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Potential versus pH (Pourbaix) DiagramsE. Protopopoff and P. Marcus, CNRS, Ecole Nationale Superieure de Chimie de Paris, Universite Pierre et Marie Curie

THE PRINCIPLE OF POTENTIAL-pH DI-AGRAMS was established in the 1940s in Bel-gium by Marcel Pourbaix (Ref 1–4). A potential-pH diagram is a graphical representation of therelations, derived from the Nernst equation, be-tween the pH and the equilibrium potentials ( E )of the most probable electrochemical reactionsoccurring in a solution containing a specic ele-ment. The standard equilibrium potentials arecomputed from thermodynamic data (standardchemical potentials, or Gibbs free energies of formation). The equilibrium relations drawn fora given concentration of the element or for agiven ratio of activities of two dissolved speciesof the element give E -pH lines. The representa-tion of the equilibrium pHs for acid-base reac-tions (independent of the potential) gives verticallines. All those lines delimit E -pH domains of stability for the various species of the element,metal, ions, oxides, and hydroxides. Potential-pH diagrams synthesize many important types of information that are useful in corrosion and inother elds. They make it possible to discern at

a glance the stable species for specic conditionsof potential and pH (Ref 1–4).The principle of E -pH diagrams may be sim-

ply understood with the case of iron in water.Corrosion in deaerated water is expressed by theelectrochemical reaction Fe r Fe 2 2e . Theequilibrium potential for the Fe 2 /Fe couple canbe calculated using the Nernst equation:

E E RT

F a

Fe Fe Fe Feo

Fe2 2 2+ + += +2

ln(Eq 1)

where E Fe Feo

2+ is the standard potential value forthe couple, R is the gas constant, T is the absolutetemperature, F is the Faraday constant, and a

Fe 2+

is activity for the ferrous ion in solution.For a given temperature and Fe 2 concentra-

tion (activity aFe 2+), the equilibrium potential is

constant and is represented as a horizontal linein a E -pH diagram (Fig. 1). This line indicatesthe potential at which Fe and Fe 2 at a givenconcentration are in equilibrium and can coexistwith no net tendency for one to transform intothe other. At potentials above the line, iron metalis not stable and tends to dissolve as Fe 2 , hencethe Fe 2 concentration increases until a newequilibrium is reached; this is a domain of sta-

bility for Fe 2 . At potentials below the equilib-rium line, the stability of the metallic iron in-creases, Fe 2 tends to be reduced, and thus itsconcentration decreases; this is the domain of stability for the metal (Fig. 1).

The diagrams of all metal-water systems havethe same common features; the lower E -pH linesgive the limit between the domain of stability of the metal and the domain of stability of eitherthe rst metallic ion or the rst metallic oxide.

For E -pH conditions below these lines, themetal is stable, and corrosion cannot take place.This is the immunity region (Fig. 1).

For E -pH conditions above the line for theequilibrium between the metal and the rst me-tallic ion, the metal is not stable, and it tends tobe oxidized and dissolved into ions. The systemis then in the corrosion or activity region of thediagram. Besides the main corrosion region inthe stability domains of the metallic ions at lowpH (acid corrosion), there is generally also asmaller domain of stability of oxygenated me-tallic ions at high pHs, leading to alkaline cor-rosion (Fig. 1).

When the reaction of the metal with water pro-duces an oxide (or hydroxide) that forms a pro-

Fig. 1 Iron E -pH diagram. Dashed lines a and b are explained in Fig. 7 and in the corresponding text.



Potential versus pH (Pourbaix) Diagrams / 1

Fig. 4 Partial E -pH diagram for the equilibri8H 6e 2H2O NO NH2 4

Fig. 3 Partial E -pH diagram for the equilibriumNi H2O NiO 2H 2e

The Nernst equation can be written as follows:

E E RT

zF aa

RT F

NiO Nio NiO

Ni2

pH

+ = + 2.303

−

log

.2 303(Eq 10)

where the standard potential E o is given by:

E F

eo NiO0

H0 0

Ni0

H O0

2=+ + − −+ −µ µ µ µ µ2 2

2( )

From the data in Ref 4:

E o K

V

298 15215 940 0 0 0 237 190

2 96 487

0 11

., ,

,

.

( ) ( )( )( )

= − + + − − −×

= +

The NiO and Ni are solid phases, and they areconsidered to be pure; their activity is therefore1. Equation 10 can then be simplied, and theequilibrium potential at 25 C becomes:

E eq(NiO/Ni) (298.15 K) 0.11 0.059 pH (Eq 11)

In this case, the equilibrium potential decreaseswith an increase in pH, as represented in the par-tial E -pH diagram of Fig. 3. The diagonal linegives the value of the equilibrium potential of the NiO/Ni couple at all pH values. Above theline, NiO is stable, and below it, nickel metal isstable.

Potential-pH diagrams are very general andcan also be applied to electrochemical reactionsinvolving nonmetallic elements. An example in-volving the reduction of nitrite ion ( NO 2

−) to am-monium ion ( NH 4

+) is given here. In this case,the metal of the electrode supports the reaction

by giving or taking away electrons, as follows:

NO H NH H O2 4 2− + − ++ + +8 6 2e

The Nernst equation gives:

E E RT

F

a

a

RT F

= +

−

−

+

o NO

NH

2

4

2.3038

pH

2 3036

6

. log

(Eq 12)

where the standard potential is expressed as:

E F

eo NO H NH H O2 4 2

6=

+ 8 + 6 − −− + − +µ µ µ µ µ0 0 0 0 02( )

From the data in Ref 4:

E o K298 15

34 520 0 0 79 500 2 237 190

6 96 487

.

, , ,

,

( )( ) ( )( )

( )=

− + + − − − −×

== +0 90. V

The equilibrium potential at 25 C is thengiven by:

E a

a298 15 0 90 0 010 0 079. . . log .K pHNO

NH

2

4

( )= + −−

+ (Eq 13)

This E -pH relation is represented for equal ac-tivity in NO 2

− and NH 4+ by the line drawn in Fig.

4.

Above the line, the ratio a aNO NH2 4− +( ) ishigher than unity, so this is a region where NO

2−is predominantly stable. Below the line, the ratio

a aNO NH2 4

− +( ) is lower than unity, so this is aregion where NH 4+ is predominantly stable.

Acid-Base Reactions. Consider a typicalacid-base chemical reaction in aqueous solution,between the acid form C and the basic form B:

cC d H2O bB mH (Eq 14)

When the reaction is in thermodynamic equi-librium:

∆r B

0

H C

0

H O

eq

2

2.303 KG b m c d

RT

0 0 0

= + − −= −+µ µ µ µlog

where DrG0 is the standard Gibbs free energy

change, l 0 represents the standard chemical po-tentials of the different substances, and K eq is theequilibrium constant for the reaction:Keq a a a a

b m c d B H C H O2( ) ( ) ( ) ( )+ .

The activity of water may be taken equal tounity in not too concentrated aqueous solutions.

If B or C is a pure solid phase (metal, oxide, orhydroxide), a B or a C is equal to unity. Using pH

− +log aH , the previous equation may be rear-

ranged as:

log log.

K pHeqB

C

r= − = −a

am

G RT

b

c

( )( )

∆ 0

2 303 (Eq

This equation shows that the ratio of the ac-tivities of the basic form to the acid form in-creases with pH. The pH at equilibrium corre-sponding to a given ratio r (a B)b /(a C)c candetermined from:

pHpK

eqeq= +

m

r

mlog( )

(Eq

with pK eq log K eq DrG0 /2.303 RT.

