Standard electrode potentials involving radicals in aqueous solution: inorganic radicals (IUPAC Technical Report)

David A. Armstrong, Robert E. Huie, Willem H. Koppenol, Sergei V. Lymar, Gábor Merényi, Pedatsur Neta, Branko Ruscic, David M. Stanbury, Steen Steenken, and Peter Wardman
  • 1 Department of Chemistry, University of Calgary, Alberta, Canada
  • 2 National Institute of Standards and Technology, Formerly of the Physical and Chemical Properties Division, Gaithersburg, MD 20899, USA
  • 3 Institute of Inorganic Chemistry, Swiss Federal Institute of Technology, CH-8093 Zürich, Switzerland
  • 4 Brookhaven National Laboratory, Chemistry Department, Upton NY 11973, USA
  • 5 The Royal Institute of Technology, Department of Applied Physical Chemistry, S-10044, Stockholm 70, Sweden
  • 6 National Institute of Standards and Technology, Physical and Chemical Properties Division, Gaithersburg, MD 20899, USA
  • 7 Argonne National Laboratory, Chemical Sciences and Engineering Division, Argonne, IL, 60439, USA, and Computation Institute, University of Chicago, Chicago, IL, 60637, USA
  • 8 Department of Chemistry and Biochemistry, Auburn University, Auburn, AL 36849, USA
  • 9 Formerly of Max-Planck-Institute für Strahlenchemie, D-45413 Mülheim, Germany
  • 10 Gray Cancer Institute, Department of Oncology, Formerly of the University of Oxford, Old Road Campus Research Building, Roosevelt Drive, Oxford OX3 7DQ, UK
David A. Armstrong, Robert E. Huie, Willem H. Koppenol, Sergei V. Lymar, Gábor Merényi, Pedatsur Neta, Branko Ruscic, David M. Stanbury, Steen Steenken and Peter Wardman

Abstract

Recommendations are made for standard potentials involving select inorganic radicals in aqueous solution at 25 °C. These recommendations are based on a critical and thorough literature review and also by performing derivations from various literature reports. The recommended data are summarized in tables of standard potentials, Gibbs energies of formation, radical pKa’s, and hemicolligation equilibrium constants. In all cases, current best estimates of the uncertainties are provided. An extensive set of Data Sheets is appended that provide original literature references, summarize the experimental results, and describe the decisions and procedures leading to each of the recommendations.

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1 Introduction

Radicals, both organic and inorganic, tend to be highly reactive. Nevertheless, they are widely encountered as intermediates in chemical reactions; their individual reactivities are central among the factors that determine the rates and products of the overall reactions in which they are involved. For reactions where the radicals are present in the aqueous phase, electrode potentials involving the radicals are among the most powerful indicators of reactivity. Electrode potentials involving radicals are often more directly related to reactivity than are electrode potentials of non-radicals, because the former more often correlate to specific steps in the reaction mechanisms.

The determination of radical electrode potentials has greatly expanded in the last three decades, largely through the application of pulse radiolysis and flash photolysis. These techniques are well suited to the generation of transient radicals and the measurement of their reaction equilibria. It is largely through the manipulation of the radical equilibrium constants that the current bounty of radical electrode potentials has been obtained.

In 1989, two comprehensive reviews on radical standard potentials appeared. Wardman’s review emphasized organic radicals [1], while Stanbury’s review considered inorganic radicals exclusively [2]. Both of these reviews are now rather dated. Another valuable compendium is Steenken’s 1985 list of electron transfer equilibria involving radicals [3]. A related review emphasizing H-atom bond dissociation “free” (Gibbs) energies has also appeared [4]. The relevant primary literature has expanded greatly and numerous major corrections have been made. With the benefit of these prior reviews, we are now in an improved position to appreciate the interconnected complexity of the various measurements. The work of the current IUPAC Task Group differs from the two prior reviews in that it doesn’t attempt to make recommendations on all known radical electrode potentials, but rather focuses on a subset that has been judged to be of greater importance. It also makes a greater effort to apply the principles of error propagation in assessing the various potentials. This document presents the results of the IUPAC Task Group as they relate to inorganic radicals. Of necessity, some careful consideration of organic radicals is also included, because in some cases the inorganic radical potentials are derived from measurements of equilibrium constants for reactions with organic radicals. Some of the standard potentials discussed here were presented at the “Medicinal Redox Inorganic Chemistry” conference held at the University of Erlangen-Nürnberg in 2013 [5].

2 Definitions and conventions

We limit the scope to those species, radical or otherwise, having sufficient lifetime to be vibrationally equilibrated with the solvent; this restriction allows the full forces of classical thermodynamics to be employed. We consider radicals to be species, either neutral or ionic, that bear an unpaired electron, and we exclude transition-metal complexes as a matter of convenience.

