Mean Activity Coefficients of NaNO3 and the Mixing Ion- Interaction Parameters in the Ternary System (NaNO3+CsNO3+H2O) at 298.15K by EMF Method

Ion-selective electrodes directly respond to the activity of target ions without destroying the existing form of the original electrolyte, so ion-selective electrodes have been widely used in various fields. Mean activity coefficient of NaNO3 in the ternary system (NaNO3 +CsNO3 +H2O) at 298.15K was measured by electromotive force (EMF) with the cell: Na + ionselective electrode (Na-ISE)|NaNO3 (mA), CsNO3 (mB)|NO3 ion-selective electrode (NO3-ISE) with total ionic strengths from 0.01 to 4.5mol·kg at different ionic strength fractions (0, 0.1, 0.2, 0.4, 0.6, and 0.8). The results showed that the Na-ISE and NO3-ISE have a good Nernst response, and the mean activity coefficients of NaNO3 are obtained via the Nernst equation. Based on the data of mean activity coefficients of NaNO3, the relationship diagrams of activity coefficients of NaNO3 against ion strengths in the ternary system were demonstrated, and the Pitzer mixing ion-interaction parameters θNa,Cs and ψNa, Cs, N O3 were obtained.


Introduction
Electrolyte solutions widely exist in salt lake, marine, underground water, oil/gas-field water, and the engineering of inorganic chemistry and hydrometallurgy [1]. The mean activity coefficients of the electrolytes are essential for the design development of processes such as salt chemical industry and desalination. In China, cesium levels in many salt lake brine range from 10 to 20 mg/L [2]. Therefore, it is of great significance to determine the activity coefficients of the solution of cesium salts.
A series of ion-interaction models of electrolytes have been proposed to predict the activity coefficients of solute and osmotic coefficients of the aqueous systems. Pitzer's ion-interaction model is one of the most commonly used models [3,4]. The research methods of the thermodynamic properties of aqueous electrolytes involve the isopiestic vapor pressure [5][6][7], electromotive force method [8][9][10], volume properties method [11], hygrometric method, and calorimetric method [12,13]. Compared with other methods, the electromotive force (EMF) method has the advantages of good selectivity, rapid response, and easy to achieve continuous assay.
The mixed ion-interaction parameter of the ternary system provides basic thermodynamic data for the separation and extraction of pure salts from salt lake brines. The ther-modynamic properties of aqueous mixed-electrolyte solutions have received considerable attention. Using EMF method in Hu's research group [14][15][16][17][18], the mean ionic activity coefficients in the following ternary systems (CsCl + Cs 2 SO 4 +H 2 O), (CsF + Cs 2 SO 4 + H 2 O), (CsF + CsBr + H 2 O), (CsF + CsNO 3 +H 2 O), (CsCl + CaCl 2 + H 2 O), and (CsCl + MgCl 2 + H 2 O) have been reported systematically, but the activity coefficients of (NaNO 3 +CsNO 3 +H 2 O) system at 298.15 K have not been reported in the literature till now. Therefore, the electromotive forces of the ternary system at 298.15 K were measured by EMF, and the mean activity coefficients of NaNO 3 and the mixing ion-interaction parameters θ Na,Cs and ψNa, Cs, NO 3 are obtained for the first time.

Experimental
All of the instructions of the chemical reagents used in this work are shown in Table 1, and they were used without further purification. The deionized distilled water (DDW) produced by ULUP-II-10T (Chongqing Jiuyang Co. Lt., China), whose conductivity is less than 1.0 × 10 −4 S·m −1 and pH = 6.60 at 298.15 K, was used during the whole experiment.
The Na-ISE and NO 3 -ISE were purchased from Shanghai Miriam Electric Science Instruments Co., Ltd. Before use, the Na-ISE and NO 3 -ISE were activated at least 2 h in a sodium nitrate with a concentration of 0.001 mol/L and purified with deionized water to a blank potential. Both electrodes were calibrated before use, and they had an excellent Nernst response and selectivity. The ion analyzer was PHSJ-4F with an uncertainty of ±0.1 mV.
The double-walled glass bottle was held at a constant temperature at (298.15 ± 0.02) K by water circulation from a thermostat.
The cell arrangements in this work were as following: (a) Na-ISE|NaNO 3 (m A0 )|NO 3 -ISE Above galvanic cells contain no liquid junction. Here, m A0 and m B0 are the molalities of NaNO 3 and CsNO 3 as single salt in water, m A and m B are the molalities of NaNO 3 and CsNO 3 in the ternary system, respectively.
Each concentration of the above solutions was prepared by directly weighing the materials using a Sartorius electronic balance whose accuracy was 0.1 mg. Voltage readings were taken as final when they were constant within 0.2 mV for at least 5 min.
The electromotive force of the above three cells was measured at 298.15 K. First, the electromotive force of the cell (a) was measured to determine whether the electrode pair of Na-ISE and NO 3 -ISE had a satisfactory Nernst response, which could judge its suitability for this experiment. Cell (b) was used to measure the electromotive force of CsNO 3 solution at different concentrations, and the selectivity coefficient K pot of electrode Na-ISE to Cs + can be calculated by equation (2). The purpose was to determine the effect of the presence of Cs + on the response of Na-ISE. Finally, the EMF of cell (c) was measured under different ionic strength fractions (y B ) of CsNO 3 in the solutions.