This equilibrium pH does not depend on thepotential and will be represented on the E -diagram by a vertical line. As an example, in thecase of cobalt, Co 2 and CoO are involved in anacid-base reaction:

Co2 H2O s CoO 2H (Eq

CoO and H 2O both have activities of 1, so theapplication of Eq 16 gives:

pHpK

eqeq Co 2= − +

2 2

log a( )(Eq

with:

pK eq CoO H Co H O0

2 2= + − −+ +( ) / .µ µ µ µ0 0 02 2 303 R

By replacing the standard chemical potentialsby their values given in the Atlas of Electchemical Equilibria (Ref 4):

pK Keq 298 15

218 860 0 53 560 237 1908 3143 298

.

, , ,.

( )

( ) ( )( )= − + − − − −× .. .

.

15 2 303

12 6

×=

( )

and nally:

pH K2eq

Co2298 15 6 3. .

log( )

( )= − +a

Fig. 2 Partial E -pH diagram for the equilibriumNi2 2e Ni for various values of log a

Ni2 +



20 / Fundamentals of Corrosion

Fig. 5 Partial E -pH diagram for the Co 2 /Co and CoOCo couples for a

Co2 + 1

Thus, for an activity unity for Co 2 , pH eq6.3. This value can also be obtained by the in-tersection of two equilibrium E -pH lines. Asshown previously for nickel, there are electro-chemical equilibria between the metal and itsrst ion (Co 2 ) and between the metal and itsrst oxide (CoO). It is possible to determine theequilibrium E -pH lines for the couples Co 2 /Coand CoO/Co, as shown in Fig. 5. The two linesintersect at point P, and above them are the do-mains of stability for Co 2 and CoO. Theboundary between these two domains is a ver-tical line containing point P and located at pH6.3 for a

Co2+ 1 (Fig. 5).Figure 6(a) shows a partial E -pH diagram for

different values of log aCo 2+ in which only three

chemical species—Co, Co 2 , and CoO (or thehydroxide Co(OH) 2)—are considered. There are,however, other possible chemical species, dis-solved or solid, that must be considered. Thisintroduces new equilibria that modify the dia-gram to give Fig. 6(b).

The Water E -pH Diagram. Pourbaix dia-grams are traced for equilibrium reactions taking

place in water; consequently, the water systemmust always be considered at the same time asthe system under investigation in any E -pH di-agram. Water can be decomposed into oxygenand hydrogen, according to the following elec-trode reactions:

2 2 2H O H OH2 l 2 g aq( ) ( ) ( )+ +− −e (Eq 19)

and

H O O H2 l 2 g aq( ) ( ) ( )1

2 2 2+ ++ −e

Considering the equilibrium of water disso-

ciation/ionization into solvated protons and hy-droxide ions:

H O H H2 l aq aq( ) ( ) ( ) + ++ Ο

equilibria (Eq 19) may also be written as:

2H Haq 2 g( ) ( )+ −+ 2e

and

2OH Oaq 2 g l( ) ( ) ( )1

2 + Η Ο + 22−e

The equilibrium potentials of these two elec-

trochemical reactions can be determined by us-ing the Nernst equation. For the water/hydrogenor proton/hydrogen couple:

E E RT

F f

RT F

H H H Ho

H2 2 2

pH

+ += −

−

2 3032

2 303

.log

.(Eq 20)

where f H2 is the fugacity or pressure of hydrogennear the electrode (in fact, dimensionless fugac-ity is equal to the numerical value of the fugacity

expressed in bar). At 25 C (298.15 K), because,by denition, E

H Ho

2+ 0 V/SHE (see the article

“Electrode Potentials” in this Section of the Vol-ume), the previous equation can be rewritten as:

E f H H H

2 2K pH+ = − −298 15 0 030 0 059. . log .( ) (Eq 21)

This relation for f pH H2 2( bar)= =1 1 Fig. 6(b)

and 7 by line a, which decreases with increasingpH.For the oxygen/water or oxygen/hydroxide

couple:

E E RT

F f

RT F

O H O O H Oo

O2 2 2 2 2

pH

= +

−

2 3034

2 303

. log

.(Eq 22)

where f O2 is the fugacity of O 2 near the electrode.The water activity is, as usual, assumed to be 1.At 25 C (298.15 K), the standard potential forO2 /H 2O is 1.23 V SHE (Ref 4), so the equationcan be rewritten as:

E f O H O O2 2 2K

pH

298 15 1 23 0 015

0 059

. . . log

.

( )= +− (Eq 23)

This relation for f pO O2 2( bar)= =1 1 is rep-

resented by line b in Fig. 6(b) and 7.It is interesting to note that the pressures of

hydrogen and oxygen in the vicinity of the elec-trode are usually identical and nearly equal tothe pressure that exists in the electrochemicalcell. To be rigorous, the water vapor pressureshould be taken into account, but it is frequentlyneglected as not being very signicant at 25 C(298.15 K). When the pressure increases, line bin Fig. 7 is displaced upward in the diagram, and

line a is lowered. The result is that the domainof water stability increases with increasing pres-sure.

The water system is very important for a goodunderstanding of the corrosion behavior of met-als; it is represented (usually by dashed lines) inall Pourbaix diagrams (Ref 4).

Conventions for E -pH Diagram Construc-tion. In the construction of diagrams for binary(metal-water) systems, the authors follow theoriginal Pourbaix format (Ref 4) and delineateregions within which condensed phases are sta-ble by solid lines, whereas coexistence linesseparating the predominance areas for dissolvedspecies are drawn dashed, even in the regionswhere the condensed species are stable (Fig. 8).Also, it is common to draw the lines of separa-tion between solid compounds and dissolvedspecies for a number of different activities of thelatter. The large number of lines may render thediagram difcult to read (Fig. 8). Moreover, theamount of the chemical element considered,when summed over all dissolved species con-taining this element, should be constant over thediagram. On diagrams calculated on this princi-ple of constant total element concentration, asthe activities in the ideal solution model aretaken equal to the numerical values of the con-

centrations (molalities), the lines correspondingto the limits of the stability domain of a solidspecies are rounded where two solution speciescoexist (e.g., the boundaries between domains of Fe 2 , Fe 3 , and Fe 2O3 in Fig. 8).

When this principle is adopted rigorously, thediagrams are tedious to compute. Thereforewidely adopted convention in calculating the EpH line for the equilibrium between a solid spe-cies and a dissolved species is that the dissolvedspecies has simply an activity equal to the mo-lality equal to that it would have if it were theonly form present, that is, the selected molalityof the element in solution, divided by the numberof atoms of the element in a molecule of thespecies. The effect of this simplifying assump-tion is that all lines on the diagrams are straight.Figure 9 shows a diagram simplied with respectto the original Pourbaix format (Fig. 8). The di-agram (Fig. 9) is further simplied by limitingthe pH range from 0 to 14.

Consider the consequences of choosing a con-vention on the element concentration when con-structing a diagram. For an equilibrium between

two dissolved forms, R and O, of an element.The E -pH line calculated for equal concentrationof the two forms separates the domains of rela-tive predominance of R and O is calculated fromthe Nernst equation for equal concentrations of the element under the two forms. When thechemical formulae of the two forms contain thesame number of atoms of the element, the con-centrations of the two forms are equal, so thelogarithmic term with the ratio of activities inthe Nernst equation is equal to 0. In this case,the equation of the separation line does not de-pend on the total concentration of the element(Ref 4, 6, 41). For example, for the reaction:

SO H H S H O42

2 aq 2− + −

+ + +10 8 4e ( ) (Eq 24

the equilibrium equation is:

E E RT

F

a

a

RT F

= +

−

−o SO

H S

42

2

pH

2 3038

2 30354

. log

.