Use of the radical “dot” in chemical formulas to indicate radical species is redundant when the exact elemental composition and electronic charge of the species is specified, as is usually the case with the species in the current review. On the other hand, its use can be helpful for those who are not intimately familiar with the chemistry involved. In the present document, an effort has been made to use the dots consistently in the summary Tables, but in the supporting data sheets its use is less consistent. Both practices are in agreement with the current guidelines for inorganic nomenclature [6, 7].

By the term “standard electrode potential”, E°, we refer to half reactions of the following type:

Ox+neRed (1)

where n is an integer, often 1, either Ox or Red can be a radical, and E° is taken relative to the normal hydrogen electrode (NHE). On occasion we use here the shorthand expression “standard potential” to refer to standard electrode potentials. By convention, these reactions are always written as reductions – the associated potentials were previously known as “standard reduction potentials” – and they can be more complex than the simple example given above. Standard electrode potentials, rigorously speaking, refer to electrode potentials specified under conditions where all species are at unit activity. The standard state for such activities in the present review is usually the ideal 1 M aqueous solution. Species in solution that can also exist as gases, such as O2, can be referred to the 1 M aqueous standard state or to the 100 kPa (1 bar, ~1 atm) pressure standard state, and in such cases we have taken care to designate the state explicitly. For water the standard state is the pure solvent (at unit activity, not 55.5 M). Standard electrode potentials are related to equilibrium constants (Keq) through the relationship

E°=(RT/nF)lnKeq (2)

where Keq=aprodx/areacty, i.e. the product of the equilibrium activities of the products (aprod) divided by the product of the equilibrium activities of the reactants (areact), all raised to the power of their appropriate stoichiometric coefficients x and y. In practice, when one is dealing with radicals, it is usually easier to determine equilibrium constants than it is to measure equilibrium electrode potentials directly.

It is often necessary to report formal potentials, E°′, rather than standard potentials, because of a lack of reliable means to estimate the activity coefficients (γ). This is typically the case when the reaction involves ionic species and the measurement is performed at high ionic strength. Formal potentials are defined in the IUPAC Green Book, as in eq. 3 [8]:

Eeq=E°(RT/nF)νiln(ci/c°) (3)

Here, ci represents the concentration of species i, c° is a normalizing standard concentration (usually 1 M), and νi is that species’ stoichiometric coefficient. This definition is analogous to the Nernst equation except that it is expressed in terms of concentrations, and it allows for various species concepts. For example, in the case of S(IV) the species might be SO32,HSO3, SO2, or the sum of all. This definition also allows for E°′ values to be defined at specific nonstandard pH values. To avoid ambiguity in the species definitions, in the present work we generally write out the relevant half-cell reaction, and for reactions involving the proton we normally refer to pH 0. Formal potentials for the species’ under consideration here can often be related to standard potentials through the activity coefficients:

E°=E°+RT/nFln(γprodx/γreacty) (4)

Likewise, it is often useful or necessary to report formal equilibrium quotients (Kf) rather than equilibrium constants. These are related through the expression

Keq=Kf(γprodx/γreacty) (5)

Even further removed from the thermodynamic ideal are “midpoint” potentials, Em. These are Eeq values obtained when the oxidized and reduced species are at equal concentration. They are typically reported when the reaction is likely to be pH dependent and data are available at only a specific pH (often pH 7, E7). Note that midpoint potentials will be strongly concentration dependent when the stoichiometric coefficients, νi, are not equal. In principle, midpoint potentials can be derived from standard potentials, but the derivation requires knowledge of the pKa values involved. For a detailed discussion of these points the reader is referred to the introductory material in Wardman’s review on the potentials of radicals [1]. Related to midpoint potentials are apparent potentials, Eap°. Apparent potentials are defined at a specific pH, like midpoint potentials, but the activities of the oxidized and reduced species in the Nernst equation do not take the state of protonation into account. Thus, apparent potentials do not necessarily imply any knowledge of the pKa’s involved.

3 Methods for determination of standard potentials

A wide variety of methods have been employed to determine standard potentials involving inorganic radicals, as has been reviewed elsewhere [9]. A brief summary is given here.

