Validation of pH Standards and Estimation of the Activity Coefficients

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Validation of pH Standards and Estimation of the Activity Coefficients of Hydrogen and Chloride Ions in an Ionic Liquid, Ethylammonium Nitrate Ryo Kanzaki, Hikaru Daiba, Hitoshi Kodamatani, and Takashi Tomiyasu J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.8b08870 • Publication Date (Web): 23 Oct 2018 Downloaded from http://pubs.acs.org on October 30, 2018

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The Journal of Physical Chemistry

Validation of pH Standards and Estimation of the Activity Coefficients of Hydrogen and Chloride Ions in an Ionic Liquid, Ethylammonium Nitrate Ryo Kanzaki,* Hikaru Daiba, Hitoshi Kodamatani, Takashi Tomiyasu Department of Earth and Environmental Sciences, Graduate School of Science and Engineering, Kagoshima University, Korimoto, Kagoshima, 890-0065, Japan

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ABSTRACT

We selected and validated the pH values of three standard materials that function in the protic ionic liquid, ethylammonium nitrate (EAN). The pH values of 0.05 mol kg‒1 phthalate, oxalate acid, and phosphate buffers were 4.93 (0.04), 2.12 (0.04), and 7.13 (0.06), respectively (the values in the parentheses denote the standard deviation). Since the pH of EAN ranges from 0 to 10, with a neutral pH of 5, these materials are usable as acidic, basic, or neutral standards. The standard electrode potential of silver-silver chloride in EAN was 127.2 (1.7) mV. The activity coefficients of hydrogen and chloride ions remain equal to unity in EAN of wide concentration range, which indicates that the effective ionic strength is independent of the solute ion concentration. In addition, the estimated value of the transfer activity coefficient of chloride ion suggests a weaker solvation in EAN compared with water in spite of a ubiquitous cation (C2H5NH3+). These behaviors of ions in EAN can be explained by the unique solvation in the ionic liquid through direct ion-ion electrostatic interactions.


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Introduction Ionic liquids are electrolytes that have melting temperature below 100 C or around ambient temperature, and provide a special reaction field that is solely filled with ions. Its subclass of onium salt, namely protic ionic liquid (PIL),1-5 is primarily characterized by the cation’s dissociable hydrogen, which makes PILs highly applicable to acid catalyzing reactions,69

fuel cells,10,11 and so on. Since it is linked to the acid-base properties of PILs, a number of

studies concerned with the hydrogen behavior have been performed. In particular, a parameter pKa, based on the difference in the pKa values between the constituent anion and cation in water, exhibits empirically a possible relationship with the ionic character of PIL.1,12-16 However, ions in neat PIL experience serious perturbations in their acidity and basicity. In addition, the pKa values of the conjugate acids of the anions are often unreliable because they tend to behave as strong acids in water. Therefore, a current ongoing debate discusses the actual definition of pKa and what exactly it expresses.17 On the other hand, PILs made from a very weak acid were found to have a surprising ionic property, where hydrogen ions are expected to rarely dissociate according to their pKa values.18-23 From this point of view, the direct observation based on solvatochromism,24-31 NMR,32,33 titrimetric pKa determination,34-41 and so on, of the actual hydrogen ion activity is a significant target of current research. Recently, scaling of pH in ionic liquids using a commonly applicable pH scale is addressed.42-49 Analogous investigations were performed previously for a number of conventional non-aqueous solvents,50-56 however, these types of studies on ionic liquids are few and provide inadequate information. According to IUPAC, pH is a notational definition on the basis of the activity of hydrogen ion (aH), and only the practical procedure to determine pH is provided by