(Eq 25




Fig. 7 The water E -pH diagram at 25 C (298.15K)1 bar

Fig. 6 E -pH diagram for the cobalt-water system for various values of log aCo2 +. (a) Partial E -pH diagram. (b) Complete E -pH diagram

The equation of the limit between the areas of relative predominance of and H 2S(aq)2SO 4simplies to:

E E RT

F = −o pH2 30354. (Eq 26)

This is not true when the formula of the twodissolved forms do not contain the same numberof atoms of the element. For example, for thereaction:

S O H H S 3H O2 32

2 2− + −+ + +10 8 2e (Eq 27)

the equilibrium equation is:

E E RT

F

a

a

RT F

= +

−

−o S O

H S

2 32

2

pH

2 3038

2 30354

2. log

.

( )

(Eq 28)

In this case, the equation of the separation linedepends on the total concentration of sulfur (mo-lality mS). If it were considered that the total ele-ment amount is constant, the equation of thelimit of the areas of relative predominance wouldcorrespond to the case where half of sulfur is asH2S(aq) and the other half as S 2 . This would2O3be obtained by taking the concentration mS /2 forH2S(aq) and mS /4 for S 2 (Ref 4, 6, 41). The2O3equation of the separation line would then be:

E E RT

F m

m

RT F

= +

−

o S

S

pH

2 3038

4

2

2 30354

2. log

.

( )

or

E E RT

F m

RT F

= − −oS pH2 303

82 303

54

. log .(Eq 29)

If the simplifying convention described pre-viously is chosen, the E -pH line for equilibriumbetween two dissolved species is calculated con-sidering that each dissolved species is the onlyform of the element present in solution; for ex-ample, taking the concentration mS for H 2S(aq)and mS /2 for S 2 . Then, the equation of the2O3separation line is:

E E RT F

mm

RT F

= +

−

o S

S

pH

2 3038

2

2 30354

2. log

.

( )( )

or

E E RT

F

RT F

m RT

F

= −

− −

o

S pH

2 3038

2

2 3038

2 30354

. log

. log .

(Eq 30)

The simplication with respect to the classicPourbaix presentation of the diagrams allows again of clarity and makes easier the constructionof the more complex diagrams for multicompo-

nent systems.Diagrams for Metastable Species. It is tonoted that the species present in solution in realconditions are not necessarily the more stableones but may be metastable species that are lessstable thermodynamically but, for kinetic rea-sons, are the ones effectively present in solutionfor a nite time. A classic example is the sulfur-




Fig. 9 Simplied E -pH diagram for the iron-water system at25 C fora molalityof dissolvedironequal

to 10 6 mol/kg. Pressure of hydrogen and oxygen, 1 atm

Fig. 8 Original Pourbaix diagram for the iron-water system at 25 C (298.15 K) (oxides are considered; hydroxides arenot). Source: Ref 4

Fig. 10 Simplied E -pH diagram for the sulfur-watesystem at 25 C. The solid lines represent th

stable system. The dashed lines represent the equilibria in-volving the metastablethiosulfates instead of the stablesul-fates. Sulfur molality is 10 4 mol/kg. Pressure of hydrogeand oxygen, 1 atm

water system where the oxidized forms of sulfurpresent in solution are not necessarily the ther-modynamically stable species elemental solidsulfur, hydrogenosulfate, , and sulfate,HSO 4

, ions but can be the metastable dithionates2SO 4S2 , hydrosultes (HS 2 , S 2 ) sultes2 2O O O6 4 4(H2SO 3, , and ), tetrathionates 2HSO SO3 3(S4 ), or thiosulfates (HS 2 , S 2 ) (Ref 2 2O O O6 3 34, 6, 7, 41). Possible reactions between the metaland sulfur metastable species are of interest forprediction of corrosion in industrial systems. The E -pH diagram for the sulfur-water system show-ing the thermodynamically stable species isgiven in Fig. 10 for a sulfur activity (molarity)of 10 4 mol/kg. It exhibits a small stability do-main of solid sulfur from acid to neutral pHs.The same diagram shows the E -pH lines for thecase where the thiosulfate species are consideredas the only oxidized forms of sulfur (dashedlines). According to the construction conven-tions, the activity of the dissolved suldes con-taining one sulfur atom per molecule or ion istaken as 10 4 and the activity of thiosulfate spe-cies containing two sulfur atoms per ion as 0.5

104.

Practical Use of E -pH Diagrams

The E -pH diagram is an important tool for un-derstanding electrochemical phenomena. It pro-vides useful thermodynamic information in asimple gure. Two cases are presented here toillustrate its practical use in corrosion prediction.

Corrosion of Nickel. A rod of nickel is im-

mersed in an aqueous deaerated acid solutionthat contains 10 4 mol/L of Ni 2 ions. The sys-tem is at 25 C (77 F) under 1 atm pressure. The E -pH diagram corresponding to these conditionsis shown in Fig. 11.

At the metal-water interface, two electro-chemical reactions are possible:

Ni s Ni2 2e (Eq 31)

and

2H 2e s H2 (Eq 32)

The equilibrium potentials of the Ni 2 /Ni and

the H /H 2 electrodes can be computed. From Eq

6, E Ni Ni2+ 0.25 0.030 log a

Ni 2+, whichfor a

Ni 2+ 10 4, gives E Ni Ni2+ 0.37 V (Fig

2). From Eq 21, E H H 2

+ 0.059 pH, which,at pH 1, for example, gives E

H H 2+ 0.0

V. E E Ni Ni H H2

2+ +< up to a pH of approximately

6 (Fig. 11). Thus, when connected via an elec-trical circuit, electrons tend to ow from themore negative nickel electrode, where they are

produced by the oxidation reaction, to the lessnegative hydrogen electrode, where they areconsumed by the reduction reaction. In this case,the two electrodes are formed on the surface of the conducting nickel rod. The two reactions willproceed under a common electrode potential ormixed potential, with a value somewhere be-tween the nickel and hydrogen equilibrium po-tentials. Up to pH 6, the mixed potential, E Mis located above the Ni 2 /Ni equilibrium poten-tial in the region of Ni 2 stability and below theH /H 2 equilibrium potential in the region of Hstability (Fig. 11). Hence, nickel is not stable atlow pH in water, and it tends to oxidize (corrode)into Ni 2 , while H is reduced into hydrogengas (hydrogen evolution).

Thus, the Pourbaix diagram explains the ten-dency for nickel to corrode in acid solutions. It




Fig. 11 E -pH diagram for nickel for aNi2 + 10 4

does not indicate the rate of corrosion, however.This important information has to be obtainedfrom a kinetic experiment, for example, fromtherecording of current versus potential curvearound the corrosion potential.

