where *wij*, *uij*, and *Cijk* are binary and ternary interaction coefficients, respectively, *xi* is the mole fraction of the species *i* in the mixture. The last term in Eq.(11) is introduced to account various possible types of reference states for electrolyte in solution - pure fused salt and state of infinite dilution. The contribution from the long-range forces, i.e. Debye–Hückel interactions, is given by

$$\frac{G\_{DH}^{\rm ex}}{RT} = -\frac{4A\_x I\_x}{\rho} \ln \left( \frac{1 + \rho I\_x^{1/2}}{1 + \rho \left(I\_x^0\right)^{1/2}} \right) + \sum\_{M \ge 1} x\_M x\_X B\_{MX} g(a I\_x^{1/2}) \,\,,\tag{12}$$

$$\text{with } g(y) = 2\left[1 - (1+y)e^{-y}\right] / y^2 \tag{12a}$$

In the above equations *xM, xX* are molar fractions of ionic species in solution; *Аx* is the Debye–Hückel coefficient for the osmotic function at the molar fraction basis ( 1/2 *А А х M*s ); *Ix* is the ionic strength on the mole fraction basis which, for single-charged ions, *Ix* = 0.5(*x*M + *x*X); 0 *xI* is the ionic strength of solution in a standard state of the pure fused salt, it approaches 0 at infinite dilution for the asymmetric reference state. The parameter is equivalent to the distance of closest approach in the Debye–Hückel theory, both parameters, and , in Eq.(12) are equal to 13 for 1,1-electrolyties. *B*MX is a specific parameter for each electrolyte. For a mixture of two neutral species, 1 and 2, and a strong 1:1 electrolyte MX wth the reference state of infinite dilution, the contributions of the short and long-range force terms to the mean ionic activity coefficient of the electrolyte MX, at the mole fraction basis can be written as follows:

$$\ln \gamma\_{\mathbf{x}} = \ln \gamma\_{\mathbf{x}}^{\text{sr}} + \ln \gamma\_{\mathbf{x}}^{\text{DH}} \,, \tag{13}$$

$$\begin{split} \ln \gamma\_{\boldsymbol{x}}^{\text{DH}} &= -A\_{\text{x}} \left[ \frac{2}{\rho} \ln(1 + \rho \sqrt{I\_{\text{x}}}) + \frac{(1 - 2I\_{\text{x}}) \sqrt{I\_{\text{x}}}}{1 + \rho \sqrt{I\_{\text{x}}}} \right] + \mathbf{x}\_{\text{X}} B\_{\text{MX}} \mathbf{g}(\mathbf{a} \sqrt{I\_{\text{x}}}) - \\ &- \mathbf{x}\_{\text{M}} \mathbf{x}\_{\text{X}} B\_{\text{MX}} \left[ \frac{\mathbf{g}(\mathbf{a} \sqrt{I\_{\text{x}}})}{2I\_{\text{x}}} + \left( 1 - \frac{1}{2I\_{\text{x}}} \right) e^{-\mathbf{a} \sqrt{I\_{\text{x}}}} \right]. \end{split} \tag{13a}$$

$$\begin{split} \ln \gamma\_{x}^{\text{av}} &= \frac{\mathbf{x}\_{1} \mathbf{x}\_{2}}{f^{2}} \Bigg[ \left( 1 - f^{2} \right) w\_{12} + 2 \left( \mathbf{x}\_{1} - \mathbf{x}\_{2} \right) \frac{\mathbf{1} - f^{3}}{f} u\_{12} + \left[ \left( 1 - 2 \mathbf{x}\_{1} \right) f^{2} - 1 \right] \mathbf{Z}\_{12\text{MAX}} \\ &+ \frac{f^{2} - 1}{f} \left( \mathbf{x}\_{1} \mathcal{W}\_{1\text{MAX}} + \mathbf{x}\_{2} \mathcal{W}\_{2\text{MAX}} \right) + \frac{\mathbf{x}\_{1}}{3f^{2}} \Bigg[ f^{3} \left( 2 - 2 \mathbf{x}\_{1} + \mathbf{x}\_{1} \right) + \mathbf{x}\_{1} f^{2} \left( 3 \mathbf{x}\_{1} + \mathbf{x}\_{2} \right) - 2 \mathbf{x}\_{2} \Bigg] \mathbf{U}\_{1\text{MAX}} + \text{.(13b)} \\ &+ \frac{\mathbf{x}\_{2}}{3f^{2}} \Bigg[ f^{3} \left( 2 - 2 \mathbf{x}\_{2} + \mathbf{x}\_{1} \right) + \mathbf{x}\_{1} f^{2} \left( 3 \mathbf{x}\_{2} + \mathbf{x}\_{1} \right) - 2 \mathbf{x}\_{1} \Big] \mathbf{U}\_{2\text{MAX}} \end{split} \tag{13b}$$

In the above equations *xI* = 2*x*M = 2*x*X = 1- *x*1 - *x*2, *f* = 1 - *x*I; *w*12 and *u*12 are model parameters for the binary system (solvent 1 and solvent 2), *Wi*MX and *Ui*MX are model parameters for the binary system - solvent *i* with MX (*i* = 1 or 2), *Z*12MX is a model parameter which accounts for the triple interaction. Formula details can be found in (Lopes et al, 2001).

Electromotive Force Measurements and

H2O-C2H5OH-NaCl system at 298.15 K is drawn.

**L + S**

**L**

0.75

Ohm.

H2O

w(NaCl)

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 89

experiments performed with the use of two different ion-selective electrodes for Na+ can be considered as independent. This increases the statistical significance of the EMF values and provides information on their correctness. The potential of the cell was measured with the use of the Multitest IPL-103 ionomer. The input impedance of the ionomer was at least 1012

The concentration range of the working solution was determined by two factors. According to the manufacturer, the sodium electrode was more sensitive to protons than to sodium ions and the interfering effect of hydrogen ions can be ignored if [Na+]/[H+] > 3000 in the solution under consideration (*i.e*., at (pH – pNa) > 3.5). Therefore, the lower limit of molality in each series of solutions had to be no less than 0.03 molkg-1. To meet the condition of solution homogeneity, the highest concentration of NaCl had to be no higher than the solubility of the salt in the mixed solvent. The widest ranges of concentration were investigated in the systems with ethanol and 1-(*iso*-)propanol. All studied systems belong to the class of systems with the top critical point; the area of existence of solutions narrows with temperature increasing. To maintain the homogeneity of mixtures, the concentration of the salt in solutions was kept no higher than the upper solubility limit of sodium chloride in a mixed solvent of a given composition. In each series of experiments successive measurements were carried out for samples with constant ratios of water/alcohol components and different molalities starting with the lowest concentration. The choice of composition range is illustrated at Fig.1 where the fragment of Gibbs-Roseboom triangle of

> 0.50 w(C2H5OH)

Fig. 1. Fragment of the isothermal (298.15 K) section of sodium chloride – water – ethanol system. Symbols correspond to composition of solutions under investigation. Numbers I, II,

Symbols are met the case of real experiment with various sodium chloride molality and constant water-to-alcohol ratios. The symbols L and S denote the Liquid and Solid phases of the ternary system. Each series of solutions was studied at two or three temperatures. The EMF values of the cell were assumed to be equilibrium if the rate of the drift in EMF was no higher than 0.01-0.02 mVmin-1. The equilibrium was established, less than 30 min. The constancy of the composition of the solution was confirmed by the fact that the refractive indices measured before and after electrochemical experiments remained practically

I II III IV C2H5OH

**L + L**

III and IV are denoted to solutions with fixed water-alcohol ratio.

**L + L + S**

0.25

0.75

The approximation of the experimental data in the present study was carried out with the Pitzer and Pitzer-Simonson models. The result of this investigation can be used in future for the development of a new thermodynamic models and verification of existing ideas.

### **4. EMF measurements of galvanic cells with ternary solutions NaCl – H2O – CnH2n+1OH (n = 2-5). Experimental procedure**

Sodium chloride (reagent grade, 99.8%) was used in experiments. The salt was additionally purified by the double crystallization of NaCl during evaporation of the mother liquor. The purified salt was dried *in vacuo* at 530 К for 48 h. The isomers of alcohol were used as organic solvents: C2H5OH (reagent grade, 99.7%), *1*-C3H7OH (special purity grade, 99.94 %), *iso*-C3H7OH (reagent grade, 99.2%), *1*-C4H9OH (special purity grade, 99.99%) and *iso*-C4H9OH (reagent grade, 99.5%), *1*-C5H11OH (reagent grade, 99.6%) and *iso*-C5H11OH (reagent grade, 99.5%). To remove moisture, the alcohols were kept on zeolites 4A for 7 days and then distilled under the atmospheric pressure. The purity of alcohols was confirmed by the agreement of the measured boiling points of the pure solvents at atmospheric pressure and the refractive indices with the corresponding published data. Deionized water with a specific conductance of 0.2 µS cm-1 used in experiments was prepared with a Millipore Elix filter system.

Electrochemical measurements were carried out with the use of solutions of sodium chloride in mixed water-organic solvents at a constant water-to-alcohol weight ratio. The reagents were weighed on a Sartorius analytical balance with an accuracy of ±0.0005 g. A sample of the NaCl was transferred to a glass cell containing ~30 g of a water-alcohol solution. The cell was tightly closed with a porous plastic cap to prevent evaporation of the solution. The cell was temperature-controlled in a double-walled glass jacket, in which the temperature was maintained by circulating water. The temperature of the samples was maintained constant with an accuracy of ±0.05 К. The solutions were magnetically stirred for 30 min immediately before the experiments. All electrochemical measurements were carried out in the cell without a liquid junction; the scheme is given below (I):

$$\text{Na} \text{\textbullet\text{-}I\text{SE} } \mid \text{NaCl} (m) \text{\textbullet\text{H}\_2\text{O}} (100 \text{-} w\_{\text{alc}}) \text{\textbullet} \text{\textbullet\text{-}I\text{-}w \text{-}I\text{-}w\_{\text{Ir}} \text{\textbullet\text{H}\_2} \text{\textbullet\text{-}II\text{-}I\text{-}K} (w\_{\text{slc}}) \mid \text{Cl} \text{\textbullet\text{-}I\text{SE}}, \tag{I}$$

where *walc* is the weight fraction of alcohol in a mixed solvent expressed in percentage and *m* is the molality of the salt in the ternary solution. Concentration cell (I) EMF measurements are related to the mean ionic activity coefficient by the equation

$$E = E\_0 - \frac{2RT}{F} \ln\left(\gamma\_\pm m\right). \tag{14}$$

An Elis-131 ion-selective electrode for chloride ions (Cl- -ISE) was used as the reference electrode. The working concentration range of the Cl--ISE electrode at 293 К is from 3. 10-5 to 0.1 molL-1; the pH of solutions should be in the range from 2 to 11. A glass ion-selective electrode for sodium ions (Na+-ISE) served as the indicator electrode, which reversibly responds to changes in the composition of the samples under study. The ESL-51-07SR (Belarus) and DX223-Na+ (Mettler Toledo) ion-selective electrodes were used in experiments. Different concentration ranges of solutions were detected by two glass electrodes. The concentration range for the ESL-51-07SR electrode at 293.15 К is from 10-4 to 3.2 molL-1; the same for the Mettler electrode is lower (from 10-6 to 1 molL-1). The results of

The approximation of the experimental data in the present study was carried out with the Pitzer and Pitzer-Simonson models. The result of this investigation can be used in future for

**4. EMF measurements of galvanic cells with ternary solutions NaCl – H2O –**

Sodium chloride (reagent grade, 99.8%) was used in experiments. The salt was additionally purified by the double crystallization of NaCl during evaporation of the mother liquor. The purified salt was dried *in vacuo* at 530 К for 48 h. The isomers of alcohol were used as organic solvents: C2H5OH (reagent grade, 99.7%), *1*-C3H7OH (special purity grade, 99.94 %), *iso*-C3H7OH (reagent grade, 99.2%), *1*-C4H9OH (special purity grade, 99.99%) and *iso*-C4H9OH (reagent grade, 99.5%), *1*-C5H11OH (reagent grade, 99.6%) and *iso*-C5H11OH (reagent grade, 99.5%). To remove moisture, the alcohols were kept on zeolites 4A for 7 days and then distilled under the atmospheric pressure. The purity of alcohols was confirmed by the agreement of the measured boiling points of the pure solvents at atmospheric pressure and the refractive indices with the corresponding published data. Deionized water with a specific conductance of 0.2 µS cm-1 used in experiments was prepared with a Millipore Elix

Electrochemical measurements were carried out with the use of solutions of sodium chloride in mixed water-organic solvents at a constant water-to-alcohol weight ratio. The reagents were weighed on a Sartorius analytical balance with an accuracy of ±0.0005 g. A sample of the NaCl was transferred to a glass cell containing ~30 g of a water-alcohol solution. The cell was tightly closed with a porous plastic cap to prevent evaporation of the solution. The cell was temperature-controlled in a double-walled glass jacket, in which the temperature was maintained by circulating water. The temperature of the samples was maintained constant with an accuracy of ±0.05 К. The solutions were magnetically stirred for 30 min immediately before the experiments. All electrochemical measurements were

 Na+-ISE | NaCl(*m*)+H2O(100*-walc*)+(*1*- or *iso*-)CnH2n+1OH(*walc*) | Cl--ISE, (I) where *walc* is the weight fraction of alcohol in a mixed solvent expressed in percentage and *m* is the molality of the salt in the ternary solution. Concentration cell (I) EMF measurements

> 0 2 ln *RT EE m F*

0.1 molL-1; the pH of solutions should be in the range from 2 to 11. A glass ion-selective electrode for sodium ions (Na+-ISE) served as the indicator electrode, which reversibly responds to changes in the composition of the samples under study. The ESL-51-07SR (Belarus) and DX223-Na+ (Mettler Toledo) ion-selective electrodes were used in experiments. Different concentration ranges of solutions were detected by two glass electrodes. The concentration range for the ESL-51-07SR electrode at 293.15 К is from 10-4 to 3.2 molL-1; the same for the Mettler electrode is lower (from 10-6 to 1 molL-1). The results of

electrode. The working concentration range of the Cl--ISE electrode at 293 К is from 3.

. (14)

10-5 to

carried out in the cell without a liquid junction; the scheme is given below (I):

are related to the mean ionic activity coefficient by the equation

An Elis-131 ion-selective electrode for chloride ions (Cl-

the development of a new thermodynamic models and verification of existing ideas.

