Sn couple

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value of the standard electrode potential E°(Sn4?/Sn2?) is not known ... HClO4 to determine E°(Sn4?/Sn2?), using SnCl4(l) and ... in chloride-free systems the electrochemical cell (I) was ... y M Sn(ClO4Ю4, z M HClO4jHg, Pt ... electromotive force (e.m.f.) of the following, almost sym- ... Despite all our effort, the preparation of.
Monatsh Chem DOI 10.1007/s00706-009-0188-5

ORIGINAL PAPER

The standard electrode potential of the Sn4+/Sn2+ couple revisited Tama´s Gajda • Pa´l Sipos • Heinz Gamsja¨ger

Received: 25 July 2009 / Accepted: 3 September 2009 Ó Springer-Verlag 2009

Abstract The Sn4?/Sn2? redox couple is, thermodynamically, the connecting link between aqueous tin(IV) and tin(II) chemistry. Because the equilibrium potential E°(Sn4?/Sn2?) was not known with sufficient accuracy, we were prompted to attempt its determination by means of a potentiometric study. The equilibrium potential of the redox couple Sn4?/Sn2? has been determined in x M HClO4 ? 1 M HCl media (x = 3, 4, 5). The formal potentials determined for different electrolyte mixtures were extrapolated to zero ionic strength by the extended specific ion interaction theory approach (E°(Sn4?/ Sn2?) = 0.384 ± 0.020 V). The evaluation of the data required knowledge of the formation constants of tin(IV) chloro complexes; these were determined spectrophotometrically at five different HClO4 concentrations (4.5– 8.0 M), and were extrapolated to zero ionic strength. Keywords Aqueous tin(IV) chemistry  Standard redox potential  Sn4?/Sn2? couple  Tin(IV) chloro complexes  Formation constant

Introduction Understanding the chemical behaviour of radionuclides in a deep repository for nuclear waste is of fundamental T. Gajda (&)  P. Sipos Department of Inorganic and Analytical Chemistry, University of Szeged, PO Box 440, 6701 Szeged, Hungary e-mail: [email protected]; [email protected] H. Gamsja¨ger Lehrstuhl fu¨r Physikalische Chemie, Montanuniversita¨t Leoben, 8700 Leoben, Austria

importance for protection of the environment. The presence of 126Sn as a fission product in radioactive waste demands knowledge of basic chemistry of inorganic tin. However, surprisingly limited reliable thermodynamic data for tin(IV) are available in the literature. Even the correct value of the standard electrode potential E°(Sn4?/Sn2?) is not known. Latimer listed E°(Sn4?/Sn2?) = 0.15 V in his book [1]. This value was calculated from potentiometric measurements in HCl solutions reported in Ref. [2], without considering the formation of tin(II) and tin(IV) chloro complexes. Pourbaix’s data on DfGm°(Sn2?) and DfGm°(Sn4?) [3] were also taken from Ref. [1]. Despic et al. [4] determined the standard potential E°0 (Sn4?/ Sn2?) = 0.228 V in 4 M HCl and 1 M Na2SO4 ? 1 M H2SO4 solutions. However, during these measurements the ionic strength changed substantially, Na2SO4/H2SO4 cannot be regarded as inert electrolyte, and the authors used a doubtful simplification in the evaluation of the stability constants for the tin(IV) chloro complexes. Vasil’ev et al. [5] also performed a potentiometric study in 2, 3, and 4 M HClO4 to determine E°(Sn4?/Sn2?), using SnCl4(l) and SnCl2(cr) as starting materials. Although the authors considered the formation of tin(II) chloro and tin(IV) hydroxo complexes, they neglected the presence of tin(IV) chloro species. Only a single paper, at a single ionic strength (5 M HClO4) reports reliable formation constants for tin(IV) chloro complexes [6]. Considering the high stability of SnCl4-x (x = 1–6) species reported in Ref. [6], under the x conditions used by Vasil’ev et al. ([Cl-]TOT [ 4 9 [Sn(IV)]TOT) the concentration of uncomplexed tin(IV) is well below 1% of [Sn(IV)]TOT. As pointed out by Hummel et al. [7], Vasil’ev made an error in his calculation. Therefore they re-evaluated Vasil’ev’s data using the specific ion interaction theory (SIT), without considering the tin(IV) chloro complexes, and obtained E°(Sn4?/Sn2?)

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T. Gajda et al.

= 0.289 V [7]. It is clear that the true standard electrode potential may differ from the generally accepted value E°(Sn4?/Sn2?) = 0.15 V by several hundred mV. The aqueous chemistry of tin(IV) is further complicated by its strong tendency to hydrolyse. Only a single experimental study is available on the hydrolysis of tin(IV) under acidic conditions, using a spectrophotometric method and salicylfluorone as competing ligand [8]. Because several experimental details in Ref. [8] are disputable, the values reported can only be regarded as approximate estimates only [7]. The missing link between aqueous tin(IV) and tin(II) chemistry prompted us to perform potentiometric and spectrophotometric studies to determine E°(Sn4?/Sn2?) and the formation constants of tin(IV) chloro complexes in strongly acidic solution, in order to avoid hydrolytic processes.

potential. Therefore, the standard potential determined under these conditions (E°0 (Sn4?/Sn2?) & 0.3 V) can be regarded, at most, as a first approximation. Apparently, the solubility of tin(IV) under strongly acidic conditions can be significantly enhanced by the presence of chloride ions, because of the formation of various SnCl4-x complexes. The higher concentration of x potential-determining ions is expected to reduce the above mentioned uncertainties. However, evaluation of E°(Sn4?/ Sn2?) in chloride-containing media requires knowledge of the stepwise formation constants of the complexes SnCl2-x x 4-x and SnCl4-x under the conditions x . Such data for SnClx relevant to these studies are not available from the literature.

Results and discussion

First, we attempted the determination of the stepwise formation constants of SnCl4-x complexes from the x electromotive force (e.m.f.) of the following, almost symmetrical concentration cell (II).