  1. Electrochemical Methods.
    1. a, i)Potentiostatic methods have been used only in a few special cases, such as in the chemistry of ClO2·. The reason for this limitation is that inorganic radicals are usually highly reactive, so it is impossible to establish conditions where the concentrations are stable on the time frame of the measurements.
    2. a, ii)Cyclic voltammetry (CV) shortens the time frame of the electrochemical methods, and it has been used successfully in a few cases. However, the lifetimes of most inorganic radicals are too brief even for CV.
    3. a, iii)Pulse radiolysis provides an entry into very short time frames, and attempts have been made to apply electrochemical measurements to species generated by pulse radiolysis. Unfortunately, these efforts have not as yet provided reliable measurements or estimates of standard potentials involving inorganic radicals.
    4. a, iv)An intriguing technique is to generate photoelectrons in solution by laser irradiation of an electrode and then to use the electrode to probe the electrochemistry of the radicals generated from the photoelectrons. The method, however, remains to be developed as a reliable source of thermodynamic data.
  2. Equilibrium Constant Measurements. The vast majority of standard electrode potentials summarized in this review have been obtained by Hess’ law methods where an equilibrium constant is measured somehow and combined with other thermochemical data to derive the reported potential. These derivations frequently make use of published values of ΔfG°, and this review normally makes the assumption that the values published in the NBS tables [10] are of reference quality. The various types of radical equilibrium constants used in these derivations are described below.
    1. b, i)Solubilities. The solubilities of  ClO2· and NO have been measured unambiguously because solutions of these radicals are stable. These solubility measurements then afford a method to determine the solution-phase standard potentials from the known gas-phase energetics of these species. The solubility of  NO2· has also been measured, but in this case the method is complex and relies on an understanding of the kinetics of dissolution and of disproportionation of NO2·(aq).
    2. b, ii)Homolysis Equilibria. Homolysis at sigma bonds generally yields radicals, and determination of these equilibrium constants can lead rather directly to electrode potentials. In the case of S2O42 it has been possible to measure the homolysis equilibrium constant by direct ESR detection of the  SO2· radicals. Homolysis equilibrium constants have been measured for unstable species such as N2O4 by use of transient methods such as flash photolysis and pulse radiolysis to establish the equilibria. A third method is to derive the equilibrium constant from the ratio of the forward and reverse rate constants (Keq = kf/kr); an example of this method is provided by S2O82, where kf is determined from the kinetics of its oxidation of various substrates and kr is obtained from transient measurements on the recombination of  SO4·.
    3. b, iii)Electron-Transfer Equilibria. Equilibrium constants for electron-transfer reactions are probably the most widely used data for deriving standard potentials involving radicals. A typical example is the reaction of O3 with ClO2:
      O3+ClO2O3·+ClO2· (6)
      In this case the equilibrium constant was determined from the ratio of kf and kr, and it was used to determine the standard one-electron electrode potential of O3 relative the well-established reference potential of ClO2·. Equilibrium constants have also been measured for a substantial number of electron transfer reactions where neither of the component half reactions can be considered as having a reliable reference potential; nevertheless, such reactions are valuable in determining standard potentials, although the thermochemical derivations are necessarily more lengthy.
    4. b, iv)Acid/Base Equilibria. Proton-transfer reactions can be crucial in understanding the reactivity of radicals, as is exemplified by superoxide. HO2· has a pKa of 4.8. It is thermodynamically unstable with respect to disproportionation. Disproportionation via the reaction of HO2· with itself or O2· is very fast. However, direct disproportionation via reaction of O2· with itself is undetectably slow, so alkaline solutions of O2· are remarkably persistent. Determinations of pKa’s have been performed for a significant number of radicals, and they have been performed by a large suite of techniques. These pKa’s have been used in a large number of derivations of radical standard potentials, and, because of their intrinsic importance, they are summarized below in Table 3.
    5. b, v)Hemicolligation Equilibria. Reactions in which radicals bind to non-radical species are defined as hemicolligations. They can occur between a radical and its reduced form that produce a symmetrical radical adduct or between a radical and some other non-radical to form a non-symmetrical adduct. Two prominent such reactions are
      I·+II2· (7)
      and
      HO·+ClClOH· (8)
      Reactions of this type can have a profound effect on the net reactivity of the radicals, and they are often unavoidable in reactive systems. Equilibrium constants have been measured for a good number of hemicolligation reactions, have been used extensively in deriving radical standard potentials, and are summarized in Table 4.
    6. b, vi)Nucleophilic Displacement Equilibria. In these reactions a nucleophile displaces another nucleophile from a radical. A typical example is
      I+(SCN)2·ISCN·+SCN (9)
      Although these reactions can be considered as equivalent to the sum of two hemicolligations, their equilibrium constants often can be more easily measured than those of the component hemicolligations. These displacement equilibria are important in the present review primarily for their use in deriving standard potentials through thermochemical cycles.
  3. Methods Involving Estimates. For certain important radicals there is no complete experimental thermochemical cycle available, and portions of the cycle must be obtained by making reasonable estimates. An important example is the hydrogen atom: although equilibrium constants have been measured for reactions that convert the aqueous hydrogen atom into other species (notably the hydrated electron), none of these reactions connects to a suitable reference redox couple. The best current solution to the problem is to make an estimate of the solvation energy of the hydrogen atom and then combine this estimate with other reliable data to derive the H+/H· electrode potential. There is good reason to believe that the uncertainties introduced in this example are relatively small. In general the current report relies on such thermochemical estimates only when direct experimental data are unavailable.
  4. Quantum Calculations. It is becoming increasingly common to use quantum calculations to obtain radical electrode potentials. The methods typically entail a relatively accurate calculation of the energetics of the gas-phase radical and another calculation of the radical solvation energy. It has recently been shown that these computational methods can fail disastrously [11], so the present review makes little use of them.