**CnH2n+1OH (n = 2-5). Experimental procedure**

filter system.

experiments performed with the use of two different ion-selective electrodes for Na+ can be considered as independent. This increases the statistical significance of the EMF values and provides information on their correctness. The potential of the cell was measured with the use of the Multitest IPL-103 ionomer. The input impedance of the ionomer was at least 1012 Ohm.

The concentration range of the working solution was determined by two factors. According to the manufacturer, the sodium electrode was more sensitive to protons than to sodium ions and the interfering effect of hydrogen ions can be ignored if [Na+]/[H+] > 3000 in the solution under consideration (*i.e*., at (pH – pNa) > 3.5). Therefore, the lower limit of molality in each series of solutions had to be no less than 0.03 molkg-1. To meet the condition of solution homogeneity, the highest concentration of NaCl had to be no higher than the solubility of the salt in the mixed solvent. The widest ranges of concentration were investigated in the systems with ethanol and 1-(*iso*-)propanol. All studied systems belong to the class of systems with the top critical point; the area of existence of solutions narrows with temperature increasing. To maintain the homogeneity of mixtures, the concentration of the salt in solutions was kept no higher than the upper solubility limit of sodium chloride in a mixed solvent of a given composition. In each series of experiments successive measurements were carried out for samples with constant ratios of water/alcohol components and different molalities starting with the lowest concentration. The choice of composition range is illustrated at Fig.1 where the fragment of Gibbs-Roseboom triangle of H2O-C2H5OH-NaCl system at 298.15 K is drawn.

Fig. 1. Fragment of the isothermal (298.15 K) section of sodium chloride – water – ethanol system. Symbols correspond to composition of solutions under investigation. Numbers I, II, III and IV are denoted to solutions with fixed water-alcohol ratio.

Symbols are met the case of real experiment with various sodium chloride molality and constant water-to-alcohol ratios. The symbols L and S denote the Liquid and Solid phases of the ternary system. Each series of solutions was studied at two or three temperatures. The EMF values of the cell were assumed to be equilibrium if the rate of the drift in EMF was no higher than 0.01-0.02 mVmin-1. The equilibrium was established, less than 30 min. The constancy of the composition of the solution was confirmed by the fact that the refractive indices measured before and after electrochemical experiments remained practically

Electromotive Force Measurements and

NaCl – H2O - C2H5OH

NaCl – H2O – *1*-C3H7OH

NaCl – H2O – *iso*-C3H7OH

NaCl – H2O – *1*-C4H9OH

NaCl – H2O – *iso*-C4H9OH

*T*, К *-E*0× 103, V (0)

CnH2n+1OH solutions.

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 91

NaCl – H2O 0 0.3856 0.3917 0.4059

288.15 K 298.15 K 318.15 K

9.99 0.4232 0.4300 0.4465 19.98 0.4690 0.4770 0.4953 39.96 0.5942 0.6047 0.6290

9.82 - 0.4437 0.4631 19.70 - 0.5121 0.5366 29.62 - 0.6021 0.6339 39.56 - 0.7231 0.7664

10.00 - 0.4466 - 20.00 - 0.5207 - 30.00 - 0.6191 - 40.00 - 0.7528 - 49.90 - 0.9373 - 58.50 - 1.1581 -

3.00 0.3958 0.4035 0.4204 4.49 0.4024 0.4104 0.4279 5.66 0.4079 0.4161 0.4359

3.00 0.3999 0.4119 0.4394 4.50 0.4103 0.4231 0.4510 5.66 0.4187 0.4315 0.4597

**,** kgmol -1 γ *С*NaCl **,** kg2mol -2 *s*0(*E*) ×

104

System *w*Alc, wt. % *A*

NaCl – H2O – *1*-C5H11OH 2.00 0.3866 0.3929 - NaCl – H2O – *iso*-C5H11OH 2.00 0.3860 0.3926 -

Table 1. Debye–Hückel coefficients for the osmotic function in NaCl-H2O-(*1-, iso-)*

**,** kgmol -1 (1)

NaCl

113.4 ± 0.2 0.0653 ± 0.007 0.2672 ± 0.03 0.0037 ± 0.002 0.8

115.9 ± 0.3 0.0720 ± 0.010 0.2802 ± 0.05 0.0039 ± 0.003 1.2

123.1 ± 0.7 0.0780 ± 0.021 0.3109 ± 0.10 0.0036 ±0.007 2.6

288.15 113.7 ± 0.2 0.0766 ± 0.002 0.2177 ± 0.02 0 1.2

298.15 116.1 ± 0.3 0.0838 ± 0.002 0.2285 ± 0.03 0 1.6

318.15 123.3 ± 0.5 0.0891 ± 0.004 0.2621 ± 0.04 0 2.8

NaCl

Table 2. Pitzer parameters for solutions of sodium chloride in water.

coincided. It appeared that a change in the weight fraction of the organic solvent during experiments was at most 0.06 wt.%.

In the first step, the operation of the electrochemical cell (I) containing an aqueous sodium chloride solution (*walc* = 0) was tested at 288.15, 298.15, and 318.15 К. The mean ionic activity coefficients of NaCl are consistent with the published data (Silvester & Pitzer, 1977; Truesdell, 1968; Pitzer & Mayorga, 1973; Lide, 2007-2008) within an experimental error. In the second step, electrochemical measurements with the use of sodium chloride solutions in water-alcohol solvents were carried out at various temperatures. Each composition was measured at least two times using the ISE-Na+ and ISE-Cl- ion-selective electrodes.

### **5. Thermodynamic properties of solutions in the NaCl – H2O – CnH2n+1OH (n = 2-5) system**

### **5.1 The mean ionic activity coefficient of the sodium chloride in the ternary solutions**

The temperature-concentration dependence of the mean ionic activity coefficient of NaCl was approximated using the Pitzer and Pitzer-Simonson model for 1:1 electrolytes. As mentioned above, the electromotive force of the electrochemical cell (I) is related to the activity coefficient of the salt by Eq.(14). In the present work the mean ionic activity coefficient of the salt was calculated with the asymmetric normalization, in which a mixed solvent with a fixed water-to-alcohol ratio and the extremely dilute sodium chloride solution in this mixed solvent served as the standard state of the components of the solutions. The Debye–Hückel coefficient for the osmotic function ( *A* ) was calculated by Eq. (5a) taking into account the experimental data on the densities and dielectric constants of water and the alcohols in the temperature range under consideration, which were published in (Bald et al., 1993; Frenkel et al., 1998; Balaban et al., 2002; Lide, 2007-2008; Pol & Gaba, 2008; Omrani et al., 2010). The *A* values used for each composition of the solvent at different temperatures are given in Table 1.

The numerical values of the parameters *E*0, (0) NaCl , (1) NaCl , and *C*NaCl were determined by the approximation of the experimental EMF values for each series of measurements. For all the solutions under consideration, the parameter *C*NaCl was insignificant and the error in its determination was higher than the absolute value. Hence, we assumed *C*NaCl = 0. It's known that the term *C*NaCl in Eq. (5) makes a considerable contribution only at high concentrations of the electrolyte, so this approach is valid for systems characterized by a narrow range of the existence of ternary solutions.

The calculated Pitzer model parameters and the errors in their determination (rms deviations) for the aqueous solution of sodium chloride are given in Table 2. The rms dispersions for each series of experimental data are listed in the last column. The parameters of Eq. (5) and (14) are given with an excess number of significant digits to avoid the error due to the rounding in further calculations. As can be seen from the Table 2, the model descriptions of water-salt solutions in both cases are similar, parameters consist within errors. So all experimental data for ternary mixtures were described taking into account the parameters *E*0, (0) NaCl , and (1) NaCl (see Table 3). Some of those results were published earlier (Mamontov et al., 2010; Veryaeva et al., 2010), thermodynamic assessment of NaCl-H2O-*1*(or *iso*-)C4H9OH system is accepted to the Fluid Phase Equilibria journal.

coincided. It appeared that a change in the weight fraction of the organic solvent during

In the first step, the operation of the electrochemical cell (I) containing an aqueous sodium chloride solution (*walc* = 0) was tested at 288.15, 298.15, and 318.15 К. The mean ionic activity coefficients of NaCl are consistent with the published data (Silvester & Pitzer, 1977; Truesdell, 1968; Pitzer & Mayorga, 1973; Lide, 2007-2008) within an experimental error. In the second step, electrochemical measurements with the use of sodium chloride solutions in water-alcohol solvents were carried out at various temperatures. Each composition was measured at least two times using the ISE-Na+ and ISE-Cl- ion-selective

**5. Thermodynamic properties of solutions in the NaCl – H2O – CnH2n+1OH**

solutions. The Debye–Hückel coefficient for the osmotic function ( *A*

**5.1 The mean ionic activity coefficient of the sodium chloride in the ternary solutions**  The temperature-concentration dependence of the mean ionic activity coefficient of NaCl was approximated using the Pitzer and Pitzer-Simonson model for 1:1 electrolytes. As mentioned above, the electromotive force of the electrochemical cell (I) is related to the activity coefficient of the salt by Eq.(14). In the present work the mean ionic activity coefficient of the salt was calculated with the asymmetric normalization, in which a mixed solvent with a fixed water-to-alcohol ratio and the extremely dilute sodium chloride solution in this mixed solvent served as the standard state of the components of the

(5a) taking into account the experimental data on the densities and dielectric constants of water and the alcohols in the temperature range under consideration, which were published in (Bald et al., 1993; Frenkel et al., 1998; Balaban et al., 2002; Lide, 2007-2008; Pol & Gaba,

> NaCl , (1)

the approximation of the experimental EMF values for each series of measurements. For all

concentrations of the electrolyte, so this approach is valid for systems characterized by a

The calculated Pitzer model parameters and the errors in their determination (rms deviations) for the aqueous solution of sodium chloride are given in Table 2. The rms dispersions for each series of experimental data are listed in the last column. The parameters of Eq. (5) and (14) are given with an excess number of significant digits to avoid the error due to the rounding in further calculations. As can be seen from the Table 2, the model descriptions of water-salt solutions in both cases are similar, parameters consist within errors. So all experimental data for ternary mixtures were described taking into account the

(Mamontov et al., 2010; Veryaeva et al., 2010), thermodynamic assessment of NaCl-H2O-*1*(or

determination was higher than the absolute value. Hence, we assumed *C*NaCl

NaCl

values used for each composition of the solvent at

was insignificant and the error in its

, and *C*NaCl

in Eq. (5) makes a considerable contribution only at high

(see Table 3). Some of those results were published earlier

) was calculated by Eq.

were determined by

= 0. It's

experiments was at most 0.06 wt.%.

2008; Omrani et al., 2010). The *A*

known that the term *C*NaCl

parameters *E*0, (0)

NaCl

, and (1)

NaCl

*iso*-)C4H9OH system is accepted to the Fluid Phase Equilibria journal.

different temperatures are given in Table 1. The numerical values of the parameters *E*0, (0)

the solutions under consideration, the parameter *C*NaCl

narrow range of the existence of ternary solutions.

electrodes.

**(n = 2-5) system**

Table 1. Debye–Hückel coefficients for the osmotic function in NaCl-H2O-(*1-, iso-)*  CnH2n+1OH solutions.

Table 2. Pitzer parameters for solutions of sodium chloride in water.

Electromotive Force Measurements and

0.049 – 1.799

0.050 – 0.600

0.050- 0.600

0.050- 0.650

in Fig. 2 *a*. The calculated values of

C4H9OH are shown in Fig. 3.

wt.% of alcohol. The trend is identical at other temperatures.

*w*Alc, wt. % *m*,

4.50 % *iso*-C4H9OH

5.66 % *iso*-C4H9OH

2.00 % *1*-C5H11OH

2.00 % *iso*-C5H11OH

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 93

1 2 3 4 5 6 7

Table 3. Pitzer parameters for solutions of sodium chloride in water-alcohol solvent.

As an example, the variation of mean ionic activity coefficient versus the electrolyte molality and various mass fraction percents of ethanol-water mixed solvents at 298.15 К, are shown

represented by solid lines in Figs. 2 *b*. The transparent symbols correspond to the dependence of mean activity coefficient of the alcohol-free solution obtained in the present study. All the curves show a typical profile of the variation of with concentrations that, as is well known, are governed by two types of interactions: ion–ion and ion–solvent. For a given temperature, the minimum value of mean ionic activity decreases with the increase of

If the parameters of the thermodynamic model are defined the calculation of any thermodynamic function is a routine mathematical operation. For example, Eq. (6) may be used for the estimation of the osmotic coefficient. The concentration dependences of this function in the ternary solutions containing 19.98 wt.% of C2H5OH and 3 wt.% of *iso*-

The NaCl-H2O-C2H5OH solutions belong to the most investigated system in comparison with other analogical objects, so it's possible to estimate the quality of our experimental data not only for aqueous solvent but for mixed solvent as well. Fig.2 *a* demonstrates a good agreement between literature data and the results of the present investigation. Hereinafter the system with ethanol as organic component was accounted as an object to test the various approaches to data approximation. The aim was to reveal the main factors that affected the accuracy of partial and integral properties determination based on the EMF measurements with ion-selective electrodes. The next factors were investigated: (a) a number of

Correlation between the quantity of experimental data and the results of calculation of mean ionic activity coefficients in the NaCl-H2O-C2H5OH system at 298.15 K and wAlc = 9.99 % is illustrated by Table 4. The Pitzer's model parameters at various numbers of input data (EMF, *m*NaCl) are listed. An analysis of the data presented in Table 4 shows that an increase in the number of experimental data (i.e. expansion of concentration range) does give noticeable advantages for the description of Pitzer's model. The standard deviation of approximation for more than seven *E,m*-pairs varies slightly (from 2.4 to 2.8) unlike the

experimental points included in approximation; (b) type of thermodynamic model.