Results and Discussion
3.1. The Calibration of Electrode Pair of Na-ISE and NO 3 -ISE. For cell (a), 13 measurements of m A0 from 0.01 to 4.5 mol·kg -1 were selected to determine each corresponding potential (E a ). The Nernst equation for cell (a) can be expressed as: E 0 is the standard potential of cell (a), k = RT/F represents the theoretical Nernst slope. The R, F, and T are the gas constant, Faraday constant, and absolute temperature, respectively. The γ ±A0 is the mean activity coefficient of pure NaNO 3 in water, whose values were taken and calculated from the literature [19] and listed in Table 2.
To check their linear relationship, E a was plotted against ln ðm A0 γ ±A Þ and shown in Figure 1. By way of this line, E 0 , k , and the linear correlation coefficient (r) can be evaluated using a linear regression method, and they are 120.3, 25.96 mV, and 0.9995, respectively. The obtained value of k gets quite close to the theoretical one (25.69 mV) of the Nernst slope. Those results mean that the electrode pair used in this work have a satisfactory Nernst response and are well suitable for our measurements.

Selective Coefficient of Na-ISE Electrode for Cs Ion.
The electromotive force values of CsNO 3 solutions with different concentrations were measured and used to calculate K pot . The selective coefficient K pot of electrode Na-ISE for Cs + can be calculated according to the following equation: where γ ±B0 refers to the activity coefficients of pure CsNO 3 in water at 298.15 K, and its value was taken and calculated according to the cited literature [19]. E b is the EMF value of cell (b) at different m B0 and is shown in Table 3. The mean value of K pot is less than 1.0 × 10 -4 , which evidenced that the response of the electrode pair to Cs ion can be ignored.
The mean activity coefficients of NaNO 3 in the ternary system can be derived from the following Nernst equation and shown in Table 3.
where γ ±A and γ ±B are the mean activity coefficients of NaNO 3 and CsNO 3 , respectively. Because K pot can be neglected [20] without leading to an appreciable error, we get the simplified form the following equation: The mean activity coefficients of NaNO 3 in the aqueous ternary system can be calculated with equation (5). The related results of cell (c) are collected in Table 4 and shown in Figure 2. It can be seen from Figure 2 that when the mole fractions remain constant substantially, the mean activity coefficient of NaNO 3 decreases with the increase of ionic strength.

Harned
Rule. The Harned rule [21] is one of the earliest proposed treatments for strong electrolyte aqueous ternary systems. Concerning the studied ternary system, the Harned rule can be written as the following equation: where α AB and β AB represent the Harned interaction parameters, dependent on both ionic strength and temperature [10,22]. γ ±A0 is the mean activity coefficient of NaNO 3 in pure solutions at the same total ionic strengths I as the ternary system. The fitted results are listed in Table 5, indicating that the Harned rule can be applied to describe the ternary system accurately.
3.5. Pitzer Model. In this paper, the Pitzer and its extended Harvie-Weare model was used to fit the experimental data [23]. The mixed ion-interaction parameter can be obtained by substituting the binary interaction parameters and the mean activity coefficient of the aqueous electrolyte into equation (9). For the ternary system studied, the mean         Journal of Chemistry activity coefficients and the osmotic coefficients can be given as in the following equations: ln γ MX = ln γ M + ln γ X ð Þ /2, ð9Þ F = A ϕ I 1/2 / 1 + 1:2I 1/2 À Á + 2/1:2 ln 1 + 1:

Journal of Chemistry
where M, a, and a ' are anions. X, c, and c ' are cations. γ M , Z M, and m c are the activity coefficient, valence number, and molar concentration of the cation, respectively. γ X , Z X, and m a are the activity coefficient, valence number, and molar concentration of the anion, respectively. A ϕ is called the Debye−Hückel constant. Ψ is the ionic interaction parameters. B is the coefficient in the second dimension. For type 1-1 electrolytes, α 1 = 2.0 mol·kg -1 , α 2 = 0. Pitzer's mixing ion-interaction parameters are evaluated through equation (10) by using multiple linear regression techniques, and the result is shown in Table 6.
The mean activity coefficients of CsNO 3 and the osmotic coefficients for the ternary system at different ionic strengths are calculated by Pitzer and its extended Harvie-Weare model. These results are given in Table 6 and Figures 3 and 4. From Figure 3, we can see that for the ternary system studied, the mean activity coefficients of CsNO 3 decrease with an increase of total ionic strengths. It can be seen from Figure 4 that when the ionic strengths are constant, the osmotic coefficient of the ternary system is reduced by increasing the mole fractions of CsNO 3 in the system.
3.6. Excess Gibbs Free Energies and Water Activities of the Ternary System. The excess Gibbs free energies and water activities of the ternary system have been calculated by using