Bard a j , stratmann m , scholz f encyclopedia of electrochemistry, inorganic chemistry volume 7 (2006)

3 1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials.. 9 1.2.6 The Dependence of the Potential of Cell Reaction on the Composition 9 1.2.7 Determination of the S

Gy orgy Inzelt

Department of Physical Chemistry, E otv os Lor´and University, Budapest, Hungary

1.1 Introduction 3

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 5

1.2.1 The Problem of the Initial and Final States 6

1.2.2 Standard States and Activities 7

1.2.3 Electrolytes, Mean Activity 7

1.2.4 Electrochemical Potential, Galvani Potential Difference 8

1.2.5 Calculation of Ecell0 from Calorimetric Data and
G0,
H0,
S0from Electrochemical Measurements 9

1.2.6 The Dependence of the Potential of Cell Reaction on the Composition 9 1.2.7 Determination of the Standard Electrode Potential (E0) from Electrochemical Measurements 11

1.2.8 Determination of E0from Thermodynamic Data 11

1.2.9 The Formal Potential (Eo
c ) 12

1.2.10 The Determination of Eo
c by Cyclic Voltammetry 13

References 15

1.1

Introduction

Practically in every general chemistry

text-book, one can find a table presenting

the Standard (Reduction) Potentials in

two parts, indicating the reaction

condi-tion: acidic solution and basic solution

In most cases, there is another table

ti-tled Standard Chemical Thermodynamic

Properties (or Selected Thermodynamic

Values) The former table is referred to in

a chapter devoted to Electrochemistry (or

Oxidation – Reduction Reactions), while a

reference to the latter one can be found

in a chapter dealing with Chemical

Ther-modynamics (or Chemical Equilibria) It

is seldom indicated that the two types

of tables contain redundant information

since the standard potential values of a cell

standard molar free (Gibbs) energy change



where n is the charge number of the cell

re-action, which is the stoichiometric number

equal to the number of electrons

trans-ferred in the cell reaction as formulated,

equi-librium constant of the reaction, R is the gas constant, and T is the thermodynamic

standard potential of the electrode

reac-tion (or sometimes called half-cell reacreac-tion),

which is tabulated in the tables mentioned

It is the standard potential of the reaction

in a chemical cell which is equal to thestandard potential of an electrode reaction(abbreviated as standard electrode poten-

oxidation of molecular hydrogen to vated protons

sol-1

hydrated proton in aqueous solutionwithout specifying the hydration sphere

It means that the species being oxidized is

related to a reduction This is the reasonwhy we speak of reduction potentials Inthe opposite case, the numerical value

would differ It should be mentioned that

in old books, for example, in Latimer’sbook [1], the other sign convention wasused; however, the International Union

of Pure and Applied Chemistry (IUPAC)has introduced the unambiguous andauthoritative usage in 1974 [2, 3]

Although the standard potentials, at least

in aqueous solutions, are always related to

reaction (2), that is, the standard

hydro-gen electrode (SHE) (see Ch 18.3), it does

not mean that other reference systems

electro-chemically accessible reaction cannot be

determined by measuring cell potential,

equi-librium The cell as a whole is not at

equilibrium (for if the cell reaction reaches

however, no current flows through the

ex-ternal circuit, with all local charge-transfer

equilibria across phase boundaries (except

at electrolyte–electrolyte junctions) and

lo-cal chemilo-cal equilibria within phases being

established

val-ues in the tables cited are determined

by calorimetry and electrochemical

mea-surements, respectively It is not so; the

way of tabulations mentioned serves

prac-tical purposes only Several

have been determined electrochemically,

especially when these measurements were

easier or were more reliable On the other

mentioned have been determined mostly

by calorimetric measurements since in

many cases – owing to kinetic reasons, too

slow or too violent reactions – it has been

impossible to collect these data by using

the measurement of the electric potential

difference of a cell at suitable conditions

Quotation marks have been used in

a thermodynamic quantity

In some nonaqueous solvents, it is

nec-essary to use a standard reaction other

than the oxidation of molecular

hydro-gen At present, there is no general

choice of a standard reaction

(refer-ence electrode) Although in some cases

the traditional reference electrodes (e.g.saturated calomel, SCE, or silver/silverchloride) can also be used in organic sol-vents, much effort has been taken to findreliable reference reactions The systemhas to meet the following criteria:

1 The reaction should be a one-electrontransfer

2 The reduced form should be a tral molecule, and the oxidized form

neu-a cneu-ation

3 The two components should have largesizes and spherical structures, that

practically independent from the nature

of the solvent (the free energy of iontransfer from one solution to the other

The ferrocene/ferrocenium reference

these requirements fairly well [4–6]

so on

the nonaqueous solvent is also quently used It yields stable potentials in

in some cases its application is limited by

a chemical reaction with the solvent

values for simple inorganic reactions in

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 5

aqueous solutions mostly involving metals

and their ions, oxides and salts, as well as

some other important elements (H, N, O,

S, and halogens) In special books (series),

compli-cated reactions, for example, with the

par-ticipation of metal complexes, and organic

compounds [8–13] The last authoritative

reference work (on the standard potential

in aqueous solutions) [13] – which has

re-placed the classic book of Latimer in this

role – appeared in 1985

on rather old reports The

thermody-namic data have been continuously

re-newed by the US National Institute for

Standards and Technology (NIST, earlier

Technology) and its reports supply reliable

data, which are widely used by the

scien-tific community [14] The numerical values

of the quantities have also been changed

because of the variation of the standard

states and constants Therefore, it is not

different depending on the year of

publi-cation of the books Despite the – usually

slight – difference in the data and their

predicting the course of any redox

reac-tions including electrode processes In the

next subchapter, a short survey of the

ther-modynamic basis of the standard, formal,

and equilibrium potentials, as well as the

experimental access of these data, is given

1.2

Thermodynamic Basis of the Standard,

Formal, and Equilibrium Potentials

In the tables of standard potentials,

usually the equation of electrode (half-cell)

reactions are displayed, for example,

or just an abbreviated form is used:

chemical (cell) reaction formulated byneutral chemical species is

as heterogeneous reactions involving acharge-transfer step at the anode andthe cathode, respectively, while electronsmove through the external circuit, that

is, electric current flows until the tion reaches its equilibrium In galvanic

reac-cells, the electric current (I ) is used for

energy production Technically it is sible to measure the electric potential

pos-difference (E) between the electrodes or

more exactly between the same lic terminals attached to the electrodes

both charge-transfer reactions is high, eachelectrode is at equilibrium, despite thefact that a small current flows There is

no equilibrium at electrolyte–electrolytejunctions; however, in many cases thisjunction potential can be diminished to

a small value (<1 mV) From this

condi-tion, it follows that the accuracy of the

determination of E0 values is limited

to ca 0.1–1 mV, depending on the

sys-tem studied However, the experimental

error of the calorimetric determination

is not much smaller Especially, the

calculation of low temperature values is

sometimes problematic The

thermody-namic quantities are usually given with

an accuracy of 0.1–0.001% For instance,

should be taken into consideration that

the problem is not the possible accuracy

of the measurement of heat (temperature)

accurately

There are several theoretical and

practi-cal difficulties regarding the determination

of the exact values of the standard

poten-tial, which will be pointed out below

1.2.1

The Problem of the Initial and Final States

The free energy functions are defined by

explicit equations in which the variables

are functions of the state of the system

The change of a state function depends

only on the initial and final states It

follows that the change of the Gibbs free

energy (
G) at fixed temperature and

pressure gives the limiting value of the

electrical work that could be obtained

from chemical transformations
G is

the same for either the reversible or

the explosively spontaneous path (e.g

of (electrical) work is different Under

reversible conditions

Equation (5) shows the fundamental lationship between Gibbs free energychange of the chemical reaction and thecell potential under reversible conditions(potential of the electrochemical cell reac-tion)