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potentiometric measurements. That is, the pH value of the sample solution is determined from the potential gap of the pH indicator electrode, often using a glass electrode, from in the pHreference solution.57 For use as the pH-reference, the lists of pH values of several standard aqueous solutions57 and non-aqueous solutions of potassium hydrogen phthalate58 are provided. On the other hand, pH (or aH) can be expressed by the specific molality and the activity coefficient of hydrogen ion. These two pH values, so-called electrochemically determined and concentration-based, are confirmed to be consistent.59-62 However, appropriate pH standards have not been established yet in ionic liquids. Therefore, selection of pH standard materials, validation of their pH value, and comparison with the concentration-based value must first be achieved in ionic liquids. Ethylammonium nitrate (EAN) is the firstly described liquid salt in 1914,63 and nowadays is the most archetypical PIL. Its characteristics, such as macroscopic physicochemistry,64-72 liquid structure,73-79 dynamics,80,81 and so on, are the most widely known out of all PILs. In our previous study, we have demonstrated that EAN is capable of maintaining ordinary acid-base equilibria where the ionization profile is completely described as a function of pH using the dissociation constants.43 In addition, we have also demonstrated that the ion-sensitive field-effect transistor (ISFET) electrode acts as a pH indicator in EAN, in which a glass electrode does not work.71 Therefore, to develop the pH standard materials will promote the investigation and application of acid-base reactions in EAN. In this study, we selected pH standard materials and validated their pH values in accordance with the orthodox procedure that was applied to the conventional molecular solvents. During potentiometric measurements, we observed that the silver-silver chloride electrode acts as a stable reference electrode, and we observed unique behaviors for the activity coefficients of ions in EAN.


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Experimental Section Reagents: EAN was synthesized following previously reported procedures43,69,71 from aqueous solutions of nitric acid and ethylamine (both 70 %; Kanto Kagaku, Japan). The water content in the synthesized EAN, determined by Karl-Fisher method, was 80-200 ppm. Since a completely neutral EAN is not possible, the excess amount of HNO3 or C2H5NH2 of the synthesized EAN was quantified by separate neutralization titrations, then the same amount of distilled C3H7NH2 or TfOH was added to neutralize. Again, the acid-base balance of this stock EAN was determined by the second neutralization titrations. The excess concentration was less than 1 mM (M = mol dm–3), which was taken into account during the subsequent measurements and analyses. Molarity and molality of EAN solutions were mutually converted using the specific density (1.212), which was determined by a pycnometer. TfOH (>99 %, provided in ampoule; Kanto Kagaku), C2H5NH3Cl (>98 %; Merck, Germany), sodium chloride (99.98 %; Kanto Kagaku), potassium hydrogen phthalate (>99.95 %; Kanto Kagaku), sodium dihydrogen phosphate (99 %; Kanto Kagaku), disodium hydrogen phosphate (>99 %; Nacalai Tesque, Japan), oxalic acid anhydrate (99 %; Merck), and disodium oxalate (99.5 %; Kanto Kagaku) were used without further purification. Potentiometric titration: Potentiometric titrations were performed at 298.15 K in a glass vessel equipped with a thermostatic water jacket. The electrolyzed silver on a platinum wire was partially oxidized to silver chloride for use as a silver-silver chloride electrode. We confirmed in separate experiments that the silver-silver chloride electrode performed as expected in aqueous solution. After titrant was added to the solution with an autoburette, equilibrium was achieved


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within 5-10 minutes, then electromotive force (emf) was recorded. Hydrogen gas was bubbled in the sample to fill the vessel throughout the titration, and discharged into the atmosphere. The atmospheric pressure was given by an aneroid barometer, and assumed to be equivalent to the partial pressure of hydrogen, 𝑝H2, in the vessel.