First estimation of E°(Sn4?/Sn2?) from measurements in Cl--free systems

The stepwise formation constants of SnCl4-x complexes x

AgjAgClj(I  xÞ M HClO4 ; x M HCljjðI  x  4yÞ M HClO4 ; For determination of the standard electrochemical potential of the Sn4?/Sn2? couple for the reaction (Eq. 1): Sn4þ ðaqÞ þ H2 ðgÞ Sn2þ ðaqÞ þ 2Hþ ðaqÞ

ð1Þ

in chloride-free systems the electrochemical cell (I) was used: Pt; H2 jð2x þ 4y þ zÞ M HClO4 jjx M Sn(ClO4 Þ2 ; y M Sn(ClO4 Þ4 ; z M HClO4 jHg; Pt

ðIÞ

For the initial experiments, 0.001 M Sn(ClO4)2 in 5 M HClO4 and 0.0005 M Sn(ClO4)4 in 5 M HClO4 solutions were used. Although H2 and Ar were permanently bubbled through the reference and measurement compartments, respectively, the potential of this cell was not stable. Using high-purity H2 (99.999%), Ar (99.996%), and Hg (99.999%, which was further purified by repeated washing with HNO3 (w = 5%) and subsequently with Milli-Q water) the stability of the potential significantly increased, but still it was not satisfactory. Moreover, the reproducibility of routine titrations, when tin(IV) perchlorate was titrated by Sn(ClO4)2 solution, was not acceptable (±25 mV), and the slopes of these plots were found to be 28–38 mV. We associated these spurious potentiometer readings with the low concentration of the potential determining cations, which was dictated by the low solubility of tin(IV) in perchlorate-containing media. The sub-millimolar tin(IV) and tin(II) concentrations make the electrochemical cell unbuffered, and probably extremely oxygen-sensitive, because even traces of oxygen could significantly change the relative concentrations of Sn(IV) and thus the cell

123

x M HCl; y M Sn(ClO4 Þ4 jAgCljAg

ðIIÞ

For this, an Ag/AgCl electrode was prepared according to Refs. [9, 10]. Despite all our effort, the preparation of Ag/AgCl electrodes which are stable in concentrated perchloric acid solutions has failed. UV spectroscopy has been successfully used to determine the stability of tin(II) chloro complexes [11]. Therefore, we studied the UV spectra of tin(IV) as a function of the chloride concentration at five different ionic strengths (Table 1). Figure 1 shows the background and dilution-corrected UV spectra of tin(IV) detected at different chloride concentrations in 8 M HClO4 solution. With increasing [Cl-]TOT significant spectral changes were observed, reflecting changes in the coordination sphere of tin(IV); this provided sufficient information to derive the formation constants of the tin(IV) chloro complexes. The observed spectral changes can be best described by the formation of five species (SnCl3?, SnCl22?, SnCl4(aq), SnCl5-, and SnCl62-) at all ionic strengths (Table 2). Formation of SnCl3? was not detected. Because 119Sn NMR spectra of concentrated SnCl4 solutions seem to prove the existence of this species [12], our observation is probably because of the high similarity of the individual spectra of SnCl3? and SnCl4(aq), which prevents their differentiation by the method used. To promote the formation of SnCl62- higher [Cl-]TOT had to be applied at lower ionic strength (Table 1).

The standard electrode potential of the Sn4?/Sn2? couple revisited Table 1 Experimental conditions for data sets of the UV spectrophotometric determination of the formation complexes constants of SnCl4-x x at different ionic strengths

Im (Ic)

[Sn(IV)]0 (mM)

5.62 (4.5)

0.221

Titrant solutions

[Cl-] conc. range (M)

No. of spectra used for the calculation

0.02 M HCl ? 4.48 M HClO4

0–0.97

103

0–0.65

97

0–0.62

98

0–0.42

128

0–0.32

88

0.2 M HCl ? 4.3 M HClO4 2.0 M HCl ? 2.5 M HClO4 7.42 (5.6)

0.208

0.02 M HCl ? 5.58 M HClO4 0.2 M HCl ? 5.4 M HClO4 2.0 M HCl ? 3.6 M HClO4

8.12 (6.0)

0.219

10.03 (7.0)

0.220

0.02 M HCl ? 5.98 M HClO4 0.2 M HCl ? 5.8 M HClO4 2.0 M HCl ? 4 M HClO4 0.02 M HCl ? 6.98 M HClO4 0.2 M HCl ? 6.8 M HClO4 1.0 M HCl ? 6.0 M HClO4

12.18 (8.0)

0.221

0.02 M HCl ? 7.98 M HClO4 0.2 M HCl ? 7.8 M HClO4 1.0 M HCl ? 7.0 M HClO4

1.8 1.6

Absorbance

1.4 1.2 1 0.8 0.6 0.4 0.2 0 190

200

210

220

230

240

250

260

λ / nm

Fig. 1 UV spectral changes of tin(IV) perchlorate solution upon addition of Cl- (Ic = 8 M H(ClO4,Cl), [Sn(IV)]TOT = 0.221 mM, [Cl-]TOT = 0–0.32 M)

Nevertheless, the change in the background electrolyte (i.e., the replacement of perchlorate by chloride ion) is modest, even for the lowest ionic strength ([Cl-]/Ic B 0.22; Table 1). The symbols for ionic strength are Ic (subscript c refers to amount concentration basis) or Im (subscript m refers to molality basis). The calculated formation constants (expressed in mol kg-1) are listed in Table 2. The individual spectra of the chloro complexes formed in 8 M HClO4 are shown in Fig. 2, the species distribution curves calculated for the highest and lowest ionic strengths applied are depicted in Fig. 3. The stability of the different complexes shows notable ionic strength dependence, e.g. with increasing ionic strength the relative stability of SnCl5- and SnCl62decreases and increases, respectively (Fig. 3). The data in Table 2 confirm the relatively high stability of tin(IV)