The Pourbaix diagram also shows that whenthe pH increases to approximately 6, the differ-ence between the nickel and the hydrogen equi-librium potential decreases in magnitude, andconsequently, the corrosion tendency dimin-ishes. For pHs between 6 and 8 (limit of stabilityof Ni 2 ), Fig. 11 shows that the hydrogen elec-trode potential becomes lower than the nickelone. Under these conditions, H can no longeraccept the electrons from nickel. The mixed po-tential of the system is, in this case, below theequilibrium potential of Ni 2 /Ni, in the regionof metal immunity. Hence, in water at room tem-perature, nickel does not corrode for pH 6 to 8.No such pH range exists for the iron-water sys-tem, where the Fe 2 /Fe electrode potential is al-ways lower than the H /H 2 electrode potential(Fig. 1, 8, 9). Therefore, iron will always corrodeto ferrous ions with evolution of H 2 in acid and

neutral solutions. In contrast, the behavior of nickel makes this metal slightly noble (in thesmall pH range of 6 to 8), and, from the diagram,it is expected to resist corrosion better than iron.Moreover, an increase in hydrogen pressure, ac-cording to Eq 21, lowers the equilibrium line of H /H 2 while it does not change the equilibrium

line of Ni 2 /Ni. As a result, an increase in pres-sure leads to greater corrosion resistance fornickel. For pHs higher than 8, lms of NiO (orthe hydrated form Ni(OH) 2) and Ni 3O4 can format the surface at anodic potentials, as can be seenin Fig. 11. These oxides may, in some cases, pro-tect the metal by forming a protective layer thatprevents or mitigates further corrosion. This phe-nomenon is called passivation. It also occurs oniron with the formation of magnetite (Fe 3O4) orhematite (Fe 2O3) at anodic potentials (Fig. 8, 9).The presence of species such as chlorine ionsmay increase the corrosion tendency of metals,because these species may attack the protectivelayer and then favor corrosion. Figures 1, 8, and11 illustrate that iron or nickel may corrode (dis-solve) in very strong alkaline solutions as

or , respectively, or, more likely, HFeO HNiO2 2as the hydrated forms or . Fe(OH) Ni(OH)3 3

Corrosion of Copper. Observation of thecopper E -pH diagram in Fig. 12 immediately re-veals that the corrosion of copper immersed indeaerated acid water is not likely to occur. TheH /H 2 equilibrium potential represented by line

a is always lower than the Cu2

/Cu equilibriumpotential. The H ions are stable in contact withcopper metal, which cannot corrode (is immune)in water solutions free from oxidizing agents.

The presence of dissolved oxygen in non-deaerated solutions introduces another possiblereaction: O 2 reduction into H 2O, with an equilib-

rium potential higher than that of Cu 2 /Cu. TO2 /H 2O couple is then a good acceptor for theelectrons produced by copper oxidation. The twoelectrochemical reactions:

Cu r Cu2 2e (Eq

and

1 ⁄ 2 O2 2H 2e r H2O (Eq

take place spontaneously in acid solutions at thesurface of an immersed piece of copper at a com-mon (mixed) potential. In neutral or alkaline so-lutions, O 2 reduction will be coupledwith coppeoxidation into Cu 2O.

E -pH Diagrams for Ternary System

The E -pH diagrams for corrosion protectiongive valuable information if all the substancespresent in the actual system under investigation(metal or metalloid in aqueous solution) are

taken into account when the diagrams are con-structed. The previous discussion assumed thatthe solution did not contain chlorine, sulfur, orother species capable of forming solid com-pounds or soluble complexes with the metal. Inthe presence of such elements, other diagramsmust be considered that may reveal differentmetal corrosion behavior. Hence, diagrams forbinary metal-water (M-H 2O) systems are of limited usefulness, and diagrams for multicompo-nent systems must be calculated. For example,the simple diagram of gold in water (Au-Hsystem) does not show any solubility for thatmetal. The addition of cyanide (CN) ions to thesystem, however, leads to the formation of a gold

complex soluble in water. Hence, gold, whichdoes not corrode in pure water can dissolve inthe presence of cyanide. This property is the ba-sis of gold plating and of the hydrometallurgy of that metal. Diagrams for the ternary system Au-CN -H2O must then be constructed to show theconditions of stability for the gold complex. Ageneral bibliography of E -pH diagrams for mu

Fig. 12 Partial E -pH diagram for copper for aCu2

10 4




ticomponent systems in aqueous solutions isgiven in Ref 8.

Diagrams for ternary metal-additive-water(M-A-H 2O) systems are frequently used. In mostcases, the amount of one element in the dis-solved form is substantially greater than that of the other. If so, the reactions involving only themajor element will be practically independent of the reactions involving the minor element. Thus,the diagram of the major element alone, drawnwith dashed lines, will serve as a background forthe diagram for the combined system, drawnwith solid lines. The behavior of the minor ele-ment may be or may not be independent of thatof the major element. It will be independent if the minor element forms no stable solid com-pound or dissolved complex with the major ele-ment; in this case the diagram for the ternarysystem will just be the diagram of the minor ele-ment alone superimposed on the diagram of themajor element alone. Otherwise the diagram forthe ternary system may be drastically different.Again, the convention is that in the regions of stability of a dissolved species, the latter is con-

sidered as the only element form present. Whenthe minor element forms a dissolved complexwith the major element, this solution species isconsidered as a species of the minor element,andhence its concentration is the one of the minorelement.

Consider the case where the concentration of additive in the dissolved form is much higherthan the tolerated concentration of dissolvedmetal. First, the E -pH diagram for the A-H 2Osystem must be calculated to determine the areasof predominance for the various species of A.Then, in each area delineated with dashed lines,the E -pH equilibria lines for the various reac-tions between the metal and the predominant A

species to form metal compounds or complexesare calculated. A metal-additive dissolved com-plex is considered as a metal species.

As an example of calculations for a ternarysystem involving metal-additive solid com-pounds, consider the following reactions for theiron-sulfur-water system:● FeS 2 /Fe 2 equilibrium in sulde media:

FeS 2 4H 2e s Fe2 2H 2S(aq) (Eq 35)

or

FeS 2 2H 2e s Fe2 2HS (Eq 36)

● Fe 2 /FeS 2 equilibrium in thiosulfate media:

Fe HS O H FeS H O22 3 2 2

+ − + −+ + + +5 6 3e

(Eq 37)

or

Fe S O H FeS H O22 3 2 2

+ 2− + −+ + 6 + +6 3e (Eq 38)

● Fe 2O3 /FeS 2 equilibrium in thiosulfate media:

Fe S O H

2FeS H O2 2 3

2 2

Ο + 2 +18 +14+ 9

32− + −e

(Eq 39)

At 25 C (77 F), the equations for the previ-ously mentioned equilibria are, respectively, if mS and mFe are the molalities of sulfur and ironin solution:

E E m

m= − −

− ×

o SFe2

pH

0 059 0 059

2

2 0 059

. log .

log

.

(Eq 40)

or

E E m

m= − −

− 0

o SFe2

pH

0 059 0 059

2

059

. log .

log

.

(Eq 41)

E E m

m= + 0.0596 +

− × 0

o SFe

56

2

pH

log .

log

.

0 0596

059 (Eq 42)

or

E E m

m= + 0.059

6 +− 0

o S Fe2

pH

log .

log

.

0 059

6

059 (Eq 43)

E E m= + 0.059

7 − × 097o S

2 pHlog .

