0.7062

0.8165 0.7889 0.7733 0.7472 0.7266 0.7150 0.7007

0.8129 0.7854 0.7714 0.7453 0.7248 0.7119

0.8226 0.7956 0.7805

I /mol · kg−1

0.10 0.15 0.20 0.25 0.30

0.05 0.08 0.10 0.15 0.20 0.25 0.30

0.05 0.08 0.10 0.15 0.20 0.25

0.05 0.08 0.10 −146.4 −123.4 −112.8

−159.4 −137.0 −126.6 −107.6 −94.2 −83.8

−150.5 −128.2 117.8 −99.8 −85.5 −74.9 −66.6

−111.1 −92.3 −78.8 −68.4 −59.8

E/mV

0.35 0.40 0.45

0.30 0.35 0.40 0.45 0.50 0.55

0.35 0.40 0.45 0.50 0.55 0.60 0.65

0.45 0.50 0.55 0.60 0.65

I /mol · kg−1

0.6998 0.6905 0.6842

0.7004 0.6910 0.6824 0.6741 0.6689 0.6627

0.6913 0.6828 0.6784 0.6719 0.6669 0.6623 0.6585

0.6837 0.6771 0.6721 0.6714 0.6675

γ±,1

0.6581 0.6543 0.6518 0.6464 0.6438 0.6413

0.6627 0.6589 0.6554

0.60 0.65 0.70 0.75 0.80 0.85

y2 = 0.5 −75.2 −68.0 −61.8 −56.4 −51.4 −47.0 T = 303.15 K y2 = 0.1 −52.8 0.70 −46.5 0.80 −40.8 0.90

0.656 0.6543 0.6517 0.6491 0.6475 0.6467 0.6451

0.70 0.75 0.80 0.85 0.90 0.95 1.00

y2 = 0.3 −59.4 −53.2 −47.5 −42.6 −38.1 −34.0 −30.2

0.6501 0.6478 0.6496 0.6484 0.6497

γ±,1

1.00 1.10 1.20 1.30 1.40

I /mol · kg−1

−40.7 −35.8 −31.3 −26.9 −23.1

E/mV

TABLE 4—continued

−19.3 −12.6 −6.7

−43.0 −39.2 −35.6 −32.4 −29.4 −26.4

−26.6 −23.2 −20.1 −17.2 −14.4 −11.7 −9.2

−2.4 2.3 6.9 10.9 14.8

E/mV

1.40 1.50 1.60

0.90 0.95 1.00

1.05 1.10 1.15 1.20 1.25 1.30

1.70 1.80

I /mol · kg−1

0.6519 0.6542 0.6556

0.6384 0.6363 0.6348

0.6426 0.6428 0.6406 0.6409 0.6398 0.6397

0.6543 0.6578

γ±,1

16.2 20.0 23.5

−23.8 −21.2 −18.6

−6.9 −4.5 −2.4 −2.1 1.8 3.8

25.1 28.3

E/mV

1116 X. Ji et al.

γ±,1

0.7546 0.7362 0.7181 0.7077

0.8184 0.7870 0.7735 0.7464 0.7269 0.7117 0.6988

0.8122 0.7795 0.7661 0.7393 0.7199

0.8123 0.7816 0.7672 0.7402 0.7220

I /mol · kg−1

0.15 0.20 0.25 0.30

0.05 0.08 0.10 0.15 0.20 0.25 0.30

0.05 0.08 0.10 0.15 0.20

0.05 0.08 0.10 0.15 0.20 −148.9 −125.9 −115.0 −95.3 −81.3

−162.5 −140.0 −129.2 −109.8 −96.0

−153.2 −130.6 −119.8 −100.4 −86.7 −76.1 −67.5

−93.3 −79.5 −69.1 −60.3

E/mV

0.35 0.40 0.45 0.50 0.55

0.25 0.30 0.35 0.40 0.45

0.35 0.40 0.45 0.50 0.55 0.60 0.65

0.50 0.55 0.60 0.65

I /mol · kg−1

0.6873 0.6820 0.6746 0.6706 0.6671

0.7036 0.6947 0.6857 0.6779 0.6717

0.6910 0.6831 0.6769 0.6714 0.6663 0.6617 0.6579

0.6800 0.6735 0.6689 0.6663

γ±,1

0.6650 0.6612 0.6566 0.6529 0.6506

0.6590 0.6539 0.6530 0.6540 0.6530

0.50 0.55 0.60 0.65 0.70

y2 = 0.5 −85.6 −76.7 −69.3 −62.9 −57.2 T = 308.15 K y2 = 0.1 −54.1 0.70 −47.4 0.80 −41.7 0.90 −36.4 1.00 −31.6 1.10