(0) NaCl **,**  kgmol-1

288.15 1209 ± 0.3 0.0877 ± 0.004 0.1215 ± 0.03 1.2 298.15 1242 ± 0.3 0.0917 ± 0.004 0.1976 ± 0.03 1.4 318.15 1301 ± 0.5 0.0873 ± 0.007 0.3961 ± 0.05 2.0

288.15 124.8 ± 0.3 0.0765 ± 0.02 0.2322 ± 0.07 0.9 298.15 127.0 ± 0.3 0.0685 ± 0.02 0.3696 ± 0.07 0.9 318.15 134.2 ± 0.5 0.0179 ± 0.03 0.6969 ± 0.12 1.6

288.15 114.7 ± 0.6 0.0376 ± 0.04 0.3142 ± 0.15 1.9 298.15 117.6 ± 0.6 0.0762 ± 0.03 0.2634 ± 0.13 1.8

288.15 114.8 ± 0.4 0.0598 ± 0.02 0.2772 ± 0.08 1.1 298.15 117.3 ± 0.5 0.0768 ± 0.03 0.3012 ± 0.10 1.6

(NaCl) in mixed *1*-propanol-water solvent are

(1) NaCl **,** kgmol-1

*s*0(*E*) × 104

molkg-1 *T*, К *-E*0× 103, V

1 2 3 4 5 6 7

(0) NaCl **,**  kgmol-1

288.15 136.1 ± 0.4 0.0830 ± 0.003 0.1919 ± 0.04 2.0 298.15 138.6 ± 0.6 0.0884 ± 0.004 0.2468 ± 0.05 2.8 318.15 145.5 ± 0.8 0.0927 ± 0.006 0.2976 ± 0.07 4.3

288.15 158.3 ± 0. 0.0861 ± 0.004 0.1567 ± 0.04 2.5 298.15 160.7 ± 0.6 0.0912 ± 0.004 0.2566 ± 0.05 2.7 318.15 166.9 ± 0.7 0.0969 ± 0.005 0.3303 ± 0.06 3.9

288.15 203.2 ± 1 0.1109 ± 0.010 0.1165 ± 0.12 4.6 298.15 205.1 ± 1 0.1204 ± 0.010 0.1714 ± 0.13 4.9 318.15 212.6 ± 1 0.1189 ± 0.010 0.3497 ± 0.12 4.9

298.15 151.9 ± 0.4 0.0877 ± 0.003 0.2352 ± 0.03 2.0 318.15 159.6 ± 0.3 0.0955 ± 0.002 0.2432 ± 0.03 2.0

298.15 171.6 ± 0.2 0.0818 ± 0.003 0.2818 ± 0.02 1.0 318.15 178.3 ± 0.4 0.0906 ± 0.006 0.3442 ± 0.04 2.0

298.15 190.5 ± 0.2 0.0955 ± 0.007 0.2703 ± 0.04 1.0 318.15 197.4 ± 0.4 0.1073 ± 0.01 0.3955 ± 0.06 2.0

298.15 205.9 ± 0.3 0.0911 ± 0.01 0.5852 ± 0.04 1.0 318.15 216.4 ± 0.5 0.1120 ± 0.02 0.6472 ± 0.09 2.0

3.000 298.15 151.4 ± 0.5 0.0810±0.02 0.3417 ± 0.09 3.2

2.500 298.15 179.9 ± 0.5 0.0859 ± 0.004 0.3290 ± 0.04 2.0

2.000 298.15 198.0 ± 0.3 0.0884 ± 0.004 0.4658 ± 0.03 1.4

1.400 298.15 222.7 ± 0.5 0.0943 ± 0.007 0.6030 ± 0.06 1.0

0.952 298.15 243.6 ± 0.6 0.0939 ± 0.02 1.0109 ± 0.09 2.0

0.710 298.15 270.5 ± 0.3 0.1266 ± 0.01 1.2882 ± 0.05 1.0

288.15 118.4 ± 0.4 0.0774 ± 0.004 0.2090 ± 0.04 1.6 298.15 120.1 ± 0.4 0.0808 ± 0.004 0.2999 ± 0.03 1.5 318.15 127.7 ± 0.6 0.0881 ± 0.006 0.3200 ± 0.05 2.5

288.15 121.4 ± 0.6 0.0763 ± 0.01 0.2032 ± 0.08 2.5 298.15 123.8 ± 0.6 0.0939 ± 0.01 0.2246 ± 0.08 2.3 318.15 130.8 ± 0.5 0.0903 ± 0.01 0.3146 ± 0.07 1.8

288.15 124.0 ± 0.4 0.0952 ± 0.04 0.1501 ± 0.15 2.0 298.15 127.0 ± 0.4 0.1257 ± 0.03 0.1284 ± 0.11 1.4 318.15 134.1 ± 0.8 0.0883 ± 0.06 0.3314 ± 0.22 2.3

288.15 119.0 ± 0.6 0.0796 ± 0.006 0.1269 ± 0.06 2.8 298.15 121.3 ± 0.5 0.0839 ± 0.005 0.2565 ± 0.05 2.6 318.15 128.1 ± 0.8 0.0905 ± 0.007 0.3782 ± 0.08 4.2

(1) NaCl **,** kgmol-1

*s*0(*E*) × 104

molkg-1 *T*, К *-E*0× 103, V

*w*Alc, wt. % *m*,

0.050 - 2.999

0.050 - 2.998

0.050 - 2.000

0.0485 - 3.002

0.051 - 1.500

0.049 - 1.199

0.051 - 0.850

0.050 -

0.050 -

0.050 -

0.100 -

0.050 -

0.050 -

0.051 - 2.006

0.049 – 1.248

0.050 – 0.601

0.051 - 2.500

9.99 % C2H5OH

19.98 % C2H5OH

39.96 % C2H5OH

9.82 % *1*-C3H7OH

19.7 % *1*-C3H7OH

29.62 % *1*-C3H7OH

39.56 % *1*-C3H7OH

10.0% *iso*-C3H7OH

20.0% *iso*-C3H7OH

30.0% *iso*-C3H7OH

40.0 % *iso*-C3H7OH

49.9 % *iso*-C3H7OH

58.5% *iso*-C3H7OH

3.00 % *1*-C4H9OH

4.49 % *1*- C4H9OH

5.66 % *1*-C4H9OH

3.00 % *iso*-C4H9OH

Table 3. Pitzer parameters for solutions of sodium chloride in water-alcohol solvent.

As an example, the variation of mean ionic activity coefficient versus the electrolyte molality and various mass fraction percents of ethanol-water mixed solvents at 298.15 К, are shown in Fig. 2 *a*. The calculated values of (NaCl) in mixed *1*-propanol-water solvent are represented by solid lines in Figs. 2 *b*. The transparent symbols correspond to the dependence of mean activity coefficient of the alcohol-free solution obtained in the present study. All the curves show a typical profile of the variation of with concentrations that, as is well known, are governed by two types of interactions: ion–ion and ion–solvent. For a given temperature, the minimum value of mean ionic activity decreases with the increase of wt.% of alcohol. The trend is identical at other temperatures.

If the parameters of the thermodynamic model are defined the calculation of any thermodynamic function is a routine mathematical operation. For example, Eq. (6) may be used for the estimation of the osmotic coefficient. The concentration dependences of this function in the ternary solutions containing 19.98 wt.% of C2H5OH and 3 wt.% of *iso*-C4H9OH are shown in Fig. 3.

The NaCl-H2O-C2H5OH solutions belong to the most investigated system in comparison with other analogical objects, so it's possible to estimate the quality of our experimental data not only for aqueous solvent but for mixed solvent as well. Fig.2 *a* demonstrates a good agreement between literature data and the results of the present investigation. Hereinafter the system with ethanol as organic component was accounted as an object to test the various approaches to data approximation. The aim was to reveal the main factors that affected the accuracy of partial and integral properties determination based on the EMF measurements with ion-selective electrodes. The next factors were investigated: (a) a number of experimental points included in approximation; (b) type of thermodynamic model.

Correlation between the quantity of experimental data and the results of calculation of mean ionic activity coefficients in the NaCl-H2O-C2H5OH system at 298.15 K and wAlc = 9.99 % is illustrated by Table 4. The Pitzer's model parameters at various numbers of input data (EMF, *m*NaCl) are listed. An analysis of the data presented in Table 4 shows that an increase in the number of experimental data (i.e. expansion of concentration range) does give noticeable advantages for the description of Pitzer's model. The standard deviation of approximation for more than seven *E,m*-pairs varies slightly (from 2.4 to 2.8) unlike the

Electromotive Force Measurements and

NaCl-H2O-C2H5OH system (9.99 wt.%) at 298.15 К.

converted to the mole fraction basis by the equation

cell (I).

Number of

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 95

experimental points *-E*0× 103, V (0) NaCl **,** kgmol-1 (1) NaCl **,** kgmol-1 *s*0(*E*) × 104

7 138.6 ± 1.7 0.1074 ± 0.132 0.2132 ± 0.46 2.8 8 138.3 ± 1.1 0.0810 ± 0.053 0.2994 ± 0.23 2.6 9 138.3 ± 0.9 0.0809 ± 0.027 0.2998 ± 0.14 2.5 10 138.2 ± 0.7 0.0770 ± 0.017 0.3162 ± 0.10 2.4 11 138.4 ± 0.6 0.0823 ± 0.009 0.2889 ± 0.07 2.4 12 138.4 ± 0.5 0.0842 ± 0.007 0.2785 ± 0.06 2.4 13 138.5 ± 0.5 0.0850 ± 0.004 0.2728 ± 0.05 2.3 14 138.6 ± 0.6 0.0884 ± 0.004 0.2468 ± 0.05 2.8 Table 4. A comparison of Pitzer's model parameters with various set of input EMF data. The

For the estimation of model's type influence on the results of calculation the Pitzer theory was compared with the more complex Pitzer-Simonson model. According to the Pitzer formalism, the mean ionic activity coefficient of a strong electrolyte is defined within the molality mode related to the "ideal dilute standard". But the definitions which use mole fractions are more suitable or even necessary for the calculations of phase equilibria. The Pitzer-Simonson model is based on mole fractions. So initial values of (NaCl) were at first

> 2 s s (1 0.001 ) (1 0.001 )

, (15)

 *x m mM m mM*

where *M*s – is the mean molar mass of solvent. Calculated activity coefficients *x* were compared with those obtained by Eq. (13). This equation includes two groups of parameters for the description of the Gibbs excess energy of mixing in the frame of Pitzer-Simonson formalism: three pairs of binary parameters "salt-water", "alcohol-water", "salt-alcohol" and one ternary parameter. The long-range parameter for sodium chloride in diluted range (*BMX*) and short-range interaction parameters (*W*1NaCl and *U*1NaCl) related to salt (NaCl) and water (1) were estimated on the base of literature data (Pitzer & Mayorga, 1973) and own experiments. Results of calculation are presented in the Table 5. The binary interaction parameters for a system containing water (1) and ethanol (2) were determined by the minimization of the objective function, which was the sum of the squares of the relative deviations between the calculated and experimental values for different data sets in the H2O-C2H5OH system (see, for instance, Shishin et al. 2010; Konstantinova et al., 2011) or by using literature data (Lopes et al., 2001). The values of short-range interactions parameters *WnMX*, *VnMX*, *UnMX* (n = 1,2) related to sodium chloride and component of mixed solvent*,*  given in Table 5, were obtained from the results of EMF measurements of electrochemical

The differences between the activity coefficients of NaCl obtained from the two models are shown in Fig.4 for various temperatures and solvent compositions. The results demonstrate that both methods are adequate for treating the EMF measurements. A comparison of calculations with two models gives the largest difference of 5 % for the alcohol rich solution. At the same time the mean ionic activity coefficients of NaCl are consistent with the published data (Lopes et al., 2001) if the uniform Pitzer-Simonson model is used for data approximation; maximum error is equal to 1.5 % for the solution with *wAlc* = 19.98% at 318.15

significance of parameters; the approximation with only seven experimental points gave insignificant values. To improve a quality of description it is necessary to use more than 10 primary (*E, m*) measurements. In many cases it is impossible to extend the concentration range due to the restrictions for lower and upper limit of molality. So, a number of 12-14 points were considered as optimum set of data in each series of experiments. Other thermodynamic models (Pitzer-Simonson model or eNRTL) are less sensitive to the amount of input data. The advantage of those models is ability to use entire set of experimental data unlike Pitzer model where only the results for solution with a constant water/alcohol ratio are accounted.

Fig. 2. Mean ionic activity coefficients of NaCl in a NaCl-H2O-C2H5OH (*a*) and NaCl-H2O-*1-* C3H7OH (*b*) solution at 298.15 К. Transparent symbols (○) correspond to the NaCl-H2O solution without alcohol (Lide, 2007-2008; Silvester & Pitzer, 1977), fill symbols are the literature data (▲ - Esteso et al., 1989; ■ - Lopes et al., 2001), lines are the result of present investigation. Number I, II, III, IV and V correspond to the experimental data for solutions containing (*a*) 0, 9.99, 19.98 and 39.96 wt. % of the ethanol; (*b*) 0, 9.82, 19.70, 29.62, 39.96 wt. % 1-propanol, respectively.

Fig. 3. Osmotic coefficients in NaCl-H2O-C2H5OH (*w*Alc= 19.98%) (*a*) and NaCl-H2O-*iso-*C4H9OH (*w*Alc= 3.00%) (*b*) solutions, where the numbers I, II, and III indicate the experimental data at 288.15, 298.15, and 318.15 К, respectively.

significance of parameters; the approximation with only seven experimental points gave insignificant values. To improve a quality of description it is necessary to use more than 10 primary (*E, m*) measurements. In many cases it is impossible to extend the concentration range due to the restrictions for lower and upper limit of molality. So, a number of 12-14 points were considered as optimum set of data in each series of experiments. Other thermodynamic models (Pitzer-Simonson model or eNRTL) are less sensitive to the amount of input data. The advantage of those models is ability to use entire set of experimental data unlike Pitzer model where only the results for solution with a constant water/alcohol ratio

> I II III

(NaCl)

Fig. 2. Mean ionic activity coefficients of NaCl in a NaCl-H2O-C2H5OH (*a*) and NaCl-H2O-*1-* C3H7OH (*b*) solution at 298.15 К. Transparent symbols (○) correspond to the NaCl-H2O solution without alcohol (Lide, 2007-2008; Silvester & Pitzer, 1977), fill symbols are the literature data (▲ - Esteso et al., 1989; ■ - Lopes et al., 2001), lines are the result of present investigation. Number I, II, III, IV and V correspond to the experimental data for solutions containing (*a*) 0, 9.99, 19.98 and 39.96 wt. % of the ethanol; (*b*) 0, 9.82, 19.70, 29.62, 39.96 wt.

0.90

Fig. 3. Osmotic coefficients in NaCl-H2O-C2H5OH (*w*Alc= 19.98%) (*a*) and NaCl-H2O-*iso-*C4H9OH (*w*Alc= 3.00%) (*b*) solutions, where the numbers I, II, and III indicate the

0.92 0.94 0.96 0.98

1.00

III II I

0.78

0.66

0.54

0.42

I II

III

III II I

IV

*m*(NaCl), molkg-1

0 1.0 2.0

*m*(NaCl), molkg-1

0 1.0 2.0 3.0

V

IV

(*a*) (*b*)

0 1.0 2.0 3.0 *m*(NaCl), molkg-1

*m*(NaCl), molkg-1

(*a*) (*b*)

experimental data at 288.15, 298.15, and 318.15 К, respectively.