059(Eq 44)

Metals may form compounds in dissolvedform with sulfur (e.g., FeSO 4(aq),

). Consider the Cu 2 / FeSO , CuSO CuSO4 3 3equilibrium in sulte media in a case where mCuK mS:

Cu SO CuSO2

3

2

3

+ − − −

+ + e

(Eq 45)

E E aa

a= + 0.059 +−

+

−

oSO

Cu

CuSO32

2

3

log . log0 059

(Eq 46)

The equation of the boundary line between thedomains of relative predominance of Cu 2 and

would be obtained (if the latter were sta-CuSO 3ble) for a a

Cu CuSO23

+ −= ( mCu ):

E E o 0.059 log mS (Eq 47)

An illustration is given for the system iron-sulfur-water in water containing thiosulfates.This case is of technological importance, be-cause thiosulfates dissolved in aqueous solutionare known to be detrimental to the corrosion re-sistance of stainless steels (Ref 9–16). The con-centration of the dissolved sulfur impurity ex-pressed in molality is usually approximately10 4 mol/kg, and the molality of dissolved ironis considered to be 10 6 mol/kg. Such a smallvalue allows conservative predictions of corro-sion, because it is generally agreed that there isno corrosion when the concentration of metalthat can be dissolved in a solution initially freefrom it is lower or equal to 10 6 mol/kg. Thus,

the major element here is sulfur, and the binarydiagram used as a background is the one of themetastable sulfur-water system (compare withFig. 10), showing the thermodynamically stablesuldes (H 2S(aq) and HS ) as reduced forms of sulfur and the metastable thiosulfates ( HS O2 and S O2 3

2−) as the only oxidized forms. The ter-nary diagram for the iron-sulfur-water system isplotted in Fig. 13.

A comparison with the diagram of the binaryiron-water system (Fig. 8, 9) shows that iron in-teracts with suldes or thiosulfates in the mid-pH region to form iron sudes (FeS and FeS 2replacing Fe 2 in acid solutions and magnetite(Fe 3O4) in neutral and alkaline solutions. Be-cause metal suldes are good ionic conductors,they offer little protection against corrosion. Al-though the diagram predicts Fe 2O3 could bformed on the surface under anodic (strongly ox-idizing) conditions over a large pH range andprotect iron from corrosion, the incompatibilitybetween FeS 2 and Fe 2O3 actually preventsgrowth of an adhesive Fe 2O3 layer (Ref 17)Hence, the diagram predicts that iron passivation

will not occur in the presence of suldes or thio-sulfates in solution.

The diagram for the chromium-sulfur-watersystem is plotted in Fig. 14. There is no range of stability of chromium suldes (at least for m S10 4 mol/kg), so the diagram is identical to thebinary diagram for the chromium-water system.It shows that chromium suldes are less stablethan the chromic oxide (Cr 2O3) or hydroxide(Cr(OH) 3), which provide the exceptional cor-rosion resistance of chromium.

E -pH Diagrams for High-Temperature Aqueous Solutions

Prediction of the corrosion behavior of metalsin aqueous solutions at high temperatures is of considerable technological interest. Such a situ-

Fig. 13 E -pH diagram for the iron-sulfur-water systemat 25 C (298.15 K) in thecase wherethe meta-

stablethiosulfatesare theonly oxidizedformsof sulfur.Thestability domains are limited by the dotted lines for the wa-ter system, dashed lines for the sulfur-water system, andsolidlines for the iron-sulfur-water system. m S 10 4 mokg. mFe 10 6 mol/kg




Table 2 Standard Gibbs free energies of formation (chemical potentials) of ironcompounds at 25 and 300 C

SpeciesD f G0(298.15 K),

kJ/molD f G0(573.15 K),

kJ /mo l R eferen

Fe 0 10.155 17Fe3O4 1015.457 1072.468 17Fe2O3 742.242 777.906 17Fe2 91.563 57.497 22FeOH 275.542 272.542 22Fe(OH) 3

614.989 629.094(a) 17

Fe3 17.280 62.718 22FeOH 2 229.409 193.548(a) 17Fe(OH) 2

438.065 438.270(a) 17

2FeO 4 467.290 375.836(a) 17

FeS 100.754 124.540 23FeS 2 160.168 181.440 23

(a) Values after correction of the difference in convention for the freeenergy of formation of H (aq) at 300 C (573.15 K) between this teand Ref 17

Table 1 Standard Gibbs free energies of formation (chemical potentials) of hydrospecies and sulfur compounds(suldes and thiosulfates only) at 25 and300 C


kJ/molD f G0(573.15 K),

kJ/ mol Referenc

H2(g) 0 38.786 21O2(g) 0 59.400 21S(rh,l) 0 12.678 21H2S(g) 33.282 93.423 21

H2O(l)

237.174

263.881 22H (aq) 0 0 . .e (aq) 0 19.393 . . H2S(aq) 27.861 78.881 22HS 12.050 13.648 7, 22HS2

O3 532.414 564.840 7

S2 2O3

522.582 505.260 7

ation is steel vessels in contact with pressurizedwater at 300 C (573.15 K) in nuclear power re-actors. It was necessary to extend the E -pH equi-librium diagrams originally established at 25 C(Ref 4) to higher temperatures. The main prob-lem is that there are few thermodynamic dataavailable for chemical species dissolved in waterabove 60 C (333.15 K). The increase in watervapor pressure with temperature in closed cellsleads to high pressures. This makes it necessaryto carry out experiments in autoclaves, high-strength vessels with special seals (Ref 18). Of-ten, thermodynamic-state functions data at hightemperatures are obtained by extrapolation fromthe data at 25 C using empirical hypotheses onthe inuence of temperature on molar heat ca-pacities. In particular, entropy correspondenceprinciples have been established that make pos-sible the calculation of entropies and heat capac-ities of ions at temperatures up to 300 C fromthe entropy values at 25 C (Ref 19, 20). Analternate treatment of the problem is the calcu-lation of temperature coefcients of standardequilibrium potentials of electrochemical reac-

tions from thermodynamic data at 25 C (Ref 21). A review of these different methods of es-timation is given in Ref 8.

High-temperature Pourbaix diagrams are, bynature, less accurate than those at 25 C that arebased on experimental data, because they arebased on estimates. The effects of pressure onthe equilibria can be ignored up to 300 C be-cause the magnitude of the errors introduced iswithin the uncertainty of the data (Ref 18, 19).

At high temperature, the molar scale for activ-ities must not be used, because, due to water vol-ume changes, the molarity for a given solutequantity (number of moles of solute per liter of water) varies with temperature. One can only use

the molality (number of moles of solute per kil-ogram of water), which is equal to the molarityat 25 C (77 F) but is invariant with temperature.The standard state for each dissolved species is

the hypothetical ideal solution of the substanceat unit molality.

Thermodynamic Conventions for HighTemperature. High-temperature thermody-namic calculations for aqueous solutions requireone to specify additional conventions, and onemust be careful about which convention applieswhen using a set of high temperature data.

Standard chemical potentials, or Gibbs freeenergies of formation at a temperature T , may begiven for the formation of the substance from itselements in their standard states at T or at 25 C(77 F). Thus, in the rst convention, the stan-dard values of elements or diatomic gases arezero at any temperature, whereas, in the secondone, they are zero only at 25 C (77 F). Usingthe second convention, values are given in Table1 for hydrospecies and sulfur species at 25 and300 C. Table 2 lists the values for iron and itscompounds.

Two conventions exist for the potential scale:the “universal” convention and the “alternate”convention. In the universal convention, theelectrode potentials are referred to the potential

of the standard hydrogen electrode (SHE) at thetemperature considered; that is, the potential of the SHE ( ) p aH H2

bar,= =+1 1 is taken equal to0 V at all temperatures. Hence, the chemical po-tential (Gibbs free energy) of the conventionalelectron used in the writing of electrode (half-cell) reactions is, at all temperatures:

µ µ µe

T T T − += −0

11

20 0( ) ( ) ( ) ( )H H2 (Eq 48)

With this convention, the E -pH line for theH (aq)/H 2(g) couple passes by the point ( E 0, pH 0) at any T (Fig. 13).