chloro complexes reported earlier [6], although the numerical values are rather different. Fatouros et al. reported a non-regular tendency of stepwise stability constants (lg K3 = 2.32, lg K4 = 0.7, lg K5 = 1.75 [6]), which would indicate a change in the coordination geometry during the reaction SnCl3? ? Cl- SnCl4(aq). However, 119Sn NMR chemical shifts indicate octahedral geometry for all tin(IV) chloro complexes [12], thus a regular decrease of the stepwise formation constants can be expected. The formation constants listed in Table 2 have been used to extrapolate to I = 0 by weighted linear regression and error propagation, assuming Gaussian probability distribution, by applying the specific ion interaction theory [13]. The resulting thermodynamic constants and the corresponding De values (Appendix B) are also listed in Table 2. The ionic strength dependences of the formation constants are depicted in Fig. 4. Obviously, the extrapolation to Im = 0 using data for Im C 5.55 mol kg-1 results in higher uncertainties than predicted for the range of ionic strengths where the actual measurements were carried out. Therefore, we would prefer to define an additional key ionic strength within the range covered. The interpolated formation constants at Im = 6.41 mol kg-1 (5 M HClO4) using weighted linear regression are also listed in Table 2. Further consideration should be made concerning the formation of hydroxo complexes of tin(IV) under our conditions. The hydrolysis constants reported by the single experimental study on the hydrolysis of tin(IV) under acidic conditions [8] refer to 1 M (H,K)NO3, and can be considered only as estimates [7]. Nevertheless, Vasil’ev et al. [5] re-calculated, by an unknown procedure, the

123

T. Gajda et al. Table 2 Formation constants bx of SnCl4-x complexes (units on the molality basis) determined in HClO4 background solutions at different ionic x strength (the estimated experimental errors (3r) are in parentheses) and extrapolated values to zero ionic strength and to Im = 6.41 mol kg-1 by SIT Im (Ic)

lg b1

lg b2

lg b4

lg b5

lg b6

5.62 (4.5)

2.91 (0.36)

4.96 (0.36)

8.01 (0.30)

8.91 (0.45)

8.40 (0.50)

7.42 (5.6)

2.80 (0.30)

5.19 (0.30)

8.75 (0.30)

9.81 (0.40)

9.89 (0.40)

8.12 (6.0) 10.03 (7.0)

3.13 (0.12) 3.52 (0.15)

5.77 (0.10) 6.57 (0.12)

9.27 (0.12) 10.39 (0.10)

10.20 (0.15) 11.38 (0.10)

10.15 (0.18) 11.69 (0.12)

12.18 (8.0)

4.40 (0.30)

7.45 (0.15)

11.69 (0.10)

12.43 (0.12)

12.67 (0.15)

?0a

3.19 ± 0.50

5.95 ± 0.36

9.57 ± 0.32

10.93 ± 0.41

9.83 ± 0.49

De (kg mol-1)

-(0.26 ± 0.06)

-(0.45 ± 0.04)

-(0.64 ± 0.03)

-(0.60 ± 0.04)

-(0.67 ± 0.05)

?6.41b/

2.73 ± 0.17

5.08 ± 0.14

8.31 ± 0.14

9.38 ± 0.17

9.28 ± 0.20

a

Extrapolation to zero ionic strength by weighted linear regression and error propagation assuming Gaussian probability distribution and 95% confidence limits of parameters [31]

b

Interpolation to average ionic strength Im = 6.41 mol kg-1 4+

7000

Sn

Sn 3+ SnCl 2+ SnCl2

6000 5000

SnCl

3+

-

SnCl5 SnCl4

2-

SnCl6

80

100 x (Sn )

-1

SnCl4(aq) 4000

-

IV

SnCl5

-1

ε / M cm

2+

SnCl2

100

4+

2-

SnCl6

3000 2000

60

40

20 1000

0

0 200

210

220

230

240

250

260

λ / nm

Fig. 2 The individual spectra of the tin(IV) chloro complexes formed in 8 M HClO4

hydrolysis constants reported in Ref. [8] for 4 M HClO4 background electrolyte (lg *b11 = 0.60, lg *b12 = 0.75). On the other hand, it is known that the hydrolysis constants and the z/dM–OH values (z = charge of the cation, dM–OH = interatomic distance) show systematic correla˚ -1) and tion [14]. As the z/dM–OH values of Sn4? (1.942 A 4? -1 ˚ ) are almost identical [15], their hydrolysis Zr (1.914 A constants are probably also similar. Using the values reported by a recent review for the hydrolysis of Zr4? [16], lg *b11 = -0.45 and lg *b12 = -2.08 can be calculated for 4.5 M HClO4 solution. Finally, applying the relationship between lg *b11 and dM–OH established by Baes and Mesmer [14], and using the SIT data reported in Ref. [16] for Zr4?, lg *b11 = 0.79 can be derived for 4.5 M HClO4 solution. On the basis of the values evaluated for Zr4? in Ref. [16], hydrolysis of tin(IV) is less than 10% in 4.5 M HClO4, the other data suggest the presence of 40–50% hydrolysed species at [Sn4?]TOT = 2 9 10-4 M. Obviously, these estimates do not enable correct consideration

123

-6

-4

-2

0

-

log10 [Cl ]TOT

Fig. 3 Species distribution curves of the tin(IV) chloro complexes in HClO4 solutions as a function of chloride concentration (Im = 5.55 m (dashed lines) and 12.18 m (solid lines))

of the hydrolysis of tin(IV). On the other hand, the UV spectra of main group metal ions show considerable changes during hydrolysis [17, 18]. The UV spectra of tin(IV) in 3–8 M HClO4 are nearly identical, indicating only small (if any) changes in the speciation. However, notable changes would occur in the speciation on considering the upper estimates of the hydrolysis constants. This observation may support our approach, which neglects the formation of hydroxo species at cHClO4  4:5 M. Determination of E° from measurements in Cl--containing systems For electrochemical measurements involving chloridecontaining mixed background electrolytes the following electrochemical cell (III) was employed:

The standard electrode potential of the Sn4?/Sn2? couple revisited 7

A log10β1° = 3.19 ± 0.53

6

12

B

11

log10β2° = 5.95 ± 0.40

-1

∆ε = -(0.26 ± 0.06) kg·mol

-1

5

exp. data, error bars: 3σ 95% confidence band -1 log10β at Im = 6.41 mol·kg log10β1 + 8 D = 4.88 ± 0.17 log10β1 = 2.73 ± 0.17

