volume 7 inorganic chemistry

11Standard Potentials

Gy..orgy Inzelt

Department of Physical Chemistry, E..otv

..os Lorand University, Budapest, Hungary

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

1.2 Thermodynamic Basis of the Standard, Formal, and EquilibriumPotentials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1.2.1 The Problem of the Initial and Final States . . . . . . . . . . . . . . . . . . 61.2.2 Standard States and Activities . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.3 Electrolytes, Mean Activity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71.2.4 Electrochemical Potential, Galvani Potential Difference . . . . . . . . . 81.2.5 Calculation of E 0cell from Calorimetric Data and G

0, H 0, S 0 fromElectrochemical Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.2.6 The Dependence of the Potential of Cell Reaction on the Composition 91.2.7 Determination of the Standard Electrode Potential (E 0) from

Electrochemical Measurements . . . . . . . . . . . . . . . . . . . . . . . . . 111.2.8 Determination of E 0 from Thermodynamic Data . . . . . . . . . . . . . 11

1.2.9 The Formal Potential (Eo

c ) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12

1.2.10 The Determination of Eo

c by Cyclic Voltammetry . . . . . . . . . . . . . 13References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

31.1Introduction

Practically in every general chemistry text-book, one can nd a table presentingthe Standard (Reduction) Potentials inaqueous solution at 25 C, sometimes intwo parts, indicating the reaction condi-tion: acidic solution and basic solution.In most cases, there is another table ti-tled Standard Chemical ThermodynamicProperties (or Selected ThermodynamicValues). The former table is referred to ina chapter devoted to Electrochemistry (orOxidation Reduction Reactions), while areference to the latter one can be foundin a chapter dealing with Chemical Ther-modynamics (or Chemical Equilibria). Itis seldom indicated that the two typesof tables contain redundant informationsince the standard potential values of a cellreaction (E 0cell) can be calculated from thestandardmolar free (Gibbs) energy change(G0) for the same reaction with a simplerelationship

E 0cell =G0

nF=(

RT

nF

)lnK (1)

where n is the charge number of the cell re-action, which is the stoichiometric numberequal to the number of electrons trans-ferred in the cell reaction as formulated,

F is the Faraday constant, K is the equi-librium constant of the reaction, R is thegas constant, and T is the thermodynamictemperature. However, E 0cell is not thestandard potential of the electrode reac-tion (or sometimes called half-cell reaction),which is tabulated in the tablesmentioned.It is the standard potential of the reactionin a chemical cell which is equal to thestandard potential of an electrode reaction(abbreviated as standard electrode poten-tial), E 0, when the reaction involves theoxidation of molecular hydrogen to sol-vated protons

12H2(g) H+(aq) + e (2)

The notation H+ (aq) represents thehydrated proton in aqueous solutionwithout specifying the hydration sphere.It means that the species being oxidized isalways the H2 molecule and E 0 is alwaysrelated to a reduction. This is the reasonwhy we speak of reduction potentials. Inthe opposite case, the numerical valueof E 0 would be the same but the signwould differ. It should be mentioned thatin old books, for example, in Latimersbook [1], the other sign convention wasused; however, the International Unionof Pure and Applied Chemistry (IUPAC)has introduced the unambiguous andauthoritative usage in 1974 [2, 3].

4 1 Standard Potentials

Although the standard potentials, at leastin aqueous solutions, are always related toreaction (2), that is, the standard hydro-gen electrode (SHE) (see Ch. 18.3), it doesnot mean that other reference systemscannot be used or G0 of any electro-chemically accessible reaction cannot bedetermined by measuring cell potential,Ecell, when both electrodes are at equi-librium. The cell as a whole is not atequilibrium (for if the cell reaction reachesits equilibrium then Ecell = Gcell = 0);however, no current ows through the ex-ternal circuit, with all local charge-transferequilibria across phase boundaries (exceptat electrolyteelectrolyte junctions) and lo-cal chemical equilibriawithin phases beingestablished.

One may think that G0 and E 0 val-ues in the tables cited are determinedby calorimetry and electrochemical mea-surements, respectively. It is not so; theway of tabulations mentioned serves prac-tical purposes only. Several thermody-namic quantities (G0,H 0,S 0 etc.)have been determined electrochemically,especially when these measurements wereeasier or were more reliable. On the otherhand, E 0 values displayed in the tablesmentioned have been determined mostlyby calorimetric measurements since inmany cases owing to kinetic reasons, tooslow or too violent reactions it has beenimpossible to collect these data by usingthe measurement of the electric potentialdifference of a cell at suitable conditions.Quotation marks have been used in writ-ing thermodynamic, as E 0 is per se alsoa thermodynamic quantity.

In some nonaqueous solvents, it is nec-essary to use a standard reaction otherthan the oxidation of molecular hydro-gen. At present, there is no generalchoice 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 ndreliable reference reactions. The systemhas to meet the following criteria:

1. The reaction should be a one-electrontransfer.

2. The reduced form should be a neu-tral molecule, and the oxidized forma cation.

3. The two components should have largesizes and spherical structures, thatis, the Gsolvation should be low andpractically independent from the natureof the solvent (the free energy of iontransfer from one solution to the otheris small).

4. Equilibrium at the electrode must beestablished rapidly.

5. The standard potential must not be toohigh so that solvents are not oxidized.

6. The system must not change structureupon electron transfer.

The ferrocene/ferrocenium referenceredox system at platinum fulllsthese requirements fairly well [46].Another system which has beenrecommended is bis(biphenyl)chromium(0)/bis(biphenyl)chromium (+1) (BCr+/BCr) [5, 7]. Several other systems havebeen suggested, and used sporadically,such as cobaltocene/cobaltocenium,tris(2,2-bipyridine) iron (I)/tris(2,2-bipyridine) iron (0), Rb+/Rb(Hg), andso on.

Ag/AgClO4 or AgNO3 dissolved inthe nonaqueous solvent is also fre-quently used. It yields stable potentials inmany solvents (e.g. in CH3CN); however,in some cases its application is limited bya chemical reaction with the solvent.

The tables compiled usually contain E 0

values for simple inorganic reactions in

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

aqueous solutions mostly involving metalsand their ions, oxides and salts, as well assome other important elements (H, N, O,S, and halogens). In special books (series),one can nd E 0 values for more compli-cated reactions, for example, with the par-ticipation of metal complexes, and organiccompounds [813]. The last authoritativereference work (on the standard potentialin aqueous solutions) [13] which has re-placed the classic book of Latimer in thisrole appeared in 1985.

Many values of G0,H 0,S 0, andE 0 found in these sources are basedon rather old reports. The thermody-namic data have been continuously re-newed by the US National Institute forStandards and Technology (NIST, earlierNBS = National Bureau of Standards andTechnology) and its reports supply reliabledata, which are widely used by the scien-tic community [14]. The numerical valuesof the quantities have also been changedbecause of the variation of the standardstates and constants. Therefore, it is notsurprising that E 0 values are somewhatdifferent depending on the year of publi-cation of the books. Despite the usuallyslight difference in the data and theiruncertainty, E 0 values are very useful forpredicting the course of any redox reac-tions including electrode processes. In thenext subchapter, a short survey of the ther-modynamic basis of the standard, formal,and equilibrium potentials, as well as theexperimental access of these data, is given.

1.2Thermodynamic 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,

MnO4(aq) + 8H+(aq) + 5e Mn2+(aq) + 4H2O E 0 = 1.51V (3)

or just an abbreviated form is used:E 0 (MnO4/Mn2+) = 1.51 V. The totalchemical (cell) reaction formulated byneutral chemical species is

2KMnO4(aq) + 3H2SO4(aq) + 5H2(g)= 2MnSO4(aq) + K2SO4(aq) + 8H2O

(4a)or considering charged reacting and prod-uct species is

2MnO4(aq) + 5H2(g) + 6H+ 2Mn2+(aq) + 8H2O (4b)

The peculiarity of the cell reaction isthat the oxidation and the reduction pro-cesses are separated in space and occuras heterogeneous reactions involving acharge-transfer step at the anode andthe cathode, respectively, while electronsmove through the external circuit, thatis, electric current ows until the reac-tion reaches its equilibrium. In galvaniccells, the electric current (I ) is used forenergy production. Technically it is pos-sible to measure the electric potentialdifference (E) between the electrodes ormore exactly between the same metal-lic terminals attached to the electrodeseven at the I = 0 condition (or by usinga voltmeter of high resistance at I 0).If the exchange current density (jo) ofboth charge-transfer reactions is high, eachelectrode is at equilibrium, despite thefact that a small current ows. There isno equilibrium at electrolyteelectrolytejunctions; however, in many cases thisjunction potential can be diminished toa small value (


determination of E 0 values is limitedto ca 0.11 mV, depending on the sys-tem studied. However, the experimentalerror of the calorimetric determinationof G0,H 0, and S 0 in many casesis not much smaller. Especially, the rel-ative error in S 0 is high and thecalculation of low temperature values issometimes problematic. The thermody-namic quantities are usually given withan accuracy of 0.10.001%. For instance,G0 = 477.2 kJ mol1 can be foundfor the formation of MnO4 ions [12]. Itshould be taken into consideration that0.1 kJ mol1 is equivalent to 1 mV. In fact,the problem is not the possible accuracyof the measurement of heat (temperature)or voltage since V or J can be measuredaccurately.

There are several theoretical and practi-cal difculties regarding the determinationof the exact values of the standard poten-tial, which will be pointed out below.

1.2.1The Problem of the Initial and Final States

The free energy functions are dened byexplicit equations in which the variablesare functions of the state of the system.The change of a state function dependsonly on the initial and nal states. Itfollows that the change of the Gibbs freeenergy (G) at xed temperature andpressure gives the limiting value of theelectrical work that could be obtainedfrom chemical transformations. G isthe same for either the reversible orthe explosively spontaneous path (e.g.H2 + Cl2 reaction); however, the amountof (electrical) work is different. Underreversible conditions

G = nFEcell (5)

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

The calculation of G from the caloricdata is straightforward, independent of thepath, that is, whether the reaction takesplace in a single step or through a series ofsteps by using Hesss law and Nernst heattheorem [1517]. Furthermore, we cancalculate G for the reaction of interestfrom the combination of other reactionsinvolved for which the thermodynamicdata are known. However, both theinitial and nal states in many casesare hypothetical. Even in the case ofmeasurements executed very carefully andaccurately, there might be problems indening 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 loweracidity the product is not Mn2+ (MnSO4)but MnO2; at higher acidity and KMnO4concentration the oxidation of H2O toO2 also occurs) but also for reactionswhich seem to be relatively simple. Forinstance, Ru3+ in aqueous solutions existsin the form Ru(H2O)63+; however, inthe presence of HCl, the whole seriesof complex ions, [RuIIICln(H2O)6n]3n

has been identied in aqueous solutions,and polymerization, hydrolysis, as well asformation of mixed valence compoundsoccur during reduction to Ru2+ [1821].

Another example is the widely usedPbO2(s, cr)|PbSO4(s, cr) reversible elec-trode, where s is for solid and cr is


for crystalline. Cells containing this elec-trode can be used for the measurementsof electromotive force (EMF Ecell) ofhigh accuracy; however, the usual prepa-ration methods yield a two-phase mixtureof tetragonal and orthorhombic PbO2(cr),with the tetragonal form predominat-ing [22]. This causes a variation in the E 0

values determined in different laborato-ries with 1 mV or more. An interestingproblem has been addressed recently. Inthe last 20 years, new scanning probe tech-niques have been developed.With the helpof the electrochemical scanning tunnelingmicroscopy (ESTM), it is possible to han-dle metal clusters. It was found that forclusters containing n < 20 Ag atoms, theE 0 value determined was less by almost2 V than that obtained for the bulk metal.In fact, this is not surprising since ther-modynamic laws are valid only for highnumbers of atoms, and the small clustersdo not show the properties of a bulk metal,for example, there is no delocalization, andthe band formation needs a large numberof atoms. The effect was explained by thegreater surface energy of small clusterscompared to that of the bulkmetal [23, 24].

1.2.2Standard States and Activities

For ideal multicomponent systems, a sim-ple linear relationship exists between thechemical potential (i) and the logarithmof the mole fraction of solvent and solute,respectively.

i =(

G

ni

)T ,p,nj =ni

= 0i + RT ln xi(6)

where ni and nj are the mole numbers ofthe components, xi is the mole fractionof component i, and 0i is the hypotheti-cal standard state of unit mole fraction of

species i. Equation (6) is strictly valid onlyin the limit of innite dilution in the case ofsolutions. In order to describe the behav-ior over the entire range of compositionas a dimensionless quantity, the activityfunction (ai) has been introduced. The 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 kgsolvent, mi = ni/rsolvent in mol kg1) andthe amount of concentration or, shortly,concentration (moles of solute/volume ofsolution, ci = ni/V in mol m3 or moldm3) are used by electrochemists. Theusage of molality is more correct becausein this case, the possible volume changecauses no problem; however, in the major-ity of the experiments in liquid phase thereis no volume change, and ci is certainlymore popular than mi.