In the alternate convention, the potentials arereferred to the potential of the SHE at 25 C (77

F). Here, the chemical potential of the conven-tional electron is the same at all temperatures:

µ µ µe− += − =0

21

20 0298 15 298 15 0( ) ( ) ( )H H2 K K. .

(Eq

In this convention, the potential of the SHE de-pends on temperature, and the E -pH line for tH (aq)/H 2(g) couple intersects the vertical axisfor pH 0 above 0 V for T 25 C (Fig. 1The two conventions become identical at 25( )µe−

01 (298.15 K) ( )µe−

02 0.

Solvated H (H (aq)) is often considered aa reference substance whose standard chemicalpotential, or Gibbs free energy of formation, istaken to be zero at all temperatures. Use of theuniversal convention produces the simple rela-tion ( ) ( )µe

T −0

1 1

20µΗ 2 ( )T .

Variation of pH with Temperature. Focorrect interpretation of the high-temperaturepH diagrams, the change of pH of the solutionwith the temperature must be taken into account.The pH of an aqueous solution is determined by:●

The equilibrium constant for water dissocia-tion into solvated protons and hydroxide ions,H2O(l) H (aq) OH (aq), also call

Fig. 14 E -pH diagram for the chromium-sulfur-watersystem at 25 C (298.15 K) in the case where

the thiosulfates are the only oxidized forms of sulfur. Thestability domains are limited by the dotted linesfor the wa-ter system, dashed lines for the sulfur-water system, andsolid lines for the chromium-sulfur-water system. m S

10 4 mol/kg and m Cr 10 6 mol/kg

Fig. 15 pH at 100 and 300 C (373.15 and 573.15 K)versus pH at 25 C (298.15 K) in an unbuffered

solution (pH 200 pH300 ). Also, the correspondence be-tween the pH scales at the different temperatures is shown.




Fig. 17 E -pH diagram for the chromium-water systemat 300 C (573.15 K). mCr 10 6 mol/kg

Fig. 16 E -pH diagram for the iron-water system at 300C (573.15 K). mFe 10 6 mol/kg

the ionic product of water, (K w)T

a aH OH+ − , which increases with temperature

● The concentrations and dissociation constantsof the other constituents of the solution

Because the temperature dependence of dis-sociation constants is not the same for all acidsand bases, it is not possible to calculate the pHscale for a given temperature in a manner thatwould apply to all aqueous solutions. At least,the temperature effect can be visualized on the E -pH diagram at a given temperature by markingby vertical lines the position of three importantpH values (Ref 24):

● pH log 10 (Kw)T 0, which correspondsto a 1 molal solution of a strong (completelydissociated) acid

● pH log 10 (Kw)T (pK w)T , which corre-sponds to a 1 molal solution of a strong base

● pH 1 ⁄ 2 (pK w)T , which corresponds to neutralwater. Indeed, in neutral aqueous solutions:

a a T H n OH n wK+ −= =( ) ( ) ( )

Hence, the neutral pH is pH n − +log ( )10 aH n

1 ⁄ 2 (log 10 (Kw)T ) 1 ⁄ 2 (pK w)T .The pK w decreases from 14.00 at 25 C to

12.27 at 100 C (373.15 K) and 11.30 at 200 and300 (473.15 and 573.15 K) (Ref 22). Accord-ingly, the pH of a neutral aqueous solution is7.00 at 25 C, whereas it is 6.13 at 100 C and5.65 at 200 and 300 C.

In an unbuffered solution (with completelydissociated acid or base), the proton activity isxed only by the water ionic product (from heresimply denoted K T), which increases with T.

Thus, a solution that has a certain pH at 25 Cwill have a lower pH at a higher temperature. Inthis simple case, the change in pH can be cal-culated in the following way (Ref 23). Considerthe general case of a solution of a certain pH at25 C: From the denition of the water ionicproduct K 25 a a

H25

OH25

+ − , hence pK 25 pH 25pOH 25 . As the temperature is raised, the equi-

librium of dissociation of water will be shifted,and equivalent amounts of additional H andOH will be generated in solution. Thus:

K a a a aH OH H OHT T T x x = + = + ++ − + −

25 25( )( ) (Eq 50)

where x is the increase in ion activity as a resultof the temperature change from 25 C to T. Thisis a quadratic equation in x: x 2 ( )a a x

H25

OH25

+ −+ (K 25 K T ) 0, whose physically-

meaningful solution is:

x

a a a a T

+ =

− + + + + −+ − + −H25

OH25

H25

OH25

25K K

2

( ) ( ) ( )2

4

(Eq 51)

The pH at T is pH T − +++log ( )10

25a x H

. Ittakes limiting values:● For low pHs: pH pK

K K

K K

25

H25

25 OH25

25 H

< <>

−+ −

+

T

T

T

a a

x a

2 7

≈ ( )

++ + +25

H H25

25pH pH

a aT

T

≈

≈

● For high pHs: pH pK

K K

K K

25

H25

25 OH25

> 14 − ><

−

+ −

+

T

T

T

a a

x

2 7( )

≈

225 OH25

OH OH25

H OH25

H25

25K K K

pH

( ) ( ) → ≈

≈

a a a

a a aT

T T T

T

− − −

+ − +=

21

≈≈ ≈pH pK pK25 25+ T

● For neutral pHs: pH

K K

25

H25

OH25

25

H25

H

≈ ≈ ≈ →

≈ ( )

7

2

a a

a x a

T + −

+ + =+++

+

T

T T

T T

a

( ) ≈ ≈

2

2H

K

pH pK

The pH values at 100 and 300 C are plottedversus the pH at 25 C 15 in Fig. 15. Also, thecorrespondence between the pH scales at differ-ent temperatures is plotted. (The pH at 200 C isequal to the pH at 300 C, because pK w is prac-tically the same at these two temperatures [Ref 22].) To compare the behavior of an electrode inan unbuffered solution of given pH at 25 C withthe one in the same solution at T , the correctedpH must be employed when using the E -pH di-agram at T.

It must be noted that, in a buffered solution,the pH is xed by the equilibrium of an acid-base couple, and it is the variation of the aciddissociation constant with temperature that ispredominant in xing the pH variation.

Temperature Effects on the E -pH Diagramfor Binary Systems. The diagram for the iron-water system at 300 C is plotted in Fig. 16. Evenafter correction of the temperature effect on pH,the net effect of increase of temperature is to shiftthe diagram to lower values of pH (Ref 17, 23–25). Comparison of higher-temperaturediagramsto the diagram at 25 C (Fig. 8) gives the follow-ing trends for the inuence of temperature:● The domains of stability of the Fe 2 an

Fe 3 cations are contracted to the benet of condensed species Fe, Fe 3O4, and Fe 2O3; thais, the solubility of the latter species in acidsolutions is lower at 300 C than at 25 C.

● There is an expansion below pH 14 of thedomain of stability of the dihypoferrite ion

(or ) at the expense of Fe, HFeO Fe(OH)2 3Fe 3O4, and Fe 2O3; that is, the solubility of thecondensed species in alkaline solutions issubstantially greater at 300 C.