re-The calculation of
G from the caloric

data is straightforward, independent of thepath, that is, whether the reaction takesplace in a single step or through a series ofsteps by using Hess’s law and Nernst heattheorem [15–17] Furthermore, we can

calculate
G for the reaction of interest

from the combination of other reactionsinvolved for which the thermodynamicdata are known However, both theinitial and final states in many casesare hypothetical Even in the case ofmeasurements executed very carefully andaccurately, there might be problems indefining the states of the compounds,

or even metals (!) that take part in thereaction

This is the situation not only forreactions in which many componentsare involved and the product distributionstrongly depends on the ratio of theparticipants (e.g in reaction (3), at lower

which seem to be relatively simple For

the presence of HCl, the whole series

has been identified in aqueous solutions,and polymerization, hydrolysis, as well asformation of mixed valence compounds

Another example is the widely used

elec-trode, where s is for solid and cr is

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 7

for crystalline Cells containing this

elec-trode can be used for the measurements

high accuracy; however, the usual

prepa-ration methods yield a two-phase mixture

with the tetragonal form

values determined in different

laborato-ries with 1 mV or more An interesting

problem has been addressed recently In

the last 20 years, new scanning probe

tech-niques have been developed With the help

of the electrochemical scanning tunneling

microscopy (ESTM), it is possible to

han-dle metal clusters It was found that for

clusters containing n < 20 Ag atoms, the

2 V than that obtained for the bulk metal

In fact, this is not surprising since

ther-modynamic laws are valid only for high

numbers of atoms, and the small clusters

do not show the properties of a bulk metal,

for example, there is no delocalization, and

the band formation needs a large number

of atoms The effect was explained by the

greater surface energy of small clusters

compared to that of the bulk metal [23, 24]

1.2.2

Standard States and Activities

For ideal multicomponent systems, a

sim-ple linear relationship exists between the

of the mole fraction of solvent and solute,

hypotheti-cal standard state of unit mole fraction of

species i Equation (6) is strictly valid only

in the limit of infinite dilution in the case ofsolutions In order to describe the behav-ior over the entire range of composition

as a dimensionless quantity, the activity

ac-tivity can be expressed on different scalesdepending on the choice of the composi-tion variable (mole fraction, molality, etc.)Mostly, the molality (moles of solute/1 kg

the amount of concentration or, shortly,concentration (moles of solute/volume of

usage of molality is more correct because

in this case, the possible volume changecauses no problem; however, in the major-ity of the experiments in liquid phase there

The deviation from the ideal behavior isdescribed conveniently by a function called

the pressure Depending on the state of

vary; however, its standard state should be

i.1.2.3

Electrolytes, Mean Activity

Electrolytes contain ions in more orless solvated (hydrated) forms and sol-vent molecules; however, undissociatedmolecules or ion associations, and so onmay also be present The composition of

a solution containing one or more

elec-trolytes can be described defining the mole

ratio or any other concentration of each

ionic species Most of the formulae have a

close resemblance to those of the

nonelec-trolytes There is, however, one important

difference, namely, the concentrations of

all the ionic species are not independent

because the solution as a whole is

elec-trically neutral The electrical neutrality of

the solution can be written as



i

species i, which is a positive integer for

the ratio of the charge carried by ion i to the

charge carried by the proton No solution

of a strong (fully dissociated) electrolyte is

even approximately ideal even at highest

dilution at which accurate measurements

can be made; the infinitely dilute solution

constitutes an idealized limiting case The

activity of the ionic species i can be given as

a i,c = γ i,c ci/c0 or a i,m = γ i,m mi/m0

( 10)

electrolyte can be determined by

mea-surements, since in all processes, the

electroneutral condition prevails Note that

the indefiniteness of the individual ity coefficient is in connection with theimpossibility of the determination of thesingle electrode potential

activ-Mean activity coefficient of electrolyte B

in solution is given by



(µB– µB0) νRT



( 11)

solute B in a solution containing B and

potential of B in its standard state (seeTable 1) A mole of the solute is defined in

a way that it contains a group of ions of twokinds carrying an equal number of positive

