Determination of single-ion activity coefficients of hydrogen and bromide ions in aqueous hydrobromic acid solutions based on an ionic liquid salt bridge

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Determination of single-ion activity coefficients of hydrogen and bromide ions in aqueous hydrobromic acid solutions based on an ionic liquid salt bridge Kazuya Minami, Takashi Kakiuchi ∗ Department of Energy and Hydrocarbon Chemistry, Graduate School of Engineering, Kyoto University, Kyoto 615-8510, Japan

a r t i c l e

i n f o

Article history: Received 3 March 2013 Received in revised form 15 April 2013 Accepted 17 April 2013 Available online xxx Keywords: Single ion activity Hydrogen ion Bromide ion Hydrobromic acid Ionic liquid salt bridge pH Liquid junction potential SiS model

a b s t r a c t Single ion activity coefficients of H+ and Br− in aqueous hydrobromic acid solutions, H+ and Br− , have been estimated potentiometrically at 25 ◦ C with a hydrogen electrode and a silver–silver bromide electrode, respectively, based on the assumption that the change in the liquid junction potential at the interface between a sample solution and an ionic liquid salt bridge is negligibly small. The mean activity coefficients of HBr calculated from experimentally obtained values of H+ and Br− well agree with the literature values over the entire concentration ranges studied, 1.04 × 10−3 to 0.528 mol kg−1 . Overall dependencies of H+ and Br− on ionic strength are similar to those found previously in aqueous HCl solutions, but the degree of the dependence is distinctively stronger in both H+ and Br− . Plots of H+ and Br− as a function of the ionic strength are nearly congruent with the predictions by Fraenkel’s smaller-ion shell (SiS) model up to 0.05 mol kg−1 . However, with a further increase in HBr concentration experimental H+ and Br− more rapidly increases and decreases, respectively, in comparison with the SiS predictions. © 2013 Published by Elsevier Ltd.

1. Introduction The single ion activity coefficients of H+ and Cl− in aqueous hydrochloric acid solutions have recently been determined with reasonable accuracy [1] by use of an ionic liquid salt bridge, ILSB [2], inserted in a Harned cell. The dependences of experimental activity coefficients on the square root of ionic strength were considerably different from experimental values previously reported based on different extrathermodynamic assumptions [3,4], but agreed well up to 0.2 mol kg−1 with theoretical predictions by Fraenkel’s smaller-ion shell (SiS) model [5], which is a fundamental gener¨ alization of the Debye–Huckel theory [6] taking into account the difference in the size of cationic and anionic species in calculating their activity coefficients. At higher ionic strengths, however, the plots for the logarithm of the activity coefficients of H+ and Cl− gradually deviated upward and downward, respectively, from the SiS curves [1]; experimentally, H+ is less stabilized, but Cl− is more stabilized at higher concentrations of HCl than expected by the SiS model. Interestingly, Fraenkel very recently reported that literature values of experimental single ion activity coefficients for aqueous solutions of NaCl, LiCl, MgCl2 , CaCl2 , and K2 SO4 , which were

estimated by use of extrathermodynamic assumptions different from ours [7,8], agree with his theoretical predictions in the higher concentration range up to 1 mol kg−1 [9]. It may seem that the SiS model better describes the single ion activities in neutral solutions than acidic HCl solutions. To evaluate the concentration range to which the SiS model is applicable, it is preferable to have reliable values of single ion activities in a variety of electrolyte solutions by use of an ILSB [10], whose reliablity and traceability have been proven in determinig single ion activities in pH measurements of dilute sulfuric acid solutions [11]. This paper describes experimental evaluation of the single ion activity coefficients of H+ (H+ ) and Br− (Br− ) in aqueous hydrobromic acid solutions by use of ILSB that consists of tributylmethoxyethylphosphonium bis(pentafluoroethanesulfonyl)amide ([TBMOEP+ ][C2 C2 N− ]), as employed previously [1,12]. The deviations of experimental data from the SiS predictions are similar to those seen in HCl solutions, but more pronounced in both H+ and Br− at the HBr concentrations higher than 0.05 mol kg−1 . 2. Experimental 2.1. Materials

∗ Corresponding author. Present address: pH Science and Technology Laboratory, Mizuo 3-16-303, Ibarakishi, Osaka 567-0891, Japan. Tel.: +81 734517129. E-mail address: [email protected] (T. Kakiuchi).