The diagram for the chromium-water systemat 300 C (573.15 K) is plotted in Fig. 17. Com-pared to the diagram at 25 C (Fig. 14), CrOH 2

replaces Cr3

as the trivalent species at low pHand anodic potentials. Effects of temperaturesimilar to those described for the iron-water sys-tem are observed. The Cr 2O3 (or Cr(OH) 3) becomes less soluble (more stable) in acid solutionand more soluble (less stable) in alkaline solu-tions, where is the stable ion CrO (Cr(OH) )2 4(Ref 17, 26–28).

Similar effects are also predicted for variousother metals (Ref 17, 18, 26, 27). Thus, the mostsignicant effect of the increase of temperatureis an expansion of the domain of corrosion instrong alkaline environment, which was con-rmed experimentally (Ref 8, 23).

Temperature Effects on E -pH Diagrams fo

Ternary Systems. Diagrams for multi-compo-nent systems in high-temperature aqueous solu-tions are obviously of great interest for predict-ing corrosion behavior in numerous industrialconditions. A general bibliography of E -pH diagrams for multicomponent systems in high-




Fig. 18 E -pH diagram for the iron-sulfur-water systemat 300 C (573.15 K) in the case where the thi-

osulfates are the only oxidized forms of sulfur. m S 10 4

mol/kg, m Fe 10 6 mol/kg

temperature aqueous solutions is given in Ref 8.As an example, the diagram for the ternary sys-tem iron-sulfur-water with thiosulfates at 300 C(573.15 K), for a S 10 4 and a Fe 10 6, isshown in Fig. 18. It may be compared to thediagram at 25 C, presented previously (Fig. 13),to visualize the effects of increasing temperature.Concerning the sulfur-water system, there is anincreased stability of the acid forms of dissolvedsulfur, H 2S(aq) and HS 2 , at the expense of O3HS and S 2 . At 300 C, the diagram for the2O3iron-sulfur-water system is identical to the onefor the iron-water system (Fig. 16). Besides theeffects described previously for the iron-watersystem (contraction of the domains of stabilityof Fe 2 and Fe 3 and expansion of the domainof ), the main effect of temperature riseFe(OH) 3is that the range of stability of the sulphides FeSand FeS 2 is drastically reduced (Ref 17, 29) andeven suppressed for the sulfur activity of the di-agram ( a S 10 4).

Similarly, the diagram for the chromium-sul-fur-water system at 300 C (572 F) is identicalto the diagram for the chromium-water system

shown in Fig. 17, because it shows no chromiumsuldes.

High-temperature E -pH diagrams for variousmetal-chlorine-water systems, which are veryimportant for the interpretation and prediction of corrosion phenomena in high-salinity brines, canbe found in Ref 30. Also, the E -pH diagrams forthe quaternary system Fe-Cl-S-H 2O up to 250 C(523.15 K) are of direct interest in the phenom-enon of stress cracking in sulde-containingbrines (Ref 31).

E -pH Diagramsfor Adsorbed Species

The principle of E -pH diagrams can be ex-tended to the case of bidimensional layers of spe-cies adsorbed on metal surfaces. The solid com-pounds treated in the usual diagrams arethree-dimensional (bulk) compounds (oxides,hydroxides, suldes, etc.). However, the forma-tion of a three-dimensional solid compoundMxAy (A may be O, OH, S . . .) by reaction of gaseous or dissolved forms of A with a metal,M, is often preceded by the formation of a two-dimensional phase of A adsorbed on the metalsurface. This surface phase is more stable thanthe bulk compound (Ref 32). When there is crea-tion of a true chemical bond between A atomsand metal surface atoms (bond energies largerthan 200 kJ/mol, at least at low coverage), theadsorption is also called chemisorption. Ad-sorbed (chemisorbed) monolayers may form un-der E -pH conditions where the bulk compoundsare thermodynamically unstable, and a classicdiagram would predict only the existence of thebare metal. Chemisorption must not be ne-glected, because the presence of a chemisorbedmonolayer can induce marked changes in thereactivity of the metal. For example, it has beenshown that a monolayer of sulfur adsorbed onnickel or nickel-iron alloys enhances the anodic

dissolution and hinders the formation of the pas-sive lm, drastically affecting the corrosion re-sistance of the metallic material (Ref 33, 34).Therefore, E -pH diagrams for adsorbed speciesare of interest for predicting corrosion risk (Ref 34). The method of calculation of the equilib-rium potentials of oxidation-reduction couplesinvolving a species adsorbed on an electrode sur-face is presented subsequently.

Principle of E -pH Diagrams for AdsorbedSpecies. Consider the case where a species A(which may be an element, H, O, S or a molec-ular species, OH or H 2O) is adsorbed from so-lution on a metal surface M in the form of aneutral monolayer [denoted A ads (M)]. The ad-sorption of A from a dissolved species in aque-ous solution may result from an electrooxidationor an electroreduction reaction, depending on thevalence state of A in the dissolved species (itmay then be called electroadsorption). The ad-sorption of an atom or molecule on a metal sur-face in water involves the replacement of ad-sorbed water molecules and a competition withthe adsorption of oxygen species (atomic oxygen

O or hydroxyl OH) produced by electrooxidationof water or hydroxide (OH ) ions present in theelectrolyte. For simplici ty, a Langmuir model foradsorption is taken in which it is assumed thatthe two-dimensional (surface) phase is an idealsubstitutional solution where species adsorbcompetitively on the same sites without lateralinteractions between adsorbed species.

Under these conditions, the chemical potentialof each adsorbed species A ads (M) in the surfacephase of a metal M can be expressed as follows:

µ µ θA M A M Aads ads( ) ( )= +0 RT ln (Eq 52)

where hA is the relative coverage by adsorbed A

(0 hA 1; hA 1 for a complete monolayerof A); µA Mads ( )0 is the standard chemical potential

of A, corresponding to the saturation of the sur-face by A ads (M). The total coverage on the sur-faceisequaltounity;thecoveragebywateris θH O2

(1 hA i ), where hA i is the coverage by anyother adsorbed species.

As an example of the method of calculationof the E -pH relations, consider the adsorption ofhydroxyl on a metal surface from adsorbed wa-ter:

H2Oads (M) s OH ads (M) H e (Eq

The equilibrium potential of this half-cell re-action is obtained by applying the Nernst equa-tion, using the expression of the chemical poten-tials of adsorbed hydroxyl and water, as given inEq 52:

E E RT

F

RT F

= +

−

o OH

H O2

pH

2 303

2 303

. log

.

θθ

(Eq

where hOH and θH O2 are the relative coverages badsorbed hydroxyl and water on the M surface.

The standard potential E o on the SHE scale given by:

E F

eSHEo OH M H H O Mads 2 ads( )

( ) ( )( )= + + −+ −µ µ µ µ0 0 0 0

(Eq

The standard chemical potentials, or Gibbsfree energies of formation, for adsorbed sulfuroxygen, or hydroxyl are derived from literaturethermodynamic data on the reversible chemi-sorption of these species at the metal-water in-terface or, if not available, at the metal-gas in-terface (Ref 35–39). Adsorbed water is weaklyadsorbed on most transition metals, compared tochemisorbed species. In the absence of accuratethermodynamic data, the standard Gibbs free en-ergy of adsorption of water from the liquid statemay be neglected; that is, the standard Gibbs freeenergy of adsorbed water is approximated by thefree energy of liquid water. This value and thevalues for sulfur and oxygen adsorbed on iron,calculated for the formation of the chemisorbedspecies from S and O 2 in their standard state a25 C, are listed in Table 3.