Electrochemical Potential, Galvani Potential Difference

The chemical potential of an ionic speciesdepends on the electrical state of the phase

(β), that is,

µ βi = ˜µiβ − ziF ϕ β ( 14)

Tab 1 Standard states of mixtures

(asolvent= 1) At infinite dilution γsolvent → 1

that has the activity that such a solution would have if it obeyed the limiting law It is set by extrapolation of Henry’s law on the given basis The temperature and pressure are the same as those of the solution under consideration.

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 9

potential of phase β.

It should be emphasized that the

arbitrary from strict thermodynamic point

of view

The general condition of equilibrium of

a species i between phases α and β is

i = ˜µ β

The electrical potential difference

(Gal-vani potential difference)

can be measured only when the two phases

have identical composition, for example,

between two terminal copper wires (Cu,

Cu’) attached to the electrodes

ϕCu− ϕCu = ˜µCu



e − ˜µCu e

F

where e is for the electron

1.2.5

Calculation of Ecell 0 from Calorimetric Data

and
G0,
H0,
S0 from Electrochemical

Measurements

By combining Eq (1) with the

Gibbs-Helmholtz relation we obtain



Ecell0 +T ∂E

0 cell

so as to obtain the value of
S from

the temperature function of the heat

However, the magnitude of T
S is often small, compared to that of
G and
H , and the relative error in
S determined

in this way can be large On the other

are made over a range of temperatures, the

values are determined under conditionswhen the temperature of the whole cell isvaried, that is, both electrodes are at thesame temperature (isothermal cell) It ispossible to keep the reference electrode atroom temperature; however, in this case,the Seebeck effect (electromotive force in

a thermocouple) appears It is another ample that thermodynamically – withoutfurther assumptions, simplifications, andconventions – only the whole cell (cell re-action) can be treated and interpreted

through the effect of the liquid junction

potential can be made negligible –

It follows that (for the sake of simplicity,

the indication of phases further on is

( 25)

when the reference system is the

oxida-tion of molecular hydrogen to solvated

(hydrated) protons The standard

elec-trode potential of the hydrogen elecelec-trode

is chosen as 0 V Thermodynamically it

means that not only the standard free

is zero – which is a rule in

thermody-namics (see Table 2) – but also that of

bar) It causes a difference in the

po-tential of the SHE of + 0.169 mV, that

is, this value has to be subtracted from

dif-ferent tables Since the large majority of

least 1 mV, this correction can be glected.) When all components are in their

Ecell= E0

accessible by any electrochemical surements, and only the mean activity can

mea-be determined The cell represented by thecell diagram

path is applied between the electrodes, orthe HCl solution is divided into two partsseparated by a diaphragm

In this case, the cell reaction is as follows

Tab 2 Standard states of pure substances

formation for any element is zero.

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 11

±= (γ±cHCl/c0)2=

(γ±mHCl/m0)2

1.2.7

Determination of the Standard Electrode

Potential (E0 ) from Electrochemical

The value of the standard potential

various HCl concentrations and then by

In dilute electrolytes, where the

Debye-H¨uckel limiting law prevails,

where A is a constant.

