Molar entropy of the selenium (VI)/(IV) couple obtained by cyclic voltammetry

Abstract

An electrochemical investigation of selenium species, using cyclic voltammetry, has been carried out for the purpose of determining the molar entropy of the Se(VI)/(IV) couple. To obtain the ion interaction coefficient between HSeO₄⁻ and Na⁺, ϵ_T(HSeO₄⁻, Na⁺), the following reaction involving HSeO₄⁻ as an oxidant and the uncharged species (H₂SeO₃) as the reductant was used:

The Se(VI)/(IV) half-wave potentials were measured in acidic sodium nitrate solutions as a function of the molality of Na⁺ ranging from 0.500 to 2.00 mol kg⁻¹. The temperatures for the measurement were 288, 298, 308 and 323 K. Specific ion interaction theory was used to calculate the HSeO₄⁻/H₂SeO₃ standard redox potential, , and ϵ_T(HSeO₄⁻, Na⁺) at each temperature. The following molar entropy was derived from the temperature dependence of :

The value of ϵ_T(HSeO₄⁻, Na⁺) at 298 K was determined to be 0.29 ± 0.03 kg mol⁻¹. The following ∂ϵ/∂T was derived from the temperature dependence of ϵ_T(HSeO₄⁻, Na⁺):

Keywords:

• entropy
• selenium
• ion interaction coefficient
• cyclic voltammetry
• sodium
• specific ion interaction theory
• temperature dependence

1. Introduction

Groundwater is the transport media for radionuclides relevant to the safety assessment of the geological disposal system. Selenium-79 (⁷⁹Se) is a long-lived fission product with a half-life of 327,000 years [1]. Se aqueous species in groundwater are present as anions. Sorption of Se aqueous species is relatively small, which results in only slight retardation of Se relative to groundwater movement. Therefore, Se is one of the key radionuclides for the safety assessment of the geological disposal system. The stability ranges of the predominant Se species in aqueous systems are summarized and displayed in a potential–pH diagram [2] (Figure 1). In neutral repository groundwaters under reducing conditions, the dominant aqueous Se species is HSe⁻ [3]. On the other hand, it is necessary to estimate the sensitivity of the system to perturbations in environmental conditions. Following a review of relevant international research and a consideration of characteristics specific to Japan, uplift, subsidence and erosion were considered to be potential natural phenomena related to the long-term stability of geological environments in Japan [4]. Radiolysis of groundwater, due to radiation from the vitrified waste, generates oxidizing agents such as H₂O₂ [4]. A decrease in the depth of repositories and the existence of oxidizing agents are of particular concern for the anticipated reducing conditions of repositories. The solubility and aqueous speciation of radionuclides can be altered due to the oxidation/reduction potentials of the geologic environments. The thermodynamic calculations indicate that the predominant Se oxidation state is Se(IV) in mildly reducing environments, and it is Se(VI) in oxidizing environments. If the environmental conditions of repositories are oxidized due to decrease in the depth of repositories and/or the presence of oxidizing agents, the oxidation state of Se is changed to Se(IV) and/or Se(VI). Increasing ionic strength decreased selenate ion (SeO^{2 −}₄) sorption on amorphous iron oxide (am-Fe(OH)₃) and goethite (α-FeOOH), but did not affect selenite ion (SeO^{2 −}₃) sorption [5]. Metallic iron and siderite (FeCO₃) reduced and immobilized Se(IV) and Se(VI) as iron diselenide (FeSe₂); the decrease in Se(IV) concentration was much greater than that in Se(VI) concentration under the same conditions [6]. Because the extent of sorption and immobilization of Se(IV) is different from that of Se(VI), the accurate prediction of Se(VI)–Se(IV) ratios is crucial for understanding the migration behavior of Se in those cases where the repositories exhibit oxidizing environments. An engineered barrier system will be constructed up to a depth of 300 m or more. Because temperature is in the range of 313–323 K at a depth of 500 m and the geothermal gradient is 3 K/100 m [4], the decrease in the depth of repositories occurs at a temperature over 298 K. Therefore, accurate prediction of Se(VI)–Se(IV) ratios is required for such a temperature.

Figure 1. Potential–pH diagram for Se based on the thermodynamic data reviewed and compiled by Olin et al. [2]. The total concentration of Se is 9.3×10⁻⁴ mol kg⁻¹. The line with arrow points indicates the scan region in this study (0.449↔1.439 V vs. SHE and pH = 1.13 ± 0.26).