4 Criteria for selection of recommended data

The recommended values in the Tables of this report are based on results published in the peer-reviewed scientific literature. The Task Group has reviewed these primary publications to confirm their plausibility, scientific soundness, and adherence to established chemical principles. When there are multiple independent reports on the same results, the individual reports have been compared to determine the degree of agreement among them, and to identify outliers and assess whether there is just cause for rejecting them. Individual reports may be rejected because the experimental method or conditions are insufficiently documented and the method has been shown to be unreliable. Non-rectifiable errors have been identified in the data handling, or the results are not internally consistent. In cases where there are multiple acceptable reports of a given result, the reviewers have assigned a subjective weighting to each report based on an assessment of the care taken in the experiments and the typical accuracy of the method. These filtered results are then averaged, optimized, and their uncertainties assigned as described below.

5 Uncertainties

In the present review, all recommended data [E° values (Table 1), pKa’s (Table 3), ΔfG° values (Table 2), hemicolligation equilibrium constants (Table 4)] are presented with associated uncertainties in two significant digits, up to 19. These uncertainties are given as ±1σ, and they are intended to indicate the best estimate of the overall uncertainty as arising from all contributions. Typically the least of these contributions are the statistical fluctuations in the direct measurements of a given quantity. Much more important are systematic errors, many of which are difficult to anticipate. Many of the recommended data are derived by combining various thermochemical quantities, and hence propagation of error must be taken into account. The level of uncertainty in the NBS ΔfG° values is frequently underappreciated in the broader chemical community. For some results there are multiple independent reports for the same quantity, for example as with the pKa of HO·; in such situations each individual report is examined for plausibility and technical excellence, outliers are rejected, then remaining reports are averaged, and a subjective assessment of the uncertainty is assigned. The specific rationale for these assignments is provided in the detailed data sheets appended. In the language of metrology, these uncertainty estimates are of Type A (from statistical treatment of repeated measurements) and Type B (estimates from experience), and ISO standards mandate that both types of uncertainties are equally valid and can be freely combined; these concepts are briefly reviewed elsewhere [12].

6 Use of thermochemical networks

As is discussed above, a large number of radical equilibrium constants of various types have been measured and combined with the standard potentials of reference couples to derive standard potentials of radicals through Hess’ law-type calculations. Some of these equilibria share common radical species and hence lead to thermochemical networks. These networks can be very useful for determining radical standard potentials. When the networks are linear or branched it is a simple process to combine adjacent equilibrium constants with appropriate reference potentials to derive potentials of interest; in such calculations appropriate attention must be paid to the cumulative effects of error propagation. Occasionally there are loops in the networks, which form closed thermochemical cycles. These closed thermochemical cycles afford excellent tests of the data, because the associated Gibbs energy changes must sum to zero. Failure to meet this criterion within reasonable uncertainty limits is a signal that at least some of the data are seriously flawed. When this criterion is met, suitable adjustments of the individual equilibrium constants (within their uncertainties) can be made to achieve exact closure. Assessment and use of these thermochemical networks can be performed manually, although consistent results are difficult to achieve when the networks are large. Larger networks can be solved in an automated and consistent way through use of appropriate computerized approaches such as ATcT, Active Thermochemical Tables [13]. In the present review, some of the recommended data are the result of manual assessment while others have been generated by use of ATcT. In its standard format, the ATcT software is optimized for evaluation of gas-phase enthalpies; for the present purposes the ATcT software has been adapted to work with Gibbs energies in solution. The method thus consists of defining the reaction network, converting relevant reference potentials and equilibrium constants to ΔG° values and associated uncertainties, and localizing the thermochemical network by incorporating auxiliary values of ΔfG° (usually from the NBS tables) as network termini; the ATcT output then consists of a set of optimized ΔfG° values and uncertainties for the radicals of interest, and these are then combined with reference values of ΔfG° to derive the E° values. This method has been applied to a subset of the data presented here, as described in Data Sheet 7.

7 Important reference couples

There are a few redox couples that have attained particular significance, either because of their centrality as reference couples for determining other standard potentials or because of their general importance in inorganic radical chemistry. Aspects of these redox couples are highlighted here.

The ClO2·/ClO2 couple (ClO2·+eClO2) is of great importance in this review because it has been used extensively in establishing equilibria with other radicals and because its standard potential is known with unusually high accuracy. These characteristics are largely a consequence of the remarkable stability of both  ClO2· and ClO2 in aqueous solution and the facile inter-conversions between them. As a result, it is not difficult to obtain reversible electrochemistry with this couple, perform classical equilibrium potentiostatic measurements, and extrapolate them to conditions of thermochemical ideality. The outcome is a reliable and genuinely standard value for E°.