Methods of synthesis and purification of [TBMOEP+ ][C2 C2 N− ] have been described elsewhere [12]. Other chemicals used were of reagent grade. Water was purified with a Milli-Q system (Millipore

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Co.). Aqueous 47 % HBr solutions were obtained from Kishida Chem Co., Japan, and Kanto Chem., Japan. The concentration of HBr solutions was determined by precipitation titration with a standardized AgNO3 solution using an automatic titrator (COM01600, Hiranuma, Japan). The concentration scale was converted from molarity to molality using the density data of aqueous HBr solutions [13]. 2.2. Methods Potentiometric measurements were made using the following cell, The cell for determination of H+ was

I

II

III

10 4 mmol dm Ag AgBr

IV 3

HBr

3. Results and discussion 3.1. Activity coefficients of H+ , Br− , HBr The difference between two E values obtained with cell (1) at two different concentrations of HBr in phase V, E, is related to the ratio of the activities of H+ in phase V, aH+ ,2 /aH+ ,1 , at the two different concentrations through [10] E − (ILSB ) =

V

x mmol dm [TBMOEP ][C2 C2 N ]

aH+ ,2 RT , ln F aH+ ,1

(3)

VI 3

HBr, H2 (g)

Pt (1)

where x = 0.104, 0.520, 1.04, 5.20, 10.4, 52.0, 104, 208, 312, 416, or 520. The glass cell was of the same design as that we used previously [1]. For determination of Br− , the following cell was employed.

I

II

III

10 4 mmol dm Ag

AgBr

HBr

IV 3

V

x mmol dm [TBMOEP ][C2 C2 N ]

HBr

VI 3

AgBr (2)

where x spans the concentration range as in cell (1). The cell was a U-shaped glass cell similar to, but smaller than the one reported elsewhere[11]. Platinum electrodes for cell (1) were prepared after the procedures described by Bates [14]; a platinum electrode having the geometric area of 1 cm2 on one side was first immersed in 6 mol dm−3 HNO3 for more than 1 h, rinsed with Milli-Q water, platinized in a 3.5 % hexachloroplatinic acid solution containing 0.005 % lead acetate for 1 h at 5 mA, soaked in 1 mol dm−3 HClO4 for more than 1 day, and then stored in Milli-Q water. Hydrogen gas of the purity higher than 99.999 % supplied from a hydrogen gas generator (H2PEM-100, Parker) was presaturated with a solution of the same composition as that in phase V in cell (1). Ag|AgBr electrodes used for cell (1) were prepared by anodizing silver electrodes, following the method for preparation of Ag|AgCl electrodes.[14] For cell (2), Ag|AgBr electrodes were prepared from a silver wire of 0.5 mm diameter. The potential of the right-hand-side terminal of cell (1) or cell (2) with respect to that of the left (E) was measured with an electrometer (8240 or 8252, ADC, Japan), which was calibrated with a voltage standard (6161, ADC). Data were acquired through GPIB by a desk-top computer. During potentiometric measurements, the cells were kept in a light-shielded water bath. The temperature of the bath was maintained at 25.00 ±0.02 ◦ C. The values of E were judged to be stabilized when the variation of E in 1 h was within 0.1 mV and employed for calculation of the activity coefficients. Usually, it took 10 h before stabilization of E of cell (1). In cell (2), E became stable in 10–20 min in most of the cases. Typical time courses are given in Fig. S1 as supplementary materials (S.M.).