Taking into account Eq (30), we may

rewrite Eq (29) in the form

In this way, a more accurate

With the help of the calorimetric method,

for a given reaction, which is formulated

in such a way that the participating species

are electrically neutral compounds and notions in solution From other techniques(e.g mass spectrometry), the formation of

an ion in gaseous state can be obtained.However, in the latter case the solvation(hydration) energy of the individual ionspresent in the solution is inaccessible,since only the heat of hydration of anelectrolyte can be measured

considered as the standard chemical

chemical potential of formation of this ion,

as zero, arbitrarily When we want to

necessary to set up equilibrium betweenthe ions and the substance whose standardvalues are known This is most often thesolubility equilibrium

The solubility product is

and the entropy change can be obtained by

1.2.9

The Formal Potential (Ec o
)

fre-quently used The purpose of defining

formal potentials is to have a

‘‘condi-tional constant’’ that takes into account the

activity coefficients and side reaction

coef-ficients (chemical equilibria of the redox

species), since in many cases, it is

impos-sible to calculate the resulting deviations

because neither are the thermodynamic

equilibrium constants known, nor is it

possible to calculate the activity

coeffi-cients Therefore, the potential of the cell

reaction and the potential of the

elec-trode reaction are expressed in terms of

concentrations of the oxidized (ox) andreduced (red) forms, respectively TheNernst equation provides the relation-ship between the equilibrium electrodepotential and the composition of the elec-trochemically active species Note that theNernst equation can be used only at equi-librium conditions The formal potential issometimes called as conditional potentialindicating that it relates to specific condi-tions (e.g solution composition), whichusually deviate from the standard con-ditions In this way, the complex oracid–base equilibria are also considered,since the total concentrations of oxidizedand reduced species considered can be de-termined, for example, by potentiometrictitration; however, without a knowledge ofthe actual compositions of the complexes(see our example in Sect 1.2.1.) In the case

of potentiometric titration, the effect of thechange of activity coefficients of the elec-trochemically active components can bediminished by applying inert electrolyte

in high concentration (almost constantionic strength) If the solution equilibriaare known from other sources, it is rel-atively easy to include their parametersinto the respective equations related to

acid–base and the complex equilibria Inacid media, a general equation for the pro-ton transfer accompanying the electrontransfer is

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 13

The complex equilibria can be treated

in a similar manner; however, one should

of a metal complex depends on the pH and

ionic strength

The simplest and most frequent case is

the metal, which means that all the ligands

the complex and the ligand, respectively,

reaction (49) Under certain conditions

the complex and ν can be estimated from

plot by using the following equation:

E = Eo

c − RT

zF lnK−RT

zF lncLν ( 51)

Amalgam formation shifts the

equilib-rium potential of a metal (polarographic

direc-tion of higher potentials owing to thefree energy of the amalgam formation



+

RT nF



+

RT nF



concen-tration of the metal in the mercury It

respective diffusion coefficients

by the widely used electroanalytical niques (e.g polarography, cyclic voltam-metry [25]) The combination of the tech-niques is also useful It has beendemonstrated recently where potentiom-etry, coulometry, and spectrophotometryhave been applied [26] The case of thecyclic voltammetry is examined below

val-ues were determined in this way ever, reliable formal potentials can bedetermined only for electrochemically re-versible systems [28] For any reversibleredox system – provided that the electrodeapplied is perfectly inert, that is, there are

How-no chemical side reactions, How-no oxide

for-mation etc – the diagnostic criteria are as

follows:

1 the peak currents are equal,

Ipa= Ipc ( 54)

the scan rate

2 the difference of the peak potential,

nF = 57

n

and the peak potentials are independent of

the scan rate v,

coefficient of the respective species, it

follows

It must be emphasized again that the

simple, reversible redox reaction when

neither any experimental artifact nor

ki-netic effect (ohmic drop effect, capacitive

current, adsorption side reactions, etc.)

