IUPAC Technical Report

Valentin Radtke, Daniela Stoica, Ivo Leito, Filomena Camões*, Ingo Krossing,Bárbara Anes, Matilda Roziková, Lisa Deleebeeck, Sune Veltze, Teemu Näykki,Frank Bastkowski, Agnes Heering, Nagy Dániel, Raquel Quendera, Lokman Liv,Emrah Uysal and Nathan Lawrence

A unified pH scale for all solvents:part I – intention and reasoning(IUPAC Technical Report)https://doi.org/10.1515/pac-2019-0504Received May 16, 2019; accepted May 17, 2021

Abstract: The definition of pH, itsmeasurement and standard buffers, is well developed in aqueous solutions.Its definition in solvents other than water has been elaborated for a couple of solvents and their mixtureswith water. However, the definition of a universal pH scale spanning all solvents and phases, not to mentionstandard procedures of measurement, is still a largely uncharted territory. UnipHied is a European collabo-ration and has the goal of putting the theoretical concept of an earlier introduced (2010) unified pHabs scale onametrologicallywell-founded basis into practice. The pHabs scale enables the comparability of acidity betweendifferent phases. This article draws the connection of the concepts of unified acidity and secondary pHmeasurement.

Keywords: Chemical potential; differential potentiometry; intersolvental; liquid junction potential; pH;traceability.

Article note: Sponsoring body: IUPAC Analytical Chemistry Division (Division V): see more details on page 1059.This work was prepared by the Subcommittee on pH.

*Corresponding author: Filomena Camões, FCiencias.ID, Centro de Química Estrutural, Faculdade de Ciencias da Universidade deLisboa, Campo Grande, 1749-016 Lisboa, Portugal, e-mail: mfcamoes@fc.ul.pt. https://orcid.org/0000-0001-8582-8904Valentin Radtke and Ingo Krossing, Universität Freiburg, IAAC, Albertstr. 21, 79104 Freiburg, Germany. https://orcid.org/0000-0002-5547-1278 (V. Radtke). https://orcid.org/0000-0002-7182-4387 (I. Krossing)Daniela Stoica, Laboratoire de Metrologie et d’Essais, 1 Rue Gaston Boissier, 75015, Paris, France. https://orcid.org/0000-0002-6748-552XIvo Leito, University of Tartu, 14a Ravila Street, 50411 Tartu, Estonia. https://orcid.org/0000-0002-3000-4964Bárbara Anes, FCiências.ID, Centro de Química Estrutural, Faculdade de Ciências da Universidadede Lisboa, Campo Grande, 1749-016 Lisboa, Portugal. https://orcid.org/0000-0002-1987-5486Matilda Roziková, Czech Metrology Institute, Okružní 31/772, 638 00, Brno, Czech RepublicLisa Deleebeeck, Danish Fundamental Metrology, Kogle Alle 5 2970 Hørsholm, DenmarkSune Veltze, Danish National Metrology Institute, Hørsholm, Denmark. https://orcid.org/0000-0001-9406-3341Teemu Näykki, Suomen ympäristökeskus (SYKE), Latokartanonkaari 11, 00790 Helsinki, FinlandFrank Bastkowski and Agnes Heering, Physikalisch-Technische Bundesanstalt, Bundesallee 100, 38116 Braunschweig, Germany.https://orcid.org/0000-0002-0893-8015 (A. Heering)Nagy Dániel, Metrological and Technical Supervisory Department of the Government Office of the Capital City Budapest (BFKH),Nemetvölgyi út 37-39, 1124 Budapest, HungaryRaquel Quendera, Instituto Portugues da Qualidade, Rua António Gião, 2, 2829-513 Caparica, PortugalLokman Liv and Emrah Uysal, Electrochemistry Laboratory, Chemistry Group, The Scientific and Technological Research Council ofTurkey - National Metrology Institute (TUBITAK UME), Gebze, Kocaeli, 41470, TurkeyNathan Lawrence, ANBSensors, Unit 4, Penn Farm Studios, Haslingfield, Cambridge, CB23 1JZ, UK

Pure Appl. Chem. 2021; 93(9): 1049–1060

© 2021 IUPAC & De Gruyter. This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives4.0 International License. For more information, please visit: http://creativecommons.org/licenses/by-nc-nd/4.0/

CONTENTS1 Introduction ................................................................................................................................. 10502 The unified pH scale .....................................................................................................................1051