where (ILSB ) is the difference in the liquid junction potentials between a sample solution and the ILSB, ILSB = W − ILSB , where i being the inner potential of phase i (i = ILSB or W)), at two different solution compositions designated by the subscripts 1 and 2 on the activities on the right-hand side of Eq (3). In cell (1), the pooled standard deviation of measured E values in the entire concentration range was 0.47 mV. When x = 10.4, that is, the solution compositions on both sides of the ILSB were the same, E was −0.3125 V with 95 % confidence interval being ± 0.0012 V. This value is in fairly good agreement with −0.3118 V obtained by interpolation from E values of the cell Ag|AgBr| aq. HBr, H2 (g) | Pt reported by Towns et al [15]. The agreement suggests that the sum of the two liquid junction potentials on both sides of the ILSB in cell (1) was less than a few tenth mV. Assuming that ILSB was negligibly small and the activity coefficient of H+ , H+ , at a low con¨ centration was given by the Debye–Huckel limiting law (HDLL), we calculated the values of aH+ , and hence, H+ , at other HBr concentrations. Because E value at the lowest concentration of HBr, x = 0.104 mmol dm−3 obtained for sextuple measurements, 432.9 (± 2.3 for 95 % confidence interval) mV, was less reproducible than E at other x values (Table S1 in S.M.), we took the E value at x = 0.520 mmol dm−3 , 388.6 (± 0.9) mV, for the reference of H+ , at ¨ limiting law which H+ was assumed to be given by Debye–Huckel to be 0.969, and calculated H+ values at higher concentrations of HBr. In the calculation of ionic strength in phase V, the contribution of the solubility of [TBMOEP+ ][C2C2N− ], 0.2 mmol dm−3 [12], was taken into account.

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and numerical values of Br− are listed in Table 2. More detailed data including E values are given in Table S2 in S.M. √ Overall shapes of the plots of H+ and Br− versus Im are similar to those obtained for aqueous HCl solutions [1] and also to the predictions by the SiS model [16], but, quantitatively, the difference is significant and deserves further examination (vide infra). 3.2. Mean activity coefficients of HBr solutions

Fig. 1. Single ion activity coefficients of H+ (filled squares) and Br− (filled triangles) and mean activity coefficient of HBr (double circles) at 25 ◦ C as a function of square root of ionic strength in molality scale. Error bars indicate 95 % confidence intervals. Solid line represents thermodynamically reliable mean activity coefficient of HBr compiled by Hamer and Wu.

The logH+ values obtained are plotted in Fig. 1 as filled squares as a function of the square root of the ionic strength of HBr solu√ tions in the molality scale, Im . The error bar at each symbol in Fig. 1 indicates 95 % confidence interval estimated from at least quadruple measurements at each point. Numerical values of the averaged H+ and 95 % confidence intervals of H+ are listed in Table 1. More detailed data including E values are given in Table S1 in S.M. Fig. 1 shows that logH+ initially decreases with increasing Im , becomes minimum, where logH+  −0.06 (H+  −0.88) at Im  √ 0.5 ( Im  0.22), and then increases with Im , crossing zero line and reaching 0.1 (H+ = 1.26) at Im = 0.52. Experimental values of Br− were determined similarly with cell (2) in the concentration range, 0.52 mmol dm−3 to 0.520 mol dm−3 , by use of E − (ILSB ) = −

aBr− ,2 RT . ln F aBr− ,1

(4)

In cell (2), the reproducibility and stability of E were both much better than those in cell (1) (Table 2 and Fig. S2 in S.M.); the pooled standard deviation of E was 0.16 mV. The reference solution for calculation of Br− was, hence, chosen to be of 0.104 mmol dm−3 . Experimental logBr− values are indicated as filled triangles in Fig. 1,

Table 1 Single ion activity coefficients of H+ and Br− and mean activity coefficients of HBr in aqueous hydrobromic acid solutions at 25.0 ◦ C determined with Cells (1) and (2) c mmol dm−3

m mmol kg−1

H+

Br−

± HBr

0.104 0.520 1.04 5.20 10.4 52.4 104 208 312 416 520

0.104 0.522 1.04 5.22 10.4 52.2 105 210 315 422 528

– 0.969a 0.957±0.105 0.944±0.071 0.931±0.100 0.886±0.067 0.906±0.089 0.979±0.117 1.054±0.094 1.139±0.136 1.261±0.059

0.980a 0.967±0.088 0.962±0.088 0.923±0.088 0.896±0.088 0.801±0.086 0.714±0.088 0.644±0.087 0.589±0.090 0.544±0.092 0.518±0.109

– – 0.959±0.097 0.933±0.080 0.913±0.094 0.842±0.077 0.804±0.088 0.794±0.103 0.788±0.092 0.787±0.116 0.808±0.087

Numbers after ± indicate 95 % confidence intervals. a Calculated from Debye–Hückel limiting law, taking account of the solubility of [TBMOEP+ ][C2 C2 N− ] in phase V.