occurs, and macroscopic inlaid disc

elec-trodes are used, that is, the thickness of the

diffusion layer is much higher than that of

the diameter of the electrode

A special case is when the ically active components are attached tothe metal or carbon (electrode) surface

electrochem-in the form of mono- or multilayers,for example, oxides, hydroxides, insol-uble salts, metalloorganic compounds,transition-metal hexacyanides, clays, zeo-lites containing polyoxianions or cations,intercalative systems The submonolayers

of adatoms formed by underpotential position are neglected, since in this case,the peak potentials are determined bythe substrate–adatom interactions (com-pound formation) From the ideal surface

half-height of either the cathodic or anodic

wave, Γ is the apparent surface coverage of the electroactive species, A is the surface

respective peak current

where L is the layer (film) thickness, D is

the charge transport diffusion coefficient,

and t is the timescale of the experiment;

instead of a surface response, a regular fusional behavior develops, and thereforeEqs (57–59) can be applied

dif-The interactions within the surface layercan also affect the surface response;

1.2 Thermodynamic Basis of the Standard, Formal, and Equilibrium Potentials 15

change

Nevertheless, the mid-peak potentials

determined by cyclic voltammetry and

other characteristic potentials obtained

by different electroanalytical techniques

(such as pulse, alternating current, or

square wave voltammetries) supply

valu-able information on the behavior of the

redox systems In fact, for the

major-ity of redox reactions, especially for the

novel systems, we have only these values

(The cyclic voltammetry almost entirely

re-placed the polarography which has been

used for six decades from 1920

How-ever, the abundant data, especially the

useful sources for providing

informa-tion on the redox properties of different

systems.)

References

1 W M Latimer, Oxidation Potentials, 2nd

ed., Prentice-Hall, Englewood Cliffs, N.J,

1952.

2 R Parsons, Pure Appl Chem 1974, 37,

503.

3 I Mills, T Cvitas, Quantities, Units and

Sym-bols in Physical Chemistry, IUPAC, Blackwell

Scientific Publications, London, Edinburgh,

Boston, Melbourne, Paris, Berlin, Vienna,

6 M M Baizer, H Lund, (Eds.), Organic

Elec-trochemistry, Marcel Dekker, New York,

1983.

7 G Gritzner, Pure Appl Chem 1990, 62, 1839.

8 A J Bard, H Lund, (Eds.), The Encyclopedia

of Electrochemistry of Elements, Marcel Dekker,

New York, 1973–1986.

9 G Milazzo, S Caroli, Tables of Standard

Electrode Potentials, Wiley-Interscience, New

York, 1977.

10 G Charlot, A Collumeau, M J C Marchot,

Selected Constants Oxidation-Reduction tentials of Inorganic Substances in Aque- ous Solution, IUPAC, Batterworths, London,

Po-1971.

11 M Pourbaix, N de Zoubov, J van Muylder,

Atlas d’ Equilibres Electrochimiques a 25◦C,

Gauthier- Villars, Paris, 1963.

12 M Pourbaix, (Ed.), Atlas of Electrochemical Equilibria in Aqueous Solutions, Pergamon-

CEBELCOR, Brussels, 1966.

13 A J Bard, R Parsons, J Jordan, Standard Potential in Aqueous Solution, (Eds.), Marcel

Dekker, New York, 1985.

14 M W Case, Jr., Thermodynamical Tables

Nat Inst Stand Tech J Phys Chem Ref.

Data, Monograph G, 1998, pp 1–1951.

15 E A Guggenheim, Thermodynamics, North

Holland Publications, Amsterdam, 1967.

16 R A Robinson, R H Stokes, Electrolyte lutions, Butterworths Scientific Publications,

So-London, 1959.

17 I M Klotz, R M Rosenberg, Chemical modynamics, John Wiley, New York, Chich-

Ther-ester, Brisbane, Toronto, Singapore, 1994.

18 F A Cotton, G Wilkinson, C A Murillo

et al., Advanced Inorganic Chemistry, Wiley,

Encyclope-John Wiley, Chichester, 1994 Vol 7.

A Prakash Rao, Inorg Chem 1986, 25,

25 F Scholz, in Electrochemical Methods (Ed.:

F Scholz), Springer, Berlin, Heidelberg,

Chapter I 2.