2.1 The physical variable of the unified pH scale .............................................................................10512.2 The reference state of the unified pH scale .................................................................................10512.3 The definition of the unified pH scale ........................................................................................ 10532.4 Assembling the unified pH scale ............................................................................................... 10542.5 Connection to electrochemistry ................................................................................................. 1055

3 The practical implementation of the unified pH scale ............................................................... 10553.1 Primary pH measurement .......................................................................................................... 10553.2 Secondary pH measurement with one solvent ........................................................................... 10553.3 Secondary pH measurement with two different solvents ........................................................... 10563.4 The liquid junction potential LJP ............................................................................................... 10563.5 The ionic liquid salt bridge ILSB ................................................................................................ 10573.6 Implementation of the pHabs scale: secondary pHabs measurement ....................................... 10583.7 UnipHied tasks .......................................................................................................................... 1058

4 Summary ...................................................................................................................................... 10595 Membership of sponsoring bodies ............................................................................................. 1059References .......................................................................................................................................... 1059

1 Introduction

The proton H+, or more exactly the hydron, plays an important role in virtually all material-related processes,and the pH of solutions is probably the most prominent and widely used chemical concept, thus buildinginterdisciplinary bridges. Accurate measurement of pH values is an extremely important task in a wide varietyof media in which physical, chemical, and biological processes occur, that is, in water, solvents other thanwater, solvent mixtures, and dispersions. The concept of pH is very well defined, by Sørensen in 1909 [1], androutinely evaluated by means of potentiometric measurements valid in dilute aqueous solutions [2]. Innon-aqueous media, the pHS value, where S represents the solvent, can be defined, in principle, in the sameway (Eq. 1); however, one has to recognize that this definition is notional [3].

pHS = −lg aH+ , S = −lg(mH+ ,S  γH+ , Sm⊖ ) (1)

All parameters are expressed on the molality scale: aH+ , S is the relative activity [4] of the proton in thesolvent S, mH+ , S is its molality, γH+ , S is its activity coefficient, and m⊖ = 1 mol kg−1 is the standard molality.

Because the relative activity is used in its definition, pHS values within the same solvent can be compared toeach other, but pHS values between different solvents cannot be compared. The reason is the choice ofstandard states for solutes in solution.

Numerous attempts have been made to overcome this situation. A not completely up-to-date, butstill insightful, overview is given by Bates [5]. As quintessence, the IUPAC propagated the s

wpH scale in1985 based on the so-called primary medium effect of the proton s

wγH+ (not to be confused with the activitycoefficient in Eq. 1; Eq. 2) [3]. The left-hand subscriptw (=water) relates to the reference state of the scale,whichis the infinitely dilute aqueous solution of H+.

swpH = −lg(mH+ , S ⋅ swγH+

m⊖ ) (2)

However, a satisfactory solution of the generalization problem was presented with the unified acidity scale

pHabs [6]. The original definition allows a more tangible formulation as pHH2Oabs [7], which, like the Sørensen

scale and the swpH scale, appears as a special case of the pHabs scale. When using standard Gibbs energies of

1050 V. Radtke et al.: A unified pH scale for all solvents: part I

transfer, the swpH-scale is identical to the pH

H2Oabs scale (cf. Eq. 13 and footnote 4). Thus, the pHH2O

abs scale can be

considered as the “intersolvental” continuation of the aqueous pH scale.Some standards have been recommended for pHS scales with S consisting of a few organic solvents

(methanol, ethanol, 2-propanol, acetonitrile, dimethylsulfoxide, and 1,4-dioxane) and some of their mixtureswith water [3, 8]. However, these standards relate to measurements only within one solvent and do not covermeasurements between different solvents, what is necessary to establish an intersolvental pH scale.

The challenge of integrating the last missing link of pH standardization is being taken by a Europeancollaboration of National Metrology Institutes, universities, and companies: UnipHied.eu. The intention is thedevelopment of appropriate and internationally agreed standards as well as reference procedures of

measuring pHabs values and pHH2Oabs values. This includes accurate and rigorous measurements based on

metrological traceability chains adapted to the new matrices or solvents and a corresponding uncertaintybudget.

2 The unified pH scale

2.1 The physical variable of the unified pH scale

The need for a unified pH scale arises from the impossibility to correlate the individual pHS scaleswithout further knowledge of the considered acid–base systems. The basic problem of knowing how acidic aproton is – that is what an acidity scale or “pH” value should reflect – is closely connected to the state of theproton in its environment, that is, on the proton’s bonding conditions, etc. One can thus deduce that theknowledge of the proton’s chemical potential μH+ (or the protochemical potential, Eq. 3) is the fundamentalkey to connect all pH scales. Certainly, more convenient is “one” pH scale directly anchored to theprotochemical potential (see Eq. 8).

