1
IUPAC Technical Report 1
PAC-REP-14-05-02 2
3
Standard Electrode Potentials Involving Radicals in 4
Aqueous Solution: Inorganic Radicals 5
6
7
IUPAC Task Group on Radical Electrode Potentials 8
9
David A. Armstrong (deceased) (task group member) 10
Department of Chemistry, University of Calgary, Alberta, Canada 11
12
Robert E. Huie (task group member) 13
formerly of the Physical and Chemical Properties Division, National Institute of Standards and 14
Technology, Gaithersburg, MD 20899, USA 15
16
Willem H. Koppenol (task group member) 17
Institute of Inorganic Chemistry, Swiss Federal Institute of Technology, CH-8093 Zürich, 18
Switzerland 19
20
Sergei V. Lymar (task group member) 21
Chemistry Department, Brookhaven National Laboratory, Upton NY 11973, USA 22
23
Gábor Merényi (task group member) 24
Department of Applied Physical Chemistry, The Royal Institute of Technology, S-10044, 25
Stockholm 70, Sweden 26
27
Pedatsur Neta (task group member) 28
Physical and Chemical Properties Division, National Institute of Standards and Technology, 29
Gaithersburg, MD 20899, USA 30
31
Branko Ruscic 32
Chemical Sciences and Engineering Division, Argonne National Laboratory, Argonne, IL, 33
60439, USA, and Computation Institute, University of Chicago, Chicago, IL, 60637, USA 34
35
David M. Stanbury (task group leader) 36
BNL-111793-2016-JA
2
Department of Chemistry and Biochemistry, Auburn University, Auburn, AL 36849, USA 37
38
Steen Steenken (task group member) 39
Mülheim, Germany 40
41
Peter Wardman (task group member) 42
formerly of the University of Oxford, Gray Cancer Institute, Department of Oncology, Old Road 43
Campus Research Building, Roosevelt Drive, Oxford OX3 7DQ, U.K. 44
45
Abstract: Recommendations are made for standard potentials involving select inorganic 46
radicals in aqueous solution at 25 °C. These recommendations are based on a critical and 47
thorough literature review and also by performing derivations from various literature reports. 48
The recommended data are summarized in tables of standard potentials, Gibbs energies of 49
formation, radical pK
a
’s, and hemicolligation equilibrium constants. In all cases, current best 50
estimates of the uncertainties are provided. An extensive set of Data Sheets is appended that 51
provide original literature references, summarize the experimental results, and describe the 52
decisions and procedures leading to each of the recommendations. 53
54
Contents 55
56
1. Introduction 57
2. Definitions and Conventions 58
3. Methods for Determination of Standard Potentials 59
4. Criteria for Selection of Recommended Data 60
5. Uncertainties 61
6. Network Problems 62
7. Important Reference Couples 63
Acknowledgments 64
References 65
Tables 66
Data Sheets 1-117 67
Supplementary Data Sheets S1-S12 68
69
70
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1. Introduction 71
72
Radicals, both organic and inorganic, tend to be highly reactive. Nevertheless, they are 73
widely encountered as intermediates in chemical reactions; their individual reactivities are 74
central among the factors that determine the rates and products of the overall reactions in which 75
they are involved. For reactions where the radicals are present in the aqueous phase, electrode 76
potentials involving the radicals are among the most powerful indicators of reactivity. Electrode 77
potentials involving radicals are often more directly related to reactivity than are electrode 78
potentials of non-radicals, because the former more often correlate to specific steps in the 79
reaction mechanisms. 80
The determination of radical electrode potentials has greatly expanded in the last three 81
decades, largely through the application of pulse radiolysis and flash photolysis. These are 82
techniques that are well suited to the generation of transient radicals and the measurement of 83
their reaction equilibria. It is largely through the manipulation of the radical equilibrium 84
constants that the current bounty of radical electrode potentials has been obtained. 85
In 1989 two comprehensive reviews on radical standard potentials appeared. Wardman’s 86
review emphasized organic radicals [1], while Stanbury’s review considered inorganic radicals 87
exclusively [2]. Both of those reviews are now rather dated. Another valuable compendium is 88
Steenken’s 1985 list of electron transfer equilibria involving radicals [3]. A related review 89
emphasizing H-atom bond dissociation “free” (Gibbs) energies has also appeared [4]. The 90
relevant primary literature has expanded greatly and numerous major corrections have been 91
made. Moreover, with the benefit of these prior reviews, we are now in an improved position to 92
appreciate the interconnected complexity of the various measurements. The work of the current 93
IUPAC Task Group differs from those two prior reviews in that it doesn’t attempt to make 94
recommendations on all known radical electrode potentials but rather it focuses on a subset that 95
has been judged to be of greater importance, and it makes a greater effort to apply the principles 96
of error propagation in assessing the various potentials. This document presents the results of the 97
IUPAC Task Group as they bear on inorganic radicals. Of necessity, some careful consideration 98
of organic radicals is also included, because in some cases the inorganic radical potentials are 99
derived from measurements of equilibrium constants for reactions with organic radicals. Some of 100
the standard potentials discussed here were presented at the "Medicinal Redox Inorganic 101