Thermodynamic models are used to calculate solubility and speciation as a function of pH, redox potential and ligand concentrations. In the calculation of solubility and speciation, the reliability of the results is necessarily dependent on that of available thermodynamic data. The Se(VI)/(IV) standard redox potential, which determines Se(VI)–Se(IV) ratios at 298 K in thermodynamic models, was obtained using the following reaction [7]: (1) Because the molar entropy of the reaction, Δ_rS⁰_m, yields the temperature derivatives of the standard redox potential, Δ_rS⁰_m of the Se(VI)/(IV) couple is also required to predict Se(VI)–Se(IV) ratios at a temperature over 298 K. No existing experimental studies report the value for Δ_rS⁰_m of the Se(VI)/(IV) couple, which results in the poor prediction of Se(VI)–Se(IV) ratios. Therefore, the objective of this study is to obtain Δ_rS⁰_m of the Se(VI)/(IV) couple.

Conventionally, thermodynamic data are quoted for conditions for the standard state, i.e. zero ionic strength. The activities of all the species participating in reactions must be estimated in order to convert the thermodynamic data obtained at high ionic strengths to zero ionic strength. One method for estimating the activities is through the use of ion interaction parameters (ϵ_T(i, j)) in the specific ion interaction theory (SIT) model [8] to calculate the ion activity coefficients (γ_i). SIT was used in the Nuclear Energy Agency chemical thermodynamics project sponsored by the Organization for Economic Cooperation and Development (OECD) [8] and Japan Atomic Energy Agency Thermodynamic Data Base review [9]. OECD has critically evaluated available thermodynamic data for Se [2]. Because no experimental data were available at that time, these reviews estimated ϵ_T(i, j) for Se species using an analogy with sulfur (S). The uncertainty in ϵ_T(i, j) for Se species estimated by Olin et al. [2] was the same as that in ϵ_T(i, j) for the similar S species. However, after that, Philippini et al. [10] and Doi [7] experimentally determined ϵ_T(i, j) for Se species and reported differences between ϵ_T(i, j) for Se species and S species. Based on these experimental investigations, the applicability of an analogy with S to estimate ϵ_T(i, j) for Se species is questionable. Therefore it is necessary to determine ϵ_T(i, j) for Se species by experimental investigations. Previous reports [7,11,12] determined the stoichiometric sum of ϵ_T(i, j), Δϵ_T(i, j), instead of ϵ_T(i, j). This was because ϵ_T(i, j) for both an oxidant and a reductant had to be considered when the half-wave potentials, E_1/2(T, I_m), determined experimentally at different ionic strengths were corrected by extrapolating to zero ionic strength to obtain the standard redox potential. If either an oxidant or a reductant is an uncharged species, then ϵ_T(i, j) for the other species can be determined because ϵ_T(i, j) for an uncharged species is zero [2]. To obtain the value for ϵ_T(HSeO₄⁻, Na⁺), the following reaction involving HSeO₄⁻ as the oxidant and the uncharged species (H₂SeO₃) as the reductant was used in this study: (2) In spite of the fact that the pH of groundwater is anticipated to be 7 to 9 [4], the above reaction occurring in an acidic solution was used. The standard thermodynamic data for the following protonation reactions are available [2]: (3) (4) (5) Because the Se speciation is calculated using a thermodynamic database including the standard thermodynamic data for these protonation reactions, it is possible to calculate the Se speciation at the anticipated pH of groundwater even though the standard thermodynamic data of the Se(VI)/(IV) couple included in a thermodynamic database are those of the reaction occurring in acidic conditions. Because this study assigned a priority to the determination of ϵ_T(i, j) for the Se species, the thermodynamic values for the reaction in Equation (2) were evaluated as functions of temperature and ionic strength.

2. Experimental

Cyclic voltammograms were obtained by using an electrochemical analyzer (BAS Co., Ltd., ALS Model 1100). A three-electrode system was employed. The working, the reference and the counter electrodes were a platinum disk (BAS Co., Ltd., 002013 PTE) with an exposed area of 2.0 mm², Ag/AgCl with a saturated solution of KCl (BAS Co., Ltd., 002058 RE-1C) and a platinum wire (BAS Co., Ltd., 002233 VC-3), respectively. The working electrode was polished using a 0.05 μm alumina paste before each cyclic voltammetry experiment.