The deviation from the ideal behavior isdescribed conveniently by a function calledactivity coefcient (i)

ai = i,mmi/m0i or ai = i,cci/c 0i (7)For the gases (it is of importance for gas

electrodes)

ai = fi/f 0 or ai = pi/p 0 (8)where f is for the fugacity and p is forthe pressure. Depending on the state ofreference, the numerical value of ai willvary; however, its standard state should bechosen in such a way that i = 0i .

1.2.3Electrolytes, 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 dening themoleratio or any other concentration of eachionic species. Most of the formulae have aclose resemblance to those of the nonelec-trolytes. There is, however, one importantdifference, namely, the concentrations ofall the ionic species are not independentbecause the solution as a whole is elec-trically neutral. The electrical neutrality ofthe solution can be written as

i

zimi = 0 or

zici = 0 (9)

where zi is the charge number of ionicspecies i, which is a positive integer forcations andnegative for anions. In fact, zi isthe ratio of the charge carried by ion i to thecharge carried by the proton. No solutionof a strong (fully dissociated) electrolyte iseven approximately ideal even at highestdilution at which accurate measurementscan be made; the innitely dilute solutionconstitutes an idealized limiting case. Theactivity of the ionic species i can be given as

ai,c = i,cci/c 0 or ai,m = i,mmi/m0(10)

However, only the mean activity (a)or mean activity coefcient () of anelectrolyte can be determined by mea-surements, since in all processes, theelectroneutral condition prevails. Note that

the indeniteness of the individual activ-ity coefcient is in connection with theimpossibility of the determination of thesingle electrode potential.

Mean activity coefcient of electrolyte Bin solution is given by

a = exp[(B 0B)

RT

](11)

where B is the chemical potential of thesolute B in a solution containing B andother species, and 0B is the chemicalpotential of B in its standard state (seeTable 1). A mole of the solute is dened ina way that it contains a group of ions of twokinds carrying an equal number of positiveand negative charges B = Kz++Az, and = + + , zii = 0. It follows that

a = a1/B = (a++ a )1/ (12)

and

= ( ++ )1/ (13)

1.2.4Electrochemical Potential, Galvani PotentialDifference

The chemical potential of an ionic speciesdepends on the electrical state of the phase(), that is,

i = i ziF (14)

Tab. 1 Standard states of mixtures

Solvent in solution The reference state is the pure solvent at the same temperature(asolvent = 1) At innite dilution solvent 1

Solute i in solution The reference state is a hypothetical state at xi = 1 orm = 1 mol kg1 or c = 1 mol dm3 solution, that is, a statethat has the activity that such a solution would have if itobeyed the limiting law. It is set by extrapolation of Henryslaw on the given basis. The temperature and pressure are thesame as those of the solution under consideration.


where i is the electrochemical potentialof ion i in phase , and is the innerpotential of phase .

It should be emphasized that thedecomposition of i into a chemical (i)and an electrical (ziF) component isarbitrary from strict thermodynamic pointof view.

The general condition of equilibrium ofa species i between phases and is

i = i (15)The electrical potential difference (Gal-

vani potential difference)

= i iziF

(16)

can bemeasured only when the two phaseshave identical composition, for example,between two terminal copper wires (Cu,Cu) attached to the electrodes.

Cu Cu = Cue Cue

F

= Ecell = EMF (17)where e is for the electron.

1.2.5Calculation of E 0cell from Calorimetric Dataand G0, H0, S0 from ElectrochemicalMeasurements

By combining Eq. (1) with the Gibbs-Helmholtz relation we obtain

H 0 = nF(E 0cell +

T E 0cell

T

)(18)

S 0 = nF(

E 0cell

T

)=

(G0

T

)p

(19)H can be determined calorimetrically,

so as to obtain the value of S from

the temperature function of the heat ca-pacities (Cp = (H/T )p = T (S/T )p).However, the magnitude of TS is oftensmall, compared to that of G and H ,and the relative error in S determinedin this way can be large. On the otherhand, if accurate measurements of EMFare made over a range of temperatures, thetemperature coefcient of Ecell providesa more accurate value of S. (EcellT )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 ina thermocouple) appears. It is another ex-ample that thermodynamically withoutfurther assumptions, simplications, andconventions only the whole cell (cell re-action) can be treated and interpreted.

1.2.6The Dependence of the Potential of CellReaction on the Composition

If the stoichiometric equation of the cellreaction is

i

i Ai = 0 (20)

where Ai is for the components and forthe phases

G =

i

i i (21)

At equilibrium between each contactingphases for the common constituents

i

i i = 0 (22)

If we consider a cell without liquidjunction which in fact is nonexistent,


through the effect of the liquid junctionpotential can be made negligible

G =

i

i i = nFEcell (23)

It follows that (for the sake of simplicity,the indication of phases further on isneglected)

Ecell = 1nF

i0 RT

nFi ln ai

= E 0cell RT

nFi ln ai (24)

If the reference electrode is the SHE

E 0cell=1

F

(0H+ 0.50H2

) 1

nFi

0i

(25)It has been mentioned that E 0cell = E 0

when the reference system is the oxida-tion of molecular hydrogen to solvated(hydrated) protons. The standard elec-trode potential of the hydrogen electrodeis chosen as 0 V. Thermodynamically itmeans that not only the standard freeenergy of formation of hydrogen (0H2 )is zero which is a rule in thermody-namics (see Table 2) but also that ofthe solvated hydrogen ion 0H+ = 0!. (Theold standard values of E 0 were cal-culated using p 0 = 1 atm = 101325 Pa.The new ones are related to 105 Pa (1bar). It causes a difference in the po-tential of the SHE of + 0.169 mV, that

is, this value has to be subtracted fromthe E 0 values given previously in dif-ferent tables. Since the large majority ofthe E 0 values have an uncertainty of atleast 1 mV, this correction can be ne-glected.) When all components are in theirstandard states (ai = 1 and p 0 = 1 bar)Ecell = E 0cell = E 0. However, ai is notaccessible by any electrochemical mea-surements, and only the mean activity canbe determined. The cell represented by thecell diagram

Cu(s)|Pt(s)|H2(g)|HCl(aq)|AgCl(s)|Ag(s)|Cu(s) (26)

p = 1 bar c = 1 mol dm3

is usually considered a cell without liquidjunction. It is not entirely true, since theelectrolyte is saturated with hydrogen andAgCl near the Pt and Ag|AgCl electrodes,respectively. In order to avoid the directreaction between AgCl and H2, a longpath 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

AgCl + 12H2 Ag + Cl + H+(27)

From Eq. (24)

Ecell = E 0Ag/AgCl RT

Fln aH+aCl (28)

Tab. 2 Standard states of pure substances

Solid Pure solid in most stable form at p 0 = 1 bar (100 kPa) and the speciedtemperature (T) (usually T = 298.15 K) the standard free energy offormation for any element is zero.

Liquid Pure liquid in most stable form at p 0 = 1 bar and T.Gas Pure gas at unit fugacity; for ideal gas, fugacity is unity at p 0 = 1 bar and

T (f = p for ideal gas).

The activity of a pure solid or pure liquid at p 0 = 1 bar is equal to 1 at any temperature.


where aH+aCl = a2 = (cHCl/c 0)2 =(mHCl/m0)2

1.2.7Determination of the Standard ElectrodePotential (E 0) from ElectrochemicalMeasurements

Considering Eq. (28) we may write

Ecell + 2RTF

lnmHCl/m0 = E 0Ag/AgCl

2RTF

ln (29)

The value of the standard potentialcan be determined by measuring Ecell atvarious HCl concentrations and then byextrapolation to mHCl 0, where 1, E 0 can be obtained.

In dilute electrolytes, where the Debye-Huckel limiting law prevails,

lg = AmHCl (30)where A is a constant.

Taking into account Eq. (30), we mayrewrite Eq. (29) in the form

Ecell + 2RTF

lnmHCl/m0 = E 0Ag/AgCl

+ 2RTF

A

mHCl (31)

In this way, a more accurate ex-trapolation to mHCl 0 can be madefrom the Ecell + 2RT

FlnmHCl/m

0 versus

A

mHCl plot.

1.2.8Determination of E 0 from ThermodynamicData

With the help of the calorimetric method,G0, H 0, and S 0 can be determinedfor a given reaction, which is formulatedin such a way that the participating species

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

For a simple metal, dissolu-tion/deposition

M+(aq) + 12H2 M(s) + H+(aq)(32)

In accordance with Eq. (25), the forma-tion of the chemical potential of the hy-drated ion, M+ (aq), can be determined as

E 0cell = E 0 1

nF0M+ (33)

since 0M = 0. However, 0M+ cannot beconsidered as the standard chemical poten-tial ofM+ ion. Itmay be called the standardchemical potential of formation of this ion,since0M+ is related to the formation of thehydrated hydrogen ion, and0H+ was takenas zero, arbitrarily. When we want to cal-culate E 0 from thermodynamic data, it isnecessary to set up equilibrium betweenthe ions and the substance whose standardvalues are known. This is most often thesolubility equilibrium.

M+A(s) +M+(aq) + A(aq)(34)

For the equilibrium of a solid electrolyteand its saturated solution, one can write

MA(s) = = MA(aq) (35)

Ks = exp[0MA(s) +0M 0A

RT

]

= a+M a

A

(a 0)(36)


The solubility product is

Ksp = c+M cA (37)and therefore,

Ks = Ksp(c 0)

(38)

The standard Gibbs energy of reaction(34) is

G0 = RT lnKs (39)and the entropy change can be obtained bythe temperature dependence of Ks .

1.2.9The Formal Potential (Eo

c )

Beside E 0cell and E0, the so-called for-

mal potentials, Eo

cell,c and Eoc , are fre-

quently used. The purpose of deningformal potentials is to have a condi-tional constant that takes into account theactivity coefcients and side reaction coef-cients (chemical equilibria of the redoxspecies), since in many cases, it is impos-sible to calculate the resulting deviationsbecause neither are the thermodynamicequilibrium constants known, nor is itpossible to calculate the activity coef-cients. Therefore, the potential of the cellreaction and the potential of the elec-trode reaction are expressed in terms ofconcentrations

Ecell = Eocell,c RT

nFi ln

ci

c 0(40)

E = Eoc RT

nFi ln

ci

c 0(41)

where

Eo

cell,c = E 0cell RT

nFi lni (42)

and

Eo

c = E 0 RT

nFi lni (43)

when SHE is the reference electrode(aH+ = (pH2/p 0) = 1). Equation (41) isthe well-known Nernst equation

E = Eoc +RT

nFln

coxox

credred

(44)

where is for the multiplication of theconcentrations 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 specic condi-tions (e.g. solution composition), whichusually deviate from the standard con-ditions. In this way, the complex oracidbase 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 caseof potentiometric titration, the effect of thechange of activity coefcients of the elec-trochemically active components can bediminished by applying inert electrolytein 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 toEo

c . The most common equilibria are the

acidbase and the complex equilibria. Inacid media, a general equation for the pro-ton transfer accompanying the electrontransfer is

Ox + ne + mH+ HmRed(mn)+

Eo

c (45)


HmRed(mn)+ Hm1Red(mn1)+

+ H+ Ka1 (46)Hm1Red

(mn1)+ Hm2Red

(mn2)+ + H+ Ka2(47)

and so on. For m = n = 2E = Eoc

+ RTnF

ln

(cox

cred

1 + Ka1aH+ + a2H+Ka1Ka2

)

(48)The complex equilibria can be treated

in a similar manner; however, one shouldnot forget that each stability constant (Ki)of a metal complex depends on the pH andionic strength.

The simplest and most frequent case iswhen metal ions (Mz+) can be reduced tothemetal, whichmeans that all the ligands(Lp ) will be liberated, that is,

ML(zn)+ (aq) + ze = M(s) + Lp(aq)(49)

In this case, the equilibrium potential isas follows:

E = Eoc,ML/M +RT

zFln

cML

cL(50)

where cML and cL are the concentrations ofthe complex and the ligand, respectively,and Eo

c,ML/M is the formal potential of

reaction (49). Under certain conditions(cM+ cL), the stability constant (K) ofthe complex and can be estimated fromthe equilibrium potential E versus ln cLplot by using the following equation:

E = Eoc RT

zFlnK RT

zFlncL (51)

Amalgam formation shifts the equilib-rium potential of a metal (polarographic

half-wave potential, E1/2) into the direc-tion of higher potentials owing to thefree energy of the amalgam formation(Gamal).