Results and Discussion Standard Potential of the Silver Chloride: The silver-silver chloride electrode is one of the best choices as a reference electrode in water. Its standard electrode potential in water is determined in a hydrochloric acid solution with using a Harned cell.57,82 HCl dissociates completely in water to form equal amounts of lyonium H3O+ and solvated Cl–. Instead of HCl,82,83 we used the EAN solution containing equimolar TfOH and C2H5NH3Cl because TfOH is supposed to dissociate completely in EAN to form equal amount of HNO371 and C2H5NH3Cl is the solvate of Cl–. Consequently, this solution is considered to be equivalent to HCl solution during electrochemical measurements. The following represents the Harned cell that we used in these experiments: Pt (H2) | EAN (H+, Cl‒) | Ag/AgCl

(1)

Figure 1 shows the emf of the cell, E, while titration with TfOH + C2H5NH3Cl solution, which corresponds to 0.1 mol kg‒1 or 0.01 mol kg‒1 HCl solution of EAN. The Nernst equation of this cell is expressed as follows:

𝐸 = 𝐸AgCl°(EAN) ―

𝑅𝑇 ( ) 𝐹 ln 𝑎H𝑎Cl

𝑅𝑇

― 2𝐹ln

𝑝H2 𝑝°

(2)


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where EAgCl(EAN) is the standard silver chloride redox potential in EAN, R = 8.314 J/molK, T = 298.15 K, F = 96485 C/mol, and the standard pressure, p, is 1013 hPa. The effect of the atmospheric pressure on E is negligible, and is hereafter ignored. Using the molalities of H+ and Cl‒ (mH and mCl, respectively), E is expressed by the following equation: 𝐸 = 𝐸AgCl°(EAN) ―

𝑚H𝑚Cl 𝑅𝑇ln 10 𝐹 log 𝑚°2

―

2𝑅𝑇 𝐹 ln 𝛾 ±

(3)

where  is the mean activity coefficient of H+ and Cl‒, given by 𝛾 ± = 𝛾H𝛾Cl, and m = 1 mol kg‒1. Unlike the HCl aqueous solution, mH and mCl are not strictly identical due to two experimental reasons, i.e., (1) imbalance of HNO3 and C2H5NH2 in synthesized EAN, and (2) not completely equimolar TfOH and C2H5NH3Cl in the titrant. As shown in Figure 1, E of log (mHmCl/m2) falls along a straight line with a slope of 59.73 (0.60) mV (the values in parentheses denote the standard deviation). This value, which is consistent with RT ln 10/F = 59.16 mV at 298.15 K, indicates that there is an ideal Nernst response of the Harned cell in EAN. In addition, excellent linearity suggests that the  value remains constant throughout the molality range. Therefore, E vs. log (mHmCl/m2) was reanalyzed with the ideal slope (59.16 mV), as shown by the solid line in Figure 1. Finally, we obtained EAgCl(EAN) of 127.2 (1.7) mV from the intercept. The experimental points shown in Figure 1 span a region that is significantly diluted. In particular, several data points at the right of the graph plot along the line only when autoprotolysis of EAN is taken into account in mH. One can consider that this is an infinitely dilute condition, where  should be unity. Consequently,  = 1 is retained throughout the concentration range observed. We discuss the activity coefficients for each of the respective ions later.


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600 500 400

2

E + RT/2F ln (pH / p°) / mV

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300 200 100 0

0

1

2 3 4 5 2 –log(mH mCl/m° )

6

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Figure 1. Electromotive force of the Harned cell. Neat EAN was titrated with 0.1 mol kg‒1 (filled symbols) or 0.01 mol kg‒1 (blank symbols) TfOH + C2H5NH3Cl solution of EAN. A least squares regression provides (127.2  1.7) mV ‒ 59.16 log (mHmCl/m2).

Validation of the pH of standards: According to the IUPAC recommendations,58 0.05 mol kg‒1 of potassium hydrogen phthalate was chosen as the primary pH standard for several non-aqueous solutions. We thus adopted the identical condition for the first pH standard. The emf of the Harned cell (1) was recorded in an EAN solution of 0.05 mol kg‒1 potassium hydrogen phthalate with changing the chloride ion molality by titration. The titrant solution (0.1 mol kg‒1 C2H5NH3Cl along with 0.05 mol kg‒1 potassium hydrogen phthalate) was prepared from the same solution of the titrand in order to keep the analytical concentration of potassium hydrogen phthalate constant throughout the titrations. The emf value, E, in this solution is described using the chloride molality mCl by the following equation.