4

3

0

2

4

6

8

Im / mol kg

10

log10 β2 + 14 D

log10 β1 + 8 D

Fig. 4 Extrapolation to Im = 0 of the formation constants of complexes using SIT SnCl4-x x (x = 1 (a), 2 (b), 4 (c), 5 (d), 6 (e))

8

exp. data, error bars: 3σ 95% confidence band -1 log10β at Im = 6.41 mol·kg log10β2 + 14 D = 8.84 ± 0.14 log10β2 = 5.08 ± 0.14

7

5

12

0

6

8

10

12

-1

D 18 log10β5° = 10.93 ± 0.44

-1

12

exp. data, error bars: 3σ 95% confidence band -1 log10β at Im = 6.41 mol·kg log10β4 + 20 D = 13.68 ± 0.14 log10β4 = 8.31 ± 0.14

10 8 2

4

6

8

Im / mol kg

10

12

-1

log10 β5 + 20 D

-1

14

0

4

Im / mol kg

∆ε = -(0.64 ± 0.03) kg·mol

16

2

-1

log10β4° = 9.57 ± 0.34

log10 β4 + 20 D

9

6

C

18

∆ε = -(0.45 ± 0.04) kg·mol

10

∆ε = -(0.60 ± 0.04) kg·mol

16

14 exp. data, error bars: 3σ 95% confidence band -1 log10β at Im = 6.41 mol·kg log10β5 + 20 D = 14.75 ± 0.17 log10β5 = 9.38 ± 0.17

12

10 0

2

4

6

8

10

12

-1

Im / mol kg

E

18

log10β6° = 9.83 ± 0.52 -1

∆ε = -(0.67 ± 0.05) kg·mol

log10 β6 + 18 D

16 14

exp. data, error bars: 3σ 95% confidence band -1 log10β at Im = 6.41 mol·kg log10β6 + 18 D = 14.11 ± 0.20 log10β6 = 9.28 ± 0.20

12 10 8 0

2

4

6

Im / mol kg

Pt; H2 j1 M HCl; ðI  1Þ M HClO4 jjx M SnCl2 ; y M SnCl4 ; 1 M HCl; ðI  1Þ M HClO4 jHg, Pt

ðIIIÞ

Further preliminary experiments indicated that only a limited ionic strength range (x M HClO4 ? 1 M HCl, x = 3, 4, 5) is available for the potentiometric measurements, because at x [ 5 a grayish precipitate on the mercury surface resulted in unstable potentials whereas at x \ 3 the chloride content of the background electrolyte is too high, and it cannot be regarded as ‘‘perchlorate medium’’. Under such conditions, the experimental complications mentioned with cell (I) were not experienced: the electrode potentials were found to be stable within ±0.2 mV after 30–60 min (as the system is relatively ‘‘well buffered’’ against O2 traces). The reproducibility of the parallel runs was found to be reasonable (±4 mV; Fig. 5), the slope of the experimental plots was found to be close to the

8

10

12

-1

theoretical value (29.58 mV/decade), i.e. this experimental setup should provide a reliable Sn4?/Sn2? redox potential. Evaluation of the experimental data requires a knowledge of the formation constants bx of complexes SnCl2-x x and SnCl4-x defined by the reactions Sn2? ? xClx

SnCl2-x and Sn4? ? xCl- SnCl4-x at a given x x ionic strength I (Table 3). Because a mixed background electrolyte was used, the true formation constants are not available. In the case of tin(IV) we used the constants determined by us for HClO4 background to extra/interpolate to the given ionic strength. In the case of tin(II) the data set for NaClO4 background electrolyte, evaluated by the OECD/NEA TDB Phase III Chemical Thermodynamics of Tin Review Team [19], was used. Although in the case of tin(II) b1 and b2 determined for NaClO4 could be converted to HClO4, a similar conversion cannot be made for b3 (e(H?, SnCl3-) is unknown) and b4 (De and

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T. Gajda et al.

0.14

0.13

A exp. data, error bars: ± 0.005 V linear fit, fixed slope: k/2 = 0.02958 V / decade E° = (0.2797 ± 0.0123) V

E/V

0.12

0.11

0.10

298.15 K (3M HClO4 + 1M HCl)

0.09 -6.2

-6.0

-5.8

-5.6 4+

log10([Sn 0.12

0.11

-5.4 2+

]/[Sn free

-5.2

-5.0

]) free

B exp. data, error bars: ± 0.004 V linear fit, fixed slope: k/2 = 0.02958 V / decade E° = (0.2732 ± 0.0066) V

E/V

0.10

0.09

298.15 K (4M HClO4 + 1M HCl)

0.08

-6.6

-6.4

-6.2

-6.0 4+

log10([Sn 0.09

0.08

-5.8 2+

free

]/[Sn

free

-5.6

-5.4

])

C exp. data, error bars: ± 0.004 V linear fit, fixed slope: k/2 = 0.02958 V / decade E° = (0.2627 ± 0.0087) V

E/V

0.07

0.06

0.05

298.15 K (5M HClO4 + 1M HCl)

0.04 -7.2

-7.0

-6.8

-6.6 4+

log10([Sn

-6.4 2+

]/[Sn free

-6.2

-6.0

]) free

Fig. 5 The observed E values of cell (III) as a function of lg ([Sn4? free]/ -1 = 4.73 (a), 6.22 (b) and 7.88 (c) (see also [Sn2? free]) at Im/mol kg Table 3)

e(H?, SnCl42-) are unknown). In addition, because we used mixed background electrolytes it seemed more reliable to assume similar ionic strength dependence in NaClO4 and HClO4/HCl background electrolytes.