E =Eoc (

Gamal

nF

)

+(

RT

nF

)ln (cM + /cM) (52)

E1/2 = Eoc (

Gamal

nF

)

+(

RT

nF

)ln cM(sat) (53)

where cM(sat) is the saturation concen-tration of the metal in the mercury. Itis assumed that aHg is not altered, andDred = Dox, where Dred and Dox are therespective diffusion coefcients.

In principle, Eo

c can be determinedby the widely used electroanalytical tech-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.

1.2.10The Determination of Eo

c by Cyclic

Voltammetry

Cyclic voltammetry has perhaps becomethe most popular electroanalytical, elec-trochemical technique [23, 27], and manyreports have appeared in which Eo

c val-

ues were determined in this way. How-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


no chemical side reactions, no oxide for-mation etc. the diagnostic criteria are asfollows:

1. the peak currents are equal,

Ipa = Ipc (54)Ip is proportional to the square root of

the scan rate.2. the difference of the peak potential,

Epa Epc = 2.218 RTnF

= 57n

mV at 298 K (55)

and the peak potentials are independent ofthe scan rate v,

3. |Ep Ep/2| = 2.218RTnF

(56)

where Ep/2 is measured at half of the peakcurrent, Ip/2.

Since

Epc = Eoc 1.1RT

nF RT

2nFln(

Dox

Dred

)1/2(57)

Epa = Eoc + 1.1RT

nF+ RT

2nFln(

Dox

Dred

)1/2(58)

where Dox and Dred are the diffusioncoefcient of the respective species, itfollows

Eo

c = 0.5(Epa + Epc) (59)It must be emphasized again that the

mid-peak potential is equal to Eo

c for asimple, reversible redox reaction whenneither any experimental artifact nor ki-netic effect (ohmic drop effect, capacitivecurrent, adsorption side reactions, etc.)occurs, and macroscopic inlaid disc elec-trodes are used, that is, the thickness of thediffusion layer is much higher than that ofthe diameter of the electrode.

A special case is when the electrochem-ically active components are attached tothe metal or carbon (electrode) surfacein 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 submonolayersof adatoms formed by underpotential de-position are neglected, since in this case,the peak potentials are determined bythe substrateadatom interactions (com-pound formation). From the ideal surfacecyclic voltammetric responses,Eo

c can also

be calculated as

Eo

c = Epa = Epc (60)Other diagnostic criteria for the ideal

surface responses are as follows:

Ipa = Ipc (61)

Ip = n2F 2

4RTA (62)

and

Ep,1/2 = 3.53RTnF

(63)

where Ep,1/2 is the total width at half-height of either the cathodic or anodicwave, is the apparent surface coverage ofthe electroactive species, A is the surfacearea, is the scan rate, and Ip is therespective peak current.

If L (2 Dt)1/2 (64)where L is the layer (lm) thickness, D isthe charge transport diffusion coefcient,and t is the timescale of the experiment;instead of a surface response, a regular dif-fusional behavior develops, and thereforeEqs (5759) can be applied.

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


however, even so, Eo

c can be derivedin many cases, since only Ep,1/2 willchange.

Nevertheless, the mid-peak potentialsdetermined by cyclic voltammetry andother characteristic potentials obtainedby different electroanalytical techniques(such as pulse, alternating current, orsquare wave voltammetries) supply valu-able information on the behavior of theredox systems. In fact, for the major-ity of redox reactions, especially for thenovel systems, we have only these values.(The cyclic voltammetry almost entirely re-placed the polarography which has beenused for six decades from 1920. How-ever, the abundant data, especially thehalf-wave potentials, E1/2, are still veryuseful sources for providing informa-tion on the redox properties of differentsystems.)

References

1. W. M. Latimer, Oxidation Potentials, 2nded., 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, BlackwellScientic Publications, London, Edinburgh,Boston, Melbourne, Paris, Berlin, Vienna,1993.

4. Z. M. Koepp, H. Wendt, H. Strehlow,Z. Elektrochem. 1960, 64, 483.

5. G. Gritzner, J. Kuta, Pure Appl. Chem. 1984,56, 461.

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,MarcelDekker,New York, 19731986.

9. G. Milazzo, S. Caroli, Tables of StandardElectrode Potentials, Wiley-Interscience, NewYork, 1977.

10. G. Charlot, A. Collumeau, M. J. C. Marchot,Selected Constants. Oxidation-Reduction Po-tentials of Inorganic Substances in Aque-ous Solution, IUPAC, Batterworths, London,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 ElectrochemicalEquilibria in Aqueous Solutions, Pergamon-CEBELCOR, Brussels, 1966.

13. A. J. Bard, R. Parsons, J. Jordan, StandardPotential in Aqueous Solution, (Eds.), MarcelDekker, New York, 1985.

14. M. W. Case, Jr., Thermodynamical TablesNat. Inst. Stand. Tech. J. Phys. Chem. Ref.Data, Monograph G, 1998, pp. 11951.

15. E. A. Guggenheim, Thermodynamics, NorthHolland Publications, Amsterdam, 1967.

16. R. A. Robinson, R. H. Stokes, Electrolyte So-lutions, Butterworths Scientic Publications,London, 1959.

17. I. M. Klotz, R. M. Rosenberg, Chemical Ther-modynamics, John Wiley, New York, Chich-ester, Brisbane, Toronto, Singapore, 1994.

18. F. A. Cotton, G. Wilkinson, C. A. Murilloet al., Advanced Inorganic Chemistry, Wiley,New York, 1999, pp. 10101039.

19. S. E. Livingstone, in Comprehensive InorganicChemistry (Eds.: J. C. Bailar, M. J. Emeleus,R. Nyholm et al.,) Pergamon Press, Oxford,1973, pp. 11631370, Vol. 3.

20. B. Chandret, S. Sabo-Etienne, in Encyclope-dia of Inorganic Chemistry (Ed.: R. B. King),John Wiley, Chichester, 1994. Vol. 7.

21. M. M. Taqui Khan, G. Ramachandraiah,A. Prakash Rao, Inorg. Chem. 1986, 25,665.

22. J. G. Albright, J. A. Rard, S. Serna et al.,J. Chem. Thermodyn. 2000, 32, 1447.

23. A. J. Bard, L. R. Faulkner, ElectrochemicalMethods, John Wiley, New York, Chichester,Neinheim, Brisbane, Singapore, Toronto,2001.

24. A. Henglein, Ber. Bunsen-Ges. Phys. Chem.1990, 94, 600.

25. F. Scholz, in Electrochemical Methods (Ed.:F. Scholz), Springer, Berlin, Heidelberg,New York, 2002, 2005, pp. 928,Chapter I. 2.

26. M. T. Ramrez, A. Rojas-Hernandez, I. Gon-zalez, Talanta 1997, 44, 31.


27. F. Marken, A. Neudeck, A. M. Bond, inElectrochemical Methods (Ed.: F. Scholz),Springer, Berlin, Heidelberg, New York,2002, 2005, pp. 5197, Chapter II. 1.

28. G. Inzelt, in Electrochemical Methods (Ed.:F. Scholz), Springer, Berlin, Heidelberg,New York, 2002, 2005, pp. 2948,Chapter I. 3.

17

2Standard, Formal, and OtherCharacteristic Potentials ofSelected Electrode Reactions

Gy..orgy Inzelt

E..otv

..os Lorand 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

18 2 Standard, Formal, and Other Characteristic Potentials of Selected Electrode Reactions

2.16 Group 16 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

2.17 Group 17 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

2.18 Group 18 Elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74

19

Over the last 2030 years not too mucheffort has been made concerning thedetermination of standard potentials. Itis mostly due to the funding policyall over the world, which directs thesources to new and fashionable researchand practically neglects support for thequest for accurate fundamental data. Anotable recent exception is the workdescribed in Ref. 1, in which the stan-dard potential of the cell Zn(Hg)x (twophase)|ZnSO4(aq)|PbSO4(s)|Pb(Hg)x (twophase) has been determined. Besides themeasurements of electromotive force, de-terminations of the solubility, solubilityproducts, osmotic coefcients, water activ-ities, and mean activity coefcients havebeen carried out and compared with theprevious data. The detailed analysis revealsthat the uncertainties in some funda-mental data such as the mean activitycoefcient of ZnSO4, the solubility prod-uct of Hg2SO4, or even the dissociationconstant of HSO4 can cause uncertain-ties in the E 0 values as high as 34 mV.The author recommends this comprehen-sive treatise to anybody who wants to godeeply into the correct determination ofE 0 values.

There are only a few groups thatdeal 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 effectson MxHg1x |MCl or MCl2|AgCl|Ag cells(M = Rb, Cs, Sr, Ba) were investigated,and Ref. 4, in which the inuence ofthe activity of the supporting electrolyteon the formal potentials of ferrice-nium/ferrocene and decamethylferrice-nium/decamethylferrocene systems werestudied with the help of the following cell:

Ag|AgClO4 or TBAClO4(CH3CN) or(H2O)|poly[Ru(vbpy)3(ClO4)n]|Pt, wherevbpy is 4-methyl-4-vinyl-2,2-bipyridineand TBA is tetra-n-butylammonium ion.

This chapter gives a selected compilationof the standard and other characteristic(formal, half-wave) potentials, as well asa compilation of the constant of solu-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 themost important reactions arepresented. The data have been taken exten-sively from previous compilations [513]where the original reports can be found,as well as from handbooks [1316], butonly new research papers are cited. Theconstant of solubility and complex equilib-ria were taken from Refs 611, 13, 1721.The oxidation states (OSs), ionization ener-gies (IEs) (rst, second, etc.), and electronafnities (EAs) of the elements and the


hydration enthalpy of some ions (Hhydr)calculated on the basis of Hhydr(Cs

+) =Hhydr (I) are also given. With the sym-bol of elements, the atomic number (lowerindex) and the mean relative atomic mass(upper index), the values that correspondeither to the current best knowledge (IU-PAC 2005) of the elements in naturalterrestrial sources or to the mass numberof the nuclide with the longest half-life, arealso indicated. The electrode reactions andequilibria are organized according to thepositions of the elements in the periodictable, starting from hydrogen and group1 to group 18, including lanthanides andactinides [22, 23].

2.1Group 1 Elements

Hydrogen (1.00791H,21H), OS: +1, 0, 1;

IE: 1312 kJ mol1; EA: 72.77 kJ mol1.Hhydr = 1090 kJ mol1.

H+/1/2H2 couple

H+(aq) + e 12H2(g)E 0 = 0.000 V

The standard potential of the hydrogenelectrode is taken as zero at all tempera-tures by convention [24, 25]. H does notrefer to isotopically pure hydrogen 11Hbut to a mixture of 11H, and

21H (deu-

terium, 2.014D) at the levels of naturalabundance (99.985% of 11H and 0.015%of 21H). H2 molecules possess nuclear spinisomers (ortho and para forms) that havesignicantly different physical and chem-ical properties. At ambient temperature,the equilibrium mixture is 3 : 1 for 11H2(ortho to para) and 2 : 1 for 21H2. Thepara form becomes predominant below200 K.

Taking into account the ionizationconstant of water (Kw = aH+aOH ) at298.15 K, the equilibrium potentials canbe calculated with the help of the Nernstequation at different pH values. SinceKw = 1.008 1014 at pH2 = 1 bar.

EH+/H2 = 0.414 V(pH 7) (1)EH+/H2 = 0.828 V(pH 14) (2)

At pH > 0, the Hammett acidity func-tion (Ho) [26, 27] can be used to estimateEH+/H2:

E = RTF

ln aH+ = RTF

ln cH+ = RTF

Ho (3)

The other strategy to determine thedependence of the equilibrium potentialof any redox reaction on the hydrogenion activity is the use of relative hydrogenelectrode (RHE); that is, a hydrogenelectrode immersed in the same solution.If the peak potential does not shift as afunction of pH, it means that the hydrogenion activity is involved in the same wayas that characteristic of the hydrogenelectrode (simple e, H+ reaction). Fromthe magnitude of the shift of Ep values, aconclusion can be drawn for the numberof hydrogen ions accompanying the redoxtransformations of the species (e.g. 2e,H+; e, 2H+).

The equilibrium potential can be mea-sured by using inert metals (EM+/M >EH+/H2) and the exchange current den-

sity (jo) for reaction H+ + e 12H2,which is higher than 104 A cm2. Be-sides Pt, Ir, Os, Pd, Rh, and Ru may beused. Because of the dissociative adsorp-tion of H2 molecules at these metals, nooverpotential is needed to cover the ratherhigh (431 kJ mol1) HH bond energy.

2.1 Group 1 Elements 21

On the other hand, the metalhydrogenatom bond energy is not too high; there-fore, it does not hinder the desorptionprocess.

In aqueous solution, the potential win-dow of stability of water is 1.23 V whenpH2 = pO2. However, at many electrodes,the hydrogen and oxygen evolution are ki-netically hindered; therefore, it is possibleto achieve a higher cell potential. Typicalexamples are Hg and Pb, in which log(jo/A cm2) = 11.9 and 12.6, respec-tively.