μH+ = ( ∂G∂nH+

)T , p, nX≠H+

(3a)

μH+ = μH+ − Fφ (3b)

The tilde brings the dependence of an ion’s partial molar Gibbs energy on the Galvani potentialφ of a phase tomind, and μH+ denotes the electrochemical potential of the proton [9, 10].1 nH+ is the amount of H+ and F theFaraday constant. Equation 3 implies that the chemical potential of single ions is an unmeasurable quantityalthough certain combinations of individual ionic activities are measurable in a thermodynamically exactmanner [11]. This instance is the source of long-lasting discussions, and widespread is the view that single-ionactivities are without physicalmeaning. On the other hand, physical reality is attributed to the electrochemicalpotential, although this quantity is not measurable either. It has been pointed out that physical significance isnot linked to measurability alone [12]. As long as no experiment is operable thermodynamically stringent incharacter the need of methods outside of exact thermodynamics is widely accepted and the determination ofsingle-ion activities is performed.

2.2 The reference state of the unified pH scale

An appropriate reference state should have two key properties: it should be maximally simple and maximallyextensive. To achieve this, we take the ideal proton gas at p = p⊖ = 105 Pa and T = 298.15 K as the reference state(Fig. 1). The adjective “ideal” suggests that no interactions between the protons (e.g., of coulombic nature)

1 Equations 3a and 3b accordingly are given as recommended by IUPAC without a tilde on G or U, respectively. It is a legitimatequestion whether confusion would be avoided or evoked if the tilde is used with G and U, too.

V. Radtke et al.: A unified pH scale for all solvents: part I 1051

occur. Thus, we actually consider an isolated proton in the gas phase and add, according to Bartmess [13] thestandard terms for entropy and enthalpy to reach 298.15 K and 105 Pa.2 This state corresponds to the standardstate of ideal neutral gases (Eq. 4) [10]. We arbitrarily set the chemical potential of the proton in this state to0 kJ mol−1.

μ⊖H+(g, T) = μH+(T, p, yH+) − RT  ln(yH+ ⋅ p

p⊖ )∶= 0 kJ mol−1 (4)

yH+ is the mole fraction of the proton in a gas mixture and, hence, unity in the pure gas.To achieve ideal behavior of solutes in solution, that is, the absence of interactions between the solutes, a

hypothetical state of the solute is established, in which the solute behaves as if infinitely dilute, marked by theinfinity symbol, but at the standard pressure p⊖ and at the standardmolalitym⊖. This state is the standard stateof solutes in solution [10]. Because solute–solvent and solvent–solvent interactions are still operative and eachsolvent interacts differently with a solute B and with itself, each solvent is accompanied by an individualstandard state which normally differs from the standard states in (or of) other solvents. This results in relativeactivities, Eq. 5, and is the reason for the incomparability of conventional pHS values (and redox potentialvalues) in different solvents.

aB, S = exp(μB, S − μ⊖B, S

RT) (5)

In accordance with the IUPAC definition, the standard chemical potential of the solvated proton in the solventS can be expressed using Eq. 6.

μ⊖H+ , S(T) = [μH+ , S(T , p⊖,mH+ ) − RT  ln(mH+ , S

m⊖ )]∞ (6)

Both reference states (Eqs. 4 and 6) are consistent with the IUPAC recommendations of the Commissionon Thermodynamics of the Physical Chemistry Division [14]. Although the definition of the standard stateof a solute in solution is comprehensible, the process of a particle’s solvation and the corresponding

Fig. 1: The (hypothetical)reference state of the unifiedpHabs scale and thethermodynamic relations tothe Brønsted-acidity in allphases. The Gibbs energy ofsolvation ΔsolvG(H+,S) is notspecified here becausedifferent definitions exist, seetext. Similarly, ΔintG(H+,S)and ΔrG(H+,S) are also notspecified.

2 Hydrons include H+ (0.999885 of natural abundance, mole fraction) and D+ (0.000115, mole fraction). The distinction betweenfermions and bosons leads to complications. A “pD” scalewould demand Bose–Einstein statistics instead of Fermi–Dirac statistics.Treating all hydrons as “Boltzons” the electron convention with Boltzmann statistics (EC-B convention) has to be used. Theconversion from one convention into another can be executed according to the requirements.