123

The experimentally observed potential values as a function of lg([Sn(IV)free]/[Sn(II)free]) are depicted in Fig. 5. Extrapolation to lg([Sn(IV)free]/[Sn(II)free]) = 0 resulted in the standard potentials E°0 (Sn4?/Sn2?) at the different ionic strengths applied, which are also listed in Table 3. Considering the uncertainties related to the formation constants of the chloro complexes and the mixed background electrolyte, the uncertainties of E°0 (Sn4?/Sn2?) have been assigned as three times the mean deviation between the measured and calculated E values of cell (III). The extrapolation of the determined standard potentials to zero ionic strength by linear regression and error propagation, assuming Gaussian probability distribution, by applying the SIT approach (Fig. 6, dotted line; Appendix B) resulted in E°(Sn4?/Sn2?) = (0.396 ± 0.011) V. However, in Im [ 3 M HClO4 solution the activity coefficients deviate strongly from those calculated by the simple SIT approach. Therefore, the use of extended SIT (Appendix B) is more appropriate in our case. There are two accepted ways of extending the validity of SIT to high ionic strengths (see (ii) and (iii) in Appendix B). From Eqs. 18 and 22 (Fig. 6, dashed and solid line) E°(Sn4?/Sn2?) = (0.382 ± 0.011) V and E°(Sn4?/Sn2?) = (0.385 ± 0.011) V can be calculated. From the slopes of the dashed and solid lines in Fig. 6, De = 0.21 and 0.16 kg mol-1 can be derived for Eq. 1, which corresponds to e(Sn4?,ClO4-) = 0.69 and 0.64 kg mol-1, respectively. Although, these values are somewhat smaller than expected for an M4? cation, they are obviously much higher than e(Sn2?,ClO4-) = 0.20 kg mol-1 [19]. The above E°(Sn4?/Sn2?) value is more positive than the so far generally accepted value of 0.15 V. The latter value was based on measurements conducted in HCl media [2], however, the formation of chloro complexes was neglected. Because tin(IV) forms much more stable chloro 2? complexes than tin(II), and therefore [Sn4? free]/[Snfree]  [Sn(IV)]TOT/[Sn(II)]TOT, the considerably more positive value determined by us is understandable. Indeed, assuming identical ionic strength dependence of tin(II) and tin(IV) chloro complexes in perchlorate and chloride media, E°(Sn4?/Sn2?) & 0.36 V can be estimated from the data published in Ref. [2], which validates the high positive value derived by us. The relatively high uncertainty of E°(Sn4?/Sn2?) originates from the uncertainties associated with both formation constants and the mixed background electrolyte applied. The extrapolation to Im = 0 poses the same problem as mentioned above for the formation constants of chloro complexes, therefore we define a standard potential E°0 (Sn4?/Sn2?, 6.41 m (5 M) HClO4) = (0.318 ± 0.011) V. For the Sn4?/Sn2? standard electrode potential we estimate a larger uncertainty, because of the long extrapolation to Im = 0 which has to be taken into account, thus E°(Sn4?/Sn2?, 298.15 K) = (0.384 ± 0.020) V. Because

The standard electrode potential of the Sn4?/Sn2? couple revisited Table 3 The formation constants used for evaluation at different ionic strength (also see text) and the calculated standard potentials Applied formation constants (molar values) for SnCl2-n n

Applied formation constants (molar values) for SnCl4-n n

E°0 (Sn4?/Sn2?) (V)

4.73 (3 M HClO4 ? 1 M HCl)

lg b1 = 1.26, lg b2 = 1.98, lg b3 = 1.97, lg b4 = 2.46,

lg b1 = 2.43, lg b2 = 4.59, lg b4 = 7.69, lg b5 = 8.91, lg b6 = 8.74,

0.2797 ± 0.0123

6.22 (4 M HClO4 ? 1 M HCl)

lg b1 = 1.47, lg b2 = 2.36, lg b3 = 2.35, lg b4 = 2.88,

lg b1 = 2.78, lg b2 = 5.18, lg b4 = 8.56, lg b5 = 9.73, lg b6 = 9.71,

0.2732 ± 0.0066

7.88 (5 M HClO4 ? 1 M HCl)

lg b1 = 1.74, lg b2 = 2.83, lg b3 = 2.84, lg b4 = 3.41,

lg b1 = 3.22, lg b2 = 5.94, lg b4 = 9.67, lg b5 = 10.79, lg b6 = 10.94,

0.2627 ± 0.0087

Conclusions Although several intelligent guesses had to support this evaluation, the first reliable data on the standard redox potential of the Sn4?/Sn2? couple have been reported. In addition, the first detailed solution equilibrium study on the tin(IV) chloro complexes has been performed. The results will contribute to basic knowledge of aqueous tin(IV) chemistry.

0.44

E°' + 5kD, Eq. (14) E°' + k(5D + ε1.5, tot Im ), Eq. (18)

of the experimental limitations, high ionic strength and mixed background electrolyte, the ion interaction coefficient can be estimated only crudely as e(Sn4?,ClO4-, 298.15 K) = (0.7 ± 0.2) kg mol-1.

0.43

SIT analysis, Eq. (14) 4+

ε (Sn ) = 0.49 kg mol

E° = (0.396 ± 0.011) V

-1

ext. SIT analysis, Eq. (18) E° = (0.382 ± 0.011) V -1 ε (Sn ) = 0.69 kg mol ext. SIT analysis, Eq. (22) E° = (0.385 ± 0.011) V 4+ -1 ε (Sn ) = 0.64 kg mol 4+

0.42 0.41 0.40 0.39 0.38

0

1

2

3

4 +

5

6

7

E°' + k (5 D + εlg, tot Im log10Im ), Eq. (22)

Im (IM) (mol kg-1)

8

-1

m (H ) ~ Im / mol kg

Fig. 6 Extrapolation of the E data of cell (III) for the reaction Sn4?(aq) ? H2(g) Sn2?(aq) ? 2H?(aq) to Im = 0 using the SIT (dotted line, calculated by Eq. 14 in Appendix B) and extended SIT (dashed line—Eq. 18 and solid line—Eq. 22)

Experimental Reagents and solutions For the experiments, the following analytical reagent grade chemicals were used: HClO4 (w & 70%, Sigma–Aldrich); HCl (w & 36%, Molar Chemicals); HNO3 (w & 62%, Reanal); SnCl45H2O (Riedel de Haen); SnCl2 (Reanal); SnO2 (Reanal); Cu(ClO4)2 and CuCl2 (Sigma–Aldrich); Sn (w & 99.999%, Sigma–Aldrich); Hg (w & 99.999%, Fluka). For solution preparation bi-distilled water was used. In order to avoid the presence of chloride in the tin(II) and tin(IV) stock solutions used for determination of the formation constants of the chloro complexes, the corresponding perchlorate solutions were prepared. Tin(II) perchlorate was obtained according to Tobias [20], using cleaned metallic tin and copper(II) perchlorate of known concentration under argon atmosphere. The redox reaction is quantitative [20] and yields Sn(II) perchlorate solution. The metallic copper formed by reduction and the remaining metallic tin was separated from the solution by filtration. The solutions were prepared just before the titrations. Iodometric determination of tin(II) concentration agreed well with the Cu(II) concentration of the starting solution.