D+/1/2D2 coupleSince the properties (e.g. dissoci-

ation energy, solvation enthalpy) of21H(D) substantially differ from those of11H, it is expected that the equilibriumpotential under the same conditions willbe different. The estimated value for thereaction is given as follows:

D+(aq) + e 12D2(g)E 0 = 0.013 V (calcd)

1/2H2/H couple

12H2(g) + e H(aq)

E 0 = 2.25 V (calcd)

Solubility of H2 in 100 g water at 1 barand 20 C is 1.75 104 g.

Lithium (6.9413Li), OS: +1, 0; IE:520.2 kJ mol1.Hhydr = 515 kJ mol1.

Li+(aq) + e Li(s)E 0 = (3.04 0.005)V

Li+(aq) + e + (Hg) Li(Hg)E1/2 = 2.34 V

Lithium intercalation in graphite(1 mol dm3 LiAsF6, ethylenecarbonate:

dimethylcarbonate 1 : 3) [28]

LiC72 + Li+ + e 2LiC36Eo

c = 0.218 V versus Li/Li+

4LiC27 + 5Li+ + 5e 9LiC12Eo

c = 0.128 V

LiC12 + Li+ + e 2LiC6Eo

c = 0.086 V

Solubility equilibrium:

Li2CO3 2Li+ + CO32Ksp = 3.1 101

Sodium (22.98911Na), OS: +1, 0; IE:495.8 kJ mol1.Hhydr = 405 kJ mol1.

Na+(aq) + e Na(s)E 0 = 2.714(0.001) V

Na+(aq) + e + (Hg) Na(Hg)E1/2 = 2.10 V


NaHCO3 Na+ + HCO3Ksp = 1.2 103

Potassium (39.09819K), OS: +1, 0; IE:418.8 kJ mol1.Hhydr = 321 kJ mol1.

K+(aq) + e K(s)E 0 = (2.924 0.001)V

K+ + e + (Hg) K(Hg)E1/2 = 2.13 V

Solubility equilibria:

KClO4 K+ + ClO4Ksp = 8.9 103

K2PtCl6 2K+ + PtCl62Ksp = 1.4 106


Rubidium (85.46737Rb), OS: +1, 0; IE:403 kJ mol1. Hhydr = 296 kJ mol1.

Rb+(aq) + e Rb(s)E 0 = (2.924 0.001)V

Rb+(aq) + e + (Hg) Rb(Hg)E1/2 = 2.12 V


RbClO4 Rb+ + ClO4Ksp = 3.8 103

Cesium (132.90555Cs), OS: +1, 0; IE:375.7 kJ mol1.Hhydr = 263 kJ mol1.

Cs+(aq) + e Cs(s)E 0 = (2.923 0.001)V

Cs+(aq) + e + (Hg) Cs(Hg)E1/2 = 2.09 V


CsClO4 Cs+ + ClO4Ksp = 3.2 103

Francium (223.0287Fr)No data are available

2.2Group 2 Elements

Beryllium (9.01214Be), OS: +2, (+1),0; IE: 899, 1757.1 kJ mol1. Hhydr =4038 kJ mol1.

Be2+(aq) + 2e Be(s)E 0 = 1.97 V (calcd)

Be2+(aq) + 2e + (Hg) Be(Hg)E1/2 1.8 V


Be(OH)2 Be2+ + 2OHKsp = 2.7 1010

Magnesium (24.30512Mg), OS: +2, (+1),0; IE: 737.7, 1450.7 kJ mol1. Hhydr =1922 kJ mol1.

Mg2+(aq) + 2e Mg(s)E 0 = 2.356 V (calcd)

Mg(OH)2(s) + 2e Mg(s) + 2OH(aq)

E 0 = 2.687 V (calcd)Mg2+(aq) + e Mg+(aq)

E 0 = 2.657 V (calcd)Mg(OH)2(s) + 2H2O + 4e

MgH2(aq) + 4OH(aq)E 0 = 1.663 V (calcd)

Mg2+(aq) + 2e + (Hg) Mg(Hg)E1/2 2.53 V


Mg(OH)2(s) Mg2+ + 2OHKsp = 1.5 1011

MgNH4PO4 Mg2+ + NH4PO42Ksp = 2.5 1012

MgC2O4 Mg2+ + C2O42Ksp = 8.6 105

MgF2 Mg2+ + 2FKsp = 6.4 109

Calcium (40.07820Ca), OS: (+4), +2,(+1), 0, 2; IE: 589.8, 1145.4 kJ mol1.


Hhydr = 1616 kJ mol1.Ca2+(aq) + 2e Ca(s)

E 0 = (2.84 0.01)VCa(OH)2(s) + 2e

Ca(s) + 2OH(aq)E 0 = 3.026 V

Ca2+(aq) + 2e + (Hg) Ca(Hg)Eo = (2.000 0.003) V(E1/2 = 1.974 V)


Ca(OH)2 Ca2+ + 2OHKsp = 7.9 106

CaCO3 Ca2+ + CO32Ksp = 3.8 109

CaC2O4 H2O Ca2+ + C2O42 + H2O

Ksp = 2.3 109CaSO4 2H2O

Ca2+ + SO42 + 2H2OKsp = 2.4 105

CaCrO4 Ca2+ + CrO42Ksp = 7.1 104

Ca(H2PO4)2 Ca2+ + 2H2PO4Ksp = 1.0 103

Ca3PO4 3Ca2+ + 2PO43Ksp = 1.0 1025

CaF2 Ca2+ + 2FKsp = 3.9 1011

Strontium (87.6238Sr), OS: +2, 0; IE: 549.5,1064.2 kJ mol1.

Sr2+(aq) + 2e Sr(s)

E 0 = (2.89 0.01)VSr(OH)2(s) + 2e

Sr(s) + 2OH(aq)E 0 = 2.99 V

Sr2+(aq) + 2e + (Hg) Sr(Hg)Eo = 1.901 V


Sr(OH)2 8H2O Sr2+ + 2OH + 8H2O

Ksp = 3.2 104SrCO3 Sr2+ + CO32

Ksp = 9.4 1010SrCrO4 Sr2+ + CrO42

Ksp = 3.6 105SrSO4 Sr2+ + SO42

Ksp = 2.8 107

Barium (137.32756Ba), OS: +2, 0;IE: 503, 965.2 kJ mol1. Hhydr =1339 kJ mol1.Ba2+(aq) + 2e Ba(s)

E 0 = (2.92 0.01)VBa(OH)2(s) + 2e Ba(s) + 2OH(aq)

E 0 = 2.99 VBa2+(aq) + 2e + (Hg) Ba(Hg)

Eo = 1.717 V(E1/2 = 1.694 V)


BaSO4 Ba2+ + SO42Ksp = 1.1 1010

Ba(OH)2 8H2O Ba2+ + 2OH + 8H2O

Ksp = 5 103


BaCO3 Ba2+ + CO32Ksp = 8.1 109

BaCrO4 Ba2+ + CrO42Ksp = 2.0 1010

BaF2 Ba2+ + 2FKsp = 1.7 106

Radium (226.025488Ra), OS:+2, 0; IE: 509.3,979 kJ mol1.

Ra2+(aq) + 2e Ra(s)E 0 = 2.916 V (calcd)

Ra2+(aq) + 2e + (Hg) Ra(Hg)E1/2 1.85 V


RaSO4 Ra2+ + SO42Ksp = 4.2 1015

2.3Group 3 Elements

Scandium (44.95521Sc), OS: +3, 0; IE: 631,4258 (I + II + III) kJ mol1.Sc3+(aq) + 3e Sc(s)

E 0 = 2.03 VSc3+(aq) + 3e + (Hg) Sc(Hg)

E1/2 = 1.51 VSc(OH)3(s)+3e Sc(s)+3OH(aq)

E 0 = 2.60VSolubility and complex equilibria:

Sc(OH)3 Sc3+ + 3OHKsp = 4 1031

Sc3+(aq) + F(aq) ScF2+(aq)

K = 1.2 107ScF2+(aq) + F(aq) ScF2+(aq)

K = 6.5 105ScF2+(aq) + F(aq) ScF3(aq)

K = 3.0 104ScF3(aq) + F(aq) ScF4(aq)

K = 7 102

Yttrium (88.95839Y), OS:+3, 0; IE: 617, 3760(I + II + III) kJ mol1.

Y3+(aq) + 3e Y(s)E 0 = 2.37 V (calcd)

Y3+(aq) + 3e + (Hg) Y(Hg)E1/2 1.6 V


Y(OH)3(s) Y3+(aq) + 3OH(aq)Ksp = 3.2 1025

Lanthanum (138.90557La), OS: +3, 0; IE:538, 3457 (I + II + III) kJ mol1. Hhydr(La3+) = 3235 kJ mol1.

La3+(aq) + 3e La(s)E 0 = 2.38 V

La3+(aq) + 3e + (Hg) La(Hg)E1/2 = 1.76 V


La(OH)3 La3+ + 3OHKsp = 2 1022

Cerium (140.11658Ce), OS: +4, +3,0; IE: 534, 1047, 1940 kJ mol1.Hhydr(Ce

3+) = 3370 kJ mol1.


Acidic solutions

Ce4+(aq) + e Ce3+(aq)E 0 = 1.72 V(1 mol dm3 HClO4)

Ce3+(aq) + 3e Ce(s)E 0 = 2.34 V

Ce3+(aq) + 3e Ce(s)Eo

c = 3.065 V versus Ag|AgCl

(x = 103)KClLiCl eutecticmelt, 700 C [29]

Ce3+(aq) + 3e + (Hg) Ce(Hg)E1/2 = 1.73 V

Basic solutions

CeO2(s) + e + 2H2O Ce(OH)3 + OH(aq)

E 0 = 0.7 VCe(OH)3 + 3e Ce(s) + 3OH(aq)

E 0 = 2.78 VSolubility equilibria:

CeO2(s) + 2H2O Ce4+(aq) + 4OH(aq)

Ksp = 1 1063Ce(OH)3 Ce3+ + 3OH

Ksp = 7.9 1023Ce2(C2O4)3 2Ce3+ + 3C2O42

Ksp = 2.5 1029

Praseodymium (140.90759Pr), OS: +4,+3, 0; IE: 522, 1018, 2090 kJ mol1.Hhydr(Pr

3+) = 3413 kJ mol1.Pr4+(aq) + e Pr3+(aq)

E 0 = 3.2 V (calcd)

Pr3+(aq) + 3e Pr(s)E 0 = 2.35 V

Pr3+(aq) + 3e + (Hg) Pr(Hg)E1/2 = 1.71 V

Pr3+(aq) + 3e + (Cd)x Pr(Cd)xEo

c = 0.561 V versus

Pr (III)/Pr coexisting two

phases: Pr Cd11 and Cd, LiClKClmelt 673 C [30]

Pr3+(aq) + 3e + (Bi)x Pr(Bi)xEo

c = 0.741 V versus

Pr (III)/Pr coexisting two phases:

PrBi and PrBi2, 673C [30]

Neodymium (144.2460Nd), OS: +4, +3,+2, 0; IE: 530, 1034, 2128 kJ mol1.Hhydr(Nd

3+) = 3442 kJ mol1.

Nd4+(aq) + e Nd3+(aq)E 0 = 4.9 V (calcd)

Nd3+(aq) + e Nd2+(aq)E 0 = 2.6 V (calcd)

Nd3+(aq) + 3e Nd(s)E 0 = 2.32 V

Nd3+(aq) + 3e + (Hg) Nd(Hg)E1/2 = 1.68 V


Nd2(C2O4)3 2Nd3+ + 3C2O42Ksp = 5.9 1029

Promethium ([144.912]61Pm), OS: +3,0; IE: 536, 1052, 2140 kJ mol1.


Hhydr(Pm3+) = 3478 kJ mol1.

Pm3+(aq) + 3e Pm(s)E 0 = 2.29 V

Samarium (150.3662Sm), OS: +3, +2, 0; IE:542, 1068, 2285 kJ mol1. Hhydr(Sm3+)= 3515 kJ mol1.Sm3+(aq) + e Sm2+(aq)

E 0 = 1.55 V(E1/2 = 1.44 V)

Sm3+(aq) + 3e Sm(s)E 0 = 2.30 V

Sm3+(aq) + 3e + (Hg) Sm(Hg)E1/2 = 1.73 V

Europium (151.96463 Eu), OS: +3, +2, 0; IE:547, 1085, 2425 kJ mol1. Hhydr(Eu3+)= 3547 kJ mol1.Eu3+(aq) + e Eu2+(aq)

E 0 = 0.35 V(E1/2 = 0.39 V)

EuCl63 + e Eu2+ + 6ClEo


(x = 9.4 103)NaClKCl melt [31]Eu3+(aq) + 3e Eu(s)

E 0 = 2.99 VEu3+(aq) + 3e + (Hg) Eu(Hg)

E1/2 = 2.23 V

Gadolinium (157.2564Gd), OS: +3, 0; IE:595, 1172, 1999 kJ mol1. Hhydr(Gd3+)= 3571 kJ mol1.Gd3+(aq) + 3e Gd(s)

E 0 = 2.28 VGd3+(aq) + 3e + (Hg) Gd(Hg)

E1/2 = 1.68 VTerbium (158.92565 Tb), OS: +4, +3, 0; IE:

569, 1112, 2122 kJ mol1. Hhydr(Tb3+)= 3605 kJ mol1.