0 1.0 2.0 3.0

are accounted.

0.8

0.7

(NaCl)

0.88

0.92

0.96

1.00

1.04

0.6

0.5

0.4

% 1-propanol, respectively.

0.9

Table 4. A comparison of Pitzer's model parameters with various set of input EMF data. The NaCl-H2O-C2H5OH system (9.99 wt.%) at 298.15 К.

For the estimation of model's type influence on the results of calculation the Pitzer theory was compared with the more complex Pitzer-Simonson model. According to the Pitzer formalism, the mean ionic activity coefficient of a strong electrolyte is defined within the molality mode related to the "ideal dilute standard". But the definitions which use mole fractions are more suitable or even necessary for the calculations of phase equilibria. The Pitzer-Simonson model is based on mole fractions. So initial values of (NaCl) were at first converted to the mole fraction basis by the equation

$$\gamma\_x = \gamma\_m (1 + 0.001 m M\_s) = \left(\gamma\_\pm\right)^2 m (1 + 0.001 m M\_s) \,\,\,\,\tag{15}$$

where *M*s – is the mean molar mass of solvent. Calculated activity coefficients *x* were compared with those obtained by Eq. (13). This equation includes two groups of parameters for the description of the Gibbs excess energy of mixing in the frame of Pitzer-Simonson formalism: three pairs of binary parameters "salt-water", "alcohol-water", "salt-alcohol" and one ternary parameter. The long-range parameter for sodium chloride in diluted range (*BMX*) and short-range interaction parameters (*W*1NaCl and *U*1NaCl) related to salt (NaCl) and water (1) were estimated on the base of literature data (Pitzer & Mayorga, 1973) and own experiments. Results of calculation are presented in the Table 5. The binary interaction parameters for a system containing water (1) and ethanol (2) were determined by the minimization of the objective function, which was the sum of the squares of the relative deviations between the calculated and experimental values for different data sets in the H2O-C2H5OH system (see, for instance, Shishin et al. 2010; Konstantinova et al., 2011) or by using literature data (Lopes et al., 2001). The values of short-range interactions parameters *WnMX*, *VnMX*, *UnMX* (n = 1,2) related to sodium chloride and component of mixed solvent*,*  given in Table 5, were obtained from the results of EMF measurements of electrochemical cell (I).

The differences between the activity coefficients of NaCl obtained from the two models are shown in Fig.4 for various temperatures and solvent compositions. The results demonstrate that both methods are adequate for treating the EMF measurements. A comparison of calculations with two models gives the largest difference of 5 % for the alcohol rich solution. At the same time the mean ionic activity coefficients of NaCl are consistent with the published data (Lopes et al., 2001) if the uniform Pitzer-Simonson model is used for data approximation; maximum error is equal to 1.5 % for the solution with *wAlc* = 19.98% at 318.15

Electromotive Force Measurements and

Section 3.

electrolyte systems.

where *ex Gx* and NaCL 0

solutions ( NaCl 0

**5.2 Integral properties of ternary solutions**

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 97

The integral properties of solutions were calculated with the Pitzer, Pitzer-Simonson model and by the Darken method. In the former case, the molality concentration scale was used, and the mixed solvent and the extremely dilute solution of the salt in this solvent were taken as the base. The formulas used for the calculation of the integral functions are listed in

One of the features of the EMF-experiment with ion-selective electrodes is a step-by-step increase of the molality at a fixed ratio of the solvent components in every experiment. As a result, the composition of the system under investigation is changing through the quasibinary section of ternary system. This allows to use the Darken method for the calculation of the integral properties of such solutions. The essence of this procedure is an integration of the Gibbs-Duhem equation in the ternary solution at a constant ratio for any two components. This method is widely used for the results of the electrochemical measurements for ternary metal alloys but has not been applied yet for the aqueous

Since solutions from one series of the EMF-measurements belong to particular NaCl- [H2O+Alc]H2O/Alc section of the ternary system with fixed relation of alcohol and water, the

NaCl

NaCl 0 2 NaCl 0 NaCl

sodium chloride equal to *x*NaCl or 0, respectively. The excess chemical potential of NaCl is

 ex NaCl Alc w Alc Alc ln 2ln ln 1 0.001 1

*RT RT x m m x M xM*

where *M*w, *M*Alс are the molar masses of water and alcohol, and Alc *x* is the mole fraction of alcohol in salt-free solvent. The temperature-concentrations dependences of the mean ionic activity coefficient of NaCl and the excess Gibbs energies of water-alcohol binary

solutions according to Eq. (16). The former may be obtained from the approximation of the results of the EMF measurements. In the case of ISE two unknown values – *E*0 and are presented in Eq.(14) unlike common galvanic cells with one unknown . The Darken method has obvious advantages for the processing of electrochemical experiments with common electrodes due to the possibility to provide a numerical integration of the Gibbs-Duhem equation. The result of this calculation does not depend upon the type of the model; thus the error in integral properties determination may be reduced. The approximation of EMF-ISE measurements includes a choice of a thermodynamic model. In such situation Darken method can be considered as an alternative way to calculate Gibbs energy of solution in molar mode. For instance, if the Pitzer formalism is used then

*ex Gx* are the excess integral Gibbs energy of solution at mole fractions of

, (17)

*ex Gx* ) are necessary for the calculation of integral properties of ternary

*x*

1-

ex NaCl

> Alc H O2

. (16)

*x x*

following equation can be used for the excess Gibbs energy of such solutions:

(1 )

*x x*

*x ex ex*

NaCL

*G xG dx*

connected with the activity coefficient in various concentration scales by the relation

К. An analysis of the data presented in Table 3 and Table 5 confirms the conclusion of Lopes that the variation of the activity coefficients of salt with the temperature or with the alcohol content is always smoother when the Pitzer–Simonson equations are used.

Fig. 4. The difference between Pitzer-Simonson and Pitzer model calculations at 288.15 К (*a*) and 298.15 К (*b*). A number I, II and III corresponds to various composition of solvent: 9.99, 19.98 and 39.96 w.%, respectively.

Table 5. Interaction parameters of the Pitzer-Simonson model for the binary NaCl-H2O and ternary NaCl-H2O-C2H5OH solutions.

Unlike in the Pitzer formalism, some of the binary interaction parameters in the Pitzer-Simonson model are defined independently by the approximation experimental data in Water-Alcohol and Water-Salt systems. In principle, the difference in those parameters can cause discrepancies in the results of calculation from various scientific groups. For the estimation of possible error we calculate the mean ionic activity coefficients with a various sets of water-ethanol interaction parameters. Model parameters were calculated using the primary experimental data about vapour-liquid equilibria that were obtained by various authors in the H2O-C2H5OH system. It was revealed that this factor does not affect to the result of x calculation; the difference in values is less than a hundredth of a percent.

### **5.2 Integral properties of ternary solutions**

96 Electromotive Force and Measurement in Several Systems

К. An analysis of the data presented in Table 3 and Table 5 confirms the conclusion of Lopes that the variation of the activity coefficients of salt with the temperature or with the alcohol

0

*T,* K 288.15 298.15 318.15 *w*12 1.1934 1.2051 1.2285 *u*12 0.2123 0.2583 0.3505 *W*1*NaCl* 6.1366 5.9187 5.6356 *U*1*NaCl* 4.5747 4.1214 3.5427 *BNaCl* 12.6266 12.8566 14.2752 *Z*12*NaCl* 7.2780 2.0676 3.0343 *W*2*NaCl* 35.1662 24.7911 16.9476 *U*2*NaCl* 31.0909 27.0080 15.8373

1.5

,PS - ,P, %

Fig. 4. The difference between Pitzer-Simonson and Pitzer model calculations at 288.15 К (*a*) and 298.15 К (*b*). A number I, II and III corresponds to various composition of solvent: 9.99,

*-E*0*(wAlc*-9.99%*)*×103*,*V 373.67 373.76 377.08 *-E*0*(wAlc-*19.98*%)*×103*,* V 439.95 428.07 411.08 *-E*0*(wAlc-*39.96%*)*×103*,* V 600.63 552.08 488.78 s0(E)×103 4.2 4.4 4.4

Table 5. Interaction parameters of the Pitzer-Simonson model for the binary NaCl-H2O and

Unlike in the Pitzer formalism, some of the binary interaction parameters in the Pitzer-Simonson model are defined independently by the approximation experimental data in Water-Alcohol and Water-Salt systems. In principle, the difference in those parameters can cause discrepancies in the results of calculation from various scientific groups. For the estimation of possible error we calculate the mean ionic activity coefficients with a various sets of water-ethanol interaction parameters. Model parameters were calculated using the primary experimental data about vapour-liquid equilibria that were obtained by various authors in the H2O-C2H5OH system. It was revealed that this factor does not affect to the

result of x calculation; the difference in values is less than a hundredth of a percent.

3.0

4.5

0 0.02 0.04 0.06

I II III

*x*(NaCl)

content is always smoother when the Pitzer–Simonson equations are used.

I II III

*x*(NaCl) 0 0.02 0.04 0.06

19.98 and 39.96 w.%, respectively.

ternary NaCl-H2O-C2H5OH solutions.

0

1.5

,PS - ,P, %

3.0

4.5

The integral properties of solutions were calculated with the Pitzer, Pitzer-Simonson model and by the Darken method. In the former case, the molality concentration scale was used, and the mixed solvent and the extremely dilute solution of the salt in this solvent were taken as the base. The formulas used for the calculation of the integral functions are listed in Section 3.

One of the features of the EMF-experiment with ion-selective electrodes is a step-by-step increase of the molality at a fixed ratio of the solvent components in every experiment. As a result, the composition of the system under investigation is changing through the quasibinary section of ternary system. This allows to use the Darken method for the calculation of the integral properties of such solutions. The essence of this procedure is an integration of the Gibbs-Duhem equation in the ternary solution at a constant ratio for any two components. This method is widely used for the results of the electrochemical measurements for ternary metal alloys but has not been applied yet for the aqueous electrolyte systems.

Since solutions from one series of the EMF-measurements belong to particular NaCl- [H2O+Alc]H2O/Alc section of the ternary system with fixed relation of alcohol and water, the following equation can be used for the excess Gibbs energy of such solutions:

$$\mathbf{G}\_{\rm x}^{\rm cx} = \left(\mathbf{1} - \mathbf{x}\_{\rm NaCl}\right) \left[\mathbf{G}\_{\rm x\_{\rm NaCl} = 0}^{\rm cx} + \int\_{0}^{\mathbf{x}\_{\rm NaCl}} \frac{\mu\_{\rm NaCl}^{\rm ex}}{\left(\mathbf{1} \cdot \mathbf{x}\_{\rm NaCl}\right)^{2}} d\mathbf{x}\_{\rm NaCl}\right]\_{\frac{\mathbf{x}\_{\rm Alk}}{\mathbf{x}\_{\rm H\_2O}}}.\tag{16}$$

where *ex Gx* and NaCL 0 *ex Gx* are the excess integral Gibbs energy of solution at mole fractions of sodium chloride equal to *x*NaCl or 0, respectively. The excess chemical potential of NaCl is connected with the activity coefficient in various concentration scales by the relation

$$\mu\_{\text{NaCl}}^{\text{ex}} = RT \ln \gamma\_{\text{x}} = RT \left( 2 \ln \gamma\_{\pm} + \ln \left( m \left( \mathbf{1} + 0.001 m \left| \left( \mathbf{1} - \mathbf{x}\_{\text{Ak}}^{\text{w}} \right) M\_{\text{w}} + \mathbf{x}\_{\text{Ak}}^{\text{w}} M\_{\text{Ak}} \right| \right) \right) \right) \tag{17}$$

where *M*w, *M*Alс are the molar masses of water and alcohol, and Alc *x* is the mole fraction of alcohol in salt-free solvent. The temperature-concentrations dependences of the mean ionic activity coefficient of NaCl and the excess Gibbs energies of water-alcohol binary solutions ( NaCl 0 *ex Gx* ) are necessary for the calculation of integral properties of ternary solutions according to Eq. (16). The former may be obtained from the approximation of the results of the EMF measurements. In the case of ISE two unknown values – *E*0 and are presented in Eq.(14) unlike common galvanic cells with one unknown . The Darken method has obvious advantages for the processing of electrochemical experiments with common electrodes due to the possibility to provide a numerical integration of the Gibbs-Duhem equation. The result of this calculation does not depend upon the type of the model; thus the error in integral properties determination may be reduced. The approximation of EMF-ISE measurements includes a choice of a thermodynamic model. In such situation Darken method can be considered as an alternative way to calculate Gibbs energy of solution in molar mode. For instance, if the Pitzer formalism is used then

Electromotive Force Measurements and

0 0.02 0.04 0.06 0.08

0 0.01 0.02 0.03 0.04 0.05

*x*(NaCl)

VI

I

IV

(*a*) (*b*)

(*a*) the weight fraction of alcohol in solvent; (*b*) the mole fraction of NaCl.

mix

0

I II III

are connected by a solid line.

mix

*H*, Jmol-1

III

V

VII

II

0

*G*, Jmol-1

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 99

VII

VI

*x*(NaCl) *x*(Alc)/{*x*(Alc) + *x*(H2O)}

I

II III

I

II III

IV

*x*(Alc)/{*x*(Alc) + *x*(H2O)}

mix

Fig. 5. The isothermal (298.15 K) sections of Gibbs energy surface of solutions of H2O–*iso*-С3H7OH–NaCl with constant (*a*) the ratio of water and alcohol; (*b*) the weight fraction of alcohol in solvent. The numbers correspond to solutions with the weight fraction of alcohol in solvent is: (I) 0, (II) 10.0, (III) 20.0, (IV) 30.0, (V) 40.0, (VI) 49.9, (VII) 58.5 wt. % (*a*); and with mole fraction of sodium chloride equal to: (I) 0, (II) 0.01, (III) 0.02, (IV) 0.03, (V) 0.04, (VI) 0.05, (VI) 0.06 (*b*). Dashed lines indicate the extrapolated values of the Δmix*G* function outside the range of experimental research. The line width increases with the increasing of

mix

Fig. 6. Isothermal sections of the surface of the enthalpy of mixing of the NaCl–H2O–*iso*-С4H9OH solution at 298.15 К along the sections with constant water-to-alcohol ratios (*a*); the weight fraction of the alcohol in the solvent (*wAlc*) is (I) - 3.0; (II) - 4.5; (III) - 5.66 wt. %, dashed line – without alcohol; (*b*) along the sections with constant mole fractions of sodium chloride; *x*NaCl is (I) - 0.01; (II) - 0.02; (III) - 0.03; (IV) - 0.04. The points in each section at (*b*)

*H*, Jmol-1

0

*G*, Jmol-1

IV V

0

the excess Gibbs energy of the ternary solution is calculated by the equation (for more detail see Mamontov et al., 2010):

$$\begin{aligned} G\_x^{\text{cr}} &= \frac{G\_{\text{NaCl}}^{\text{cr}} - 0}{\{1 + 0.001 \cdot mM\}} + \\ &\frac{2RT \cdot M}{\left(1000 + mM\right)} \Bigg( -\frac{2}{1.2} A\_\vartheta m \ln(1 + 1.2m^{1/2}) + \beta\_\text{NaCl}^{(0)} \cdot m^2 + \frac{\beta\_\text{NaCl}^{(1)} m}{2} (1 - (1 + 2m^{1/2}) \exp(-2m^{1/2})) + \\ &\left( \frac{C\_\text{NaCl}^{\text{cr}}}{2} m^3 + \frac{1}{2} \Big( m \cdot \ln(m) - 2m + \frac{1000}{M} (1 + 0.001 mM) \ln(1 + 0.001 mM) \Big) \right) \end{aligned} \tag{18}$$

To calculate the excess Gibbs energies of water-alcohol binary solutions it is necessary to construct a thermodynamic model of those solutions. The model parameters of aqueous solutions of alcohols were proposed in numerous studies (see, for example, Gmehling & Onken, 1977 or subsequent Editions). In the present study we used a results of own assessment of Water-Alcohol systems with NRTL model (Shishin et al., 2010; Konstantinova et al., 2011). The main merit of our approach is a use of unified equation of the Gibbs energy of a water-alcohol solution for the description of various types of equilibria: vapor-liquid and liquid-liquid.