1052 V. Radtke et al.: A unified pH scale for all solvents: part I

thermodynamic parameters may cause – although clearly defined – confusion. This is amplified by the use ofdifferent symbols and, of course, standard states and conventions. Hünenberger and Reif [15] elaborated aconsistent notation expanding on the recommendations by the IUPAC [10], leaving no room for ambiguity.However, due to its complexity, the introduction of this notation goes beyond the scope of this report.

ΔsolvG∗ describes the transfer of a particle from a fixed point in the ideal gaseous phase (G∗, at

c⊖ = 1 mol L−1) to a fixed point in the ideal solvation state (cG⊖, at c⊖ = 1 mol L−1) at the same p and T in bothphases (conveniently p⊖ and 298.15 K) and is considered as reflecting the solvation process physically mostappropriate [16]. The standard Gibbs energy of solvation Δ c

solvG⊖ or Δ m

solv G⊖ is then defined, specifying the

transition of the proton from the gaseous standard state (at p⊖ = 105 Pa) to the solution standard state in thesolvent S, either at the standard amount concentration c⊖ = 1 mol L−1 (cG⊖), Eq. 7a, or at the standard molality

m⊖ = 1 mol kg−1 (mG⊖), Eq. 7b. The conversion from concentration- to molality-based standard states and viceversa is straightforward, Eq. 7c; therefore, in Fig. 1, ΔsolvG(H+, S) is not specified.

Δ csolvG

⊖ = ΔsolvG∗ + ΔcG⊖→∗ with ΔcG⊖→∗ = RT  ln

RTc⊖

p⊖ (7a)

Δ msolv G

⊖ = ΔsolvG∗ + ΔmG⊖→∗ with ΔmG⊖→∗ = RT  ln

RTm⊖ρ⊖Sp⊖ ; ρ⊖S is the density of the solvent S (7b)

Δ msolv G

⊖ = Δ csolvG

⊖ + ΔGc→m with ΔGc→m = ΔmG⊖→∗ − ΔcG⊖→∗ = RT  lnm⊖ρ⊖Sc⊖

(7c)

Further discussion on the distinction betweenmolality and amount concentration scale is not required as longas it is consistently used.

In this way, the standard states of each solvent are traced to the more extensive gaseous standard stateand the direct comparability between different solvents is ensured. This also holds for all homogeneous andisotropic solid or liquid media. It follows from Eq. 3 that under standard conditions, ΔsolvG

⊖(H+, S) = μ⊖abs,H+ , S

holds true, keeping in mind the chosen reference state and using the subscript “abs” to indicate that allprotochemical potentials obtained in this way can be compared to each other.

2.3 The definition of the unified pH scale

With Eqs. 4 and 5, all absolute protochochemical potentials μabs,H+ can be related to each other. On this basis,

the pHabs scale was defined unifying all phases (Eq. 8) [6].

pHabs = − μabs,H+

RT  ln 10(8)

The absolute state is referenced to the gas phase connecting all media; thus, no indication in terms of mediumis necessary and all pHabs values can be compared to each other regardless of the medium. Because theconventional pHS (Eq. 1) is defined by the relative activity, it can be formulated in an atypical way as

pHS = −μH+ , S−μ⊖H+ , SRT  ln10 . Conversely, using the absolute activity [4] λH+ = aabs,H+ = exp(μabs,H+

RT ), one can derive a more

familiar form of pHabs, Eq. 9a.

pHabs = −lg aabs,H+ (9a)

pHabs can even be translated in terms of H+ pressure, Eq. 9b.

p(H+, g) = 10−pHabs  p⊖ (9b)

Because the aqueous pH scale (i.e., pHH2O) is the most prominent, it is favorable to define the pHH2Oabs value to

align the zero values (not the reference states!) of the pHabs and the conventional pHH2O scale (Eq. 10) [7].

V. Radtke et al.: A unified pH scale for all solvents: part I 1053

pHH2Oabs = pHabs + ΔsolvG

⊖(H+,H2O)RT ln 10

(10)

The magnitude of one pHS, pHabs, and pHH2Oabs unit is identical, that is, unity in terms of pH measure, according

toRT·ln10 in terms of caloricmeasure or (RT/F) · ln10 in terms of electricmeasure. Thus, the pHH2Oabs value serves

as a thermodynamically well-defined link between the acidity in water and the acidity in any other mediumwith respect to the aqueous system (Fig. 2).

