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

Figures & data

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).

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

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.

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. 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}.

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

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.

Olin Å, Noläng B, Öhman LO, Osadchii EG, Rosén E. Chemical thermodynamics of selenium. Amsterdam: Elsevier; 2005.

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