The hydroxyl radical is of general importance because it is one of the three radicals intrinsic to water (HO·, H·, and eaq), it is the only one of the three to have its electrode potential determined without extra-thermodynamic assumptions or approximations, and occupies a central position in the largest of the thermochemical networks in this review. Its potential has been determined by two independent routes. The first of these has its origins in thallium chemistry and rests specifically on the redox potentials of the unstable species Tl2+, which are determined relative to the well-established Fe3+/Fe2+ reference potential. The second route depends on the pKa of HO·, the hemicolligation of O·– with O2, the electron-transfer equilibrium of O3· with ClO2·, and the use of the ClO2·/ClO2 redox couple as a reliable reference. The excellent agreement between these two routes provides strong support for the recommended potential of this important species.

Br2· is widely used as an oxidant, and equilibrium constants have been measured for at least 12 of its reactions. Its electrode potential is considered well established because of the good agreement between several independent derivations. Notable among these are a derivation based on the equilibrium constants for 1) its reaction with OH to form BrOH·– and bromide and 2) the dissociation of BrOH·– to form Br and HO·.

The trinitrogen(·) radical, N3·, is important generally because it is often used as a mild nonspecific oxidant. It holds special importance in this review because of its frequent use in establishing redox equilibria that can be used to establish electrode potentials that involve radicals. The standard electrode potential of the N3·/N3 redox couple has been determined in several ways with good agreement. It has been measured electrochemically (under irreversible conditions), and it has been derived from equilibria with four other reference redox couples ([IrCl6]2–/[IrCl6]3–, [Ru(bpy)3]3+/[Ru(bpy)3]2+, ClO2·/ClO2, and Br2·/2Br). Note that use of N3·/N3 as a reference potential at very high azide concentrations requires consideration of the association between N3· and N3 (Data Sheet 86).

There are also some organic radicals that are important in providing reference potentials for the inorganic radicals recommended here. These include species such as the phenoxyl radical, TEMPO, the tryptophan radical cation, and the promethazine (phenothiazine) radical. Evaluations of their electrode potentials are provided in the supplementary data sheets.

8 Tables

Table 1

Inorganic standard electrode potentials.