± The mean activity coefficients of an aqueous HBr solution, HBr , calculated from experimental values of H+ and Br− are plotted in Fig. 1 as double circles, together with the solid line representing the ± data compiled by Hamer and Wu [17]. The numerical values of HBr are listed in the fifth column in Table 1. The agreement between ± the experimental values of HBr and thermodynamically reliable mean activity coefficients over the entire concentration range studies suggests consistency of H+ and Br− values obtained by the present method based on the ILSB. We note that, although H+ and Br− were determined independently with two different types of the cell, both were obtained based on the same extrathermodynamic assumption, that is, the negligible liquid junction potentials between the ILSB and acidic solutions up to the ionic strength of about 0.5 mol kg−1 . This point is further discussed below in *****Section 3.4

3.3. Comparison with Fraenkel’s SiS model Given marvelous success of SiS model in explaining and reasoning physicochemical behavior of electrolyte solutions [5,9,16,18] and a good agreement of SiS predictions with our previous data on HCl solutions, it is imperative to compare the results in Fig. 1 with the SiS model predictions for aqueous HBr solutions. Fig. 2a compares the experimental data H+ with the theoretical SiS curve (curve 1), which was calculated from the SiS equation with Fraenkel’s ion size parameters for HBr [16]. Fig. 2a shows that experimental H+ values go along with theoretical curve within the confidence interval up to the ionic strength of about 0.05 mol kg−1 . However, the experimental points at higher ionic strengths increasingly go off upward beyond the confidence intervals. At the highest concentration studied, the point lies above the theoretical curve by 0.11 in the unit of the logarithm of H+ . This difference corresponds to 6.5 mV in the unit of the potential, which is significantly greater than the confidence intervals of experimental points. Also shown in Fig. 2a are the SiS curve for H+ in aqueous HCl solutions (curve 3) [16] and corresponding experimental data (open squares) previously obtained [1] based on the same ILSB and the same extrathermodynamic assumption, that is, (ILSB ) being negligibly small over the entire concentration range of HCl. Regarding the experimental data, the plot of logH+ in HBr lies above that of logH+ in HCl. In the case of aqueous HCl solutions, the discrepancy between the experimental points and the SiS curve √ becomes visible only when Im is greater than 0.5. Such an elevation of H+ with increasing size of the anion is interpreted by the SiS model in terms of the thicker smaller inner shell around H+ in HBr than that in HCl [16]; the central H+ ion surrounded by the larger number of ions with the same sign has larger escaping tendency. It is clearly seen in Fig. 2a that the ILSB-based experimental data are located above the SiS curves in both HCl and HBr solutions, and the gap between the ILSB-based experimental data and the SiS model predictions is considerably greater in HBr than that in HCl. Similarly, experimental logBr− values (filled triangles) are compared with the SiS curve (curve 1) in Fig. 2b. In contrast to the √ case of H+ , logBr− monotonously decreased with Im . The agree−1 ment is good up to 0.05 mol kg , as is the case of logH+ , but at

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Table 2  based on equilibrium partitioning model calculated using standard ion transfer potentials in nitrobenzene–water two-phase systems at Effect of Br− partitioning on W ILSB 25 ◦ C 0,W cHBr mol dm−3

W  ILSB mV

c ILSB H+ mol dm−3 × 106

c ILSB Br− mol dm−3 × 106

c W+ H mol dm−3 × 104

c W− A mol dm−3 × 104

0 2 × 10−2 5 × 10−2 1 × 10−1 2 × 10−1 5 × 10−1 1

−18.50 −18.47 −18.42 −18.34 −18.18 −17.71 −16.97

0 0.0196 0.0491 0.0985 0.1983 0.5049 1.039

0 0.5559 1.387 2.766 5.497 13.59 26.22

2.106 2.104 2.100 2.093 2.080 2.042 1.984

2.106 2.109 2.113 2.120 2.133 2.172 2.236

0.1 mol kg−1 , the experimental point deviates to the lower side from the SiS curve (curve 1), with the magnitude exceeding the confidence interval. The gap between experimental points and curve 1 becomes wider at higher concentrations; Br− is increasingly more stabilized with an increase in HBr concentration than is predicted by the SiS model. As is the case of H+ data in Fig. 2a, experimental points start to deviate from the SiS curve at about ten time smaller ionic strength compared with the case of HCl (shown as curve 3 and open triangles).