A solution of Se was prepared by the addition of Se standard (1003 ppm Se in 0.10 mol dm⁻³ HNO₃, Kanto Kagaku Co., Ltd., 37808-1B) and sodium nitrate (NaNO₃, Wako Jyunyaku Kogyo Co., Ltd., 195-02545) into 0.1000 mol dm⁻³ HNO₃. The concentration of Se was 9.3×10⁻⁴ mol kg⁻¹ in this solution. The molality of a sodium ion, m_Na+, was adjusted to 0.500, 1.00, 1.50 and 2.00 mol kg⁻¹. The tetravalent Se species was H₂SeO₃ because the values of −log₁₀ a_H+ were estimated to be 1.13 ± 0.26 as described in Section 3.1. The solution not containing Se (henceforth referred to as the “blank” solution) was prepared by dissolving NaNO₃ into 0.1000 mol dm⁻³ HNO₃. Aliquots of solution were transferred to the glass cell (BAS Co., Ltd., 001056). The temperature of the solution in the glass cell was maintained by the thermostat water bath (AS ONE Co., Ltd., Thermax TM-1). The temperatures for the measurements were selected to be 288, 298, 308 and 323 K because the values of the Debye–Hückel constants, A(T), are available for these temperatures [8]. Before and after the cyclic voltammetry experiment, pH values at each temperature controlled by the thermostat water bath were measured using the combination glass pH electrode (TOA Co., Ltd., ION METER IM-55G). Because the reference electrode was immersed in the solution in the glass cell, it is reasonable to assume that the temperature of the internal solution of the reference electrode was same as that of the solution in the glass cell. All solutions were thoroughly degassed with nitrogen gas prior to recording cyclic voltammograms. For all the cyclic voltammetry experiments, the scan region was 0.250↔1.240 V vs. Ag/AgCl, which corresponded to 0.449↔1.439 V vs. SHE at 298 K, described as a line with arrow points in Figure 1. The scan rate was 0.6 V s⁻¹ except while investigating the dependence of the peak current and potential on the scan rate.

3. Data analysis

3.1. Dependence of the half-wave potential on the molality of a sodium ion

When the redox process is reversible or quasi-reversible and the diffusion coefficient of a reductant is equal to that of an oxidant, E_1/2(T, I_m) is the potential when the concentration of a reductant is equal to that of an oxidant [11]. Nernst's equation for the redox reaction, , is (6) The application of Nernst's equation to the HSeO₄⁻/H₂SeO₃ couple and the Ag/AgCl couple yields E_1/2(T, I_m) and E_Ref(T, I_Ref), respectively, given by (7) (8) where (9) J is constant. In this study, the value of 2log₁₀ a_Cl− in Equation (8) is equal to the common logarithm of the equilibrium constant, log₁₀ K₁(T, 0), for the following reaction occurring in an internal solution of the Ag/AgCl reference electrode: (10) SIT [8] gives a good estimation of the activity coefficient in an ionic medium of up to 3.5 mol kg⁻¹. SIT was used to estimate a value of log₁₀ in Equation (7). Because the cations were Na⁺ and H⁺ in a solution of Se, log₁₀ is described by (11) where (12) D(T, I_m) is the Debye–Hückel term [8]. The values of A(T) calculated from the static dielectric constant and the density of water as functions of temperature and pressure are listed in TDB-2 [8]. The values of A(T) at a pressure of 1.00 bar for temperatures of 288, 298, 308 and 323 K were taken from TDB-2. By substituting Equation (11) for log₁₀ in Equation (7), the following equations are finally obtained: (13) where (14) (15) The values of Y are plotted against m_Na+. As one would predict from Equation (13), the extrapolation of Y to gives a straight line where the slope and intercept correspond to ϵ_T(HSeO₄⁻, Na⁺) and Y_intercept, respectively. Using Equation (15), can be calculated from Y_intercept.

Measurements of E_1/2(T, I_m) were made four times at each m_Na+. Using Equation (14), Y was calculated from an average of E_1/2(T, I_m), E_1/2^ave(T, I_m). The uncertainty 1.96σ of the four measurements, representing the 95% confidence level, was assigned to E^ave_1/2(T, I_m).