Pure alcohol and water, along with a hypothetical infinitely dilute solution of NaCl in the mixed solvent, were chosen as the standard state of the solution components during integration by the Darken's method. To go to the unified reference system (pure solvents and the extremely dilute solution of the salt in water), the so-called Born contribution accounting for the change in the Gibbs energy ( ex *G*Born ) was used (see Eq.(4)). The Gibbs energy of formation of the solution in this reference system can be written as follows:

$$\Delta\_{\rm mix} G = RT \cdot \left( \mathbf{x}\_{\rm H\_2O} \ln \mathbf{x}\_{\rm H\_2O} + \mathbf{x}\_{\rm Alc} \ln \mathbf{x}\_{\rm Alc} + \mathbf{x}\_{\rm NaCl} \ln \mathbf{x}\_{\rm NaCl} \right) + G\_x^{\rm ex} + G\_{\rmBorn}^{\rm ex} \,. \tag{19}$$

Other thermodynamic functions were obtained from Eq.(19) by means of common thermodynamic relations, for example, Gibbs-Helmholtz equation. Next figures illustrate some results of the calculation. Fig. 5 *a,b* shows the isothermal (298.15 K) sections of Gibbs energy surface for the solution formed by sodium chloride, water, and *iso*-propanol with a constant ratio of water and alcohol in solvent, and with a constant mole fraction of sodium chloride. Since all electrochemical measurements were carried out with the use of homogeneous mixtures, no anomalies are observed in the curves in Fig. 5 in the region of the measured compositions (solid lines), and they are shifted with respect to each other in the expected way. Fig. 6 shows the sections of the surface of the enthalpy of mixing of the solution with *iso*-butanol at a constant composition of the solvent and a constant fraction of NaCl at 298.15 К. The relative enthalpy of the ternary solution changes only slightly in the temperature range under consideration.

The Darken method is theoretically justified, so there is no reason to doubt the correctness of the results. Additionally we compared the values of thermodynamic function been calculated with this approach and Pitzer-Simonson model. As can be seen from the Fig.7 the results are in excellent agreement.

the excess Gibbs energy of the ternary solution is calculated by the equation (for more

NaCl

*mM C m mmm mM mM M*

To calculate the excess Gibbs energies of water-alcohol binary solutions it is necessary to construct a thermodynamic model of those solutions. The model parameters of aqueous solutions of alcohols were proposed in numerous studies (see, for example, Gmehling & Onken, 1977 or subsequent Editions). In the present study we used a results of own assessment of Water-Alcohol systems with NRTL model (Shishin et al., 2010; Konstantinova et al., 2011). The main merit of our approach is a use of unified equation of the Gibbs energy of a water-alcohol solution for the description of various types of equilibria: vapor-liquid

Pure alcohol and water, along with a hypothetical infinitely dilute solution of NaCl in the mixed solvent, were chosen as the standard state of the solution components during integration by the Darken's method. To go to the unified reference system (pure solvents and the extremely dilute solution of the salt in water), the so-called Born contribution accounting for the change in the Gibbs energy ( ex *G*Born ) was used (see Eq.(4)). The Gibbs energy of formation of the solution in this reference system can be written as

2 2

Other thermodynamic functions were obtained from Eq.(19) by means of common thermodynamic relations, for example, Gibbs-Helmholtz equation. Next figures illustrate some results of the calculation. Fig. 5 *a,b* shows the isothermal (298.15 K) sections of Gibbs energy surface for the solution formed by sodium chloride, water, and *iso*-propanol with a constant ratio of water and alcohol in solvent, and with a constant mole fraction of sodium chloride. Since all electrochemical measurements were carried out with the use of homogeneous mixtures, no anomalies are observed in the curves in Fig. 5 in the region of the measured compositions (solid lines), and they are shifted with respect to each other in the expected way. Fig. 6 shows the sections of the surface of the enthalpy of mixing of the solution with *iso*-butanol at a constant composition of the solvent and a constant fraction of NaCl at 298.15 К. The relative enthalpy of the ternary solution changes only slightly in the

The Darken method is theoretically justified, so there is no reason to doubt the correctness of the results. Additionally we compared the values of thermodynamic function been calculated with this approach and Pitzer-Simonson model. As can be seen from the Fig.7 the

H O H O Alc Alc NaCl NaCl Born *mixG RT x x x x x x G G* ln ln ln *x* . (19)

*m Am m m m m RT M*

(1000 ) 1 1000 ln( ) 2 (1 0.001 )ln(1 0.001 ) 2 2

2 ln(1 1.2 ) (1 (1 2 )exp( 2 )) 2 1.2 2

(1)

1/2 (0) 2 NaCl 1/2 1/2

ex ex

(18)

detail see Mamontov et al., 2010):

NaCL 0

*mM*

temperature range under consideration.

results are in excellent agreement.

(1 0.001 )

*ex*

*G*

*ex x*

*x*

and liquid-liquid.

follows:

*G*

3

*NaCl*

Fig. 5. The isothermal (298.15 K) sections of Gibbs energy surface of solutions of H2O–*iso*-С3H7OH–NaCl with constant (*a*) the ratio of water and alcohol; (*b*) the weight fraction of alcohol in solvent. The numbers correspond to solutions with the weight fraction of alcohol in solvent is: (I) 0, (II) 10.0, (III) 20.0, (IV) 30.0, (V) 40.0, (VI) 49.9, (VII) 58.5 wt. % (*a*); and with mole fraction of sodium chloride equal to: (I) 0, (II) 0.01, (III) 0.02, (IV) 0.03, (V) 0.04, (VI) 0.05, (VI) 0.06 (*b*). Dashed lines indicate the extrapolated values of the Δmix*G* function outside the range of experimental research. The line width increases with the increasing of (*a*) the weight fraction of alcohol in solvent; (*b*) the mole fraction of NaCl.

Fig. 6. Isothermal sections of the surface of the enthalpy of mixing of the NaCl–H2O–*iso*-С4H9OH solution at 298.15 К along the sections with constant water-to-alcohol ratios (*a*); the weight fraction of the alcohol in the solvent (*wAlc*) is (I) - 3.0; (II) - 4.5; (III) - 5.66 wt. %, dashed line – without alcohol; (*b*) along the sections with constant mole fractions of sodium chloride; *x*NaCl is (I) - 0.01; (II) - 0.02; (III) - 0.03; (IV) - 0.04. The points in each section at (*b*) are connected by a solid line.

Electromotive Force Measurements and

298.15 K

22.4 ± 0.4

44.6 ± 0.6

89.0 ± 1.0

0.7

0.6

0.6

0.7

318.15 K

22.5 ± 0.6

43.6 ± 0.7

89.3 ± 1.0

23.2 ± 0.8 -

41.9 ± 0.7 -

61.0 ± 0.7 -

80.0 ± 0.8 -

CnH2n+1OH (*walc*%) mixed solvent at various temperatures.

288.15 K

9.99 22.4 ± 0.4

19.98 44.6 ±

39.96 89.5 ±

0.5

1.0

9.82 - 22.4 ±

19.70 - 42.1 ±

29.62 - 61.0 ±

39.56 - 76.4 ±

3.00 -4.7 ± 0.4

4.49 -7.7 ± 0.6

5.66 -10.3 ± 0.4

2.00 -1 ±

0.6

walc, %

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 101

Water-ethanol solvent

K 298.15 K 318.15

2170 ± 60 1910 ± 100 (Mazzarese & Popovych, 1983 5600 ± 100 (Kalida et al., 2000)

4300 ± 60 3880 ± 100 (Mazzarese & Popovych, 1983) 6400 ± 100 (Kalida et al., 2000)

8590 ± 100 (\*) 8330 ± 100 (Mazzarese & Popovych, 1983) 8000 ± 100 (Kalida et al., 2000)

2161 ± 70 2036 ± 80 (Gregorowicz et al., 1996)

4062 ± 60 3908 ± 80 (Gregorowicz et al., 1996)

5885 ± 60 5649 ± 80 (Gregorowicz et al., 1996)

7371 ± 70 7451 ± 80 (Gregorowicz et al., 1996)

390 ± 40

740 ± 58

1050 ± 40

640 ± 70 (Chu et al., 1987) 430 ± 60

960 ± 100 (Chu et al., 1987) 720 ± 50

1200 ± 120 (Chu et al., 1987) 1040 ± 80

K

2140 ± 80

4210 ± 70

8620 ± 100

2238 ± 80

4042 ± 70

5885 ± 70

7718 ± 80

288.15

2.16 ± 0.04

4.30 ± 0.05

8.64 ± 0.10

Water-*n*-propanol solvent

Water-*n*-butanol solvent

Water-*n*-pentanol solvent

It can be seen that the values of the standard functions of transfer determined in the present study do not contradict to those recommended in the literature. Data for the propanols are in satisfactory agreement with results (Gregorowicz et al., 1996). In the case of butanols the values of the standard functions of transfer at 298.15 К are shifted to smaller values

0.5 - 99 ± 58 147 ± 48 -

450 ± 40

740 ± 60

990 ± 40

Table 6. Standard Gibbs energy of transfer of NaCl from H2O to the H2O (100-*walc*%) +

Fig. 7. The difference between results of Gibbs energy calculation of the NaCl-H2O-C2H5OH solution at 298.15 K (*a*) ad 318.15 К (*b*) with Darken method and Pitzer-Simonson model. A number I, II, III corresponds to various composition of solvent: 9.99, 19.98 and 39.96 w.%, respectively.

### **5.3 Standard thermodynamic functions of transfer of salt from water to the mixed solvent**

The electrochemical measurements allowed us not only to calculate the mean ionic activity coefficients, the Gibbs energies, and the enthalpies of mixing of ternary solutions but also to estimate the standard thermodynamic functions of transfer of salt from water to a mixed solvent. The standard Gibbs energy of transfer is defined as the difference between the standard Gibbs 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 energy of the solute when it is transferred from one solvent to another at infinite dilution and can be easily calculated according to the expression:

$$
\Delta\_{\rm tr} G\_T^0 = -F(E\_{0,s} - E\_{0,\rm w}) \tag{20}
$$

where *E*0,s and *E*0,w are the standard electrode potentials of the electrochemical cell (I) for the mixed solvent and water, respectively. The values o tr*GТ* were calculated for each temperature and the composition of the solution based on the data presented in Table 6. Fig. 8 *a* shows tr*G vs*. *n* (number of carbon atoms in *n*- and *iso*-alcohol) for ternary solutions with *w*Alc = 5 % at 298 K. It is surprising the decrease of Gibbs energy of transfer for aqueousalcohol mixtures with n > 3. Apparently, this phenomenon requires further investigation.

mix

Fig. 7. The difference between results of Gibbs energy calculation of the NaCl-H2O-C2H5OH solution at 298.15 K (*a*) ad 318.15 К (*b*) with Darken method and Pitzer-Simonson model. A number I, II, III corresponds to various composition of solvent: 9.99, 19.98 and 39.96 w.%,

**5.3 Standard thermodynamic functions of transfer of salt from water to the mixed**

The electrochemical measurements allowed us not only to calculate the mean ionic activity coefficients, the Gibbs energies, and the enthalpies of mixing of ternary solutions but also to estimate the standard thermodynamic functions of transfer of salt from water to a mixed solvent. The standard Gibbs energy of transfer is defined as the difference between the standard Gibbs 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 energy of the solute when it is transferred from one solvent to another at infinite dilution and can be easily

where *E*0,s and *E*0,w are the standard electrode potentials of the electrochemical cell (I) for the mixed solvent and water, respectively. The values o tr*GТ* were calculated for each temperature and the composition of the solution based on the data presented in Table 6. Fig. 8 *a* shows tr*G vs*. *n* (number of carbon atoms in *n*- and *iso*-alcohol) for ternary solutions with *w*Alc = 5 % at 298 K. It is surprising the decrease of Gibbs energy of transfer for aqueousalcohol mixtures with n > 3. Apparently, this phenomenon requires further investigation.

0

0.02

0.04

0.06

*G*PS- mix

*G*P, Jmol-1

I II III

*x*(NaCl)

o tr*G FE E Т* ( ) 0,s 0,w (20)

I II III

(*a*) (*b*)

0 0.02 0.04 0.06 *x*(NaCl)

calculated according to the expression:

mix

0

respectively.

**solvent**

0.02

0.04

0.06

*G*PS- mix

*G*P, Jmol-1

Table 6. Standard Gibbs energy of transfer of NaCl from H2O to the H2O (100-*walc*%) + CnH2n+1OH (*walc*%) mixed solvent at various temperatures.