The SiS model predicts at a given ionic strength a slight increase in Br− than that in Cl− as shown in curves 1 and 3 in Fig. 2b. In contrast, experimental points of Br− at higher ionic strengths are all positioned below the corresponding points of Cl− . This inversion of the trend in X− , where X− is a halogenide ion, in the anion size dependency is noteworthy. 3.4. Liquid junction potential at ILSB-sample solution interface As in other extrathermodynamic assumptions for evaluating single ion activities, there is no thermodynamically endorsable way of validating the assumption employed in the present study, i.e., W   0. However, the long history of discussion on pH deterILSB mination [19–22] tells us that the nonthermodynamic nature of single ion activities does not mean that single ion activity is a mathematical device [23] or the emperor’s new cloths [24]; they can indeed be estimated with reasonable accuracy in ideal or well-designed experimental conditions, however difficult in other conditions [25–27]. There are several conceivable factors that can lead us to overestimate H+ and underestimate Br− (Fig. 2a and b).  and single ion activity coefficients 3.4.1. W ILSB As long as the partitioning of ILSB-constituent ions, TBMOEP+ and C2 C2 N− , dictates W , the value of W  stays constant. ILSB ILSB However, the partitioning of other ions in the sample solution side becomes appreciable, W  drifts away from the constant value. ILSB According to a partition equilibrium model of the phase-boundary potential at the IL|water interface [28] and the mixed potential the ory at the liquid|liquid interface [29], the positive shift in W ILSB with increasing HBr concentration can be caused by partitioning of Br− into ILSB. When W  = W - ILSB shifts to the positive direction by ILSB (W ), the potential of the right-hand-side terminal in cell (1), ILSB ER , shifts to the positive direction by the same amount. Because ER referred to the potential in phase V is related to the activity of H+ through ER =

RT ln aH+ + const., F

(5)

a positive shift in ER in turn results in an overestimation of the H+ activity by (logH+ ) =

F (W ILSB ). ln(10)RT

(6)

In cell (2), ER is given by ER = − Fig. 2. (a) Comparison of experimental single ion activities of H+ in HBr (filled squares) with calculated curve based on SiS model for HBr (curve 1) and comparison of single ion activities of H+ in HCl (open squares) with calculated curve (curve 3) ¨ limiting is shown as dashed line based on SiS model for HCl. Slope of Debye–Huckel 2. (b) Comparison of experimental single ion activities of Br− in HBr (filled triangles) with calculated curve based on SiS model for HBr (curve 1) and comparison of single ion activities of Cl− in HCl (open triangles) with calculated curve based on SiS model ¨ limiting is shown as dashed line 2. for HCl (curve 3). Slope of Debye–Huckel

RT ln aBr− + const., F

(7)

and, hence, the same positive drift in W  with increasing HBr ILSB concentration results in overestimation of a decrease in Br− by the same magnitude as is the case of H+ , (logBr− ) = −

F (W ILSB ) ln(10)RT

(8)

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Fig. 4. Difference between measured E values and corresponding values of SiS predictions cell (1) (filled circles) and cell (2) (open circles).

Fig. 3. Difference between measured E values and corresponding values of Nernst slopes in cell (1) (a) and cell (2) (b).

Thus, the positive drift of W  can cause both an increase in ILSB logH+ and a decrease in logBr− by the same magnitude in the method based on cells (1) and (2), and can give rise to the deviations of experimental H+ and Br− values from the corresponding true values, to the directions shown in Fig. 2a and b for logH+ and logBr− values from the SiS curves. To examine the magnitude of a possible contribution of the drift  to the activity coefficients, the magnitude as well as the of W ILSB sign of (W ) in the presence of HBr in W need to be evaluated. ILSB Before doing this estimation, it is meaningful to examine experimental values of E for cells (1) and (2). Fig. 3a and b shows the deviation of E values from the Nernst slope for cells (1) and (2) as a function of logmHBr , respectively. In Fig. 3a and b, ENernst stands for E at a given value of mHBr when the activity coefficient of the ion is unity. The deviation directly translates to a change in logH+ (Fig. 3a) and logBr− (Fig. 3b). E − ENernst first decreases with mHBr = Im and then increases to become positive in Fig. 3a, as has been