In this experiment, the measured pH might be different from the value of −log₁₀ a_H+ because of the difference between the activity factor of the calibration buffer and high ionic strength solution. Therefore, the measured pH was not used to calculate Y. The value of is calculated by (16) The H⁺ concentration is calculated from the amount of HNO₃. During the cyclic voltammetry experiment, no oxygen gas bubble was found on the electrode surface. The pH value measured after the cyclic voltammetry experiment was the same as that measured before the cyclic voltammetry experiment. Therefore, it was considered that the cyclic voltammetry experiment made no changes in the H⁺ concentration. The value of log₁₀ γ_H+ is calculated using SIT as follows: (17) The value of is 0.07 ± 0.01 kg mol⁻¹ [8]. The following relationship was proposed on the basis of a few experimental values for Δϵ_T(i, j) [13]: (18) Using Equation (18) with ϵ_T(i, j) and in place of Δϵ_T(i, j) and , the correction for ϵ_T0(NO₃⁻, H⁺) was calculated to be less than 0.006 kg mol⁻¹ for the temperature range of 288–323 K. Because this correction was smaller than the assigned uncertainty in ϵ_T0(NO₃⁻, H⁺), ϵ_T(NO₃⁻, H⁺) at 288, 308 and 323 K was equal to ϵ_T0(NO₃⁻, H⁺) in this study.

The values of log₁₀ a_H2O are calculated by (19) where φ is the osmotic coefficient of the mixture and the summation extends over all solute species k with molality m_k present in the solution [2]. The following equations yield the osmotic coefficient for a mixed electrolyte [14]: (20) (21) (22) (23) where f ^φ is the Debye–Hückel term extended to include osmotic effects and c is an index covering all cations, while a covers all anions. The parameters of β⁽⁰⁾_ca and β⁽¹⁾_ca define the second virial coefficient, and C^φ_ca defines the third virial coefficient [15].

The E_Ag/AgCl(T, 0) values are calculated using the following equation, which is applicable for any temperature from 273 to 368 K [16]: (24) The standard molar Gibbs energy of formation of K⁺ and Cl⁻ [2] and that of KCl [17] were used to calculate log₁₀ K₁(T₀, 0). Equation (25) can be used to calculate equilibrium constant for any temperature from 273 to 473 K [18]: (25) Equation (25) was used to calculate log₁₀ K₁(T, 0) at 288, 308 and 323 K. The standard molar enthalpy of formation of KCl, K⁺ and Cl⁻ [17] were used to calculate Δ_rH⁰_m (T₀) of Equation (10). Following the simplification that the heat capacity for any temperature is equal to that at 298 K for the temperature range between 273 and 423 K [18], the standard molar heat capacity of KCl, K⁺ and Cl⁻ [17] were used to calculate Δ_rC⁰_{p, m} of Equation (10).

3.2. Temperature dependence of the standard redox potential

The Gibbs–Helmholtz equation [12] is represented by (26) On the other hand, (27) Equation (28) is obtained by substituting Equation (27) into Equation (26) [12]: (28) Equation (28) indicates that the determination of E_Ox/Red(T, 0) as a function of temperature allows us to determine Δ_rS⁰_m.

4. Results and discussion

Figure 2 shows the cyclic voltammogram of a solution containing H₂SeO₃ after repetitive potential cycling. Peaks were assigned as arising from Se species present in solution. This was because no voltammetric peaks associated with the oxidation–reduction reaction of NaNO₃ and HNO₃ were observed in a voltammogram of the blank solution. With increasing number of cycles, two peaks appear clearly, consistent with electrochemical investigations of Se species, using cyclic voltammetry conducted with the working platinum electrode [7,19]. As described in the previous work [7], this voltammetric behavior arises from a passivating layer covering the electrode surface. The drop of the anodic current at the upper reversal potential, observed during the course of the second cycle, suggests a decrease in the active electrode area available for the electron-transfer process owing to the formation of a passivating layer. The growth of the redox wave is indicative of the increase in the active electrode area owing to the removal of this layer by repetitive potential cycling. The cyclic voltammogram became steady by the 35th cycle in this study. The complete removal of this passivating layer resulted in a steady voltammogram. The E_1/2(T, I_m) value was obtained from the 40th cyclic voltammogram in this study.

Figure 2. Cyclic voltammogram of a solution containing H₂SeO₃ after repetitive potential cycling .