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𝐸 = 𝐸AgCl°(EAN) +

𝑅𝑇ln 10 𝐹 pH

―

𝑚Cl 𝑅𝑇ln 10 𝐹 log 𝑚°

―

𝑅𝑇 𝐹 ln 𝛾Cl

(4)

As shown by the filled circles in Figure 2, E as a function of ‒log mCl/m yields a straight line with a slope of 57.63 (0.38) mV. Although the difference from the ideal Nernst response (59.16 mV) was slightly larger than the standard deviation, we could not find out a thermodynamically proper reason to interpret simultaneously the smaller slope and the linearity. Therefore, we assume the ideal Nernst response in this solution. Besides, 𝛾Cl remained constant throughout the concentration range observed. As a result, similar to the way for obtaining EAgCl(EAN), we reanalyzed Figure 2 with the ideal slope, as shown by the solid line. Finally, we obtain an intercept at log (mCl/m) = 0 of 418.9 mV, which yields a pH of 4.931 (0.043). Note that the neutral pH of EAN is around 5 according to the autoprotolysis constant of EAN.64,71 Therefore, potassium hydrogen phthalate is useful as a pH standard for neutral EAN.

800 700

E / mV

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


600 500 400 300 0

1

2

3

4

–log (mCl/m°)


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Figure 2. Electromotive force of the Harned cell. EAN solutions of 0.05 mol kg‒1 phthalate (circles), phosphate (squares), and oxalate (triangles) buffers were titrated with a C2H5NH3Cl + 0.05 mol kg‒1 buffer solution of EAN.

We expect that a pair of NaH2PO4 and Na2HPO4 will produce a basic pH buffer according to the pKa value (pKa,2 = 7.6643). Figure 2 filled squares show E for cell (1) depending on Cl‒ molality in the EAN solution containing 0.05 mol kg‒1 of 1:1 NaH2PO4 and Na2HPO4. The cell yields a linear relationship between E and ‒log mCl/m with a slope of 56.16 mV. Following the same procedure mentioned above, we observed a pH of 7.135 (0.056). For an acidic buffer, although its pKa was not known at this stage, we selected oxalic acid. Figure 2 triangles display E for cell (1) depending on Cl‒ molality in the EAN solution containing 0.05 mol kg‒1 of 3:1 H2(ox) and Na2(ox) (ox2‒ = oxalate). The slope was 57.17, and a pH of 2.122 (0.038) was given. These pH values of three buffer solutions are summarized in Table 1. They cover the acidic, neutral, and basic region of EAN. We here compare these pH values with those based on the hydrogen ion molality. Taking into account the acid dissociation constants of phthalic acid in EAN, i.e., pKa,1 = 3.73 and pKa,2 = 5.88,43 a 0.05 mol kg‒1 potassium hydrogen phthalate solution yields an mH of 1.1910‒5 mol/kg. Since acid dissociation constants are molarity-based values, the molality and molarity of all compounds involved in this calculation are simply converted using the specific density of EAN. Finally, this yields a pH = ‒log HmH/m of 4.92, where we apply H = 1 as mentioned later. This value agrees with the pH determined from the electrochemical procedure mentioned above within the standard deviation. With regard to the phosphoric acid solution, using pKas,43 we


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found that ‒log HmH/m is equal to 7.13, which agrees with the pH determined electrochemically. With regard to oxalic acid, the acid dissociation constants in EAN were determined in this work by the separate titrations. The detailed procedure has been described elsewhere.43 Typically, 5 cm3 EAN solution of 10 mM sodium oxalate was titrated by EAN solution of 0.25 M TfOH. In Figure 3, three series of titration data are plotted. By means of least squares fitting, we obtained pKa,1 and pKa,2 of 1.96 (0.06) and 5.28 (0.02), respectively (for only pKas, values in parentheses denote three standard deviations). The calculation curve using the obtained pKa values is drawn by the solid line in Figure 3, which reproduces excellently the experimental points. Using these pKas, ‒log HmH/m is equal to 2.22. This value satisfactorily agrees with the electrochemically determined pH, while the difference is larger than the standard deviation. Overall, these pH buffer solutions associate well with the hydrogen ion concentration.