For the preparation of tin(IV) perchlorate stock solution, the dissolution of SnO2 (both crystalline and freshly prepared from SnCl4) in 2, 5, and 8 M hot HClO4 under reflux proved to be unsuccessful, the solid did not dissolve, or the solutions obtained were unstable (i.e., SnO2 precipitated on aging of the solutions). The most useful method was oxidation of the freshly prepared Sn(II) perchlorate solution by air or ozone. Oxidation by air was rather slow, therefore ozone was bubbled through the solution which resulted in rapid quantitative oxidation to Sn(IV). The above mentioned procedure was applied using several Sn(IV) (0.5, 1, 2, 5, 10 9 10-3 M) and perchloric acid (3, 5, and 8 M) concentrations. The exact concentration of Sn(IV) was determined by ICP–AES using a standard addition technique. Only negligible traces of Cu2? were detected by ICP–AES in these solutions. As a result of this procedure, a stable (i.e., non-precipitating) stock solution was obtained only in 8 M (12.18 mol kg-1) HClO4 and at B1 mM tin(IV) concentrations. The solution of 0.002 M tin(IV) in 8 M HClO4 was stable only for *2 months. In 3 M and 5 M HClO4 even the less concentrated solution became turbid in 1– 2 days and 2–3 weeks, respectively.

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In chloride-containing media the stock solution of tin(IV) (*0.1 M) was prepared by dissolving a known amount of SnCl45H2O in the given background electrolyte (x M HClO4 ? 1 M HCl, x = 3–7), and its concentration was determined by ICP–AES. Sn(II) solutions (*0.03 M) were prepared by Tobias’ method [20] using 0.03 M CuCl2 dissolved in the given background electrolyte (x M HClO4 ? 1 M HCl, x = 3–7). The accurate Sn(II) concentration of the solution was determined iodometrically immediately after preparation. The total tin content of the solutions was determined by ICP–AES, and was practically identical with the initial CuCl2 concentrations determined by complexometry. The densities of the perchloric acid solutions were taken from the literature [21]. Those of the mixed electrolytes were determined experimentally, and were found to be close to the theoretical values (Appendix A). Potentiometric measurements For the potentiometric measurements, an electrochemical cell was designed and constructed. The cell consists of two thermostated (25 ± 0.1 °C) compartments (Vmax = 10 cm3 each), separated by a glass tube and G3 glass frit as liquid junction. For the left side, a well insulating, tightly fitted Teflon-made lid was constructed, with three inlets: one for the H2/Pt electrode, the second for bubbling H2, and the third for allowing excess H2 to leave (which provides a permanent overpressure to avoid oxygen diffusion into the system). For the right side, an Hg-pool electrode was constructed; this was connected to the outside environment via a Pt wire welded into the bottom of the glass wall of the compartment. This compartment also has a tightly fitting Teflon lid with three inlets: through one, high purity (99.996%) Ar purging gas is led to the system; the second is for admitting titrant solutions into the cell; the third is for venting. The quality of Ar was checked by bubbling the gas through an alkaline pyrogallol solution; extensive bubbling, for a couple of hours, did not cause any discolouration of the solution, which proves the O2 content of the Ar gas can be regarded as insignificant. The lack of O2 was also checked by adding Iions to our background solutions; this resulted in no visually detectable I2 formation (in strongly acidic solutions O2 readily oxidizes I- ion). This control reaction also proved that other oxidants (i.e., traces of ClO3-, Cl2) were absent from our HClO4 and HClO4–HCl background electrolytes. Platinised Pt-electrodes were prepared according to the literature [22]. The electrode consists of high-purity (99.999%) Pt wire (d = 1.5 mm) and 5 mm 9 8 mm highpurity (99.999%) Pt sheets. The platinisation was performed (after careful cleaning as described in Ref. [9]), by use of H2PtCl6 in strongly acidic HCl ([HCl]TOT = 0.2 M)

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solution. The two electrodes were connected to a highimpedance multimeter via crocodile clips. Spectrophotometric measurements The stepwise formation constants of tin(IV) chloro complexes were determined by a spectrophotometric method, following the spectral changes between 200 and 260 nm of tin(IV) perchlorate solution upon addition of H(Cl,ClO4) solution, using a Unicam Helios a spectrophotometer. The experimental conditions used for spectrophotometric titrations are listed in Table 1. The computer program PSEQUAD [23] was used to derive the stepwise formation constants and the individual spectra of the chloro complexes. Acknowledgments The authors thank Professor Wolfgang Voigt (TU Bergakademie Freiberg, Germany) for helpful discussions and Professor Erich Ko¨nigsberger (Murdoch University, Australia) for constructive comments. This work was supported by the OECD/NEA Thermodynamic Data Base, Phase III Project.