The anodic peak current of the 40th cyclic voltammogram after repetitive potential cycling is plotted as a function of v^1/2 in Figure 3. The linear dependence of the anodic peak current on v^1/2 is indicative of the diffusion-controlled process [20,21]. The peak at about 1.0 V vs. Ag/AgCl and that at about 0.4 V vs. Ag/AgCl are attributed to the oxidation of H₂SeO₃ to HSeO₄⁻ and to the corresponding reduction of HSeO₄⁻ to H₂SeO₃, respectively.

Figure 3. Dependence of the anodic peak current on v^1/2. The eight filled circles corresponding to each scan rate in the figure are obtained from the 40th cyclic voltammogram after repetitive potential cycling measured in a solution containing H₂SeO₃ . The solid line is the linear least-squares fit of data. The linear dependence of the anodic peak current on v^1/2 is indicative of the diffusion-controlled process.

Compared with the cathodic wave, an extra increase in the anodic current occurs in the potential range 0.87 ± 0.08 V vs. Ag/AgCl, where the stripping peak was observed in the cyclic voltammogram of a solution containing 1×10⁻³ mol dm⁻³ of SeO₂ [22]. Similar behavior was observed in the cyclic voltammogram of a solution containing Se species [7,19]. The stripping peak is associated with the removal of a previously deposited film of Se [23] and can be considered independent of the oxidation of H₂SeO₃ to HSeO₄⁻. The anodic current is the sum of the current associated with the removal of the Se film and that associated with the oxidation of H₂SeO₃ to HSeO₄⁻. The cathodic wave is associated only with the corresponding reduction of HSeO₄⁻ to H₂SeO₃. The similarity in the peak shape between the anodic wave and the cathodic wave indicates that the contribution of the removal of the Se film to the anodic current is not significant. Without subtracting this contribution from the total anodic current, evidence of a diffusion-controlled process was obtained as described earlier. These voltammetric features were seen from the voltammogram of a solution containing SeO₃²⁻ [7]. Therefore, as was the case of the cyclic voltammogram of a solution containing SeO₃²⁻, the peak potential and current of the anodic wave were determined without any correction in this study.

E_p(Ox), E_p(Red) and E_1/2(T, I_m) of the 40th cyclic voltammogram after repetitive potential cycling, measured at different scan rates are listed in Table 1. As confirmed by the data in Table 1, E_1/2(T, I_m) is independent of the scan rate. This feature corresponds to the quasi-reversible reaction [11,12]. Assuming that the diffusion coefficient of H₂SeO₃ is equal to that of HSeO₄⁻, E_1/2(T, I_m) is the potential when the concentration of H₂SeO₃ is equal to that of HSeO₄⁻. Based on this assumption, Equation (7) was used to determine at each temperature in this study.

Table 1. E_p(Ox), E_p(Red) and E_1/2(T, I_m) of the 40th cyclic voltammogram after repetitive potential cycling, measured at different scan rates in a solution containing H₂SeO₃ .

	Ep(Ox)	Ep(Red)	E1/2(T, Im)
	(V vs. Ag/	(V vs. Ag/	(V vs. Ag/
v (V s^−1)	AgCl)	AgCl)	AgCl)
0.80	1.0535	0.3992	0.7264
0.60	1.0515	0.4009	0.7262
0.50	1.0408	0.4118	0.7263
0.40	1.0372	0.4153	0.7263
0.30	1.0319	0.4207	0.7263
0.20	1.0247	0.4279	0.7263
0.10	1.0247	0.4279	0.7263
0.08	1.0247	0.4279	0.7263

Table 2 shows a summary of the cyclic voltammetry experiments to measure the half-wave potentials for the HSeO₄⁻/H₂SeO₃ couple in acidic sodium nitrate solutions as a function of m_Na+. A plot of the Y values vs. m_Na+ is shown in Figure 4. The values of Y_intercept and ϵ_T(HSeO₄⁻, Na⁺) are obtained by using the extrapolations of weighted linear regression [24] through Y determined at various m_Na+, which correspond to the lines in Figure 4. Using Equation (15), were calculated from Y _intercept, E_Ag/AgCl(T, 0) and log₁₀ K₁(T, 0). The values of Y _intercept, ϵ_T(HSeO₄⁻, Na⁺), E_Ag/AgCl(T, 0), log₁₀ K₁(T, 0) and are listed in Table 3. A plot of the values vs. temperature is shown in Figure 5, where the solid line represents a weighted linear regression of . The slope of this line corresponds to Δ_rS⁰_m/2F given by

Table 2. Summary of the cyclic voltammetry experiments to measure the half-wave potentials for the HSeO₄⁻/H₂SeO₃ couple in acidic sodium nitrate solutions as a function of m_Na+.