Half-reactionElectrode potential/VData Sheet #
Table 1.1: Electron, Hydrogen and Oxygen
e ⇋ e·–(aq)–2.88 ± 0.021.1
H+ + e ⇋ H·(aq)–2.31 ± 0.031.3
O(3P) + e ⇋ O·–+1.6 ± 0.12
O(3P) + H+ + e ⇋ HO·+2.3 ± 0.12
O2(g) + e ⇋ O2·−–0.35 ± 0.023
O2(aq) + e ⇋ O2·−–0.18 ± 0.023
1ΔgO2(g) + e ⇋ O2·−+0.64 ± 0.014
1ΔgO2(aq) + e ⇋ O2·−+0.81 ± 0.014
O2(g) + e + H+ ⇋ HO2·–0.07 ± 0.023
O2(aq) + H+ + e ⇋ HO2·+0.10 ± 0.023
HO2· + e + H+ ⇋ H2O2+1.46 ± 0.015
H2O2 + e + H+ ⇋ HO· + H2O+0.80 ± 0.016
HO· + e + H+ ⇋ H2O+2.730 ± 0.0177
OH· + e ⇋ OH+1.902 ± 0.0177
O3(g) + e ⇋ O3·–+0.91 ± 0.0223
O3(aq) + e ⇋ O3·–+1.03 ± 0.0223
Table 1.2: Halogens
Table 1.2a: Chlorine
Cl· (aq) + e ⇋ Cl(aq)+2.432 ± 0.0187
Cl2·–(aq) + e ⇋ 2Cl(aq)+2.126 ± 0.0177
Cl2(aq) + e ⇋ Cl2·–(aq)+0.666 ± 0.0177
ClOH·–(aq) + e ⇋ Cl + OH(aq)+1.912 ± 0.0187
ClOH·–(aq) + e + H+(aq) ⇋ Cl(aq) + H2O(l)+2.740 ± 0.0187
HOCl(aq) + e ⇋ ClOH·–(aq)+0.25 ± 0.087
ClO2·(aq) + e ⇋ ClO2+0.935 ± 0.00324
ClO3·(aq) + e ⇋ ClO3(aq)+2.38 ± 0.037
ClO·(aq) + e ⇋ ClO(aq)+1.39 ± 0.0325
Table 1.2b: Bromine
Br2·–(aq) + e ⇋ 2Br(aq)+1.63 ± 0.0226
Br2(aq) + e ⇋ Br2·–(aq)+0.55 ± 0.0226
Br·(aq) + e ⇋ Br(aq)+1.96 ± 0.0226
BrO2·(aq) + e ⇋ BrO2(aq)+1.290 ± 0.00540
Table 1.2c: Iodine
I2·– + e ⇋ 2I+1.05 ± 0.0245
I· + e ⇋ I+1.35 ± 0.0245
I2(aq) + e ⇋ I2·–+0.19 ± 0.0245
Table 1.3: Chalcogens
SO4·–(aq) + e ⇋ SO42–(aq)+2.437 ± 0.0197
S2O82–(aq) + e ⇋ SO4·–(aq) + SO42–(aq)+1.44 ± 0.087
SO3·–(aq) + e ⇋ SO32–(aq)+0.73 ± 0.0259
SO5·–(aq) + e ⇋ SO52–+0.81 ± 0.0166
S2O3·–(aq) + e ⇋ S2O32–+1.35 ± 0.0371
S4O6•3–(aq) + e ⇋ 2S2O32–+1.10 ± 0.0171
HS·(aq) + H+ + e ⇋ H2S(aq)+1.54 ± 0.0377
S·– + e + H+ ⇋ HS+1.33 ± 0.0377
S·– + e + 2H+ ⇋ H2S(aq)+1.74 ± 0.0377
HS·(aq) + e ⇋ HS+1.13 ± 0.0377
HS2 + e ⇋ HS2·2––1.13 ± 0.0577
SeO3·– + e ⇋ SeO32–+1.68 ± 0.0378
SeO3·– + H+ + e ⇋ HSeO3+2.18 ± 0.0378
TeO3·– + e ⇋ TeO32–+1.74 ± 0.0379
TeO3·– + H+ + e ⇋ HTeO3+2.31 ± 0.0379
Table 1.4: Group 5
NO3·(aq) + e ⇋ NO3(aq)+2.466 ± 0.0197
N3·(aq) + e ⇋ N3(aq)+1.33 ± 0.0180
NO·(aq) + H+ + e ⇋ HNO(aq)–0.15 ± 0.0222
HNO(aq) + H+ + e ⇋ H2NO·(aq)+0.52 ± 0.0487
H2NO· + 2H+ + e ⇋ NH3OH++1.253 ± 0.01087
H2NO· + H+ + e ⇋ NH2OH+0.900 ± 0.01087
NO2·(aq) + e ⇋ NO2+1.04 ± 0.0288
PO3·2– + H+ + e ⇋ HPO32–+1.54 ± 0.0496
H2PO4· + e ⇋ H2PO4+2.75 ± 0.0197
Table 1.5: Group 4
CO2(aq) + e ⇋ CO2·––1.90 ± 0.0298
CO3·–(aq) + e ⇋ CO32–+1.57 ± 0.0399
CO2·– + H+ + e ⇋ HCO2+1.52 ± 0.03100
SCN· + e ⇋ SCN+1.61 ± 0.02101
(SCN)2·– + e ⇋ 2SCN+1.30 ± 0.02101
Table 1.6: Group 3
Tl2+ + e ⇋ Tl++2.225 ± 0.00721
Tl3+(aq) + e ⇋ Tl2+(aq)+0.34 ± 0.087
TlOH+(aq) + e + H+(aq) ⇋ Tl+(aq) + H2O(l)+2.507 ± 0.0137
TlOH2+(aq) + e ⇋ TlOH+(aq)+0.12 ± 0.087
TlOH2+(aq) + e + H+(aq) ⇋ Tl2+(aq) + H2O(l)+0.40 ± 0.087
Table 1.7: Zn, Cd, Hg
HgCl2(aq) + e ⇋ HgCl(aq) + Cl–0.55 ± 0.02102
Table 2

Gibbs energies of formation, ΔfG°.

RadicalΔfG°/kJ mol–1Data Sheet #
eaq+278 ± 21.1
O·–+93.1 ± 1.72
OH·+26.3 ± 1.67
O2·–+33.8 ± 1.93
HO2·(aq)+7 ± 23
O3·–+75 ± 223
H·(aq)+223 ± 21.1
Cl·(aq)+103.4 ± 1.77
Cl2·–(aq)–57.3 ± 1.67
ClOH·–(aq)–104.0 ± 1.77
ClO·(aq)+97 ± 325
ClO2·(aq)+110 ± 1024
ClO3·(aq)+221.6 ± 37
Br2·––51 ± 226
Br·+85 ± 226
BrO2·(aq)+152 ± 440
BrOH·––93 ± 226
BrSCN·–+129 ± 326
I2·––2.1 ± 1.945
I·+78.8 ± 245
IOH·––82.7 ± 245
S·–+140 ± 377
HS·+121 ± 377
HSS·2–+129 ± 477
SO3·––416 ± 259
SO4·–(aq)–509.4 ± 1.87
SO5·–(aq)–506 ± 366
S2O3·––392 ± 871
S4O6·3––939 ± 871
SeO3·––202 ± 378
HSeO4·2––358 ± 378
TeO3·––214 ± 379
HTeO4·2––394 ± 379
TeO4·3––319 ± 379
N3·(aq)+476 ± 880
NO·(aq)+102.0 ± 0.290
H2NO·(aq)+66 ± 387
NO2·(aq)+62.3 ± 0.588
NO3·(aq)+126.7 ± 1.87
CO2·––205 ± 298
CO3·––373 ± 399
SCN·+248 ± 2101
(SCN)2·–+310 ± 2101
ISCN·–+152 ± 245
Tl2++182.3 ± 1.27
TlOH+–27.6 ± 1.37
Table 3

Inorganic radical pKas and related hydrolysis.