0.6556 0.6553 0.6518 0.6508 0.6483 0.6454 0.6468

0.70 0.75 0.80 0.85 0.90 0.95 1.00

y2 = 0.3 −60.0 −53.6 −47.9 −42.8 −38.2 −34.0 −30.1

0.6525 0.6501 0.6505 0.6518

γ±,1

1.00 1.10 1.20 1.30

I /mol · kg−1

−35.6 31.1 −26.9 −22.9

E/mV

TABLE 4—continued

−19.4 −12.7 −6.5 −0.8 4.2

−52.2 −47.5 −43.3 −39.4 −35.7

−26.4 −22.8 −19.7 −16.6 −13.8 −11.2 −8.4

−1.4 3.4 8.0 12.3

E/mV

1.40 1.50 1.60 1.70 1.80

0.75 0.80 0.85 0.90 1.00

1.05 1.10 1.15 1.20 1.25 1.30

1.70 1.80

I /mol · kg−1

0.6561 0.6576 0.6596 0.6629 0.6674

0.6466 0.6431 0.6421 0.6409 0.6358

0.6448 0.6456 0.6427 0.6423 0.6430 0.6423

0.6558 0.6584

γ±,1

17.3 21.1 24.7 28.2 31.6

−32.4 −29.3 −26.2 −23.3 −18.2

−6.0 −3.5 −1.4 0.7 3.0 5.0

26.7 29.9

E/mV

Mean activity of NaCl 1117

γ±,1

0.7073 0.6966

0.8202 0.7893 0.7747 0.7461 0.7249 0.7116 0.6994

0.8240 0.7899 0.7739 0.7467 0.7256

I /mol · kg−1

0.25 0.30

0.05 0.08 0.10 0.15 0.20 0.25 0.30

0.05 0.08 0.10 0.15 0.20 −163.8 −141.0 −130.2 −110.5 −96.7

−155.1 −132.1 −101.6 −87.8 −76.9 −68.1 −60.6

−70.5 −61.6

E/mV

0.25 0.30 0.35 0.40 0.45

0.35 0.40 0.45 0.50 0.55 0.60 0.65

0.60 0.65

I /mol · kg−1

0.7108 0.7000 0.6894 0.6815 0.6742

0.6901 0.6809 0.6761 0.6709 0.6661 0.6632 0.6599

0.6642 0.6609

γ±,1 1.20 1.30 0.70 0.75 0.80 0.85 0.90 0.95 1.00 0.50 0.55 0.60 0.65 0.70

y2 = 0.3 −54.2 −48.3 −43.1 −38.4 −34.0 −30.0 −26.3 y2 = 0.5 −85.9 −77.0 −69.6 −63.1 −57.4

I /mol · kg−1

−27.2 −23.2

E/mV

TABLE 4—continued

0.6689 0.6642 0.6600 0.6568 0.6537

0.6568 0.6558 0.6529 0.6513 0.6520 0.6498 0.6494

0.6526 0.6530

γ±,1

−52.2 −47.5 −43.2 −39.2 −35.5

−22.7 −19.5 −16.4 −13.3 −10.6 −7.9 −5.4

8.8 13.1

E/mV

0.75 0.80 0.85 0.90 0.95

1.05 1.10 1.15 1.20 1.25 1.30

I /mol · kg−1

0.6503 0.6486 0.6470 0.6453 0.6443

0.6481 0.6484 0.6451 0.6455 0.6446 0.6460

γ±,1

−32.1 −28.8 −25.7 −22.8 −20.0

−2.9 −0.8 1.5 3.6 5.8

E/mV

1118 X. Ji et al.

Mean activity of NaCl

1119

4. Conclusion glass i.s.e. |NaCl (m 1 ), NaHCO3 (m 2 )|Cl− solid-state i.s.e. was successfully used in the determination of mean ionic activity coefficients of NaCl in (sodium chloride + sodium bicarbonate + water), at T = 293.15 K to T = 308.15 K and at NaHCO3 molality fractions up to 0.5. Unlike the values reported by Butler and Huston, the results of this work are close to the calculated values from the Pitzer equation. In this range of NaHCO3 molality fractions, the interference of NaHCO3 on the Na+ i.s.e. can be neglected. A cell of Na+

The financial support received from the National Natural Science Foundation of P. R. C. (No. 29376244), Natural Science Foundation of Jiangsu province of P. R. C. (BK 97124), the outstanding young teacher Foundation of Education Ministry of P. R. C., the outstanding youth of National Nature Science Foundation of P. R. C. (29925616) and the Alexander-von-Humboldt Foundation of Germany is greatly appreciated. REFERENCES 1. Peiper, J. C.; Pitzer, K. S. J. Chem. Thermodynamics 1982, 14, 613–638. 2. Butler, J. N.; Roy, R. N. Activity Coefficients in Electrolyte Solution. Pitzer, K. S.: editor. Boston. 1991, p. 155. 3. Butler, J. N.; Huston, R. J. Phys. Chem. 1970, 74, 2976–2983. 4. Harned, H. S.; Scholes, S. R. Jr J. Am. Chem. Soc. 1941, 63, 1706–1909. 5. Harned, H. S.; Davis, R. Jr J. Am. Chem. Soc. 1943, 65, 2030–2037. 6. Harned, H. S.; Bonner, F. T. J. Am. Chem. Soc. 1945, 67, 1026–1031. 7. Roy, R. N.; Gibbons, J. J.; Trower, J. K.; Lee, G. A.; Hartley, J. J.; Mack, J. G. J. Chem. Thermodynamics 1982, 14, 473–482. 8. Pitzer, K. S. Activity Coefficients in Electrolyte Solution. Pitzer, K. S.: editor. Boston. 1991, p. 75. 9. Ji, X.; Lu, X.; Li, S.; Zhang, L.; Wang, Y.; Shi, J. J. Solution Chem. Accepted, 1999. 10. Zhang, L.; Lu, X.; Wang, Y.; Shi, J. J. Solution Chem. 1993, 22, 137–150. 11. Ji, X.; Lu, X.; Li, S.; Zhang, L.; Wang, Y.; Shi, J.; Lu, B. C.-Y. J. Chem. Eng. Data 2000, 45, 29–33. 12. Bates, R. G.; Dickson, A. G.; Gratzl, M.; Hrabeczy-Pall, A.; Lindner, E.; Pungor, E. Anal. Chem. 1983, 55, 1275–1280. 13. Haghtalab, A.; Vera, J. H. J. Chem. Eng. Data 1991, 36, 332–340. 14. Ji, X.; Lu, X.; Li, S.; Zhang, L.; Wang, Y.; Shi, J. J. Chem. Eng. Data 2000, 45, 29–33. (Received 15 May 2000; in final form 21 December 2000)

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