T (K)		D(T, Im)^a			E1/2^ave(T, Im)^b (V vs. Ag/AgCl)	Y^c
288.4 ± 0.6	0.500	0.18	1.14 ± 0.00	−0.0083	0.7137 ± 0.0025	28.65 ± 0.09
	1.00	0.20	1.14 ± 0.01	−0.0148	0.7200 ± 0.0035	28.75 ± 0.13
	1.50	0.22	1.13 ± 0.01	−0.0212	0.7274 ± 0.0010	28.95 ± 0.04
	2.00	0.23	1.11 ± 0.01	−0.0275	0.7332 ± 0.0009	29.15 ± 0.05
298.3 ± 1.1	0.500	0.18	1.15 ± 0.00	−0.0083	0.7137 ± 0.0000	27.90 ± 0.01
	1.00	0.21	1.15 ± 0.01	−0.0148	0.7269 ± 0.0022	28.23 ± 0.08
	1.50	0.22	1.14 ± 0.01	−0.0212	0.7290 ± 0.0001	28.21 ± 0.04
	2.00	0.23	1.12 ± 0.01	−0.0275	0.7332 ± 0.0017	28.28 ± 0.07
308.1 ± 1.4	0.500	0.19	1.16 ± 0.00	−0.0083	0.7222 ± 0.0009	27.22 ± 0.07
	1.00	0.21	1.16 ± 0.01	−0.0148	0.7276 ± 0.0010	27.48 ± 0.04
	1.50	0.23	1.14 ± 0.01	−0.0212	0.7324 ± 0.0009	27.59 ± 0.06
	2.00	0.24	1.13 ± 0.01	−0.0275	0.7371 ± 0.0020	27.73 ± 0.08
323.4 ± 0.5	0.500	0.19	1.17 ± 0.00	−0.0083	0.7283 ± 0.0009	26.40 ± 0.03
	1.00	0.22	1.16 ± 0.01	−0.0148	0.7326 ± 0.0000	26.51 ± 0.03
	1.50	0.23	1.15 ± 0.01	−0.0212	0.7362 ± 0.0000	26.60 ± 0.03
	2.00	0.24	1.13 ± 0.01	−0.0275	0.7436 ± 0.0009	26.80 ± 0.05

^aD(T, I_m) is Debye-Hückel term [8].

^bE_1/2^ave(T, I_m) is an average of E_1/2(T, I_m) in four measurements at each .

, where J = RT/2Flog₁₀ e (= 0.02958 V at 298.2 K).

Table 3. Values of Y_intercept, ϵ_T(HSeO₄⁻, Na⁺), E_Ag/AgCl(T, 0), log₁₀ K₁(T, 0) and . The intercept and slope of each line in Figure 4 correspond to Y _intercept and ϵ_T(HSeO₄⁻, Na⁺), respectively, at each temperature.

		ϵT(HSeO4^−, Na^+)	EAg/AgCl(T, 0)
T (K)	Y intercept^a	(kg mol^−1)	(V vs. SHE)	log10 K1(T, 0)^b	(V vs. SHE)
288.4 ± 0.6	28.44 ± 0.10	0.35 ± 0.06	0.2287 ± 0.0003	0.697 ± 0.041	1.0226 ± 0.0037
298.3 ± 1.1	27.76 ± 0.03	0.29 ± 0.03	0.2225 ± 0.0006	0.805 ± 0.055	1.0203 ± 0.0035
308.1 ± 1.4	27.12 ± 0.08	0.32 ± 0.06	0.2155 ± 0.0008	0.897 ± 0.065	1.0171 ± 0.0049
323.4 ± 0.5	26.26 ± 0.04	0.25 ± 0.03	0.2031 ± 0.0003	1.012 ± 0.035	1.0133 ± 0.0022

^aY_intercept = [ – E_Ag/AgCl(T, 0)]/J + log₁₀ K₁(T, 0), where J = RT/2Flog₁₀ e (= 0.02958V at 298.2 K).

^bK₁(T, 0) is the equilibrium constant of the reaction (KCl K⁺ + Cl⁻) occurring in an internal solution of the Ag/AgCl reference electrode.