2.4 Assembling the unified pH scale

For solutions, Eq. 8 can be expressed in terms of the Gibbs energy of solvation (Eq. 11).

pHabs = −ΔsolvG⊖(H+, S)

RT ln 10+ pHS (11)

pHS is the conventional pH value in the solvent S according to Eq. 1. Thus, the knowledge of the Gibbs energy ofsolvation and of the relative activity of the proton in the solvent S suffices to determine the corresponding pHabs

value. However, the determination of Gibbs energies of solvation for single ions is anything but straightfor-ward, and data are scarce.3 The difference of Gibbs energies of solvation of a species B in two solvents S1 and S2is called the Gibbs energy of transfer between these solvents and is related to the medium effect (Eq. 12).

ΔsolvG⊖(B, S2) − ΔsolvG

⊖(B, S1) = ΔtrG⊖(B, S1 → S2) = RT  ln S2

S1γ⊖B (12)

With Eqs. 10, 11, and 12 (if S1 is water), one can formulate the pHH2Oabs as Eq. 13.4

pHH2Oabs = −ΔtrG

⊖(H+,H2O→ S2)RT ln 10

+ pHS (13)

The determination of ΔtrG⊖( i, S1 → S2) of single ions i is an intricating task best described as a vicious

circle and has been tackled by quite a number of distinguished scientists during the past century. So far,extra-thermodynamic assumptions have been used to get around the problem [19]. The values ofGibbs energies of transfer obtained with extra-thermodynamic assumptions, however, are afflicted with

Fig. 2: The absolute protochemical potential μabs,H+ and the relation to the pHabs, pHH2O, and pHH2Oabs scales based on

ΔsolvG⊖(H+,H2O)=−1104.5 kJmol−1. The colored areas represent theprotochemicalwindowsof someselectedmedia, determinedby the respective autoprotolysis constant pKAP, with the vertical bars being their respective neutral points (defined with pKAP/2);data were taken from Ref. [17].

3 A recommended value for ΔsolvG⊖(H+,H2O) is (−1104.5 ± 8) kJ mol−1 (according to the electron convention, Boltzmann statistics

(EC-B) by Bartmess) obtained with the cluster-pair approximation [18]. Another recommended value is (−1100.0 ± 5) kJ mol−1

(according to the electron convention, Fermi–Dirac statistics (EC-FD)) [15]. For the proton, the EC-B value is shifted by about−3.6 kJ mol−1 with respect to the EC-FD value. As hydration is considered the distinction between themol L−1- and themol kg−1-scaleis negligible (approx. 0.007 kJ mol−1).4 Further, with s

wγH+ = γH+ , S ⋅ swγ⊖H+ and Eq. 1 it follows that pHH2O

abs = swpH.

1054 V. Radtke et al.: A unified pH scale for all solvents: part I

uncertainties, which cannot be determined exactly but only can be estimated. These estimations depend onthe method. Optimistic estimations lie in the range of 1 pH unit, cautious estimations in the range of roughly2 to 12 pH units, and rise up to 20 pH units applied on model systems [20]. Here, we suggest approaching theproblem with a direct method based on potentiometric measurements with a determined consistency ofabout 0.1 pH unit (see below).

2.5 Connection to electrochemistry

The aforementioned connection from the gaseous state to the solution state also leads in a straightforwardmanner to the standard state used in electrochemistry. However, one must note that the standard state,that is, the standard hydrogen electrode (SHE),5 in electrochemistry is not as unambiguously defined asthe pH value is in acid–base chemistry (see Eq. 1). In Ref. [10], the SHE definition includes “a solution of H+ atunit activity” without specifying the concentration scale. Although sometimes it is clearly defined in themolality scale, tables of standard redox potentials list values under atmospheric pressure in preference to105 Pa [22].

The Gibbs energy of a reaction, divisible in a reduction (electronation) and oxidation (de-electronation)partial reaction, is connected to the electric potential difference Ecell of an appropriate electrochemical cell byEq. 14.

ΔrG = −nF  Ecell (14)

n is the number of electrons in the cell reaction and F is the Faraday constant.

3 The practical implementation of the unified pH scale

3.1 Primary pH measurement

The primary method of measuring the pH of dilute aqueous solutions is laid out in the 2002 IUPACRecommendations [2]. This method, commonly referred to as the Harned cell method, relies on the potentialdifference measurement of cell I.