Tb4+(aq) + e Tb3+(aq)E 0 = 3.1 V (calcd)

Tb3+(aq) + 3e Tb(s)E 0 = 2.31 V

Tb3+(aq) + 3e + (Hg) Tb(Hg)E1/2 = 1.65 V

Dysprosium (162.50066 Dy), OS: +4, +3,+2, 0; IE: 567, 1126, 2230 kJ mol1.Hhydr(Dy

3+) = 3637 kJ mol1.Dy4+(aq) + e Dy3+(aq)

E 0 = 5.4 V (calcd)Dy3+(aq) + e Dy2+(aq)

E 0 = 2.5 VDy3+(aq) + 3e Dy(s)

E 0 = 2.29 VHolmium (164.93067 Ho), OS: +3, 0; IE: 574,

1139, 2221 kJ mol1. Hhydr(Ho3+) =3667 kJ mol1.Ho3+(aq) + 3e Ho(s)

E 0 = 2.33 VHo3+(aq) + 3e + (Hg) Ho(Hg)

E1/2 = 1.61 VErbium (167.25968 Er), OS: +3, 0; IE: 581,

1151, 2207 kJ mol1. Hhydr(Er3+) =3691 kJ mol1.


Er3+(aq) + 3e Er(s)E 0 = 2.32 V

Er3+(aq) + 3e + (Hg) Er(Hg)E1/2 = 1.60 V

Thulium (168.93469Tm), OS: +3, +2, 0; IE:589, 1163, 2305 kJ mol1. Hhydr(Tm3+)= 3717 kJ mol1.Tm3+(aq) + e Tm2+(aq)

E 0 = 2.3 VTm3+(aq) + 3e Tm(s)

E 0 = 2.32 VTm3+(aq) + 3e + (Hg) Tm(Hg)

E1/2 = 1.57 V

Ytterbium (173.0470Yb), OS: +3, +2, 0; IE:603, 1175, 2408 kJ mol1. Hhydr(Yb3+)= 3739 kJ mol1.

Yb3+(aq) + e Yb2+(aq)E 0 = 1.05 V(E1/2 = 1.13 V)

Yb3+(aq) + 3e Yb(s)E 0 = 2.22 V

Yb3+(aq) + 3e + (Hg) Yb(Hg)E1/2 = 1.73 V

Lutetium (174.96771Lu), OS: +3, 0; IE: 513,1341, 2054 kJ mol1. Hhydr(Lu3+) =3760 kJ mol1.

Lu3+(aq) + 3e Lu(s)E 0 = 2.30 V

Lu3+(aq) + 3e + (Hg) Lu(Hg)E1/2 = 1.54 V

Actinium ([227.027]89 Ac), OS:+3, 0; IE: 4284(I + II + III) kJ mol1 [32].

The IE of all the actinides are estimatedvalues based on the dependence of E 0 onIE [32].

Ac3+(aq) + 3e Ac(s)E 0 = 2.15 V


Ac(OH)3 Ac3+ + 3OHKsp = 1.26 1021

Thorium (232.038190Th), OS: +4, (+3), 0;IE: 3628 (I + II + III) kJ mol1.

Th4+(aq) + 4e Th(s)E 0 = 2.56 V

Th4+(aq) + e Th3+(aq)E 0 = 3.8 V


Th(OH)4 Th4+ + 4OHKsp = 2.5 1049

Protactinium (231.035891Pa), OS: +5, +4,+3, 0; IE: 568 kJ mol1

PaOOH2+(aq) + e + 3H+ Pa4+(aq) + 2H2OE 0 = 0.1 V

Pa4+(aq) + 4e Pa(s)E 0 = 1.46 V

Pa4+(aq) + e Pa3+(aq)E 0 = 1.4 V

Uranium (238.028992U), OS: +6, +5, +4,+3, 0; IE: 5023 (I + II + III) kJ mol1.


UO22+(aq) + e UO2+(aq)E 0 = 0.16 V

UO2+(aq) + e + 4H+ U4+(aq) + 2H2O

E 0 = 0.38 VU4+(aq) + e U3+(aq)

E 0 = 0.52 VU3+(aq) + 3e U(s)

E 0 = 1.66 VEo


(1 wt % AgCl) (LiClKCleutectic salt, 450 C) [33]


U(OH)3 U3+ + 3OHKsp = 6.31 1023

Neptunium ([237.0482]93Np), OS: +7, +6,+5, +4, +3, 0; IE: 4853 (I + II + III)kJ mol1.

NpO3+(aq) + e + 2H+

NpO22+(aq) + H2O

E 0 = 2.04 VNpO2

2+(aq) + e NpO2+(aq)E 0 = 1.24 V

NpO2+(aq) + e + 4H+

Np4+(aq) + 2H2OE 0 = 0.66 V

Np4+(aq) + e Np3+(aq)E 0 = 0.18 V

Np3+(aq) + 3e Np(s)E 0 = 1.79 V

Eo

c = 1.484 V versus Ag|AgCl(LiClKCl eutectic salt, 450 C) [33]


Np(OH)3 Np3+ + 3OHKsp = 3.99 1023

Plutonium ([244.0642]94 Pu), OS: +7, +6, +5,+4, +3, 0; IE: 4531 (I + II + III) kJ mol1.PuO22+(aq) + e PuO2+(aq)

E 0 = 1.02 VPuO2+(aq) + e + 4H+

Pu4+(aq) + 2H2OE 0 = 1.04 V

Pu4+(aq) + e Pu3+(aq)E 0 = 1.01 V

Pu3+(aq) + 3e Pu(s)E 0 = 2.0 VEo


(LiClKCl eutectic salt, 450 C) [33]or Eo

c = 1.571 V [34]

PuO53 + H2O + e

PuO42 + 2OH(aq)Eo

c = 0.95 V (1 mol dm3 NaOH)


Pu(OH)3 Pu3+ + 3OHKsp = 2.5 1023

Americium ([243.061]95 Am),OS:+6,+5,+4,+3, +2, 0; IE: 4405 (I + II + III) kJ mol1.AmO22+(aq) + e AmO2+(aq)

E 0 = 1.6 V


AmO2+(aq) + e + 4H+ Am4+(aq) + 2H2O

E 0 = 0.82 VAm4+(aq) + e Am3+(aq)

E 0 = 2.62 V (calcd)Am4+(aq) + 4e Am(s)

E 0 = 0.9 VAm3+(aq) + 3e Am(s)

E 0 = 2.07 VAm2+ + 2e Am(s)

Eo

c = 1.642 V versus Ag|AgCl(LiClKCl eutectic salt, 450 C) [33]

Curium ([247.07]96 Cm), OS: (+4), +3, 0; IE:4424 (I + II + III) kJ mol1.

Cm4+(aq) + e Cm3+(aq)E 0 = 3.1 V (calcd)

Cm3+(aq) + 3e Cm(s)E 0 = 2.06 V (calcd)

Berkelium ([247.07]97 Bk), OS: (+4), +3, 0;IE: 4513 (I + II + III) kJ mol1.

Bk4+(aq) + e Bk3+(aq)E 0 = 1.67 VEo

c = 1.54 V (1 M HClO4),

1.37 V (1 M H2SO4)

Bk3+(aq) + 3e Bk(s)E 0 = 2.0 V (calcd)

Californium ([251.079]98 Cf), OS: (+4), +3,+2, 0; IE: 4646 (I + II + III) kJ mol1.

Cf4+(aq) + e Cf3+(aq)

E 0 = 3.2 V (calcd)Cf3+(aq) + e Cf2+(aq)

E 0 = 1.6 VCf3+(aq) + 3e Cf(s)

E 0 = 1.91 VCf2+(aq) + 2e Cf(s)

E 0 = 2.1 V

Einsteinium ([252.083]99 Es), OS: (+4), +3,+2, 0; IE: 4531 (I + II + III) kJ mol1.

Es4+(aq) + e Es3+(aq)E 0 = 4.5 V (calcd)

Es3+(aq) + 3e Es(s)E 0 = 1.98 V

Es3+(aq) + e Es2+(aq)E 0 = 1.5 V

Fermium ([257.095]100 Fm), OS: (+4), +3, 0;IE: 4598 (I + II + III) kJ mol1.

Fm4+(aq) + e Fm3+(aq)E 0 = 5.2 V (calcd)

Fm3+(aq) + 3e Fm(s)E 0 = 2.07 V

Fm3+(aq) + e Fm2+(aq)E 0 = 1.15 V

Fm2+(aq) + 2e Fm(s)E 0 = 2.37 V

Mendelevium ([258.098]101 Md), OS: +3, +2,0; IE: 4973 (I + II + III) kJ mol1.

Md3+(aq) + 3e Md(s)E 0 = 1.74 V


Md3+(aq) + e Md2+(aq)E 0 = 0.15 V

Nobelium ([258.098]102 No), OS: +3, +2, 0; IE:5526 (I + II + III) kJ mol1.

No3+(aq) + 3e No(s)E 0 = 1.26 V

No3+(aq) + e No2+(aq)E 0 = 1.4 V

No2+(aq) + 2e No(s)E 0 = 2.5 V

Lawrencium ([262.109]103 Lr), OS: +3, 0; IE:4479 (I + II + III) kJ mol1.

Lr3+(aq) + 3e Lr(s)E 0 = 2.1 V (calcd)

2.4Group 4 Elements

Titanium (47.86722Ti), OS: +4, +3, +2, (+1),0; IE: 658 kJ mol1.

Acidic solutions

TiO2+(aq) + e + 2H+ Ti3+(aq)E 0 = 0.1 V (calcd)

2TiO2(s) + 2e + 2H+ Ti2O3(s) + H2O(both oxides are unhydrated)

E 0 = 0.556 V (calcd)Ti3+(aq) + e Ti2+(aq)

E 0 = 2.3 V (calcd) orE 0 = 0.37 V (calcd)

Ti3+(aq) + 3e Ti(s)

E 0 = 1.209 V (calcd)Ti2+(aq) + 2e Ti(s)

E 0 = 1.628 V (calcd)Ti(s) + e + H+ TiH(s)

E 0 = 0.65 V (calcd)Ti(s) + 2e + 2H+ TiH2(s)

E 0 = 0.45 V (calcd)TiF62(aq) + 4e Ti(s) + 6F(aq)

E 0 = 1.19 V (calcd)TiF4(s) + 4e Ti(s) + 4F(aq)

E 0 = 0.89 V (calcd)[Ti( C5H5)2]2+(Cl)2 aq) + e

[Ti( C5H5)2]+Cl(aq) + Cl(aq)Eo

c = 0.44 V Eo

c = 0.63 V

versus Ag+/Ag (DMF,

0.1 M TEAP)

Basic solution

2TiO2(s) + 2e + H2O Ti2O3(s) + 2OH(aq)

E 0 = 1.38 V (calcd)

Standard potentials are calculated val-ues. The electrochemical measurementshave supplied contradictory values. Thisis mainly due to the formation of ox-ides and hydride lms on the Ti surface,which causes it to behave as a noblemetal. Titanium dissolves rapidly onlyin HF.

Zirconium (91.22440Zr), OS: +4, +3, +2,+1, 0; IE: 661 kJ mol1.

Zr4+(aq) + 4e Zr(s)E 0 = 1.55 V (calcd)


ZrO2(s) + 4e + 4H+ Zr(s) + 2H2O

E 0 = 1.45 V (calcd)Solubility equilibrium:

Zr(OH)4 Zr4+ + 4OH

Ksp 1 1056

Hafnium (178.4972Hf), OS: +4, +3, +2, +1,0; IE: 681 kJ mol1.

Hf4+(aq) + 4e Hf(s)E 0 = 1.7 V (calcd)

HfO2(s) + 4e + 4H+ Hf(s) + 2H2O

E 0 = 1.57 V (calcd)The experimental determination of

E 0 values is hindered by the forma-tion of surface oxides and polymericspecies with oxo and hydroxo bridgesin the solution. Hydrolysis practically al-ways takes place even in strongly acidicmedia.

Rutherfordium ([261.108]104 Rf)No data are available.