It can be seen that the values of the standard functions of transfer determined in the present study do not contradict to those recommended in the literature. Data for the propanols are in satisfactory agreement with results (Gregorowicz et al., 1996). In the case of butanols the values of the standard functions of transfer at 298.15 К are shifted to smaller values

Electromotive Force Measurements and

pp. 121-133, ISSN 0031-9104

1547-5905

112, ISSN 0378-3812

5905

**7. Acknowledgment**

**8. References**

Thermodynamic Modelling of Sodium Chloride in Aqueous-Alcohol Solvents 103

This work was supported by the RFBR (project 09-03-01066) and the URALCHEM holding.

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$$
\Delta E\_0 = E\_{0,s} - E\_{0,w} = N\_h k\_\text{g} \log w \tag{21}
$$

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Fig. 8. Plot of tr*G vs*. n (in C*n*H2*n+*1OH*)* (*a*) and *N*hyd *vs*. n (*b*) ; the filled symbol - present work, the transparent symbol (Mazzarese & Popovych, 1983; Chu et al., 1987). *T* = 298.15 K

### **6. Conclusion**

Systematic studies of electrochemical cells with Na+ and Cl- ion-selective electrodes in aqueous-alcohol solvents were performed. Analysis of the results have shown that the major sources of uncertainty of the partial properties in the EMF measurements with the ISE are the choice of model solution and the amount of input data that take into account at the approximation. Therefore, when comparing the activity coefficients of electrolyte obtained in various researches groups should pay particular attention to the method of data processing.

The Darken method was first used to calculate the integral properties of electrolyte solutions. It was shown that the Gibbs energy of mixing calculated by the Pitzer-Simonson model and the Darken method are in excellent agreement.

The results of present investigation can be used to the verification of proposed thermodynamic models and for the development of alternative theories of electrolyte solutions.

### **7. Acknowledgment**

This work was supported by the RFBR (project 09-03-01066) and the URALCHEM holding.

### **8. References**

102 Electromotive Force and Measurement in Several Systems

compared to those recommended in the study (Chu et al., 1987). In all cases an increase in the standard Gibbs energy of transfer is observed with the increase of alcohol in the mixture, which would indicate a decrease in hydration of electrolyte in the mixture. Using the Feakins and French equation (Feakins & French, 1957), it is possible to estimate the primary hydration number of the electrolyte based on the dependency between the standard electromotive force of the cell and the logarithm of the mass fraction of water in the mixture:

where *k*B is a is the Boltzmann constant. This value varies from 8 for methanol to 0.5 for butanol and coincides for different homologs of alcohols within error. Fig. 8 *b* shows the plot of *N*hyd *vs*. n*.* The solid lines in both graphics have no physical meaning, they represent a

*N*hyd

0

Fig. 8. Plot of tr*G vs*. n (in C*n*H2*n+*1OH*)* (*a*) and *N*hyd *vs*. n (*b*) ; the filled symbol - present work, the transparent symbol (Mazzarese & Popovych, 1983; Chu et al., 1987). *T* = 298.15 K

Systematic studies of electrochemical cells with Na+ and Cl- ion-selective electrodes in aqueous-alcohol solvents were performed. Analysis of the results have shown that the major sources of uncertainty of the partial properties in the EMF measurements with the ISE are the choice of model solution and the amount of input data that take into account at the approximation. Therefore, when comparing the activity coefficients of electrolyte obtained in various researches groups should pay particular attention to the method of data

The Darken method was first used to calculate the integral properties of electrolyte solutions. It was shown that the Gibbs energy of mixing calculated by the Pitzer-Simonson

The results of present investigation can be used to the verification of proposed thermodynamic models and for the development of alternative theories of electrolyte

8

6

4

2

trend.

trG, Jmol-1

500

0

**6. Conclusion**

processing.

solutions.

1000

0 1 2 3 4 5

n in CnH2n+1OH

model and the Darken method are in excellent agreement.

*s* ,0,00 *w h* B log *wkNEEE* (21)

0 1 2 3 4 5

n in CnH2n+1OH

Electromotive Force Measurements and

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ISSN 0044-4537

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256

6106

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**6**

Yuji Kurata

*Japan*

**Application of Electromotive Force**

Liquid lead and lead-bismuth eutectic(LBE) are promising candidate materials as coolant of fast reactors with improved safety because of their good thermal-physical and chemical properties. Liquid LBE is also a primary candidate material for high-power spallation targets and coolant of accelerator driven systems (ADSs) for transmutation of long-lived radioactive wastes. In order to apply these liquid lead and LBE to nuclear systems, development of systems for controlling oxygen concentration in the liquid mediums is one of important research subjects (Gromov et al., 1999; Shmatko & Rusanov, 2000; OECD/NEA Handbool, 2007). Liquid lead and LBE are corrosive for steels at high temperatures and likely to cause plugging due to PbO formation in low-temperature components of systems. It is generally accepted that maintaining a certain level of oxygen concentration in them is crucial from the viewpoints of mitigating corrosion attack at high-temperature parts and avoiding PbO formation at low-temperature parts. The active oxygen control within the range between Fe3O4 and PbO formation has been proposed (Shmatko & Rusanov, 2000; Li,

Effective control of the oxygen concentration requires devices for removing and adding oxygen in liquid lead alloys and oxygen sensors for monitoring the oxygen concentration. It is essential to measure oxygen concentration correctly in lead alloys online for the active oxygen control. Electromotive force measurement using oxygen sensors with a solid electrolyte is a useful means to measure oxygen concentration in liquid lead alloys. Oxygen sensors employing yttria-stabilized zirconia (YSZ) and magnecia-stabilized zirconia (MSZ) as a solid electrolyte enable us to measure oxygen concentration in lead alloys. While oxygen sensors using YSZ as a solid electrolyte and Pt/gas as a reference system are often used in automobile industries, the operating temperature of the sensors is generally rather high. It has been reported that oxygen sensors were used in liquid lead and LBE in Russia where research on nuclear systems using them has been conducted for a long term (Gromov et al., 1999; Shmatko & Rusanov, 2000). The special sensor using YSZ as a solid electrolyte and Mo/Bi-Bi2O3 as a reference system gave accurate measurement of oxygen concentration and long service lifetime(Shmatko & Rusanov, 2000). Recently, oxygen sensors for use in

liquid lead alloys have been manufactured and examined worldwide.

**1. Introduction**

2002; OECD/NEA Handbool, 2007).

**Measurement in Nuclear Systems**

**Using Lead Alloys**

*Japan Atomic Energy Agency*

## **Application of Electromotive Force Measurement in Nuclear Systems Using Lead Alloys**

Yuji Kurata *Japan Atomic Energy Agency Japan*

### **1. Introduction**

106 Electromotive Force and Measurement in Several Systems

Taboada, M. E.; Graber, T. A.; & Cisternas, L. A. (2004). Sodium carbonate extrective

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equilibria of mixed solvent electrolyte systems using the extended electrolyte

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solutions by salting-out extraction. *J. Chem. Technol. Biotechnol*. Vol. 76, No. 7, pp.

Liquid lead and lead-bismuth eutectic(LBE) are promising candidate materials as coolant of fast reactors with improved safety because of their good thermal-physical and chemical properties. Liquid LBE is also a primary candidate material for high-power spallation targets and coolant of accelerator driven systems (ADSs) for transmutation of long-lived radioactive wastes. In order to apply these liquid lead and LBE to nuclear systems, development of systems for controlling oxygen concentration in the liquid mediums is one of important research subjects (Gromov et al., 1999; Shmatko & Rusanov, 2000; OECD/NEA Handbool, 2007). Liquid lead and LBE are corrosive for steels at high temperatures and likely to cause plugging due to PbO formation in low-temperature components of systems. It is generally accepted that maintaining a certain level of oxygen concentration in them is crucial from the viewpoints of mitigating corrosion attack at high-temperature parts and avoiding PbO formation at low-temperature parts. The active oxygen control within the range between Fe3O4 and PbO formation has been proposed (Shmatko & Rusanov, 2000; Li, 2002; OECD/NEA Handbool, 2007).

Effective control of the oxygen concentration requires devices for removing and adding oxygen in liquid lead alloys and oxygen sensors for monitoring the oxygen concentration. It is essential to measure oxygen concentration correctly in lead alloys online for the active oxygen control. Electromotive force measurement using oxygen sensors with a solid electrolyte is a useful means to measure oxygen concentration in liquid lead alloys. Oxygen sensors employing yttria-stabilized zirconia (YSZ) and magnecia-stabilized zirconia (MSZ) as a solid electrolyte enable us to measure oxygen concentration in lead alloys. While oxygen sensors using YSZ as a solid electrolyte and Pt/gas as a reference system are often used in automobile industries, the operating temperature of the sensors is generally rather high. It has been reported that oxygen sensors were used in liquid lead and LBE in Russia where research on nuclear systems using them has been conducted for a long term (Gromov et al., 1999; Shmatko & Rusanov, 2000). The special sensor using YSZ as a solid electrolyte and Mo/Bi-Bi2O3 as a reference system gave accurate measurement of oxygen concentration and long service lifetime(Shmatko & Rusanov, 2000). Recently, oxygen sensors for use in liquid lead alloys have been manufactured and examined worldwide.

Application of Electromotive Force Measurement in Nuclear Systems Using Lead Alloys 109

where *P*o2(reference) is the oxygen partial pressure at the reference electrode and *P*o2 is the oxygen partial pressure at the working electrode. The EMF is formed across the solid electrolyte between the different oxygen partial pressures. The EMF, *E* is expressed as

2

where *R* is the gas constant, *T* temperature and *F* the Faraday constant. When the gas containing a given oxygen concentration is used at the reference electrode side, the oxygen partial pressure at the working electrode, *P*o2 can be calculated using the Eq. (1). The EMF can be measured using a voltmeter shown in Fig.1. A voltmeter with high impedence is

Solid electrolyte

O2-

Electrode Electrode O2+4e=2O2- 2O =O2+4e 2-

VV

Fig. 1. Principle diagram for measurement of oxygen concentration using a solid electrolyte. Figure 2 shows a schematic diagram of an oxygen sensor and interface reaction in measurement of oxygen concentration in liquid LBE using YSZ as a solid electrolyte and Pt/gas reference electrode. The following interface reaction occurs on porous Pt as

 O2 +4e = 2O2- (2) Type 304SS was used as a working electrode in liquid LBE. Since oxygen dissolves into liquid LBE as O atom, the following interface reaction occurs at the YSZ surface in the liquid

2O2- = 2[O] +4e (3)

Voltmeter

O

4 *RT P*

*E*

recommended in measurement using solid electrolyte sensors.

*P*O2 (Reference)

electrocatalyst at the YSZ surface in the reference electrode side:

LBE side:

high

2

*F P* (1)

*P*O2 low

O (reference) ln

follows according to the Nernst equation:

Konys et al. (Konys et al., 2001, 2004) and Schroer et al. (Schroer et al., 2011) showed that YSZ sensors using a Pt/air reference electrode and a Mo/Bi-Bi2O3 reference electrode were promising in LBE as a result of tests of sensors using Pt/air, Mo/Bi-Bi2O3 and Mo/In-In2O3 reference electrodes. Furthermore, it was reported that the Pt/air reference electrode sensor exhibited better reliability and longer lifetime than the Mo/Bi-Bi2O3 reference electrode (Konys et al., 2004). Courouau et al. (Courouau et al., 2002a, 2002b; Courouau, 2004) mainly used the YSZ sensor with the Mo/Bi-Bi2O3 reference electrode as a result of tests of several Mo/metal-metal oxide electrodes. Calibration was also conducted for the Mo/Bi-Bi2O3 reference electrode sensors manufactured at the laboratory scale (Courouau et al., 2002b). The calibration method firstly proposed by Konys et al. (Konys et al., 2001) is based on measurement of electromotive force (EMF) of the oxygen sensor following temperature variation under the condition close to oxygen saturation in LBE. Calibration methods using Co/CoO or Fe/Fe-oxide equilibrium in liquid LBE besides Pb/PbO equilibrium (oxygensaturated condition) were also attempted (Schroer et al., 2011). The YSZ sensors with the Mo/Bi-Bi2O3 reference electrode have been manufactured and used by other researchers (Li, 2002; Kondo et al., 2006; Num et al., 2008). Although sensors with the Mo/In-In2O3 reference electrode have been also developed, the temperature range where measured EMF values agree with theoretical values in the calibration test is very narrow (Konys et al., 2001; Courouau, 2004; Fernandez et al., 2002; Colominas et al., 2004). Furthermore, experience has been reported on use of Russian sensor with the Bi-Bi2O3 reference and sensors with the In-In2O3 reference in liquid Pb-Bi or liquid Pb (Foletti et al., 2008).

The following two problems have been pointed out in case of using the oxygen sensor with the Mo/metal-metal oxide reference electrode: this type of sensor often exhibits time drift that EMF values change with increase in service time (OECD/NEA Handbool, 2007) and measured EMF values disagree with the theoretical ones (Konys et al., 2001; Colominas et al., 2004). We have also tested YSZ sensors using Pt/air reference and Mo/Bi-Bi2O3 reference electrodes in LBE. We had experience that even the sensor with the Pt/air reference electrode exhibited incorrect EMF values in LBE after long-term use as a reliable oxygen sensor. Investigation of the cause of the incorrect outputs and re-activation of the Pt/air reference sensor was reported (Kurata et al., 2010). Importance of interface reaction at electrode/medium and electrocatalyst was pointed out in measurement of electromotive force using YSZ oxygen sensors. Furthermore, calibration methods with high reliability and convenience were required for oxygen sensors for use in liquid lead alloys.

In this chapter, the EMF measurement using the YSZ sensor with the Pt/gas reference system is investigated from basic to practical viewpoints together with re-activation treatments of the YSZ sensor. In addition, the usage record of the YSZ sensors with the Pt/air reference system for a long time and situation of oxygen control in liquid LBE in a static corrosion apparatus are described.