seen in Fig. 1. On the contrary, in Fig. 3b, E - ENernst increases monotonically with logmHBr . If the partitioning of Br− causes the drift in W , we would see monotonous deviation from the Nernst slope ILSB in both Fig. 3a and b. We would then be able to say that the drift in W  is at least not big enough to invert the decrease in H+ to be ILSB less than unity, and hence W  is probably small, if any. ILSB When mHBr is higher than 0.05 mol kg−1 , both plots in Fig. 3a and b become positive. Even in such higher concentrations of HBr, where the partitioning of Br− can be more significant, the magnitude of the deviation is much greater in cell (2) than that in cell (1). This fact suggests that the deviation of E − ENernst from zero in the higher concentration range reflects rather intrinsic changes in logH+ and logBr− , or at least is not inundated by the drift of W . ILSB Another way of examining a possible Br− partitioning would be to check the magnitudes of the difference between experimental values of logH+ and logBr− from the SiS predictions, as shown in Fig. 4. No significant deviations of experimental points from the SiS predictions are seen up to ca 0.05 mol kg−1 , but at higher concentrations the deviations sharply grow to the opposite directions. The magnitudes of the deviations is greater in E in cell (2) and the difference between the magnitudes is beyond the confidence intervals of the E values. Obviously, this inequality in the deviations cannot be explained by the partitioning of Br− and the resultant positive shift in W . ILSB Although no data are available for the transfer Gibbs energies of relevant ions between [TBMOEP+ ][C2 C2 N− ] and water, a semiquantitative measure of the magnitude of Br− partitioning in ILSB is available by use of transfer Gibbs energies of ions between water and nitrobenzene (NB) [28,30,31], thanks to the fact that moderately hydrophobic ionic liquids are likened to polar aprotic solvents [32]. We consider the partition equilibrium between an ILSB and an aqueous solution of HBr. The values of W  ILSB were calculated for given values of standard ion transfer potentials of ions, W 0 , the volume ratio of the two phases, and NB i the initial concentration of HBr in W. The activity coefficients of all ionic species were assumed to be unity. Literature values of W 0 for TBMOEP+ , C2 C2 N− , H+ , and Br− employed for the calNB i culation were −0.236 [33], 0.199 [34], 0.377 [35], and −0.288 [35] V, respectively. These values of W 0 for TBMOEP+ , and C2 C2 N− NB i employed in the calculation give −0.0185 mV for W  in the ILSB absence of Br− partitioning, and 0.2 mmol dm−3 for the theoretical

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solubility of [TBMOEP+ ][C2 C2 N− ], the latter of which coincides with the experimental value [12]. W  calculated at several different initial concentrations of ILSB

did not show evidence of such electrochemical processes (data not shown) and, second, the deviation of E from the Nernst slope are seen in Fig. 3a and b for both cells (1) and (2).

0,W cHBr = 0.5 mol dm−3 , which is the highest concentration studied with cells (1) and (2) above, W 0 shifts by 0.8 mV to the positive NB i direction, which is caused by the partitioning of Br− in ILSB, whose concentration is 13 ␮mol dm−3 . The electrical neutrality in W is mainly maintained by the change in the dissolved C2 C2 N− in W. 0,W Even at cHBr = 1 mol dm−3 , the shift in W 0 is only 1.5 mV. This NB i W model calculation of ILSB  suggests that the contribution of Br− partitioning to the results in Figs. 3 and 4 is nominal, and would not be the main source of the large deviations of H+ and Br− values from the SiS predictions in Fig. 2.