2.5Group 5 Elements

Vanadium (50.94123V), OS: +5, +4, +3, +2,0; IE: 650 kJ mol1.

VO2+(aq) + e + 2H+ VO2+(aq) + H2O

E 0 = 1.0 VH2V10O284(aq) + 10e + 24H+

10VOOH+(aq) + 8H2O

E 0 = 0.723 VV2O5(s) + 2e + 6H+

2VO2+(aq) + 3H2OE 0 = 0.958 V

VO2+(aq) + 2H+ + e VO3+(aq) + H2O

E 0 = 0.337 VV4O92(aq) + 4e + 6H+

2V2O3(s) + 3H2OE 0 = 0.536 V

V3+(aq) + e V2+(aq)E 0 = 0.255 V

V2+(aq) + 2e V(s)E 0 = 1.13 V

V5+(aq) + e V4+(aq)Eo

c = 1.02 V (1 M HCl)

Eo

c = 1.02 V (1 M HClO4)Eo

c = 1.0 V (1 M H2SO4)


c = 0.36V (1 M H2SO4)


c = 0.267V (1 M HCl)

[V( C6H5)2]2+(ClO4)2(aq)+ e [V( C6H5)2]+Cl(aq)+ Cl(aq)

Eo

c = 0.32V (0.1 M HClO4)1-[As2VW17O62]

7 + e 1-[As2VW17O62]

8

Eo

c = 0.575 V versus


SCE (saturated calomel electrode)

SCE (pH 7) [35]

1-[PVW17O62]7 + e

1-[PVW17O62]8

Eo

c = 0.506 V versusSCE (pH 7) [35]

1,2,3-[As2Mo2VW15O62]7 + e

1,2,3-[As2Mo2VW15O62]8

Eo

c = 0.489V versusSCE (pH 7) [35]

2-[H4PVW17O62]8 + e

2-[H4PVW17O62]9

Eo

c = 0.291V versusSCE (pH 7) [35]

Eo

c values of several other Dawson-typeV-substituted polyoxometalates can befound in Ref. 35 and the citations therein.

Selected equilibria:

V2O5(s) + 2H+ 2VO2+ + H2OK = 3.42 102

10VO2+ + 8H2O H2V10O284 + 14H+

K = 1.8 107VO22+ + H2O VOOH+ + H+

K = 4.4 106V2O3(s) + 6H+ 2V3+ + 3H2O

K = 1.56 1013V3+ + H2O VOH2+ + H+

K = 1.17 103VO(s) + 2H+ V2+ + H2O

K = 3 1010

Uncertainties concerning the nature ofthe hydrolyzed and associated species callforth uncertainties in E 0 values.

Niobium (92.90641Nb), OS: (+7), +5, +4,+3, +2, (+1), 0, ( 1); IE: 664 kJ mol1.

Nb2O5(s) + 10e + 10H+ 2Nb(s) + 5H2O

E 0 = 0.65 V (calcd)NbO(SO4)2

+ 2e + 2H+ Nb3+(aq) + H2O + 2SO42(aq)

E 0 0.1 VNb3+(aq) + 3e Nb(s)

E 0 = 1.1 V (calcd)Niobium is always covered with an oxide

layer. In aqueous solutions only someniobium compounds are soluble, mostlyin the form niobate anions, for example,[HxNb6O19](8x).

Tantalum (180.94873Ta), OS: +5, +4, +3, 0;IE: 761 kJ mol1.

Ta2O5 + 10e + 10H+ 2Ta(s) + 5H2O

Eo

c = 0.81 V (pH 1)TaF7

2(aq) + 5e Ta(s) + 7F(aq)Eo

c = 0.45 V

Dubnium ([262.114]105 Db)No data are available.

2.6Group 6 Elements

Chromium (51.99624Cr), OS: +6, +3, +2, 0;IE: 652 kJ mol1.

HCrO4(aq) + 3e + 7H+


Cr3+(aq) + 4H2OE 0 = 1.38 V (calcd)

Cr2O72(aq) + 6e + 14H+

2Cr3+(aq) + 7H2OE 0 = 1.36 V

Cr3+(aq) + e Cr2+(aq)E 0 = 0.424 V

Cr3+(aq) + 3e Cr(s)E 0 = 0.74 V

Cr2+(aq) + 2e Cr(s)E 0 = 0.9 V

CrO42(aq) + 3e + 4H2O Cr(OH)3(s)

E 0 = 0.11 VCr(CN)6

3 + e Cr(CN)64

Eo

c = 1.143 V (1 M KCN)[Cr( C6H6)2]+(aq) + e

[Cr( C6H6)2](aq)Eo

c = 0.97 V (pH 212)

Eo

c = 0.93 V(0.1 M TEAP, CH3CN)

Data for chromium amino carboxylatecomplexes can be found in Ref. 36.

Solubility and complex equilibria:

Cr(OH)3 Cr3+ + 3OHKsp = 1 1030

Cr(H2O)63+

[Cr(H2O)5OH]2+ + H+

K = 1.6 104Cr(H2O)6

3+ + Cl

[Cr(H2O)5Cl]2+ + H2O

K = 0.1Molybdenum (95.9442Mo), OS: +6, +5, +4,

+3, +2, 0; IE: 685 kJ mol1.Acidic solutions

2H2MoO4(aq) + 2e + 4H+ Mo2O42+(aq) + 4H2O

E 0 = 0.50 V (calcd)H2MoO4(aq) + 6e + 6H+

Mo(s) + 4H2OE 0 = 0.114 V (calcd)

[MoO2Cl4]2(aq) + 2e + 4H+ [Mo(H2O)Cl4](aq)

Eo

c = 0.15 V (1 M HCl)[MoOCl5]

2(aq) + 2e + 2H+ [Mo(H2O)Cl5]

2(aq)

Eo

c = 0.38 V (1 M HCl)Mo(CN)8

3(aq) + e Mo(CN)8

4(aq)

Eo

c = 0.725 V (pH 7)Basic solutions

MoO42(aq) + 2e + 2H2O MoO2(s) + 4OH(aq)

E 0 = 0.78 V (calcd)MoO2(s) + 4e + 2H2O

Mo(s) + 4OH(aq)E 0 = 0.98 V (calcd)

In solution Mo(VI) exists in the formof colorless MoO42 anion at pH > 6.Acid hydrolysis results in the formation ofpolyanions, for example, [Mo8O26]4 (pH


> 1) or [Mo36O112]8, [H2Mo2O6]2+ (pH> 1). In the presence of other oxanionsheteropolyanions are formed, for example,[SiMo12O40]4, H3[PMo12O40].

Tungsten (183.8474W), OS: +6, +5, +4, +3,+2, +1, 0; IE: 770 kJ mol1.

Acidic solutions

WO3(s) + 6e + 6H+ W(s) + 3H2O

E 0 = 0.09 VWO2Cl3(aq) + e + 2H+ + 2Cl

WOCl52(aq) + H2OEo

c = 0.36 V (12 M HCl)

2WOCl52(aq) + 4e + 4H+

W2Cl93(aq) + H2O + Cl

Eo

c = 0.05V (12 M HCl)W(CN)8

3(aq) + e W(CN)8

4(aq)

Eo

c = 0.457 VCoW12O406(aq) + 2e + 2H+

H2CoW12O406(aq)Eo

c = 0.046 V (1 M H2SO4)

PW12O403(aq) + e PW12O404(aq)

Eo

c = 0.218 V (1 M H2SO4)

Basic solutions

W(OH)4(CN)43(aq) + e

W(OH)4(CN)44(aq)

Eo

c = 0.74 V (pH 13.7)WO42(aq) + 6e + 4H2O

W(s) + 8OH(aq)

E 0 = 1.074 V (calcd)

Seaborgium ([266.122]106 Sg)No data are available.

2.7Group 7 Elements

Manganese (54.93825Mn), OS: +7, +6, +5,+4, +3, +2, +1, 0, 1; IE: 717 kJ mol1.

Acidic solutions

MnO4(aq) + e MnO42(aq)E 0 = 0.56 V

MnO4(aq) + 5e + 8H+ Mn2+(aq) + 4H2O

E 0 = 1.51 V (calcd)MnO42(aq) + e MnO43(aq)

E 0 0.27 VMnO2(s) + 2e + 4H+

Mn2+(aq) + 2H2OE 0 = 1.23 V (calcd)

Mn3+(aq) + e Mn2+(aq)E 0 1.5 V (calcd)

Mn2+(aq) + 2e Mn(s)E 0 = 1.18 V (calcd)

[Mn(CN)6]3(aq) + e [Mn(CN)6]4(aq)

E 0 = 0.24 VBasic solutions

MnO4(aq) + 5e + 4H2O Mn(OH)2(s) + 6OH(aq)

E 0 = 1.34 V (calcd)


MnO4(aq) + 3e + 2H2O MnO2(s) + 4OH(aq)

E 0 = 0.06 V (calcd) -MnO2(s) + e + H2O

-MnO(OH)(s) + OH(aq)E 0 = 0.3 V (calcd)

Mn(OH)2(s) + 2e Mn(s) + 2OH(aq)

E 0 = 1.56 V (calcd)The determination of equilibrium (stan-

dard) potentials is rather problematic forseveral reasons; for instance, hydroly-sis and disproportionation reactions, theexistence of a large number of struc-tural forms (e.g. -, -, -, -MnO2),strong dependence on pH and ionic ex-change processes, and the instability ofthe species in contact with water (e.g. Mn-metalhydrogen evolution, MnO4 oxy-gen evolution; however, these processesare rather slow).


Mn(OH)2 Mn2+ + 2OHKsp = 4 1014

MnS Mn2+ + S2Ksp = 5.6 1016

MnCO3 Mn2+ + CO32Ksp = 5.1 1010

Technetium ([97.907]43 Tc), OS: +7, +6, +5,+4, +2, +1, 0, (1); IE: 702 kJ mol1.

Acidic solutions

TcO4(aq) + 3e + 4H+ TcO2(s) + 2H2O

E 0 = 0.738 V

TcO4(aq) + 7e + 8H+ Tc(s) + 4H2O

E 0 = 0.472 V (calcd)Tc2+(aq) + 2e Tc(s)

E 0 = 0.40 V (calcd)Basic solutions

Tc(OH)(s) + e + H+ Tc(s) + H2O

E 0 = 0.031 VTc(OH)2(s) + 2e + 2H+

Tc(s) + 2H2OE 0 = 0.072 V

Tc(OH)3(s) + 3e + 3H+ Tc(s) + 3H2O

E 0 = 0.185 VTc(OH)4(s) + 4e + 4H+

Tc(s) + 4H2OE 0 = 0.294 V

Rhenium (186.20775Re), OS: +7, +6, +5,+4, +3, +2, +1, 0, 1; IE: 760 kJ mol1.

Acidic solutions

ReO4(aq) + 7e + 8H+ Re(s) + 4H2O

E 0 = 0.34 VReO4(aq) + 3e + 4H+

ReO2(s) + 2H2OE 0 = 0.51 V

ReO4(aq) + e + 2H+ ReO3(s) + H2O

E 0 = 0.768 V


Re(s) + e Re(aq)E 0 = 0.1 V (calcd)

Basic solutions

ReO4(aq) + 7e + 4H2O Re(s) + 8OH(aq)

E 0 = 0.604 VReO4(aq) + e + H2O

ReO3(s) + 2OH(aq)E 0 = 0.89 V

2ReO4(aq) + 8e + 5H2O Re2O3(s) + 10OH(aq)

E 0 = 0.808 V (calcd)Re2O3(s) + 6e + 3H2O

Re(s) + 6OH(aq)E 0 = 0.333 V (calcd)

Bohrium ([264]107Bh)No data are available.

2.8Group 8 Elements

Iron (55.84526 Fe), OS: (+6), +3, +2, 0; IE:759 kJ mol1.

Acidic solutions

Fe3+(aq) + e Fe2+(aq)E 0 = 0.771 V

Fe3+(aq) + 3e Fe(s)E 0 = 0.037 V (calcd)

Fe2+(aq) + 2e Fe(s)E 0 = 0.44 0.04 V

FeO42(aq) + 3e + 8H+ Fe3+(aq) + 4H2O

Eo

c = 2.25 V [37][Fe(CN)6]3(aq) + e

[Fe(CN)6]4(aq)

E 0 = 0.3610 (0.0005) VEo

c = 0.69 V (1 M H2SO4)

[Fe(CN)6]4(aq) + 2e

Fe(s) + 6CN(aq)E 0 = 1.16 V

[Fe(C2O4)3]3+(aq) + e

[Fe(C2O4)3]4(aq)

Eo

c = 0.005 V(Na2C2O4, c < 0.2M)

[Fe(C2O4)3]3(aq) + e

[Fe(C2O4)2]2(aq) + C2O42(aq)

Eo

c = 0.035 V(Na2C2O4, c > 0.1M)

[Fe(-C5H5)2]+(aq) + e ferricenium

[Fe(-C5H5)2](aq, slightly soluble)

ferrocene

E 0 = (0.400 0.007)V[Fe(-C5H5)2]

+(s) + e [Fe(-C5H5)2](saturated)

Eo

c = 0.637 V (1 M KCl,0.01 M NH4Cl)

Eo

c = 0.618 V (1 M NaClO4,0.01 M HClO4)

Eo

c = 0.605 V (1.01 M HCl)


Eo

c = 0.539 V versusSHE (HCONH2)

Eo

c = 0.19 V versus SHE (CH3CN)Eo

c = 0.348 V versusSHE(aq) (CH3CN)

The formal potential of the substitutedferrocenes can be found in Ref. 38.