ReactionKa/MpKaData Sheet #
H·(aq) ⇋ e(aq) + H+(2.48 ± 0.24) × 10–101.2
OH·(aq) ⇋ O·– + H+11.7 ± 0.1116
HO2·(aq) ⇋ O2·– + H+4.8 ± 0.13
HO3·(aq) ⇋ O3·– + H+No recommendation23
Cl·(aq) + H2O(l) ⇋ ClOH·– + H+5 × 10–6, within a factor of 27
Br·(aq) + H2O(l) ⇋ BrOH·– + H+10.50 ± 0.0726
I·(aq) + H2O(l) ⇋ IOH·– + H+13.3 ± 0.545
HS·(aq) ⇋ S·– + H+3.4 ± 0.777
HS4O6·2– ⇋ S4O6·3– + H+6.271
NH2OH·+ ⇋ NH2O· + H+<–5105
NH2O· ⇋ NHO·– + H+12.6 ± 0.3105
HPO3·– ⇋ PO3·2– + H+5.75 ± 0.05106
H2PO3· ⇋ HPO3·– + H+1.1107
H3PO3·+ ⇋ H2PO3· + H+54107
H2PO4· ⇋ HPO4·– + H+5.7 ± 0.4108
HPO4·– ⇋ PO4·2– + H+8.9 ± 0.2108
HPO5·– ⇋ PO5·2– + H+3.4 ± 0.2109
As(OH)4· ⇋ As(OH)3O·– + H+7.38 ± 0.06110
As(OH)4· ⇋ HAsO3·– + H2O + H+3.85 ± 0.05110
HAsO3·– ⇋ AsO3·2– + H+7.81 ± 0.04110
HCO2· ⇋ CO2·– + H+NR100
HCO3· ⇋ CO3·– + H+< 099
SCN· + H2O ⇋ HOSCN·– + H+12.5 ± 0.1111
Tl2+ + H2O(l) ⇋ TlOH+ + H+(1.7 ± 0.3) × 10–57
Table 4

Hemicolligation equilibria.

ReactionK/M–1Data Sheet #
O2(aq) + O·– ⇋ O3·–(1.4 ± 0.1) × 10623
Cl·(aq) + Cl ⇋ Cl2·–(1.4 ± 0.2) × 10510
OH·(aq) + Cl ⇋ ClOH·–0.70 ± 0.1312
Br·(aq) + Br ⇋ Br2·–(3.9 ± 1.2) × 10533
OH·(aq) + Br ⇋ BrOH·–3.2 × 102 within factor of 234
I·(aq) + I ⇋ I2·–1.35 × 10552
S·– + SH ⇋ HSS·2–(9 ± 2) × 103117
S2O3·– + S2O32– ⇋ S4O6·3–Log K = 4.1 ± 0.571
N3·(aq) + N3 ⇋ N6·–0.24 ± 0.0885
HAsO3·– + H2O ⇋ As(OH)3O·–pK = 3.53 ± 0.11110
SCN·(aq) + SCN ⇋ (SCN)2·–(2.0 ± 0.3) × 105101
S2O3·– + SCN ⇋ SCNS2O3·2–1.2 × 103 within a factor of 275
Tl(aq) + Tl+ ⇋ Tl2+140 ± 7112
Tl+ + OH·(aq) ⇋ TlOH+(5.8 ± 1.0) × 10319
Tl2+ + Cl ⇋ TlCl+(6.2 ± 0.7) × 104113
TlCl+ + Cl ⇋ TlCl2(1.9 ± 0.4) × 103114
TlCl2 + Cl ⇋ TlCl313 ± 3115

Acknowledgments

We thank IUPAC, ETH & ETH Stiftung for financial support of this project. The work at Argonne National Laboratory was supported by the US Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences and Biosciences under Contract No. DE-AC02-06CH11357. This material is partially based upon work at Brookhaven National Laboratory supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences, and Biosciences under contract DE-AC02-98CH10886.

References

  • [1]

    P. Wardman. J. Phys. Chem. Ref. Data18, 1637 (1989).

  • [2]

    D. M. Stanbury. Adv. Inorg. Chem.33, 69 (1989).

  • [3]

    S. Steenken. “Electron transfer equilibria involving radicals and radical ions in aqueous solutions”, in Landolt-Börnstein, New Series, Vol. 13e, H. Fischer (Ed.), p. 147. Springer-Verlag, New York (1985).

  • [4]

    J. J. Warren, T. A. Tronic, J. M. Mayer. Chem. Rev.110, 6961 (2010).

  • [5]

    D. A. Armstrong, R. E. Huie, S. Lymar, W. H. Koppenol, G. Merenyi, P. Neta, D. M. Stanbury, S. Steenken, P. Wardman. Bioinorg. React. Mech.9, 59 (2013).