PtH2

H+(of  primary standard buffer),Cl− AgCl Ag I

Cell I is a cell without transference and is, therefore, assumed to exclusively reflect the Gibbs energy of theassociated cell reaction.6

Similarly, for some organic solvents and their mixtures with water, primary standards were defined andmeasured with cell I [3, 24]. However, measurements concerning intersolvental pH scales demand cells withconcomitantly different solvents inside (solvation cells). Consequently, the primarymethod cannot be applied.

3.2 Secondary pH measurement with one solvent

Due to the restrictions imposed by the primary method, pH measurements more commonly include themeasurement of potential difference of two electrodes immersed in two separate aqueous solutions, known as

5 The recommended definition of the absolute electrode potential includes the real potential α and takes into account the surfacepotential of the phase under consideration [4]. Since our method of measurements results in Gibbs energies of transfer, we use thedefinition including the chemical potential [21], sometimes called “intrinsic” potential [15], due to its absence of surface potentialcontributions.6 However, even in this case a liquid junction potential arises [23].

V. Radtke et al.: A unified pH scale for all solvents: part I 1055

secondary pH measurements. In effect, the used electrochemical cell contains one or more liquid–liquidjunctions, each accompanied by a potential drop, called liquid junction potential (LJP).

Secondary pHmeasurements canbe performedwith, e.g., cell II, which enables themeasurement of the pHdifference between the solutions on the left and the right side of cell II [25].

IndaH+ , S1┊┊ SB ┊┊d aH+ , S1

Ind II

d(≠0) is a factor indicating that the (relative) proton activity in both solutions may or may not be equal. Ind isan indicator electrode selective exclusively (as far as practically possible) to protons and SB is a salt bridge.Note that both solutions contain H+ (solv) within the identical solvent S1. Each of the single vertical barsrepresent a phase boundary, and the double-dashed vertical bars pertain to liquid–liquid junctions, in whichthe LJP has been assumed to be eliminated. In the case of aqueous solutions and using a SB filled with anaqueous solution of KCl (c ≥ 3.5 mol L−1), this assumption works quite satisfactorily and the double-dashedvertical bars are virtually reasonable. Secondary pH measurements are generally accepted and in widespreaduse. To some extent, this is also true for solvents other than water [3, 8].

3.3 Secondary pH measurement with two different solvents

As discussed above, themeasurement of pH difference between different solvents requires solvation cells, thatis, cells with different solvents in each half cell. Although possible in principle, solvation cells can beimplemented, e.g., as cell II for secondary pHmeasurements (note that in this case, the solutions on the left andthe right side of the cell contain H+ (solv) within different solvents S1 and S2). To the authors’ knowledge, suchsecondary pH measurements have been performed by only one team so far, and only for aqueous organicsolvents [7, 25]. UnipHied is working on filling the gap.

The measurement of pH values and the measurement of transfer energies of the proton can be consideredequivalent. Consider the transfer reaction of a proton from one solvent S1 to another S2, Eq. 15.

7

H+(solv, S1)→ H+(solv, S2) (15)

The assembly of cell II with suitable indicator electrodes permits the use of Eq. 15, and in combination withEq. 14, one obtains Eq. 16; EII is the potential difference in cell II according to the Stockholm conventions [26].

ΔtrG(H+, S1 → S2) = −F  EII (16)

Using different solvents, the double-dashed vertical bars in cell II are not reasonable anymore. Thus, cell IIIbetter reflects reality.

IndaH+ , S2 ┊

LJP2SB ┊

LJP1d aH+ , S1

Ind III

The single-dashed vertical bars represent liquid–liquid junctions including the potential drop occurring atthese boundaries – the liquid junction potentials (LJPs). Thus, Eq. 16 has to be modified (Eq. 17).

ΔtrG(H+, S1 → S2) = F  ( − EII + Ej1 − Ej2) (17)

Ej1 and Ej2 are LJP1 and LJP2. For further discussion, it is helpful to first take a glimpse at the topic of LJPs.

3.4 The liquid junction potential LJP

The LJP results from a non-equilibrated state at the phase boundary, in which flows of particles (ions andsolvent molecules) and forces (chemical and electric potential differences) are mutually dependent. Its

7 Reduction: H+ (solv, S1) + e− (g) → ½ H2 (g) (15a) Oxidation: ½ H2 (g) → H+ (solv, S2) + e− (g) (15b).

1056 V. Radtke et al.: A unified pH scale for all solvents: part I

description demands the implementation of non-equilibrium thermodynamic principles. Applying theOnsager reciprocal relations results in the generally accepted Eq. 18 [27].