26 M T Ram´ırez, A Rojas-Hern´andez, I

Gon-z´alez, Talanta 1997, 44, 31.

27 F Marken, A Neudeck, A M Bond, in

Electrochemical Methods (Ed.: F Scholz),

Springer, Berlin, Heidelberg, New York,

2002, 2005, pp 51–97, Chapter II 1.

28 G Inzelt, in Electrochemical Methods (Ed.:

F Scholz), Springer, Berlin, Heidelberg,

Chapter I 3.

2

Standard, Formal, and Other

Characteristic Potentials of

Selected Electrode Reactions

Gy orgy Inzelt

E otv os Lor´and University, Budapest, Hungary

2.1 Group 1 Elements 20

2.2 Group 2 Elements 22

2.3 Group 3 Elements 24

2.4 Group 4 Elements 30

2.5 Group 5 Elements 31

2.6 Group 6 Elements 32

2.7 Group 7 Elements 34

2.8 Group 8 Elements 36

2.9 Group 9 Elements 39

2.10 Group 10 Elements 41

2.11 Group 11 Elements 43

2.12 Group 12 Elements 47

2.13 Group 13 Elements 50

2.14 Group 14 Elements 53

2.15 Group 15 Elements 57

2.16 Group 16 Elements 63

2.17 Group 17 Elements 68

2.18 Group 18 Elements 73

Acknowledgment 73

References 74

Over the last 20–30 years not too much

effort has been made concerning the

determination of standard potentials It

is mostly due to the funding policy

all over the world, which directs the

sources to new and fashionable research

and practically neglects support for the

quest for accurate fundamental data A

notable recent exception is the work

described in Ref 1, in which the

phase) has been determined Besides the

measurements of electromotive force,

de-terminations of the solubility, solubility

products, osmotic coefficients, water

activ-ities, and mean activity coefficients have

been carried out and compared with the

previous data The detailed analysis reveals

that the uncertainties in some

funda-mental data such as the mean activity

The author recommends this

comprehen-sive treatise to anybody who wants to go

deeply into the correct determination of

There are only a few groups that

deal with the study of the

thermody-namics of the electrochemical cell

Be-sides Ref 1, it is appropriate to mention

Refs 2, 3, where the medium effects

and Ref 4, in which the influence ofthe activity of the supporting electrolyte

on the formal potentials of nium/ferrocene and decamethylferrice-nium/decamethylferrocene systems werestudied with the help of the following cell:

and TBA is tetra-n-butylammonium ion.

This chapter gives a selected compilation

of the standard and other characteristic(formal, half-wave) potentials, as well as

a compilation of the constant of bility and/or complex equilibria Mostly,data obtained by electrochemical mea-surements are given In the cases whenreliable equilibrium potential values can-not be determined, the calculated values(calcd) for the most important reactions arepresented The data have been taken exten-sively from previous compilations [5–13]where the original reports can be found,

solu-as well solu-as from handbooks [13–16], butonly new research papers are cited Theconstant of solubility and complex equilib-ria were taken from Refs 6–11, 13, 17–21.The oxidation states (OSs), ionization ener-gies (IEs) (first, second, etc.), and electronaffinities (EAs) of the elements and the

hydration enthalpy of some ions (
Hhydr)

sym-bol of elements, the atomic number (lower

index) and the mean relative atomic mass

(upper index), the values that correspond

either to the current best knowledge

(IU-PAC 2005) of the elements in natural

terrestrial sources or to the mass number

of the nuclide with the longest half-life, are

also indicated The electrode reactions and

equilibria are organized according to the

positions of the elements in the periodic

table, starting from hydrogen and group

1 to group 18, including lanthanides and

The standard potential of the hydrogen

electrode is taken as zero at all

tempera-tures by convention [24, 25] H does not

isomers (ortho and para forms) that have

significantly different physical and

chem-ical properties At ambient temperature,

para form becomes predominant below

200 K

Taking into account the ionization

298.15 K, the equilibrium potentials can

be calculated with the help of the Nernstequation at different pH values Since

At pH > 0, the Hammett acidity

If the peak potential does not shift as afunction of pH, it means that the hydrogenion activity is involved in the same way