### **2. Theory of oxygen concentration measurement**

Figure 1 shows a principle diagram for measurement of oxygen concentration using a solid electrolyte. A solid electrolyte separates two domains characterized by different oxygen partial pressures. When the electrolyte is an oxygen-ion (O2-) conductor, an electrochemical galvanic cell using a solid electrolyte is presented as follows:

 *P*o2(reference)//solid electrolyte//*P*o2

Konys et al. (Konys et al., 2001, 2004) and Schroer et al. (Schroer et al., 2011) showed that YSZ sensors using a Pt/air reference electrode and a Mo/Bi-Bi2O3 reference electrode were promising in LBE as a result of tests of sensors using Pt/air, Mo/Bi-Bi2O3 and Mo/In-In2O3 reference electrodes. Furthermore, it was reported that the Pt/air reference electrode sensor exhibited better reliability and longer lifetime than the Mo/Bi-Bi2O3 reference electrode (Konys et al., 2004). Courouau et al. (Courouau et al., 2002a, 2002b; Courouau, 2004) mainly used the YSZ sensor with the Mo/Bi-Bi2O3 reference electrode as a result of tests of several Mo/metal-metal oxide electrodes. Calibration was also conducted for the Mo/Bi-Bi2O3 reference electrode sensors manufactured at the laboratory scale (Courouau et al., 2002b). The calibration method firstly proposed by Konys et al. (Konys et al., 2001) is based on measurement of electromotive force (EMF) of the oxygen sensor following temperature variation under the condition close to oxygen saturation in LBE. Calibration methods using Co/CoO or Fe/Fe-oxide equilibrium in liquid LBE besides Pb/PbO equilibrium (oxygensaturated condition) were also attempted (Schroer et al., 2011). The YSZ sensors with the Mo/Bi-Bi2O3 reference electrode have been manufactured and used by other researchers (Li, 2002; Kondo et al., 2006; Num et al., 2008). Although sensors with the Mo/In-In2O3 reference electrode have been also developed, the temperature range where measured EMF values agree with theoretical values in the calibration test is very narrow (Konys et al., 2001; Courouau, 2004; Fernandez et al., 2002; Colominas et al., 2004). Furthermore, experience has been reported on use of Russian sensor with the Bi-Bi2O3 reference and sensors with the In-

The following two problems have been pointed out in case of using the oxygen sensor with the Mo/metal-metal oxide reference electrode: this type of sensor often exhibits time drift that EMF values change with increase in service time (OECD/NEA Handbool, 2007) and measured EMF values disagree with the theoretical ones (Konys et al., 2001; Colominas et al., 2004). We have also tested YSZ sensors using Pt/air reference and Mo/Bi-Bi2O3 reference electrodes in LBE. We had experience that even the sensor with the Pt/air reference electrode exhibited incorrect EMF values in LBE after long-term use as a reliable oxygen sensor. Investigation of the cause of the incorrect outputs and re-activation of the Pt/air reference sensor was reported (Kurata et al., 2010). Importance of interface reaction at electrode/medium and electrocatalyst was pointed out in measurement of electromotive force using YSZ oxygen sensors. Furthermore, calibration methods with high reliability and

In this chapter, the EMF measurement using the YSZ sensor with the Pt/gas reference system is investigated from basic to practical viewpoints together with re-activation treatments of the YSZ sensor. In addition, the usage record of the YSZ sensors with the Pt/air reference system for a long time and situation of oxygen control in liquid LBE in a

Figure 1 shows a principle diagram for measurement of oxygen concentration using a solid electrolyte. A solid electrolyte separates two domains characterized by different oxygen partial pressures. When the electrolyte is an oxygen-ion (O2-) conductor, an electrochemical

In2O3 reference in liquid Pb-Bi or liquid Pb (Foletti et al., 2008).

convenience were required for oxygen sensors for use in liquid lead alloys.

static corrosion apparatus are described.

**2. Theory of oxygen concentration measurement**

galvanic cell using a solid electrolyte is presented as follows:

 *P*o2(reference)//solid electrolyte//*P*o2

where *P*o2(reference) is the oxygen partial pressure at the reference electrode and *P*o2 is the oxygen partial pressure at the working electrode. The EMF is formed across the solid electrolyte between the different oxygen partial pressures. The EMF, *E* is expressed as follows according to the Nernst equation:

$$E = \frac{RT}{4F} \ln \frac{P\_{\text{O\_2}} \text{(reference)}}{P\_{\text{O\_2}}} \tag{1}$$

where *R* is the gas constant, *T* temperature and *F* the Faraday constant. When the gas containing a given oxygen concentration is used at the reference electrode side, the oxygen partial pressure at the working electrode, *P*o2 can be calculated using the Eq. (1). The EMF can be measured using a voltmeter shown in Fig.1. A voltmeter with high impedence is recommended in measurement using solid electrolyte sensors.

Fig. 1. Principle diagram for measurement of oxygen concentration using a solid electrolyte.

Figure 2 shows a schematic diagram of an oxygen sensor and interface reaction in measurement of oxygen concentration in liquid LBE using YSZ as a solid electrolyte and Pt/gas reference electrode. The following interface reaction occurs on porous Pt as electrocatalyst at the YSZ surface in the reference electrode side:

$$\rm O\_2 + 4e = 2C^{2-} \tag{2}$$

Type 304SS was used as a working electrode in liquid LBE. Since oxygen dissolves into liquid LBE as O atom, the following interface reaction occurs at the YSZ surface in the liquid LBE side:

$$2\mathbf{C}^2 = 2[\mathbf{C}] + 4\mathbf{e} \tag{3}$$

Application of Electromotive Force Measurement in Nuclear Systems Using Lead Alloys 111

these two reference electrode sensors using standard Gibbs energy of PbO and Bi2O3 (Courouau et al., 2002a; Konys et al., 2004). The equation derived by Courouau et al.

 *E*Saturation=1.129-5.858x10-4*T* (6)

 *E*=0.791-4.668x10-4*T*-4.309x10-5*T*ln*C*o (7)

 *E*Saturation=0.128-6.368 x10-5*T* (8)

 *E*=-0.210+5.538x10-5*T*-4.309x10-5*T*ln*C*o (9) Thermoelectric voltages occur between Mo wire and austenitic stainless steels such as 304SS in measurement using the Mo/Bi-Bi2O3 reference electrode sensor. The influence of the thermoelectric valgtages on measurement was investegated in detail (Schroer et al., 2011).

V V

Fig. 3. Schematic diagram of oxygen sensors in liquid LBE: (a) Pt/air reference system and

While YSZ sensors with the Pt/gas reference electrode and the Mo/Bi-Bi2O3 reference electrode were prepared, the former was mainly used in this study. The Pt/gas reference sensor made by Sukegawa Electric Co., Ltd. was the one-end closed YSZ tube with outer diameter of 15mm and inner diameter of 11mm. The Pt/gas reference system was put inside the YSZ tube. The inner Pt electrode was made by a process of painting Pt-paste inside the YSZ tube and baking it. The porous Pt electrode made through this process has good catalytic activity that enables to measure oxygen concentration at lower temperatures. The fully stabilized zirconia (ZrO2) with 8 mol% Y2O3 produced by Nikkato Corp. was used as a solid electrolyte on account of its good electronic behavior and thermo-mechanical

Bi-Bi2O3

304SS 304SS

LBE LBE

**3. Electromotive force measurement using oxygen sensors**

Mo (a) (b)

(Courouau et al., 2002a) was used in this study.

For Pt/air reference sensor

Pt

For Mo/Bi-Bi2O3 reference sensor

air

(b) Mo/Bi-Bi2O3 reference system.

The oxygen activity, o*a* in equilibrium with an oxygen pressure *P*o2 is written assuming that dissolution of oxygen into liquid LBE obeys the Henry's law:

$$a\_o = \gamma\_o \mathbf{C}\_o = \frac{\mathbf{C}\_o}{\mathbf{C}\_o^s} = \left(\frac{P\_{o\_2}}{P\_{o\_2}^s}\right)^{\frac{1}{2}}\tag{4}$$

where O is an activity coefficient, *C*o the oxygen concentration in LBE, s *C*o the saturated oxygen concentration in LBE and 2 *s Po* the oxygen concentration in gas in equilibrium with oxygen-saturated LBE. The activity o*a* becomes unity when the oxygen dissolved in LBE attains the level of saturation (*C*o = s *C*o ). The saturated oxygen concentration in LBE is calculated using the following Orlov's equation (Gromov et al., 1999):

$$
\log \mathcal{C}\_o^s(wt\%) = 1.2 - \frac{3400}{T} \tag{5}
$$

Fig. 2. Reaction at interfaces of solid electrolyte of an oxygen sensor.

Figure 3 shows a schematic diagram to measure oxygen concentration in liquid LBE using two types of oxygen sensors. Oxygen sensors using YSZ as a solid electrolyte and Pt/gas (a) or Mo/Bi-Bi2O3 (b) as a reference system were used in this study. When measurement was conducted in LBE, air was used as the reference gas in Pt/gas reference system. The 304SS rod was used as an electrode immersed in LBE. Therefore, the system for measurement in LBE is represented by Pt/air//YSZ//LBE/304SS or Mo/Bi-Bi2O3//YSZ//LBE/304SS. The relationship between the EMF and the oxygen concentration in LBE has been calculated for these two reference electrode sensors using standard Gibbs energy of PbO and Bi2O3 (Courouau et al., 2002a; Konys et al., 2004). The equation derived by Courouau et al. (Courouau et al., 2002a) was used in this study.

For Pt/air reference sensor

110 Electromotive Force and Measurement in Several Systems

The oxygen activity, o*a* in equilibrium with an oxygen pressure *P*o2 is written assuming

o oo s s

oxygen-saturated LBE. The activity o*a* becomes unity when the oxygen dissolved in LBE attains the level of saturation (*C*o = s *C*o ). The saturated oxygen concentration in LBE is

3400 log ( %) 1.2 *C wt*

Solid Electrolyte

(YSZ)

Electrode (304SS)

*a C*

calculated using the following Orlov's equation (Gromov et al., 1999):

*P*O2 (Reference)

(Porous Pt)

high

Interface reaction:

o

Gas LBE

O2+4e=2O2-

Figure 3 shows a schematic diagram to measure oxygen concentration in liquid LBE using two types of oxygen sensors. Oxygen sensors using YSZ as a solid electrolyte and Pt/gas (a) or Mo/Bi-Bi2O3 (b) as a reference system were used in this study. When measurement was conducted in LBE, air was used as the reference gas in Pt/gas reference system. The 304SS rod was used as an electrode immersed in LBE. Therefore, the system for measurement in LBE is represented by Pt/air//YSZ//LBE/304SS or Mo/Bi-Bi2O3//YSZ//LBE/304SS. The relationship between the EMF and the oxygen concentration in LBE has been calculated for

Fig. 2. Reaction at interfaces of solid electrolyte of an oxygen sensor.

2 2

2 o o

o o *C P*

O is an activity coefficient, *C*o the oxygen concentration in LBE, s *C*o the saturated

*C P*

1

*s Po* the oxygen concentration in gas in equilibrium with

[O]

O2- low

2O =2[O]+4e 2-

*T* (5)

Electrode

(4)

that dissolution of oxygen into liquid LBE obeys the Henry's law:

where

oxygen concentration in LBE and 2

s

$$E\_{\text{Saturation}} = 1.129 \text{-} 5.858 \times 10^{-4} T \tag{6}$$

$$E = 0.791 \text{--} 4.668 \text{x} 10 \text{-} 4 \text{T-} 4.309 \text{x} 10 \text{-} 5 \text{T} \ln C\_{\text{o}} \tag{7}$$

For Mo/Bi-Bi2O3 reference sensor

$$E\_{\text{Saturation}} = 0.128 \text{-} 6.368 \times 10^{\circ}T \tag{8}$$

$$E = 0.210 + 5.538 \text{x} 10^{\circ} \text{T} \text{-} 4.309 \text{x} 10^{\circ} \text{T} \text{ln} \, C\_0 \tag{9}$$

Thermoelectric voltages occur between Mo wire and austenitic stainless steels such as 304SS in measurement using the Mo/Bi-Bi2O3 reference electrode sensor. The influence of the thermoelectric valgtages on measurement was investegated in detail (Schroer et al., 2011).

Fig. 3. Schematic diagram of oxygen sensors in liquid LBE: (a) Pt/air reference system and (b) Mo/Bi-Bi2O3 reference system.

### **3. Electromotive force measurement using oxygen sensors**

While YSZ sensors with the Pt/gas reference electrode and the Mo/Bi-Bi2O3 reference electrode were prepared, the former was mainly used in this study. The Pt/gas reference sensor made by Sukegawa Electric Co., Ltd. was the one-end closed YSZ tube with outer diameter of 15mm and inner diameter of 11mm. The Pt/gas reference system was put inside the YSZ tube. The inner Pt electrode was made by a process of painting Pt-paste inside the YSZ tube and baking it. The porous Pt electrode made through this process has good catalytic activity that enables to measure oxygen concentration at lower temperatures. The fully stabilized zirconia (ZrO2) with 8 mol% Y2O3 produced by Nikkato Corp. was used as a solid electrolyte on account of its good electronic behavior and thermo-mechanical

Application of Electromotive Force Measurement in Nuclear Systems Using Lead Alloys 113

The relationship between the EMF and tempeerature is shown in Fig. 5 (Kurata et al., 2010). The theoretical line calculated from Eq. (1) is also drawn in this figure. The EMF values approach the theoretical line of the Nernst relation while it seems to take time to attain the stable outputs below 500C. This calibration method in gas was often used to investigate

**300 350 400 450 500 550 600 650**

**Reference gas: 10.45%O2 + He Measured gas: 502 ppm O2 + He Reference gas: 10.45%O2+He**

**Measured gas: 502ppmO2+He**

**( C )**

**0.5h**

**Theoretical value**

**Temperature ( C)**

Fig. 5. Relationship between EMF and temperature measured in gas using Pt/gas reference

An apparatus for corrosion tests in LBE (Kurata et al., 2008) was used for the calibration test in LBE. Components contacting liquid LBE were made of quartz. About 7kg of LBE was put into the pot and melted under Ar cover gas with purity of 99.9999% for the calibration test in LBE. The chemical compositions of LBE were 55.60Bi-0.0009Sb-0.0002Cu-0.0001Zn-0.0005Fe-0.0007As-0.0005Cd-0.0001Sn-Bal.Pb(wt%). Initial oxygen content in LBE was usually from 10-4 to 10-3 wt% in this treatment. Figure 6 depicts a photo showing the Pt/gas reference oxygen sensor under measurement in liquid LBE. A thin PbO film was observed

Figure 7 shows the relationship between EMF and temperature measured in LBE using Pt/gas reference sensor (Kurata et al., 2010). Air was used as reference gas of the YSZ oxygen sensor. Open circles indicate EMF values measured in oxygen-saturated LBE with pure Ar cover gas. The theoretical line calculated from Eq. (6) for the oxygen-saturated LBE is written with a thick solid line. The measured EMF values are almost on the theoretical line for the oxygen-saturated LBE above 450C. From the measured EMF value at 550C, it is estimated that the oxygen concentration in the LBE is about 10-3wt%. The measured EMF

**3.2 Estimation of outputs of the Pt/gas reference sensor in liquid LBE**

on the surface of the liquid LBE with pure Ar cover gas at 450C.

correctness of Pt/gas reference sensors.