Figure 4. Determination of the standard redox potential for the HSeO₄⁻/H₂SeO₃ couple using SIT. Experimental data as a function of are shown as the solid bars with a vertical bar showing the standard deviation in each data point. The solid line is a weighted linear regression [24] of data. The slope and intercept of each line correspond to ϵ_T(HSeO₄⁻, Na⁺) and Y_intercept, respectively, at each temperature. , where J = RT/2F log₁₀ e. Y_intercept = [ – E_Ag/AgCl(T, 0)]/J + log₁₀ K₁(T, 0).

Figure 5. Determination of the molar entropy for the HSeO₄⁻/H₂SeO₃ couple. The HSeO₄⁻/H₂SeO₃ standard redox potential as a function of temperature is shown as the filled circle with vertical bar showing the standard deviation in each data point. The solid line is a weighted linear regression [24] of data. The slope of this line corresponds toΔ_rS⁰_m/2F = −0.3 ± 0.1 mV K^{− 1}.

The OECD-selected values for the standard molar enthalpy of the formation of HSeO₄⁻, H₂SeO₃ and H₂O are −582.700 ± 4.700 kJ mol⁻¹, −505.320 ± 0.650 kJ mol⁻¹ and −285.830 ± 0.040 kJ mol⁻¹, respectively [2]. From these values, Δ_rH⁰_m (T₀) of Equation (2) was calculated to be −208.450 ± 4.745 kJ mol⁻¹. This calculated value was compared with the Δ_rH⁰_m (T₀) value calculated from our experimental results. The following relationship permits calculation of Δ_rH⁰_m: (29) Using Equation (27), Δ_rG⁰_m(T₀) of Equation (2) was calculated to be −196.90 ± 0.68 kJ mol⁻¹ from listed in Table 3. Using Equation (29), from Δ_rG⁰_m(T₀) and Δ_rS⁰_m obtained by this study using cyclic voltammetry, Δ_rH⁰_m(T₀) of Equation (2) was calculated to be −212 ± 6 kJ mol⁻¹, which agrees with the Δ_rH⁰_m(T₀) value calculated from the OECD-selected values within the uncertainty limits. The result of this study will make a contribution to more reliable prediction of the Se speciation at a temperature over 298 K in oxidized groundwater. The standard thermodynamic data of Equation (2) are summarized in Table 4.

Table 4. Standard thermodynamic data for the Se(VI)/(IV) couple.

	Reaction HSeO4^− + 3H^+
	+ 2e^− H2SeO3 + H2O	Reference
	1.0203 ± 0.0035 V vs. SHE	This study
ΔrG^0m(T0)	−196.90 ± 0.68 kJ mol^−1	This study
ΔrH^0m(T0)	−208.450 ± 4.745 kJ mol^−1	Olin et al. [2]
ΔrS^0m	−0.05 ± 0.02 kJ K^−1 mol^−1	This study

The value of was determined to be 0.29 ± 0.03 kg mol⁻¹ in this study. Available literature values for are −0.01 ± 0.02 kg mol⁻¹ [2] and 0.11 ± 0.05 kg mol⁻¹ [25]. The difference was found between and . The ion interaction coefficient is dependent on the size and charge of the ion [8]. The relationship between the size of monovalent anions and the ion interaction coefficient for Na⁺ was surveyed. We compare the ionic radius of F⁻, Cl⁻, Br⁻ and I⁻, which increase in that order [26]. This order is the same as found for the magnitude of the ion interaction coefficient for Na⁺, i.e. [8]. Among these monovalent anions, the larger the size, the larger the magnitude of the ion interaction coefficient for Na⁺ is. The ionic radius of Se⁶⁺ is longer than that of S⁶⁺ [26]. From the fact that the interatomic distances of H₂Se, SeO₄²⁻ and SeO₂ are longer than those of H₂S, SO₄²⁻ and SO₂, respectively [27], the interatomic distances of HSeO₄⁻ are considered to be longer than those of HSO₄⁻. Therefore, the size of HSeO₄⁻ is likely to be larger than that of HSO₄⁻, which is consistent with the relationship of .