Chemistry" conference held at the University of Erlangen-Nürnberg in 2013 [5]. 102
103
2. Definitions and Conventions 104
105
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We limit the scope to those species, radical or otherwise, having sufficient lifetime to be 106
vibrationally equilibrated with the solvent; this restriction allows the full forces of classical 107
thermodynamics to be employed. We consider radicals to be species either neutral or ionic that 108
bear an unpaired electron, and we exclude transition-metal complexes as a matter of 109
convenience. 110
Use of the radical “dot” in chemical formulas to indicate radical species is redundant 111
when the exact elemental composition and electronic charge of the species is specified, as is 112
usually the case with the species in the current review. On the other hand, its use can be helpful 113
for those who are not intimately familiar with the chemistry involved. In the present document, 114
an effort has been made to use the dots consistently in the summary Tables, but in the supporting 115
data sheets its use is less consistent. Both practices are in agreement with the current guidelines 116
for inorganic nomenclature [6, 7]. 117
By the term “standard electrode potential”, E°, we refer to half reactions of the following 118
type: 119
120
Ox + ne
–
⇌ Red (1) 121
122
where n is an integer often 1, either Ox or Red can be a radical, and E° is taken relative to the 123
normal hydrogen electrode (NHE). On occasion we use here the shorthand expression “standard 124
potential” to refer to standard electrode potentials. By convention, these reactions are always 125
written as reductions – the associated potentials were previously known as “standard reduction 126
potentials” − and they can be more complex than the simple example given above. Standard 127
electrode potentials, rigorously speaking, refer to electrode potentials specified under conditions 128
where all species are at unit activity. The standard state for such activities in the present review is 129
usually the ideal 1 M aqueous solution. Species in solution that can also exist as gases, such as 130
O
2
, can be referred to the 1 M aqueous standard state or to the 100 kPa (~1 atm) pressure 131
standard state, and in such cases we have taken care to designate the state explicitly. For water 132
the standard state is the pure solvent (at unit activity, not 55.5 M). Standard electrode potentials 133
are related to equilibrium constants (K
eq
) through the relationship 134
135
E° = –(RT/nF)lnK
eq
(2) 136
137
where K
eq
=
Π
a
prod
x
/
Π
a
react
y
, i.e., the product of the equilibrium activities of the products (a
prod
)
138
divided by the product of the equilibrium activities of the reactants (a
react
), all raised to the power 139
of their appropriate stoichiometric coefficients x and y. In practice, when one is dealing with 140
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radicals, it is usually easier to determine equilibrium constants than it is to measure equilibrium 141
electrode potentials directly. 142
It is often necessary to report formal potentials, E°', rather than standard potentials 143
because of a lack of reliable means to estimate the activity coefficients (
γ
). This is typically the 144
case when the reaction involves ionic species and the measurement is performed at high ionic 145
strength. Formal potentials are defined in the IUPAC Green Book as in eq 3 [8]: 146
147
E
eq
= E°' – (RT/nF)Σ
ν
i
ln(c
i
/c°) (3) 148
149
Here, c
i
represents the concentration of species i, c° is a normalizing standard concentration 150
(usually 1 M), and
ν
i
is that species stoichiometric coefficient. This definition is analogous to the 151
Nernst equation except that it is expressed in terms of concentrations, and it allows for various 152
species concepts. For example, in the case of S(IV) the species might be SO
3
2–
, HSO
3
–
, SO
2
, or 153
the sum of all. This definition also allows for E°' values to be defined at specific nonstandard pH 154
values. To avoid ambiguity in the species definitions, in the present work we generally write out 155
the relevant half-cell reaction, and for reactions involving the proton we normally refer to pH 0. 156
Formal potentials for the species’ under consideration here can often be related to standard 157
potentials through the activity coefficients: 158
159
E° = E°' + RT/nFln(
Πγ
prod
x
/
Πγ
react
y
) (4) 160
161
Likewise, it is often useful or necessary to report formal equilibrium quotients (K
f
) rather than 162
equilibrium constants. These are related through the expression 163
164
K
eq
= K
f
(
Πγ
prod
x
/
Πγ
react
y
) (5) 165
166
Even further removed from the thermodynamic ideal are “midpoint” potentials, E
m
. 167
These are E
eq
values obtained when the oxidized and reduced species are at equal concentration. 168
They are typically reported when the reaction is likely to be pH dependent and data are available 169
at only a specific pH (often pH 7, E
7
). Note that midpoint potentials will be strongly 170
concentration dependent when the stoichiometric coefficients,
ν
i
, are not equal. In principle, 171
midpoint potentials can be derived from standard potentials, but the derivation requires 172
knowledge of the pK
a
values involved. For a detailed discussion of these points the reader is 173
referred to the introductory material in Wardman’s review on the potentials of radicals [1]. 174
Related to midpoint potentials are apparent potentials, E°
ap
. Apparent potentials are defined at a 175
specific pH, like midpoint potentials, but the activities of the oxidized and reduced species in the 176