**0**

**20**

**40**

**60**

**12h**

**EMF (mV)**

sensor (Kurata et al., 2010).

**80**

**100**

**120**

performance. The Mo/Bi-Bi2O3 reference sensor was a sensor using the one-end closed tube of YSZ with the sizes of 8mm in outer diameter, 5mm in inner diameter and 300mm in length. The Mo/Bi-Bi2O3 reference electrode was made inside the YSZ tube in our laboratory. The ratio of Bi to Bi2O3 was 9:1 in weight. The upper part of the YSZ tube was sealed using alumina cement. This sensor with the Mo/Bi-Bi2O3 reference electrode was similar to the Mo/Bi-Bi2O3 reference sensor manufactured in other institutes (Courouau et al., 2002b; Konys et al., 2004; Kondo et al., 2006).

The following two methods were employed for calibration of oxygen sensors: (1) comparison between measured EMF values and theoretical ones using two kinds of gases with different oxygen concentrations for the reference electrode and the working electrode, and (2) comparison between measured EMF values and theoretical ones in LBE with the parameter of temperature under the condition close to oxygen saturation in LBE. The advantage of the former method is easiness of preparing the reliable working electrode with the correct oxygen concentration in gas in case of employing a ceramic vessel. The latter method has been often employed as a calibration test in LBE (Konys et al., 2001; Courouau et al., 2002b). An electrometer with high impedence of 1014 was used for measurement of the EMF both in gas and in LBE. Schroer et al. conducted calibration tests using not only Pb/Pb-monoxiside (PbO) but also Co/Co-monoxide (CoO) and Fe/Fe-oxide equilibria in liquid LBE (Schroer et al., 2011).

### **3.1 Measurement of oxygen concentration in gas**

Figure 4 shows a schematic drawing (a) and appearance (b) of the Pt/gas reference sensor used in measurement of oxygen concentration in gas (Kurata et al., 2010). Platinum paste was painted on the lower part of the outer YSZ surface to measure oxygen concentration in gas. In this test, 10.45%O2-He gas was used as reference gas and 502ppmO2-He gas as working gas. The temperature range was 350C - 600C and the temperature was kept for about 24h to investigate change of the EMF values at each temperature.

Fig. 4 Schematic drawing (a) of the YSZ oxygen sensor with Pt/gas reference system and appearance(b) of the YSZ oxygen sensor with outer Pt electrode for measurement of oxygen concentration in gas (Kurata et al., 2010).

performance. The Mo/Bi-Bi2O3 reference sensor was a sensor using the one-end closed tube of YSZ with the sizes of 8mm in outer diameter, 5mm in inner diameter and 300mm in length. The Mo/Bi-Bi2O3 reference electrode was made inside the YSZ tube in our laboratory. The ratio of Bi to Bi2O3 was 9:1 in weight. The upper part of the YSZ tube was sealed using alumina cement. This sensor with the Mo/Bi-Bi2O3 reference electrode was similar to the Mo/Bi-Bi2O3 reference sensor manufactured in other institutes (Courouau et

The following two methods were employed for calibration of oxygen sensors: (1) comparison between measured EMF values and theoretical ones using two kinds of gases with different oxygen concentrations for the reference electrode and the working electrode, and (2) comparison between measured EMF values and theoretical ones in LBE with the parameter of temperature under the condition close to oxygen saturation in LBE. The advantage of the former method is easiness of preparing the reliable working electrode with the correct oxygen concentration in gas in case of employing a ceramic vessel. The latter method has been often employed as a calibration test in LBE (Konys et al., 2001; Courouau et al., 2002b). An electrometer with high impedence of 1014 was used for measurement of the EMF both in gas and in LBE. Schroer et al. conducted calibration tests using not only Pb/Pb-monoxiside (PbO) but also Co/Co-monoxide (CoO) and Fe/Fe-oxide equilibria in

Figure 4 shows a schematic drawing (a) and appearance (b) of the Pt/gas reference sensor used in measurement of oxygen concentration in gas (Kurata et al., 2010). Platinum paste was painted on the lower part of the outer YSZ surface to measure oxygen concentration in gas. In this test, 10.45%O2-He gas was used as reference gas and 502ppmO2-He gas as working gas. The temperature range was 350C - 600C and the temperature was kept for

> Yttria stabilized zirconia (YSZ)

Reference platinum Electrode (Inside)

Fig. 4 Schematic drawing (a) of the YSZ oxygen sensor with Pt/gas reference system and appearance(b) of the YSZ oxygen sensor with outer Pt electrode for measurement of oxygen

(b)

al., 2002b; Konys et al., 2004; Kondo et al., 2006).

**3.1 Measurement of oxygen concentration in gas**

about 24h to investigate change of the EMF values at each temperature.

Reference gas inlet Reference gas outlet

liquid LBE (Schroer et al., 2011).

Outer electric pole

concentration in gas (Kurata et al., 2010).

Reference electric pole

(a)

The relationship between the EMF and tempeerature is shown in Fig. 5 (Kurata et al., 2010). The theoretical line calculated from Eq. (1) is also drawn in this figure. The EMF values approach the theoretical line of the Nernst relation while it seems to take time to attain the stable outputs below 500C. This calibration method in gas was often used to investigate correctness of Pt/gas reference sensors.

Fig. 5. Relationship between EMF and temperature measured in gas using Pt/gas reference sensor (Kurata et al., 2010).

### **3.2 Estimation of outputs of the Pt/gas reference sensor in liquid LBE**

An apparatus for corrosion tests in LBE (Kurata et al., 2008) was used for the calibration test in LBE. Components contacting liquid LBE were made of quartz. About 7kg of LBE was put into the pot and melted under Ar cover gas with purity of 99.9999% for the calibration test in LBE. The chemical compositions of LBE were 55.60Bi-0.0009Sb-0.0002Cu-0.0001Zn-0.0005Fe-0.0007As-0.0005Cd-0.0001Sn-Bal.Pb(wt%). Initial oxygen content in LBE was usually from 10-4 to 10-3 wt% in this treatment. Figure 6 depicts a photo showing the Pt/gas reference oxygen sensor under measurement in liquid LBE. A thin PbO film was observed on the surface of the liquid LBE with pure Ar cover gas at 450C.

Figure 7 shows the relationship between EMF and temperature measured in LBE using Pt/gas reference sensor (Kurata et al., 2010). Air was used as reference gas of the YSZ oxygen sensor. Open circles indicate EMF values measured in oxygen-saturated LBE with pure Ar cover gas. The theoretical line calculated from Eq. (6) for the oxygen-saturated LBE is written with a thick solid line. The measured EMF values are almost on the theoretical line for the oxygen-saturated LBE above 450C. From the measured EMF value at 550C, it is estimated that the oxygen concentration in the LBE is about 10-3wt%. The measured EMF

Application of Electromotive Force Measurement in Nuclear Systems Using Lead Alloys 115

above 450C in liquid LBE. Solid triangles indicate EMF values measured in LBE after Ar-H2-H2O gas bubbling. These data were obtained in oxygen-unsaturated LBE. The theoretical lines calculated from Eq. (7) are drawn for the EMF values of oxygen concentrations of 10-3wt% to 10-10wt% in LBE. Regarding EMF values measured in LBE after Ar-H2-H2O gas bubbling, the slope and the magnitude above 450C are identical with the expected values for LBE with dissolved oxygen concentration of about 3x10-5wt%. A solid square shows the EMF value measured in LBE after Ar-4%H2 gas bubbling. Oxygen concentration of 10-9wt% in LBE can be measured using the Pt/gas reference sensor. Konys et al. and Schroer et al. also showed validation of oxygen sensors from calibration tests in saturated and unsaturated LBE (Konys et al., 2001; Schroer et al., 2011). On the basis of the results obtained in the present test, it is found that the Pt/air reference sensor enables us to measure oxygen concentration correctly in LBE above 450C. The appearance of the oxygen sensor after the test in LBE is shown in Fig. 8 (Kurata et al., 2010). Since much LBE adheres to the YSZ surface of the sensor, it is clear that the YSZ surface is wet well with liquid LBE.

Fig. 8. Appearance of the Pt/gas reference sensor after test in liquid LBE (Kurata et al.,

The Pt/air reference sensor, which exhibited good performance, had been used in LBE for about 6500h. A comparison test was conducted in LBE for the Pt/air reference sensor after long-term use and the Mo/Bi-Bi2O3 reference sensor produced in our laboratory. An apparatus shown in Fig. 9 was used for the comparison test of oxygen sensors. The vessel of the apparatus was made of 304SS and outputs from three sensors in liquid LBE could be compared. About 60 kg of LBE was used in the comparison test using 304SS vessel. The procedure similar to that in section 3.2 was employed in the comparison test in liquid LBE. Figure 10 shows the relationship between the EMF and temperature measured in LBE using Pt/air reference and Mo/Bi-Bi2O3 reference sensors (Kurata et al., 2010). In the same way as Fig. 7, the theoretical lines calculated from Eq. (6) for the Pt/air reference sensor and from Eq. (8) for the Mo/Bi-Bi2O3 reference sensor in the oxygen-saturated LBE are drawn in this figure. It is a surprise that the measured EMF values in LBE with Ar cover gas are much

2010).

**3.3 Re-activation of oxygen sensor**

Fig. 6. Photo showing the oxygen sensor under measurement in liquid LBE.

Fig. 7. Relationship between EMF and temperature measured in LBE using Pt/gas reference sensor (Kurata et al., 2010).

values are much lower than the theoretical line below 400C. Furthermore, the measured EMF value attained the stable one in LBE above 450C in short time. From the calibration test using Pb/PbO equilibrium in liquid LBE, it is possible to use the Pt/air reference sensor

**Electrode in Oxygen sensor**

**liquid LBE**

Fig. 6. Photo showing the oxygen sensor under measurement in liquid LBE.

10-8wt%

10-9wt%

10-10wt%

Oxygensaturated (*E*satutration)

**300 350 400 450 500 550 600**

10-3wt%

After Ar-H2-H2O gas bubbling

After Ar-4%H2 gas bubbling

10-4wt%

*E*saturation=1.129-5.858x10-4*T*

10-5wt%

*E*=0.791-4.668x10-4*T*-4.309x10-5*T*ln*C*o

10-6wt%

10-7wt%

Tnmp(C)

Fig. 7. Relationship between EMF and temperature measured in LBE using Pt/gas

values are much lower than the theoretical line below 400C. Furthermore, the measured EMF value attained the stable one in LBE above 450C in short time. From the calibration test using Pb/PbO equilibrium in liquid LBE, it is possible to use the Pt/air reference sensor

**Temperature (C )**

**500**

reference sensor (Kurata et al., 2010).

**600**

**700**

**800**

**900**

**EMF (mV)**

**1000**

**1100**

**1200**

above 450C in liquid LBE. Solid triangles indicate EMF values measured in LBE after Ar-H2-H2O gas bubbling. These data were obtained in oxygen-unsaturated LBE. The theoretical lines calculated from Eq. (7) are drawn for the EMF values of oxygen concentrations of 10-3wt% to 10-10wt% in LBE. Regarding EMF values measured in LBE after Ar-H2-H2O gas bubbling, the slope and the magnitude above 450C are identical with the expected values for LBE with dissolved oxygen concentration of about 3x10-5wt%. A solid square shows the EMF value measured in LBE after Ar-4%H2 gas bubbling. Oxygen concentration of 10-9wt% in LBE can be measured using the Pt/gas reference sensor. Konys et al. and Schroer et al. also showed validation of oxygen sensors from calibration tests in saturated and unsaturated LBE (Konys et al., 2001; Schroer et al., 2011). On the basis of the results obtained in the present test, it is found that the Pt/air reference sensor enables us to measure oxygen concentration correctly in LBE above 450C. The appearance of the oxygen sensor after the test in LBE is shown in Fig. 8 (Kurata et al., 2010). Since much LBE adheres to the YSZ surface of the sensor, it is clear that the YSZ surface is wet well with liquid LBE.

### **3.3 Re-activation of oxygen sensor**

The Pt/air reference sensor, which exhibited good performance, had been used in LBE for about 6500h. A comparison test was conducted in LBE for the Pt/air reference sensor after long-term use and the Mo/Bi-Bi2O3 reference sensor produced in our laboratory. An apparatus shown in Fig. 9 was used for the comparison test of oxygen sensors. The vessel of the apparatus was made of 304SS and outputs from three sensors in liquid LBE could be compared. About 60 kg of LBE was used in the comparison test using 304SS vessel. The procedure similar to that in section 3.2 was employed in the comparison test in liquid LBE.

Figure 10 shows the relationship between the EMF and temperature measured in LBE using Pt/air reference and Mo/Bi-Bi2O3 reference sensors (Kurata et al., 2010). In the same way as Fig. 7, the theoretical lines calculated from Eq. (6) for the Pt/air reference sensor and from Eq. (8) for the Mo/Bi-Bi2O3 reference sensor in the oxygen-saturated LBE are drawn in this figure. It is a surprise that the measured EMF values in LBE with Ar cover gas are much

Application of Electromotive Force Measurement in Nuclear Systems Using Lead Alloys 117

(measured)

**250 300 350 400 450 500 550**

**Temperature( C)**

Fig. 10. Relationship between EMF and temperature measured in LBE using Pt/air

Fig. 11. Appearance of oxygen sensors after measurement in liquid LBE using the

**( C )**

**0**

comparison apparatus of oxygen sensors.

**200**

**400**

**600**

**EMF(mV)**

**800**

**1000**

**1200**

Pt/air Mo/Bi-Bi 2

O3 Pt/air(measured) Mo/Bi-Bi 2

O3

**Oxygen-saturated**

**Oxygen-saturated**

reference and Mo/Bi-Bi2O3 reference sensors (Kurata et al., 2010).

higher than each theoretical line of oxygen-saturated LBE because oxygen concentration in calibration tests using LBE with Ar cover gas has been constantly in a range of 10-4 to 10-3 wt%. Therefore, it is necessary to examine whether EMF values measured by both sensors in this test showed correct oxygen concentration or not. Since Ar cover gas does not contain a reducing gas component, it is considered that fresh LBE used in the test contained oxygen of 10-4 to 10-3 wt%. In the case of the Pt/air reference sensor, the slope of the relationship between the EMF value and temperature is similar to that of the theoretical line above 400C. Similar trend is also observed in the case of the Mo/Bi-Bi2O3 reference sensor above 350C. These results suggest that oxygen concentration in LBE used in the test was close to saturated oxygen concentration.

Fig. 9. Photo of the comparison apparatus of oxygen sensors. Three sensors can be compared in liquid LBE.