[Fe(phen)3]3+(aq) + e

[Fe(phen)3]2+(aq)

(phen = 1,10 phenanthroline)Eo

c = 1.13 V

[Fe(bpy)3]3+(aq) + e

[Fe(bpy)3]2+(aq)

(bpy = 2, 2-bipyridyl)Eo

c = 1.11 V

Methemoglobin (Fe3+) + e Hemoglobin (Fe2+)

Eo

c = 0.152 V (pH 7),0.282 V [39]

Methemoglobin + e Hemoglobin

Eo

c = 0.281 V(Lumbriansterrestis) [39]

Cytochrome A (Fe3+) + e Cytochrome A (Fe2+)

Eo

c = 0.29 V (pH 7)Cytochrome B (Fe3+) + e

Cytochrome B (Fe2+)

Eo

c = 0.04 V (pH 7)Cytochrome C (Fe3+) + e

Cytochrome C (Fe2+)

Eo

c = 0.26 V (pH 7)[Fe4S4(SR)4]

+ e [Fe4S4(SR)4]2(oxidized

ferredoxin (Fe3+))(reduced

ferredoxin (Fe2+))

Eo

c = 0.45 V [40] (dependingon the source of the

ferredoxins and the pH)

[Fe2S2]2ferredoxin

+ e [Fe2S2]3Eo

c = 0.81 V [41]

(Formal potentials of metal hexacyano-ferrates can be found in Ch. 11)

Basic solutions

FeO42(aq) + 3e + 2H2O FeO2(aq) + 4OH(aq)

E 0 0.55 VFeO2(aq) + e + H2O

HFeO2(aq) + OH(aq)E 0 0.69 V

HFeO2(aq) + 2e + H2O Fe(s) + 3OH(aq)

E 0 0.8 V

The aqua complexes of Fe2+ and Fe3+,which are present in acid solutions,can hydrolyze to FeOH+, Fe(OH)2+,Fe(OH)2+, and other ions at higher pHvalues, and the respective hydroxidesprecipitate. Weak anion complexes suchas FeSO4, FeSO4+, or FeCl2+ can also beformed.


Solubility and complex equilibria:

Fe(OH)2 Fe2+ + 2OHKsp = 4.8 1016

Fe(OH)3 Fe3+ + 3OHKsp = 3.8 1038

FeS Fe2+ + S2Ksp = 3.7 1019

Fe2S3 2Fe3+ + 3S2Ksp 1 1088

FeC2O4 Fe2+ + C2O42Ksp = 2.1 107

Fe4[Fe(CN)6]3 4Fe3+ + 3[Fe(CN)6]4

Ksp = 3 1041

[Fe(CN)6]4 Fe2+ + 6CN

K = 1.3 1037[Fe(CN)6]

4 + H+ [HFe(CN)6]

3

K = 1.2 104[HFe(CN)6]

3 + H+ [H2Fe(CN)6]

2

K = 2.2 102

Ruthenium (101.0744 Ru), OS: +8, +7, +6,+4, +3, +2, 0; IE: 711 kJ mol1.Acidic solutions

RuO4(aq) + e RuO4(aq)

E 0 = 0.99 V (calcd)RuO4(aq) + 3e + 4H+

RuO2(s, hydr) + 2H2O

E 0 = 1.533 V (calcd)RuO2(s) + 4e + 4H+ Ru(s)

E 0 = 0.68 V (calcd)RuO4(aq) + e RuO22(aq)

E 0 = 0.593 V (calcd)[Ru(H2O)6]

3+(aq) + e [Ru(H2O)6]

2+(aq)

Eo

c = 0.249 V(p-toluenesulfonic acid)

[Ru(H2O)5Cl]2+(aq) + e

[Ru(H2O)5Cl]+(aq)

Eo

c = 0.086 V[Ru(CN)6]

3(aq) + e [Ru(CN)6]

4(aq)

Eo

c = (0.86 0.05)V (KCl)[Ru(NH3)6]

3+(aq) + e [Ru(NH3)6]

2+(aq)

Eo

c = (0.1 0.01)V (HClO4)The formation of polymeric and mixed-

valence complexes also occurs in aqueoussolutions.

Ruthenocenium+ + e Ruthenocene

Eo

c = 0.59 V versus Fc+/FcFormal potentials of ruthenium metal-

locenes can be found in Refs 4244.

[Ru(bpy)3]3+ + e [Ru(bpy)3]2+

Eo

c = 1.32 V[Ru(bpy)3]

2+ + e [Ru(bpy)3]+

Eo

c = 1.30 V


[Ru(bpy)3]+ + e Ru(bpy)3

Eo

c = 1.49 V versus SCERu(bpy)3 + e

[Ru(bpy)3](bpy = 2, 2-bipyridyl)

Eo

c = 1.73 V (0.1 MTBAPF4,CH3CN)

Formal potentials of dinuclear andhexanuclear Ru(II) bipyridine complexes(40 redox processes!) are given in Ref. 45.

Osmium (190.2376 Os), OS: +8, +7, +6, +5,+4, +3, +2, +1, 0; IE: 840 kJ mol1.

OsO4(aq) + 8e + 8H+ Os(s) + 4H2O

E 0 = 0.84 V (calcd)OsO4(s) + 4e + 4H+

OsO2(s) + 2H2OE 0 = 1.005 V (calcd)Eo

c = 0.964 VpH = 3.5 6.5

OsO2(s) + 4e + 4H+ Os(s) + 2H2O

E 0 = 0.687 V (calcd)[Os(Cl)6]

2(aq) + e [Os(Cl)6]

3(aq)

E 0 = 0.85 V (calcd)[Os(CN)6]

3(aq) + e [Os(CN)6]

4(aq)

E 0 = 0.634 VOs(bpy)3

3+(aq) + e Os(bpy)3

2+(aq)

E 0 = 0.885 V (calcd)

Hassium ([277]108Hs)No data are available.

2.9Group 9 Elements

Cobalt (58.93327 Co), OS: (+4), +3, +2, (+1),0; IE: 758 kJ mol1.

Acidic and nonaqueous solutions

CoO2(s) + e + 4H+ Co3+(aq) + 2H2O

E 0 = 1.416 V[Co(H2O)6]

3+(aq) + e [Co(H2O)6]

2+(aq)

Eo

c = 1.95 V (4 M HClO4)Co2+(s) + 2e Co(s)

E 0 = 0.277 V (calcd)[Co(NH3)6]

3+(aq) + e [Co(NH3)6]

2+(aq)

Eo

c = 0.058 V (7 M NH3,1 M NH4Cl)

[Co(C2O4)3]3(aq) + e

[Co(C2O4)3]4(aq)

Eo

c = 0.57 V (1 M KCl)[Co(C2H5)2]

(aq) + e (cobaltocenium)

[Co(C2H5)2]2(aq)(cobaltocene)

Eo

c = 0.918 VEo

c = 1.146 V (CH3CN)

Eo

c = 0.79 V (HCONH2)


Co(salen)+ + e Co(salen)Eo

c 0.45 V versus

Fc+/Fc (DMF)

Eo

c 0.37 V versusAg+/Ag (CH3CN)

Co-phthalocyanine (CoIIPc)

+ e (CoIPc)Eo

c = 0.602 V (pH 13) [46]

Co-hexadecauorophthalocyanine

(CoIIF16Pc) + e (CoIF16Pc)Eo

c = 0.381 V [46]

(Formal potential of other substitutedPcs can also be found in Ref. 46.)

Basic solutions

CoO2(s) + e + 2H2O Co(OH)3(s) + OH(aq)

E 0 = 0.7 VCo(OH)3(s) + e

Co(OH)2(s) + OH(aq)E 0 = 0.17 V

Co(OH)2(s) + 2e Co(s) + 2OH(aq)

E 0 = 0.733 V[Co(CO)4]2(aq) + 2e

2[Co(CO)4](aq)

E 0 = 0.4 VSolubility and complex equilibria:

Co(OH)2 Co2+ + 2OH

Ksp = 1.6 1018

Co(OH)3 Co3+ + 3OH

Ksp = 2.5 1043

CoS() Co2+ + S2Ksp = 3.1 1023

CoS() Co2+ + S2Ksp = 1.9 1027

CoS( ) Co2+ + S2Ksp = 3 1026

CoCO3 Co2+ + CO32Ksp = 1 1017

Rhodium (102.90545 Rh), OS: (+6), (+5),(+4), +3, +2, (+1), 0, (1); IE: 720 kJmol1.

2RhO2(s) + 2e + 2H+ Rh2O3(s) + H2O

E 0 = 1.73 V (calcd)Rh2O3(s) + 6e + 6H+

2Rh(s) + 3H2OE 0 = 0.88 V (calcd)

Rh3+(aq) + 3e Rh(s)E 0 = 0.758 V (calcd)(HClO4, pH 5)

[RhCl6]3(aq) + 3e Rh(s) + 6Cl(aq)

E 0 = 0.5 V (HCl)[Rh(CN)6]

3(aq) + e [Rh(CN)6]

4(aq)

E 0 = 0.9 VIridium (192.21777 Ir), OS: (+6), (+5), +4,

+3, (+2), +1, 0; IE: 880 kJ mol1.IrO2(s)+4e+4H+ Ir(s)+2H2O


Eo

c = (0.935 0.005)VIrO(s) + 2e + 2H+ Ir(s) + H2O

Eo

c = (0.87 0.02)V (1 M H2SO4)[IrCl6]2(aq) + e [IrCl6]3(aq)

Eo

c = 0.867 V (0.3 M HCl)[IrCl6]3(aq) + 3e

Ir(s) + 6Cl(aq)E 0 = 0.83 V (calcd)

[Ir(H2O)Cl5](aq) + e

[Ir(H2O)Cl5]2

Eo

c = 1.0 V (0.2 M HNO3)[Ir(H2O)3Cl3]+(aq) + e

[Ir(H2O)3Cl3](aq)

Eo

c = 1.30 V (0.4 M HClO4)[IrBr6]2(aq) + e [IrBr6]3(aq)

Eo

c = 0.883 V (1 M HClO4)[IrI6]2(aq) + e [IrI6]3(aq)

Eo

c = 0.49 V (1 M KI)

Formal potentials of Irphosphine com-plexes in nonaqueous solutions can befound in Refs 4749.

Meitnerium ([268.139]109Mt)No data are available.

2.10Group 10 Elements

Nickel (58.693428Ni), OS: (+6), +4, +3, +2, 0;IE: 757 kJ mol1.

Acidic solutions

NiO2(s) + 2e + 4H+ Ni2+(aq) + 2H2O

E 0 = 1.59 V (calcd)Ni2+(aq) + 2e Ni(s)

E 0 = 0.257 VNiS()(s) + 2e

2Ni(s) + S2(aq)E 0 = 0.814 V

NiS()(s) + 2e 2Ni(s) + S2(aq)

E 0 = 0.96 VNiS( )(s) + 2e

2Ni(s) + S2(aq)E 0 = 1.07 V

[Ni(NH3)6]2+(aq) + 2e Ni(s) + 6NH3(aq)

E 0 = 0.476 V

Basic solutions

Ni(OH)4(s) + e Ni(OH)3(s) + OH(aq)

E 0 = 0.6 V (calcd)Ni(OH)3(s) + e

Ni(OH)2(s) + OH(aq)E 0 = 0.48 V (calcd)

Ni(OH)2(s) + 2e Ni(s) + 2OH(aq)

E 0 = 0.72 VNiO(OH) + e + H2O

Ni(OH)2(s) + OH(aq)Eo

c = 1.39 V (1 M NaOH)


Solubility and other equilibria:

NiS() Ni2+ + S2Ksp = 3 1021

NiS() Ni2+ + S2Ksp = 1 1026

NiS( ) Ni2+ + S2Ksp = 2 1028

Ni(OH)2 Ni2+ + 2OHKb = 1.6 1016

[Ni(NH3)6]2+

Ni2+ + 6NH3(aq)K = 1.8 109

[Ni(CN)4]2+ Ni2+ + 4CN

K = 1 1022

Palladium (106.4246Pd), OS: (+6), +4, (+3),+2, (+1), 0; IE: 804 kJ mol1.