4. Conclusions

0,W , assuming the unity volume ratio are listed in Table 2. At HBr, cHBr

3.4.2. Other factors that can influence H+ and Br− values estimated with cells (1) and (2) In the above calculation of W , the activity coefficients of all ILSB ionic species have been neglected. Because W  ****is given by ILSB [28] W ILSB 

=

where C+

+ + W — − W — IL IL C

A

2 and A−

Acknowledgements

 W−  IL+ RT + ln AW CIL 2F  +  − C

(9)

A

N− , respectively, any

stand for TBMOEP+

and C2 C2 specific interaction of H+ and Br− with TBMOEP+ and C2 C2 N− can alter the value of W  through the second term on the right hand ILSB side of Eq. (9). Table 2 shows that the amounts of H+ and Br− dissolved in ILSB probably remains to be only small fractions, and, hence, the main concern would be the change in  W− / W+ with HBr C A concentration. For example, if the difference in 5 mV in Figs. 3 or 4 is attributed to the activity ratio in Eq. (9),  W− / W+ need to be 1.5. It C A is unlikely that any specific interactions, e.g., coordination and ion pairing between TBMOEP+ and Br− or H+ and C2 C2 N− , as well as protonation of the latter pair, are significant in W to the extent that is enough to bring such disparity between  W− and  W+ in the conA

Single ion activity coefficients of H+ and Br− in aqueous hydrobromic acid solutions at 25 ◦ C have been estimated based on the assumption that the liquid junction potential across the interface between ionic liquid and the aqueous HBr solution stays constant over the change in the HBr concentration. Dependencies of the activity coefficients on the ionic strength are similar to, and quantitatively in agreement up to 0.05 mol kg−1 with, the predictions by Fraenkel’s SiS model. However, the discrepancy between the experimental data and the SiS predictions at higher ionic strengths appears to surpass the uncertainty implied in the extrathermodynamic assumption employed in the present study. This discrepancy that starts at ten times less ionic strengths than in HCl solutions suggests that the applicability of the SiS model depends on the type and concentration of electrolytes.

This work was partly supported by Grant-in-Aid for Scientific Research (No. 21245021) from the Ministry of Education, Sports, Science, and Technology, Japan. Support by the Global COE Program, International Center for Integrated Research and Advanced Education in Materials Science (No. B-09) from the Ministry of Education, Culture, Sports, Science and Technology of Japan is highly appreciated. Appendix A. Supplementary Data Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/j.electacta. 2013.04.104.

C

centration below 1 mol dm−3 [16]. At higher concentrations of HBr, short-range interactions may alter the activities of TBMOEP+ and C2 C2 N− differently, as salting-out effects of the polarized potential window at the liquid|liquid interface suggest [36]. Another possible concern is the deviation of the response of the hydrogen electrode and Ag|AgBr electrode from the Nernstian manner, that is, the response represented by Eqs. (5) and (7); they may not respond to the single ion activity in highly concentrated solutions, e.g., 0.5 mol dm−3 HBr, or in very dilute HBr solutions, e.g., 0.1 mmol dm−3 HBr. The performance of cells without liquid junction and with hydrogen and Ag|AgBr electrodes has been examined with dilute HBr solutions by Keston, who found a Nernstian response in sub-millimolar HBr solutions [37]. Several groups studied cell voltage of cells without liquid junction and with hydrogen and Ag|AgBr electrodes at high concentrations of HBr in the range of one molal or higher [15,38–40]. No sign of deterioration in response of hydrogen and Ag|AgBr electrodes has been reported in HBr solutions below 1 mol kg−1 , though Biermann and Yamsakai noticed that the rate of establishment of equilibrium became very slow at high concentrations, and above three molal equilibrium was not reached after three days [39]. Although subnernstian and supernernstian responses are common to most of ion-selective electrodes [41], it does not seem that hydrogen electrodes and Ag|AgBr electrodes do not show nernstian response at least in the concentration range of HBr studied above. Possibilities that certain electrochemical reactions of TBMOEP+ and C2 C2 N− at the hydrogen electrode or Ag|AgBr electrode can change their equilibrium potentials are ruled out on the grounds that, first, voltammetry with a Pt electrode in [TBMOEP+ ][C2 C2 N− ]

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Please cite this article in press as: K. Minami, T. Kakiuchi, Determination of single-ion activity coefficients of hydrogen and bromide ions in aqueous hydrobromic acid solutions based on an ionic liquid salt bridge, Electrochim. Acta (2013), http://dx.doi.org/10.1016/j.electacta.2013.04.104