A plot of the ϵ_T(HSeO₄⁻, Na⁺) values vs. temperature is shown in Figure 6. The value of ∂ϵ/∂T was obtained by using the extrapolation of weighted linear regression [24] through ϵ_T(HSeO₄⁻, Na⁺) obtained at 288, 298, 308 and 323 K, which corresponds to the line in Figure 6. The slope of this line corresponds to ∂ϵ/∂T given by (30)

Figure 6. Dependence of the ion interaction coefficient ϵ_T(HSeO₄⁻, Na⁺) on temperature. The ion interaction coefficient ϵ_T(HSeO₄⁻, Na⁺) as a function of temperature is shown as the filled circle with vertical bar showing the standard deviation in each data point. The solid line is a weighted linear regression [24] of data. The slope of this line corresponds to ∂ϵ/∂T = −0.002 ± 0.002 kg mol⁻¹ K⁻¹.

The temperature dependence of the ion interaction coefficient was discussed by Lewis and Randall [28], Millero [29], Helgeson et al. [30], Oelkers and Helgeson [31] and Grenthe and Plyasunov [32]. All these studies reported that ∂ϵ/∂T are usually ≤0.005 kg mol⁻¹ K⁻¹ for temperatures below 473 K, which is consistent with our result. The small temperature dependence of ϵ_T(HSeO₄⁻, Na⁺) suggests that the change in the interatomic distance of HSeO₄⁻ is small at a temperature in the range of 288–323 K, which is consistent with the fact that the change in the interatomic distance associated with a temperature change of 50° is less than 0.01 Å [33].

5. Conclusion

An electrochemical investigation of selenium species, using cyclic voltammetry, has been carried out for the purpose of determining the molar entropy of the Se(VI)/(IV) couple. To obtain the value for ϵ_T(HSeO₄⁻, Na⁺), the following reaction involving HSeO₄⁻ as the oxidant and the H₂SeO₃ uncharged species as the reductant was used. The Se(VI)/(IV) half-wave potentials were measured in acidic sodium nitrate solutions as functions of m_Na+ ranging from 0.500 to 2.00 mol kg⁻¹ and temperature ranging from 288 to 323 K. SIT was used to calculate and ϵ_T(HSeO₄⁻, Na⁺). The following molar entropy was derived from the temperature dependence of : The value of ϵ_T(HSeO₄⁻, Na⁺) at 298 K was determined to be 0.29 ± 0.03 kg mol⁻¹. The following ∂ϵ/∂T was derived from the temperature dependence of ϵ_T(HSeO₄⁻, Na⁺):

Nomenclature

ai	=	activity of ion i
γi	=	activity coefficient of ion i
zi	=	charge of ion i
mi	=	molality of ion i (amount of ion i divided by the mass of the solvent, mol kg−1)
[i]	=	molarity or concentration of ion i (amount of ion i divided by the volume of the solution, mol dm−3)
T	=	absolute temperature (K)
T0	=	reference temperature (= 298.15 K)
Im	=	ionic strength of the working solution
IRef	=	ionic strength of a solution contained in the reference electrode (mol kg−1)
D(T, Im)	=	Debye–Hückel term
A(T)	=	Debye–Hückel constant (values taken from TDB-2 [8])
ϵT(i, j)	=	specific interaction coefficient between ion i and ion j of opposite charge (kg mol−1)
EOx/Red(T, 0)	=	standard redox potential of the Ox/Red couple
ERef(T, IRef)	=	potential of the silver–silver chloride (Ag/AgCl) reference electrode with a saturated solution of potassium chloride (KCl)
Ep(Ox)	=	anodic peak potential against the Ag/AgCl reference electrode
Ep(Red)	=	cathodic peak potential against the Ag/AgCl reference electrode
E1/2(T, Im)	=	half-wave potential {E1/2(T, Im) = [Ep(Ox) + Ep(Red)]/2} against the Ag/AgCl reference electrode
J	=	RT/2Flog10e (= 0.02958 V at 298.2 K)
E (V vs. Ag/AgCl)	=	potential against the Ag/ACl reference electrode
E (V vs. SHE)	=	potential against the standard hydrogen electrode
v	=	scan rate (V s−1)
ΔrG0m	=	the molar Gibbs energy of reaction (kJ mol−1)
ΔrH0m	=	the molar enthalpy of reaction (kJ mol−1)
ΔrS0m	=	the molar entropy of reaction (J K−1 mol−1)
ΔrC0p, m	=	the molar heat capacity of reaction (J K−1 mol−1)
K	=	the equilibrium constant of the reaction
σ	=	standard deviation

Acknowledgements

The author would like to thank Prof. Yokoyama (Kanazawa University), Dr Kamei (Japan Atomic Energy Agency) and Dr Rai (Rai Enviro-Chem, LLC) for the valuable discussions and suggestions.