PdO2(s) + 2e + 2H+ PdO(s) + H2O

E 0 = 1.263 V (calcd)E 0 = 1.47 V (measured)

PdO2(s) + 2e + 4H+ Pd2+(aq) + 2H2O

E 0 = 1.194 VPdCl62(aq) + 2e

PdCl42(aq) + 2Cl(aq)E 0 = 1.47 V (1 M HCl)

PdBr62(aq) + 2e PdBr42(aq) + 2Br(aq)

E 0 = 0.99 V (1 M KBr)PdI62(aq) + 2e

PdI42(aq) + 2I(aq)E 0 = 0.48 V (1 M KI)

Pd2+(aq) + 2e Pd(s)E 0 = (0.915 0.005)V(HClO4)

PdO(s) + 2e + 2H+ Pd(s) + H2O

E 0 = 0.917 V (calcd)E 0 = 0.79V (measured)

PdCl42(aq) + 2e Pd(s) + 4Cl(aq)

Eo

c = 0.62V (1 M HCl)PdBr42(aq) + 2e

Pd(s) + 4Br(aq)Eo

c = 0.49V (1 M KBr)

PdI42(aq) + 2e Pd(s) + 4I(aq)

Eo

c = 0.18V (1 M KI)

Palladium shows a great capacity forhydrogen absorption. This takes place withchanges in the crystalline structure ofthe metal with the formation of Pd2H orPd4H2 hydrides.

Platinum (195.07878Pt), OS: (+6), +4, (+3),+2, (+1), 0; IE: 870 kJ mol1.

PtO2(s) + 2e + 2H+ PtO(s)E 0 = 1.045 V (calcd)

PtO2(s) + 2e + 4H+ Pt2+(aq) + 2H2O

E 0 = 0.837 V (calcd)PtO(s)+2e+2H+ Pt(s)+H2O

E 0 = 0.98 V (calcd)


Pt2+(aq) + 2e Pt(s)E 0 = 1.188 V

PtCl62(aq) + 4e Pt(s) + 6Cl(aq)

E 0 = 0.744 VPtBr62(aq) + 4e

Pt(s) + 6Br(aq)E 0 = 0.657 V

PtI62(aq) + 4e Pt(s) + 6I(aq)

Eo

c = 0.4 V (1 M NaI)PtCl62(aq) + 2e

PtCl42(aq) + 2Cl(aq)E 0 = 0.726 V

PtBr62(aq) + 2e PtBr42(aq) + 2Br(aq)

E 0 = 0.613 VPtI62(aq) + 2e

PtI42(aq) + 2I(aq)E 0 = 0.329 V

PtCl42(aq) + 2e Pt(s) + 4Cl(aq)

Eo

c = 0.758 VPtBr42(aq) + 2e

Pt(s) + 4Br(aq)Eo

c = 0.698 V (3 MHClO4 and HBr)

PtI42(aq) + 2e Pt(s) + 4I(aq)

Eo

c = 0.4 V (0.5 M NaI)cis-Pt(NH3)2Cl4(aq) + 2e

Pt(NH3)2Cl2(aq) + 2Cl(aq)Eo

c = 0.669 V (1 M NaCl)

(cisplatin, cancer chemotherapy agent)Solubility and complex equilibria:

Pt(OH)2 Pt2+ + 2OH

Ksp 1024

Pt(OH)3 Pt3+ + 3OH

Ksp 1025

PtS Pt2+ + S2Ksp 1068

Darmstadtium ([271]110Ds)No data are available.


Copper (63.54629Cu), OS: +2, +1, 0; IE: 745.3,1957.3, 3577.6 kJ mol1.

Acidic solutions

Cu2+(aq) + 2e Cu(s)E 0 = 0.340 V

Cu2+(aq) + e Cu+(s)E 0 = 0.159 V

Cu+(aq) + e Cu(s)E 0 = 0.520 V

Cu2+(aq) + e + Cl(aq) CuCl(s)E 0 = 0.559 V

CuCl(s) + e Cu(s) + Cl(aq)E 0 = 0.121 V


Cu2+(aq) + e + Br CuBr(s)E 0 = 0.654 V

CuBr(s) + e Cu(s) + Br(aq)E 0 = 0.033 V

Cu2+(aq) + e + I CuI(s)E 0 = 0.861 V

CuI(s) + e Cu(s) + I(aq)E 0 = 0.182 V

2CuS(s) + 2e Cu2S(s) + S2(aq)E 0 = 0.542 V

Cu2S(s) + 2e 2Cu(s) + S2(aq)E 0 = 0.898 V

Cu(NH3)2+(aq) + e

Cu(s) + 2NH3(aq)E 0 = 0.100 V

Cu(NH3)42+(aq) + e

Cu(NH3)2+(aq) + 2NH3(aq)

E 0 = 0.10 VCu(CN)2

(aq) + e Cu(s) + 2CN(aq)

E 0 = 0.44 VCu2+(aq) + e + 2CN(aq)

Cu(CN)2(aq)E 0 = 1.12 V

Basic solutions

CuO(s) + 2e + H2O Cu(s) + 2OH(aq)

E 0 = 0.29 VCuO(s) + e + H2O

Cu2O(s) + OH(aq)E 0 = 0.22 V

Cu2O(s) + 2e + H2O 2Cu(s) + 2OH(aq)

E 0 = 0.365 V


CuCl Cu+ + ClKsp = 1.9 107

CuBr Cu+ + BrKsp = 5.9 109

CuI Cu+ + IKsp = 5.1 1012

Cu2S 2Cu+ + S2Ksp = 1.6 1048

CuS Cu2+ + S2Ksp = 7.9 1037

Cu2[Fe(CN)6] 2Cu2+ + [Fe(CN)6]4

Ksp = 1.3 1016

Cu(OH)2 Cu2+ + 2OHKsp = 1.6 1019

Complex equilibriaThe information about the composition

and stability of several Cu2+ complexeswith nitrogen-containing and polyhydrox-ylic ligands can be found in Refs 5065.

Silver (107.86247Ag), OS: (+3), (+2), +1, 0;IE: 731, 2072.6, 3359.4 kJ mol1.

Acidic solutions

Ag+(aq) + e Ag(s)E 0 = 0.7991 V


AgCl(s) + e Ag(s) + Cl(aq)E 0 = 0.2223 V

AgBr(s) + e Ag(s) + Br(aq)E 0 = 0.0711 V

AgI(s) + e Ag(s) + I(aq)E 0 = 0.1522 V

Ag(CN)2(aq) + e

Ag(s) + 2CN(aq)E 0 = 0.31 V

Ag(SCN)2(aq) + e

Ag(s) + 2SCN(aq)E 0 = 0.304 V

Ag4[Fe(CN)6](s) + 4e 4Ag(s) + [Fe(CN)6]4(aq)

E 0 = 0.1478 VAg3PO4(s) + 3e

3Ag(s) + PO43(aq)E 0 = 0.4525V

Ag(NH3)2+(aq) + e

Ag(s) + 2NH3(aq)E 0 = 0.373 V

Ag2SO4(s) + 2e 2Ag(s) + SO42(aq)

E 0 = 0.654 VAgClO4(s) + e

Ag(s) + ClO4(aq)E 0 = 0.787 V

Ag(S2O8)23(aq) + e Ag(s) + 2S2O82(aq)

E 0 = 0.01 VAg2CrO4(s) + 2e

2Ag(s) + CrO42(aq)E 0 = 0.4491 V

Ag2+(aq) + e Ag+(s)E 0 = 1.98 V

Ag2O3(s) + 4e + 6H+ 2Ag+(aq) + 3H2O

E 0 = 1.36 VAgO(s) + e + 2H+

Ag+(aq) + H2OE 0 = 1.772 V

Basic solutions

Ag2O3(s) + 2e + H2O 2AgO(s) + 2OH(aq)

E 0 = 0.739 V2AgO(s) + 2e + H2O

Ag2O(s) + 2OH(aq)E 0 = 0.604 V

Ag2O(s) + 2e + H2O 2Ag(s) + 2OH(aq)

E 0 = 0.342 V


AgCl Ag+ + Cl

Ksp = 1.77 1010


AgBr Ag+ + Br

Ksp = 5.0 1013

AgI Ag+ + I

Ksp = 8.7 1017

Ag2S 2Ag+ + S2

Ksp = 1 1050

Ag2SO4 2Ag+ + SO42

Ksp = 1.2 105

Ag2CO3 2Ag+ + CO32

Ksp = 8 1012

Ag2CrO4 2Ag+ + CrO42

Ksp = 2.7 1012

Ag2C2O4 2Ag+ + C2O42

Ksp = 1.1 1011

Ag3[Fe(CN)6] 3Ag+ + [Fe(CN)6]3

Ksp = 1 1020

Ag4[Fe(CN)6] 4Ag+ + [Fe(CN)6]4

Ksp = 8.6 1045

Gold (196.96679Au), OS: +3, (+2), +1, 0; IE:890, 1973.3, (2895) kJ mol1.

Au3+(aq) + 3e Au(s)E 0 = 1.52 VEo

c = 1.362 V (1 mol kg1 H2SO4)

AuCl4(aq) + 3e Au(s) + 4Cl(aq)

E 0 = 1.002 V

AuBr4(aq) + 3e Au(s) + 4Br(aq)

E 0 = 0.854 VAuI4(aq) + 3e

Au(s) + 4I(aq)E 0 = 0.56 V

[Au(SCN)4](aq) + 3e

Au(s) + 4SCN(aq)E 0 = 0.636 V

[Au(NH3)4]3+(aq) + 3e

Au(s) + 4NH3(aq)E 0 = 0.325 V

Au3+(aq) + 2e Au+(aq)E 0 = 1.36 V

AuCl4(aq) + 2e AuCl2(aq) + 2Cl(aq)

E 0 = 0.926 VAuBr4(aq) + 2e

AuBr2 (aq) + 2Br(aq)E 0 = 0.802 V

AuI4(aq) + 2e AuI2(aq) + 2I(aq)

E 0 = 0.55 V[Au(SCN)4]

(aq) + 2e Au(SCN)2

(aq) + 2SCN(aq)E 0 = 0.623 V

Au+(aq) + e Au(s)E 0 = 1.83 V

AuCl2(aq) + e Au(s) + 2Cl(aq)


E 0 = 1.154 VAuBr2(aq) + e

Au(s) + 2Br(aq)E 0 = 0.96 V

AuI2(aq) + e Au(s) + 2I(aq)

E 0 = 0.578 V[Au(SCN)2]

(aq) + e Au(s) + 2SCN(aq)

E 0 = 0.662 V[Au(CN)2]

(aq) + e Au(s) + 2CN(aq)

Eo

c = 0.595 V (0.5 M KCN)[Au(NH3)2]

+(aq) + e Au(s) + 2NH3(aq)

Eo

c = 0.563 V (10 M NH4NO3)Solubility equilibria:

AuCl Au+ + Cl

Ksp = 2 103

AuBr Au+ + Br

Ksp = 5 1017

AuCl3 Au3+ + 3Cl

Ksp = 3.2 1025

AuBr3 Au3+ + 3Br

Ksp = 1.6 1023

AuI3 Au3+ + 3I

Ksp = 1 1046

Au(OH)3 Au3+ + 3OH

Ksp = 1 1053

Rontgenium ([272]111Rg)No data are available.


Zinc (65.40930Zn), OS: +2, (+1), 0; IE: 906.1,1733, 3831 kJ mol1.

Acidic solutions

Zn2+(aq) + 2e Zn(s)E 0 = 0.7626 V

Zn2+(aq) + 2e + (Hg)x Zn(Hg)x (two phase)

E 0 = 0.76175 V [1][Zn(NH3)4]

2+(aq) + 2e Zn(s) + 4NH3(aq)

E 0 = 1.04 V[Zn(CN)4]

2(aq) + 2e Zn(s) + 4CN(aq)

E 0 = 1.34 VZnS(s) + 2e Zn(s) + S2(aq)

E 0 = 1.44 V

Basic solutions

Zn(OH)42(aq) + 2e

Zn(s) + 4OH(aq)E 0 = 1.285 V (calcd)

Zn(OH)2(s) + 2e Zn(s) + 2OH(aq)

E 0 = 1.246 VZnO(s) + 2e + H2O

Zn(s) + 2OH(aq)


E 0 = 1.248 VSolubility and complex equilibria:

Zn(OH)2 Zn2+ + 2OHKsp = 4.5 1017

ZnS(sphalerite) Zn2+ + S2Ksp = 2.2 1027

ZnS(wurtzite) Zn2+ + S2Ksp = 1.6 1023

ZnS(precipitated) Zn2+ + S2Ksp = 8.7 1023

ZnCO3 Zn2+ +

volume 7 inorganic chemistry

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