    • PubMed
    • Export Citation
  • [6]

    N. G. Connelly, T. Damhus, R. M. Hartshorn, A. T. Hutton. Nomenclature of Inorganic Chemistry. IUPAC Recommendations 2005, Royal Society of Chemistry, Cambridge (2005).

  • [7]

    W. H. Koppenol. Pure Appl. Chem.72, 437 (2000).

  • [8]

    E. R. Cohen, T. Cvitaš, T. G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, A. Mills, F. Pavese, M. Quack, J. Stohner, H. L. Strauss, M. Takami, A. J. Thor. Quantities, Units and Symbols in Physical Chemistry, 3rd ed., p. 70, RSC Publishing, Cambridge, UK (2007).

    • Crossref
    • Export Citation
  • [9]

    D. M. Stanbury. “Measurement of reduction potentials of inorganic radicals in aqueous solution”, in General Aspects of the Chemistry of Radicals, Z. B. Alfassi (Ed.), p. 347. John Wiley & Sons, New York (1999).

  • [10]

    D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, R. L. Nuttall. J. Phys. Chem. Ref. Data11 (Suppl. 2), 2-1–2-392 (1982).

  • [11]

    G. A. Poskrebyshev, V. Shafirovich, S. V. Lymar. J. Phys. Chem. A112, 8295 (2008).

    • Crossref
    • Export Citation
  • [12]

    B. Ruscic. Int. J. Quantum Chem.114, 1097 (2014).

  • [13]

    B. Ruscic, R. E. Pinzon, M. L. Morton, G. von Laszevski, S. J. Bittner, S. G. Nijsure, K. A. Amin, M. Minkoff, A. F. Wagner. J. Phys. Chem. A108, 9979 (2004).

    • Crossref
    • Export Citation

Footnotes

Note

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Footnotes

Supplemental Material

The online version of this article (DOI: 10.1515/pac-2014-0502) offers supplementary material, available to authorized users. The supplementary material consists of Data Sheets 1–117 and Supplementary Data Sheets S1–S12, 275 pages.

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  • [1]

    P. Wardman. J. Phys. Chem. Ref. Data18, 1637 (1989).

  • [2]

    D. M. Stanbury. Adv. Inorg. Chem.33, 69 (1989).

  • [3]

    S. Steenken. “Electron transfer equilibria involving radicals and radical ions in aqueous solutions”, in Landolt-Börnstein, New Series, Vol. 13e, H. Fischer (Ed.), p. 147. Springer-Verlag, New York (1985).

  • [4]

    J. J. Warren, T. A. Tronic, J. M. Mayer. Chem. Rev.110, 6961 (2010).

  • [5]

    D. A. Armstrong, R. E. Huie, S. Lymar, W. H. Koppenol, G. Merenyi, P. Neta, D. M. Stanbury, S. Steenken, P. Wardman. Bioinorg. React. Mech.9, 59 (2013).

    • PubMed
    • Export Citation
  • [6]

    N. G. Connelly, T. Damhus, R. M. Hartshorn, A. T. Hutton. Nomenclature of Inorganic Chemistry. IUPAC Recommendations 2005, Royal Society of Chemistry, Cambridge (2005).

  • [7]

    W. H. Koppenol. Pure Appl. Chem.72, 437 (2000).

  • [8]

    E. R. Cohen, T. Cvitaš, T. G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, A. Mills, F. Pavese, M. Quack, J. Stohner, H. L. Strauss, M. Takami, A. J. Thor. Quantities, Units and Symbols in Physical Chemistry, 3rd ed., p. 70, RSC Publishing, Cambridge, UK (2007).

    • Crossref
    • Export Citation
  • [9]

    D. M. Stanbury. “Measurement of reduction potentials of inorganic radicals in aqueous solution”, in General Aspects of the Chemistry of Radicals, Z. B. Alfassi (Ed.), p. 347. John Wiley & Sons, New York (1999).

  • [10]

    D. D. Wagman, W. H. Evans, V. B. Parker, R. H. Schumm, I. Halow, S. M. Bailey, K. L. Churney, R. L. Nuttall. J. Phys. Chem. Ref. Data11 (Suppl. 2), 2-1–2-392 (1982).

  • [11]

    G. A. Poskrebyshev, V. Shafirovich, S. V. Lymar. J. Phys. Chem. A112, 8295 (2008).

    • Crossref
    • Export Citation
  • [12]

    B. Ruscic. Int. J. Quantum Chem.114, 1097 (2014).

  • [13]

    B. Ruscic, R. E. Pinzon, M. L. Morton, G. von Laszevski, S. J. Bittner, S. G. Nijsure, K. A. Amin, M. Minkoff, A. F. Wagner. J. Phys. Chem. A108, 9979 (2004).

    • Crossref
    • Export Citation