7 6

–3

–log ([H]/mol dm )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


5 4 3 2 1

0

1 2 3 TfOH : Na2(ox)

4

Figure 3. A potentiometric titration curve of oxalic acid in EAN. The Na2(ox) solution of EAN is titrated with the TfOH solution of EAN. H means the hydrogen ion in EAN (exists as HNO3).


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The solid line represents the theoretical curve calculated from finally obtained pKa,1 and pKa,2 values.

The activity coefficients of H+ and Cl‒ in EAN: As previously mentioned, the mean activity coefficient of H+ and Cl‒, , remains constant at unity in EAN, whereas, Cl does not depend on mCl, as is shown in Figure 2. Therefore, H = 1 and Cl = 1 are supposed in wide concentration range in EAN. This is a strange behavior because, in conventional molecular liquids, the activity coefficient of ions depends strongly on their concentration. However, it can be reasonably explained by the nature of the ionic liquids. In molecular solvents, the electrostatic potential generated by an ion decays gradually by the ionic atmosphere of the coexisting ions. On the other hand, in ionic liquids, oppositely charged ions exist ubiquitously around the ion, so that the electrostatic potential is rapidly screened and possibly disappeared at the nearest neighbor by one counterion at a minimum. In other words, the effective ionic strength in the conventional meaning is saturated in ionic liquid and remains constant in spite of the addition of ions. This situation has also been found in C2mimTf2N.84 Hence, it may be a fundamental aspect of ionic liquids. In order to consider the solvation state of H+ and Cl‒ in EAN, their transfer activity coefficients from water to EAN are estimated from emf of the following cell equipped with the double junction bridge: Pt(H2) | sample EAN solution || EANint || NaClaq | Ag/AgCl

(5)

The double bars denote liquid junctions with a 4G glass filter. NaClaq denotes an aqueous solution of 0.1 M NaCl, in which silver-silver chloride is immersed, and EANint is the electrode


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internal solution, which prevents water from contaminating the EAN sample solution. As previously reported,43 the practical standard potential of the cell is ‒234 mV. Calculating the activity coefficient of Cl‒ in NaClaq using a simple assumption (log 𝛾 ± = ―0.5 0.1), we obtained the redox potential of AgCl to be 165 mV against the standard hydrogen electrode (SHE) in EAN (SHEEAN). If the liquid junction potential between the EAN internal solution and 0.1 M NaClaq is ignored this potential is considered at the same level as the redox potential of AgCl in water. Finally, as indicated in Figure 4, this hypothesis results in 57 mV higher SHEEAN than the SHE in water (SHEW), which yields the transfer activity coefficient of H+ from water to + EAN, log γW→EAN tr,H + , of 0.96. Therefore, HNO3 in EAN is a stronger acid than H3O in water.

Although a rough estimation, this value is excellently consistent with previous results suggesting that EAN is an acidic solvent that is 1 pH unit more acidic than water.43 For Cl‒, the redox potential of AgCl in EAN is 38 mV lower than that in water, resulting in a log γW→EAN of 0.64. tr,Cl ― ‒ The positive log γW→EAN (or γW→EAN tr,Cl ― tr,Cl ― > 1) indicates that Cl is destabilized in EAN, while the

W→EAN transfer Gibbs energy, Δ𝐺W→EAN tr,Cl ― = 𝑅𝑇ln γtr,Cl ― , is only less than 4 kJ/mol. The positive transfer