as that characteristic of the hydrogen

conclusion can be drawn for the number

of hydrogen ions accompanying the redox

The equilibrium potential can be

2H2,

Be-sides Pt, Ir, Os, Pd, Rh, and Ru may beused Because of the dissociative adsorp-

overpotential is needed to cover the rather

2.1 Group 1 Elements 21

On the other hand, the metal–hydrogen

atom bond energy is not too high;

there-fore, it does not hinder the desorption

process

In aqueous solution, the potential

win-dow of stability of water is 1.23 V when

the hydrogen and oxygen evolution are

ki-netically hindered; therefore, it is possible

to achieve a higher cell potential Typical

examples are Hg and Pb, in which log

respec-tively

D+/1/2 D2couple

Since the properties (e.g

dissoci-ation energy, solvdissoci-ation enthalpy) of

2

1

potential under the same conditions will

be different The estimated value for the

reaction is given as follows:

Lithium (6.9413Li), OS: +1, 0; IE:

Sodium ( 22.98911Na), OS: +1, 0; IE:

Potassium ( 39.09819K), OS: +1, 0; IE:

Rubidium ( 85.46737Rb), OS: +1, 0; IE:

Cesium ( 132.90555Cs), OS: +1, 0; IE:

Beryllium (9.01214Be), OS: +2, (+1),

Barium (137.32756Ba), OS: +2, 0;

Lanthanum ( 138.90557La), OS: +3, 0; IE:

Pr (III)/Pr coexisting two

Pr (III)/Pr coexisting two phases:

The IE of all the actinides are estimated

Uranium ( 238.028992U), OS: +6, +5, +4,

Plutonium ( [244.0642]94Pu), OS:+7, +6, +5,

Americium ( [243.061]95Am), OS:+6, +5, +4,

Curium ( [247.07]96Cm), OS: (+4), +3, 0; IE:

Einsteinium ( [252.083]99Es), OS: (+4), +3,

val-is mainly due to the formation of ides and hydride films on the Ti surface,which causes it to behave as a noblemetal Titanium dissolves rapidly only

The experimental determination of

forma-tion of surface oxides and polymeric

species with oxo and hydroxo bridges

in the solution Hydrolysis practically

al-ways takes place even in strongly acidic

SCE (saturated calomel electrode)

Dawson-type V-substituted polyoxometalates can be

found in Ref 35 and the citations therein

in the form niobate anions, for example,

Chromium ( 51.99624Cr), OS: +6, +3, +2, 0;

Data for chromium amino carboxylate

complexes can be found in Ref 36

Solubility and complex equilibria:

In solution Mo(VI) exists in the form

Acid hydrolysis results in the formation of

>1) or [Mo36O112]8−, [H2Mo2O6]2+ (pH

heteropolyanions are formed, for example,

The determination of equilibrium

(stan-dard) potentials is rather problematic for

several reasons; for instance,

hydroly-sis and disproportionation reactions, the

existence of a large number of

strong dependence on pH and ionic

ex-change processes, and the instability of

the species in contact with water (e.g

oxy-gen evolution; however, these processes

are rather slow)

The formal potential of the substituted

ferrocenes can be found in Ref 38

which are present in acid solutions,

values, and the respective hydroxidesprecipitate Weak anion complexes such

formed

Solubility and complex equilibria:

Formal potentials of dinuclear and

hexanuclear Ru(II) bipyridine complexes

(40 redox processes!) are given in Ref 45

Osmium ( 190.2376 Os), OS:+8, +7, +6, +5,

Cobalt ( 58.93327 Co), OS: (+4), +3, +2, (+1),

(Formal potential of other substituted

Pc’s can also be found in Ref 46.)