Appendix A: Density of mixed electrolyte solutions Equation 2 can be fitted to density q versus concentration c data of strong electrolytes in aqueous solutions. q ¼ q ðH2 OÞ þ ac þ bc2

ð2Þ

The density of pure water at 298.15 K was set to q°(H2O) = 0.997045 kg dm-3. A least-squares analysis of the data listed for densities of HClO4 ? H2O solutions up to 8.31 M and for densities of HCl ? H2O solutions at 298.15 K in [21] resulted in: a (HClO4) = 0.05644 kg mol-1, b (HClO4) = 0.000288 kg dm2 mol-2 (r = 0.000536, R = 0.999993) and a (HCl) = 0.01748 kg mol-1, b (HCl) = -0.000175 kg dm2 mol-2 (r = 0.000331, R = 0.999984). For HCl the data listed in Tab II-5 of the NEA, OECD volumes on Chemical Thermodynamics were also used, e.g. Ref. [16]. Density estimation Stock solutions 1 and 2 containing Ic/mol dm-3 HClO4 and HCl, respectively, were prepared. Apparent molar volume uc and density qc on amount concentration basis are related by Eq. 3, where qo is the density of pure water, c is the amount concentration, and Msolute the molar mass of the solute. 1 q  qo  uc ¼ Msolute  c ð3Þ qo c Background electrolyte solutions were obtained by mixing Y1 = c(HClO4)/[c(HClO4) ? c(HCl)] volumes of

The standard electrode potential of the Sn4?/Sn2? couple revisited Table 4 Calculated density of background electrolyte solutions assuming DmixV = 0 on an amount concentration basis, and experimental values Ic (mol dm-3)

c1 (mol dm-3)

qc,1 (kg dm-3)

qc,2 (kg dm-3)

Im,1 (mol kg-1)

Im,2 (mol kg-1)

Calc. Eq. 8a (qmix/kg dm-3)

Expt. (qmix/kg dm-3)

4.00

3.00

1.2242

1.0642

4.864

4.356

1.1842

1.1852

5.00

4.00

1.2825

1.0801

6.409

5.569

1.2420

1.2455

6.00

5.00

1.3413

1.0956

8.124

6.843

1.3003

1.2930

solution 1 with Y2 = c(HCl)/[c(HClO4) ? c(HCl)] volumes of solution 2, where the ionic strength Ic = c(HClO4) ? c(HCl). For the sake of brevity HClO4 is denoted by subscript 1 and HCl by subscript 2. The ionic strength fractions are Y1 and Y2, the apparent molar volumes are uc,1 and uc,2, the densities of the binary solutions at ionic strength Ic are qc,1 and qc,2, the mean apparent molar volume and the density of the mixed electrolyte solution at ionic strength Ic are uc,mix and qc,mix, respectively. Assuming that DmixV = 0 when aqueous solutions containing different electrolytes of the same ionic strength on an amount concentration basis are mixed, the density of the mixed background solution can be estimated. Using Eq. 3, the unit volumes of HClO4, HCl, and HClO4 ? HCl solutions are given by Eqs. 4–6. 1 ¼ Ic uc;1 þ ðqc;1  Ic M1 Þ=qo

ð4Þ

1 ¼ Ic uc;2 þ ðqc;2  Ic M2 Þ=qo

ð5Þ

1 ¼ Ic uc;mix þ qc;mix  c1 M1  c2 M2 =qo

ð6Þ

From the assumption DmixV = 0 on an amount concentration basis, Eq. 7 follows by multiplying the right-hand sides of Eqs. 4 and 5 with the ionic strength fractions and equating their sum with the right-hand side of Eq. 6. c1 uc;1 þ ðY1 qc;1  c1 M1 Þ=qo þ c2 uc;2 þ ðY2 qc;2  c2 M2 Þ=qo ¼ Ic uc;mix þ ðqc;mix  c1 M1  c2 M2 Þ=qo

ð7Þ

The terms in parentheses in Eq. 7 refer to the mass of water, which remains constant upon mixing. This results in Eqs. 8a and 8b, most simple mixing rules predicting density and mean apparent molar volume of mixed electrolytes. qc;mix ¼ Y1 qc;1 þ Y2 qc;2

ð8aÞ

uc;mix ¼ Y1 uc;1 þ Y2 uc;2

ð8bÞ

Humffray [24] pointed out that Eq. 8a is equivalent to Eq. 8b. The molality of these solutions was calculated using Eqs. 9a and 9b [25].

m1 ¼ m2 ¼

1 c1 ðq

1  c2 M 2 Þ  M 1

ð9aÞ

1 c2 ðq

1  c1 M 1 Þ  M 2

ð9bÞ

It should be emphasized that the condition DmixV = 0, when aqueous solutions containing different electrolytes of the same ionic strength on a molality basis are mixed, leads according to Eq. 10 to a different rule for prediction of the background electrolyte density. Y1 ð1 þ Im M1 Þ=qm;1 þ Y2 ð1 þ Im M2 Þ=qm;2 ¼ ð1 þ m1 M1 þ m2 M2 Þ=qm;mix

ð10Þ

The expressions in parentheses divided by densities are the unit volumes of stock and mixed electrolyte solutions, respectively. Eq. 10 has been used by Patwardhan and Kumar [26], but is not applicable here because Im,1 = Im,2. The densities calculated from Eq. 8a agree reasonably well with the experimental values (Table 4).

Appendix B: Analysis of electrochemical measurements The standard e.m.f. E° for Eq. 1 is defined as: ( "  #  4þ p H m Sn ð Þ RT ln 10 2 E ¼ E  log10  2þ  2 þ 2F m Sn m ðH Þ  ) cðSn4þ Þ þ log10 cðSn2þ Þc2 ðHþ Þ

ð11Þ

It is assumed that H2 is in its standard state, thus ln 10 ¼ 2k, and log p(H ) = 0. For the sake of brevity let RT2F  10 4þ2  cðSn Þ ¼ Ctot 2þ þ cðSn Þc2 ðH Þ " #   m Sn4þ k k  E ¼ E  log10  2þ  2 þ  log10 Ctot ð12Þ 2 2 m Sn m ðH Þ " #   m Sn4þ k k 0 E ¼ E  log10  2þ  2 þ ; 2 m Sn m ðH Þ 2 ¼ 0:02958 V at 25 C

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(i)

For an electrolyte medium consisting preponderantly of HClO4

Im & m(ClO4-) and the Debye–Hu¨ckel term pffiffiffiffiffi A Im pffiffiffiffiffi; D¼ 1 þ Baj Im at 25 °C A = 0.509 kg0.5 mol-0.5 and kg0.5 mol-0.5. log10Ctot is given according to SIT by

Baj = 1.5

 log10 cðSn4þ Þ ¼ 16D þ eðSn4þ ; ClO 4 ÞmðClO4 Þ  log10 cðSn2þ Þ ¼ 4D þ eðSn2þ ; ClO 4 ÞmðClO4 Þ