LJP = Ej = − 1F∫S2

S1

∑itridμi (18)

tri is the reduced transference numbers of all involved particles in the considered system [28]. Many attemptshave been undertaken to split the sum of Eq. 18 into different parts to reach an equation that is simpler tointerpret and calculate. Probably, the most elaborated model is given by Izutsu, who proposed the three-component breakdown (Eq. 19; here, i refers to ionic species), specifically in the context of differing solvents oneither side of the liquid junction [29].

Ej = − RTF

∫S2

S1

∑i

tizid lnai − 1

F∫S2

S1

∑i

tizidμ⊖

i + Ej, solv (19)

The first term on the right-hand side, called part A, accounts for differences in relative activities andmobilitiesof the involved ions. The second term, part B, originates fromdifferent Gibbs solvation energies of the ions. Thethird term, part C, is assigned to solvent S1–solvent S2 interactions.Without going intomore detail, the rigorouscalculation of Ej is almost never possible because for part B, Gibbs energies of transfer of the ions are needed,and part C is estimated rather than calculated.8

3.5 The ionic liquid salt bridge ILSB

Because LJP calculations are difficult and inaccurate, it is reasonable to minimize or eliminate LJP contribu-tions experimentally. Besides the above-mentioned KCl-SB, Kakiuchi presented a salt bridge containing anionic liquid without any solvent and showed its applicability for all-aqueous cells, in which both LJPs cancelwithin the 95 % confidence interval of 0.5 mV [30]. Those ILSBs are robust and led to IL-filled glass electrodes[31], which are capable of pH measurement of, e.g., rainwater samples [32].

Recently, the use of an ideal ILSB in solvation cells was proposed [20]. The ideal salt bridge “wouldalways generate the same diffusion potential, or, better still, no difference of potential, across the liquid junction,Bridge┊ Soln. X nomatter what the composition or pHof solution Xmight be” [5]. From the specified requisites forsalt bridges [33],9 one can derive the specifications for an ideal ILSB: the IL is a strong (i.e., the degree ofdissociation approaches unity) binary electrolyte – and this is of utmost importance – of which cations andanions exhibit equal transference numbers through the whole cell. Because no solvent is present, the ionicconcentration is much higher than in the half cells, and as a pure substance, the activity coefficients of theIL-constituting ions are per definition unity. The absence of solvent is crucial in the context of solvation cellsbecause no solvent–solvent interface is present in cells with the ILSB.

The potentials of cells IV with the redox system Ag+(solv)/Ag(s) turned out to be astonishingly stableagainst changes of the ionic strength of the half cells and of influx of the solvent into the salt bridge. In suchcells, parts A of each LJPs cancel [34].

AgAgZm(c, Si)

LJP2

ILSB

LJP1

AgZn(xc, Sk)Ag IV

One ILSB, which essentially meets the above-mentioned requisites, is the salt bridge filled with the IL [N2225][NTf2] (amyltriethylammonium bis(trifluoromethanesulfonyl)imide). The use of cell IV leads to Gibbs energies

8 Even in the seemingly simple case of cells including one solvent only, LJP-calculationswith thewell-knownHenderson equation,likewise derived from Eq. 18, are in poor agreement experiment in many cases.9 For those requisites, the KCl-SB is used in aqueous systems.

V. Radtke et al.: A unified pH scale for all solvents: part I 1057

of transfer of the silver ion from one solvent Sk to another solvent Si in quite good agreement with literaturedata.

3.6 Implementation of the pHabs scale: secondary pHabs measurement

The combination of cells III and IV leads to cell V and is intended to perform secondary pHabs measurementsbetween different solvent solutions.