Gibbs energy was also observed in the transfer from water to most of organic solvents,55,85 however, the it is significantly smaller than the typical values (13.2 kJ/mol for methanol to 40.3 kJ/mol for dimethylsulfoxide). The relatively small Δ𝐺W→EAN value might be surprising if Cl‒ in tr,Cl ― EAN was assumed to be fully solvated by the oppositely charged ions, C2H5NH3+, through electrostatic interactions. Even though the smaller dielectric constant of EAN80 than water should be taken into account, presumably, coexisting NO3‒ predominantly destabilize Cl‒ in EAN due to the repulsive interactions. This competitive solvation contributes negatively to the net solvation Gibbs energy. Such a significant effect of like ion is a distinguishable feature in ionic liquids


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because, in conventional solvents, like ions rarely make contact with each other and their electrostatic contribution has been almost ignored so far.

Figure 4. A potential diagram in water and EAN. Values with an asterisk denote that AgCl was immersed in water.

Conclusions In this study, we propose three pH standard buffers that function in EAN, and validated their pH values. These values cover the pH range of EAN from acidic to basic. In addition, we confirmed that these pH values are in consistent with the concentration of hydrogen ion. Hence, this set of pH standards are applicable for pH measurements in EAN solutions. Especially, it facilitates using an ISFET electrode because ISFET is a more convenient pH probe than the hydrogen


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electrode although its standard potential is always not readily available. Since EAN is an easily available ionic liquid, the result of this study may promote the understanding and application of PILs. For thermodynamics, we observed that the activity coefficients of H+ and Cl‒ remain constant at unity in EAN. This suggests that the Debye-Hückel treatment is no longer relevant for ionic liquids. In addition, the transfer activity coefficients of single ions, H+ and Cl–, were estimated from the redox potential of silver chloride in EAN. These estimations reveal that EAN destabilizes Cl‒ to some extent in comparison with water, in spite of the ubiquitously existing C2H5NH3+. Although these trends seem strange in comparison with conventional solvents, they can be explained by the fact that ionic liquids are filled with ions. It is worth noting that there is possibly a negative contribution to the solvation energy caused by the contact of like ions, which can occur exceptionally in ionic liquids. The balance of these contributions should be recognized for considering ion-solvation in ionic liquids. Further knowledge of ion’s behavior in ionic liquids is required.


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Table 1. Comparison between electrochemically determined and concentration-based pH and. ‒log HmH/m

Buffer

composition (in mol kg‒1)

emf of Harned cell pH (in mV)

Oxalate

H2(ox) 0.03836

252.7 (1.5)

2.12 (0.04) 2.22

418.9 (1.9)

4.93 (0.04) 4.92

548.7 (3.3)

7.12 (0.06) 7.13

Na2(ox) 0.01257 (ox2‒ = oxalate) Phthalate

KHPh 0.05062 (Ph2‒ = phthalate)

Phosphate

NaH2PO4 0.02476 Na2HPO4 0.02477

values in parentheses denote the standard deviation.

AUTHOR INFORMATION Corresponding Author *Ryo KANZAKI, [email protected], +81-99-285-8106 Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript. Funding Sources ACKNOWLEDGMENT This work was supported by JSPS KAKENHI Grant Numbers JP26410157 and JP18H03392


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SYNOPSIS (Table of Contents Image)


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The Journal of Physical Chemistry 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46

Page 30 of 31

Figure 4

AgCl 222

234*

AgCl in 0.1 M NaClaq

165*

AgCl

38 mV 127 AgCl

0 57 mV

in EAN

SHEW 0 in water


SHEEAN

Page 31 of 31 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46


TOC Graphic

AgCl 222

38 mV

57 mV SHEW

0 in water

234*

AgCl in 0.1 M NaClaq

165*

AgCl 127 AgCl

0 in EAN

Cl‒ in water

SHEEAN


Cl‒ in EAN

Validation of pH Standards and Estimation of the Activity Coefficients

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