2þ  log10 Ctot ¼ 10D þ ½eðSn4þ ; ClO 4 Þ  eðSn ; ClO4 Þ þ    2eðH ; ClO4 ÞmðClO4 Þ 2þ  þ  De ¼ eðSn4þ ; ClO 4 Þ  eðSn ; ClO4 Þ  2eðH ; ClO4 Þ

Now Eq. 12 reads k E ¼ Eapp  ½10D þ De mðClO 4 Þ 2

ð13Þ

The SIT approach leads to Eqs. 14 and 15 for evaluation of E° and De. k k E0 þ 10D ¼ E þ De mðClO ð14Þ 4Þ 2 2    k mðSn4þ Þ E  log10  10D 2 mðSn2þ Þm2 ðHþ Þ k ð15Þ ¼ E þ De mðClO 4Þ 2 However, the activity coefficients derived from Eq. 2, log10c(H?) = -2D ? 2e(H?, ClO4-)m(ClO4-), at Im [ 3 m deviate strongly from those determined experimentally. There are two accepted ways to extend the validity of SIT to high ionic strengths ((ii) and (iii), below): Let us assume that the analysis of log10c(H?) versus m(ClO4-) results in:  2 log10 cðHþ Þ ¼ 2D þ 2e1 ðHþ ; ClO 4 ÞmðClO4 Þ þ  1:5  ð16Þ þ 2e1:5 ðH ; ClO4 Þm ðClO4 Þ (ii)

see second ionic strength expansion in unnumbered equation [13]. For the sake of brevity e1(H?, ClO4-) = e1 and e1.5(H?, ClO4-) = e1.5. If De = e(Sn4?, ClO4-) - e(Sn2?, ClO4-) - 2e1, log10Ctot has to be modified. 1:5  log10 Ctot ¼ 10D þ DemðClO 4 Þ  2e1:5 m ðClO4 Þ

ð17Þ

The modified SIT approach leads to Eqs. 18 and 19 for evaluation of E° and De.

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The values of e1 = 0.0865 (0.10559) kg mol-1 and e1.5 = 0.0290 (0.00932) kg1.5 mol-1.5 were obtained from lg c± data at 0.1 B m(HClO4)/mol kg-1 B 8.0 [27] and 0.001 B m(HCl)/mol kg-1 B 8.0 [28], the e values of HCl are in parentheses. (iii)

 2 log10 cðH þ Þ ¼ 2D þ 2eðHþ ; ClO 4 ÞmðClO4 Þ



    k

k ¼E þ Dem ClO ð18Þ E0 þ 10Dþ2e1:5 m1:5 ClO 4 4 2 2    k mðSn4þ Þ 1:5  E  log10 m ðClO Þ  10D  2e 1:5 4 2 mðSn2þ Þm2 ðHþ Þ k ¼ E þ DemðClO ð19Þ 4Þ 2

Let us assume that analysis of log10c(H?) versus m(ClO-4) results in:

 2 log10 cðH þ Þ ¼ 2D þ 2e1 ðHþ ; ClO 4 ÞmðClO4 Þ þ   þ 2elg ðH ; ClO4 ÞmðClO4 Þ log10 ½mðClO 4 Þ

ð20Þ see App. B Ionic strength corrections Table B-6, e.g. Ref. [30]. For the sake of brevity e1(H?, ClO4-) = e1 and elg(H?, ClO4-) = elg. If De = e(Sn4?, ClO4-) - e(Sn2?, ClO4-) - 2e1, log10Ctot has to be modified. log10 Ctot ¼ 10D þ De mðClO 4Þ   2elg mðClO Þ log 10 ½mðClO4 Þ 4

ð21Þ

The modified SIT approach leads to Eqs. 22 and 23 for evaluation of E° and De. k  E0 þ f10D þ 2elg mðClO 4 Þ log10 ½mðClO4 Þg 2 k ¼ E þ De mðClO 4Þ 2 (   k mðSn4þ Þ E log10  10D 2 mðSn2þ Þm2 ðHþ Þ

ð22Þ

k    2elg mðClO 4 Þ log10 ½mðClO4 Þg ¼ E þ De mðClO4 Þ 2 ð23Þ The values of e1 = 0.1079 (0.1121) kg mol-1 and elg = 0.06506 (0.02126) kg mol-1 were obtained from lg c± data at 0.1 B m(HClO4)/mol kg-1 B 8.0 [27] and 0.001 B m(HCl)/mol kg-1 B 8.0 [28], the e values for HCl are in parentheses. As pointed out at the beginning, the measurements were carried out using a mixture of HCl and HClO4 as background electrolyte. Patwardhan and Kumar [29] showed that the reduced overall activity coefficient of a mixed electrolyte solution C* is related to the reduced activity coefficients Ci,r of the single electrolyte solutions, zi is the charge on single ionic species.

The standard electrode potential of the Sn4?/Sn2? couple revisited

log10 Cr ¼ log10 c =ðjzþ z jÞ For 1:1 electrolytes Cr ¼ c and fraction, thus: X mi log Ci;r log10 Cr ¼ I i

mi I

is the ionic strength ð24Þ

where the individual ionic activity coefficients C = c± have to be taken at mi = I. With Eq. 24 the modified formulas used for extrapolation read as Eqs. 18 and 22, but e1.5 and elg were 4Þ replaced bye1:5;tot ¼ mðHClO e1:5 ðHClO4 Þ þ mðHClÞ I I e1:5 ðHClÞ 4Þ and elg;tot ¼ mðHClO elg ðHClO4 Þ þ mðHClÞ I I elg ðHClÞ; respectively, and m(HClO4) was replaced by Im. Results allowing for replacement of HClO4 by HCl are, within experimental uncertainty, indistinguishable from those obtained by use of unmodified Eqs. 18 and 22. The extended SIT analysis, no matter which type is used, results in more realistic values for the ion interaction coefficient e(Sn4?,ClO4-, 298.15 K). It was decided to calculate the standard electrode potential E°(Sn4?/Sn2?) by use of modified Eqs. 18 and 22. Thus the ionic medium is taken into account and these types of extended SIT analyses have been recommended by NEA OECD publications on modelling in aquatic chemistry [13] and chemical thermodynamics, e.g. Ref. [30].

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