IndaH+ , S2

LJP2

ILSB

LJP1

d aH+ , S1Ind V

This is possible because, with Eqs. 13 and 16 inmind, the potential of cell V EV directly gives the pHH2Oabs value via

Eq. 20: if S1 is water, aH+ , S1 = 1 and d = 1, thus referring to an aqueous solution containing solvated protonsunder standard conditions (Eq. 20 is written assuming Nernstian slopes for both Ind electrodes).

pHH2Oabs = F

RT ln 10EV + pHS (20)

If additionally aH+ , S2 = 1, and thus the solvent S2 contains solvated protons under standard conditions,

ΔtrG⊖(H+,H2O→ S2) can be obtained. The condition, of course, is that LJP1 and LJP2 of cell V cancel or are

ineffective for some other reason.However, even if this is not the case, cell V can support valuable services. The evidence of stability and

reproducibility of the difference ofEj1–Ej2 would lead to a consistent set of data. Using cell V, the intersolventalpH measurement is in principle traceable to the primary pH method with a quite good (if the LJPs areineffective) or acceptable (if the LJPs allow consistent data) accuracy. Nevertheless, very recent results showthat parts C of the ILSB LJPs are absent and indicate that parts B are small and the difference of the LJPs in cellIV is negligible [35].10 There are no indications why this should be different in cell V.

3.7 UnipHied tasks

The main task of UnipHied is the assembly of cell V such that a reliable and reproducible pHabs measurementprocedure can be defined. This includes a number of different issues:– the choice of suitable indicator electrodes and their characterization– the choice of a suitable ionic liquid– the choice of suitable buffer solutions– the assessment of LJPs contributions– the preparation of an uncertainty budget– the definition of calibration standards

The chosen solvents for these tasks are acetonitrile, ethanol, methanol, and somemixtures of themwithwater.The execution of these tasks involves interlaboratory comparison.

10 Measurements of 87 different combinations of cell IV with four different solvents and six different counterions Z− in threedifferent concentrations were considered. A statistical analysis of the data results in a consistency of 6.3 mV or 0.6 kJ mol−1

(equivalent to 0.08 pH units), respectively.

1058 V. Radtke et al.: A unified pH scale for all solvents: part I

4 Summary

UnipHied attempts to deliver a standardized procedure on a metrological basis for the measurement andcomparison of acidities between different solvents. The theoretical background is, as presented here, thecomplete and stringent connection of the pHabs scale unifying all media – defined with the IUPAC compliantgaseous standard state of the proton as reference state– to the secondary pHmeasurementmethod. To this, weutilize the recommended specifications for the solvation of the proton, as well as for its transfer from onesolvent to another. In this context, its general electrochemical measurability is elucidated, the impossibility ofthe primary pH measurement method is discussed, and the subject of LJPs is pointed out. The practicalimplementation is considered as promisingwith the help of ideal ionic liquid salt bridges (in the sense of Bates

[5]) allowing intersolvental pH measurements with acceptable accuracy using the more convenient pHH2Oabs

scale.The given explanations permit the definition of objectives, which can be summarized as follows:

(1) The development and validation of a reliable and universally applicable measurement procedure,including proper sensors, that enable the assessment of pHabs.

(2) The creation of a reliable method for the experimental or computational evaluation of the liquid junctionpotentials between aqueous and non-aqueous solutions.

(3) The development of a coherent and validated suite of calibration standards for standardizing routinemeasurement systems in terms of pHabs values for a variety of widespread systems (e.g., industrial mix-tures, soils/waters, food products, and biomaterials).

The results of UnipHied will be published in a forthcoming part II of this report.

5 Membership of sponsoring bodies

The membership of the Analytical Chemistry Division at the start of this project wasPresident: Zoltan Mester; Past President: Jan Labuda; Vice President: Erico Marlon de Moraes Flores;Secretary: Takae Takeuchi; Titular Members: Medhat A. Al-Ghobashy, Derek Craston, Attila Felinger, IreneRodriguez Meizoso, Sandra Rondinini, David Shaw. Associate Members: Jiri Barek, M. Filomena Cam es,Petra Krystek, Hasuck Kim, Ilya Kuselman, M. Clara Magalh es, Tatiana A. Maryutina; National Represen-tatives: Boguslaw Buszewski, Mustafa Culha, D. Brynn Hibbert, Hongmei Li, Wandee Luesaiwong, SerigneAmadou Ndiaye, Mariela Pist n Pedreira, Frank Vanhaecke, Winfield Earle Waghorne, Susanne KristinaWiedmer.

Research funding: UnipHied is funded from the EMPIR program (project 17FUN09) co-financed by theParticipating States and from the European Union’s Horizon 2020 research and innovation program. The workat Tartu was additionally supported by the Estonian Research Council grant PRG690. FC.ID, whose work wasdeveloped in Centro de Química Estrutural, thanks Fundação para a Ciencia e Tecnologia for funding underproject UID/QUI/00100/2020.

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1060 V. Radtke et al.: A unified pH scale for all solvents: part I