E -pH Equations for Oxygen and Sulfur Asorbed on Iron. As an example, presented hereare the E -pH relations for the equilibria betweenoxygen and sulfur adsorbed on iron and dis-solved species in water containing suldes (Hor HS ) or thiosulfates (HS 2 ) 2O or S O3 2 3is considered that the ratio of the area of elec-

Table 3 Standard Gibbs free energies of formation (chemical potentials) for water,oxygen, and sulfur adsorbed on ironsurfaces at 25 and 300 C


kJ/molD f G0(573.15 K),

k J/mo l R eferen

H2Oads(Fe) 237.174(a) 263.881(a) 36Oads(Fe) 229 236 36Sads(Fe) 176 188 36

(a) The values taken for H 2Oads(Fe) are the values for H 2O(l). SouRef 22




trode to the volume of solution is small enoughso that the activity (molality mS) of each dis-solved sulfur species is independent of the sulfursurface coverage, hS. The uncertainty on theseequations is relatively high because of the lack of accuracy of the thermodynamic measure-ments presently available for chemisorbed sulfurand oxygen:

Sads (Fe) H2O(l) s Oads (Fe) H2S(aq) (Eq 56)

At 25 C:

log( hO / hS) 18.8 log mS (Eq 57)

At 300 C:

log( hO / hS) 7.9 log mS (Eq 58)

where hO and hS are the relative coverages by theadsorbed oxygen and sulfur on the Fe surface.

Sads (Fe) H2O(l) s Oads (Fe) HS H (Eq 59)

At 25 C:

log( hO / hS) pH 25.8 log mS (Eq 60)

At 300 C:

log( hO / hS) pH 16.4 log mS (Eq 61)

H2Oads (Fe) s Oads (Fe) 2H 2e (Eq 62)

E 25

059

= − 0.11+ 0.030 − −− 0

1

pH

O S Olog

.

θ θ θ( ) (Eq 63)

E 300

0 114= − 0.22 + 0.057 − −−

1 pH

O S Olog.

θ θ θ( ) (Eq 64)

H O Fe H S aq S Fe H O l

H

2 ads 2 ads 2( ) ( ) ( ) ( )+ ++ ++ −2 2 e (Eq 65)

E m25 0 67 0 030

0 030

0 059

= − −+ − −−

. . log

. log

.

S

S S O1

pH

θ θ θ( ) (Eq 66)

E m300 0 67 0 057

0 057

0 114

= − −+ − −−

. . log

. log

.

S

S S O1

pH

θ θ θ( ) (Eq 67)

H O Fe HS S Fe H O l

H

2 ads ads 2( ) ( ) ( )+ ++ +

−

+ −2e (Eq 68)

E m25 0 88 0 030

0 030

0 030

= − −+ − −−

. . log

. log

.

S

S S O1

pH

θ θ θ( ) (Eq 69)

E m300 0 057

0 057

0 057

= −1.15 −+ − −−

. log

. log

.

S

S S O1

pH

θ θ θ( ) (Eq 70)

2 5 2

9 8

2S Fe H O l O Fe HS O

H

ads ads 2 3( ) ( ) ( )+ ++ +

−

+ −e (Eq 71)

E m25 0 007

0 015 0 067

= 0.58−+ −

. log

. log .

S

O S

2

pH

( )( )θ θ (Eq 72)

E m300 0 014

0 028 0 128

= 0.52 −+ −

. log

. log .

S

O S

2

pH

( )( )θ θ (Eq 73)

2 5 2

10 8

S M H O l O M S O

H

ads 2 ads 2 32( ) ( ) ( )+ +

+ +

−

+ −e (Eq 74)

E m25 0 007

0 015 0 074

= 0.60++ −

. log

. log .

S

O S

2

pH

( )( )θ θ (Eq 75)

E m300 0 014

0 028 0 142

= 0.60++ −

. log

. log .

S

O S

2

pH

( )( )θ θ (Eq 76)

Potential-pH Diagrams for Oxygen andSulfur Adsorbed on Iron. The preceding equa-tions have been used to plot the E -pH diagramsfor sulfur and oxygen adsorbed on iron in water

containing suldes or thiosulfates (Ref 40). Thediagrams at 25 and 300 C for a molality of dis-solved sulfur mS 10 4 mol/kg are shown inFig. 19 and 20. The diagrams are superimposedon the iron-sulfur-water diagrams described pre-viously (Fig. 13, 18).

The domains of stability of adsorbed speciesare limited by lines corresponding to signicant

values of the surface coverage: h 0.01; 0.50.99. For hS 0.5 and a ratio hO / hS 0.01sulfur is considered as the only adsorbed speciesin the domain, and hO may be neglected in Eq66 to 70. Similarly, for hO 0.5 and a ratiohO / hS 100, oxygen is considered as the onlyadsorbed species, and hS may be neglected in Eq63 and 64. For 0.01 hO / hS 100, the adsorbedphase is a mixture of coadsorbed sulfur and ox-ygen, and both terms hS and hO must be takeninto account in the equations.

In the stability domain of H 2S(aq), the ratiohO / hS is constant (Eq 57, 58). It is negligible at25 and 300 C (for mS 10 4 mol/kg), hencehO can be neglected in Eq 66 and 67, and onlysulfur is adsorbed by replacement of water. Fora given value of hS, the ratio θ θS H O2

/ (θH O2

hS hO) is xed, and the E -pH relation forsulfur adsorption from H 2S(aq) by replacementof water (Eq 66, 67) gives a straight line (Fig.19, 20).

In the stability domain of HS , the ratiohO / hS increases with pH, according to Eq 60 and61. At 25 C, this ratio is innitesimal up to pH

14. At 300 C for mS 104

mol/kg, it becomessignicant ( 0.01) for a pH value below 14. ThepH values corresponding to hO / hS 0.01 (pH

10.4) and hO / hS 1 (pH 12.4) are rep-resented by vertical lines in the diagram (Fig.20). The rst vertical line is the left boundary of a domain, where sulfur and oxygen are coad-sorbed. In this domain, as the ratio hO / hS varie

Fig. 19 E -pH diagram for the system of sulfur, oxygen, and water adsorbed on iron at 25 C (298.15 K) in the caswhere the thiosulfates are the only oxidized forms of sulfur. The stability domains are limited by the dotted

lines for the water system, dashed lines for the sulfur-water system, and thin solid lines for the iron-sulfur-water systemand thick solid lines for the adsorbed species system. hS and hO are the relative surface coverages of adsorbed sulfur andoxygen, respectively. m S 10 4 mol/kg, m Fe 10 6 mol/kg




dimensional chemisorbed species with respect tothe three-dimensional compounds. At 300

whereas no region of stability of iron sulde ex-ists for mS 10 4 mol/kg, adsorbed sulfur istable in a large domain, which includes the do-main of Fe 3O4 and overlaps the domains of ironFe 2 , Fe 2O3, and (Fig. 20).Fe(OH) 3

The prediction of domains of thermodynamicstability of adsorbed sulfur on iron in thiosulfatesolutions supports the experimental observationof sulfur adsorption by thiosulfate reduction oniron-chromium alloys, which was invoked to ex-plain the detrimental effect of dissolved thiosul-fates on the corrosion resistance of ferritic stain-less steels (Ref 16). The diagrams indicatestability of S ads in a large part of the passivitydomain. The chemisorption of sulfur on bareiron is a process in competition with the forma-tion of Fe 3O4 (and Fe 2O3 in a limited E -pH gion). The equilibrium E -pH diagrams are constructed on a thermodynamic basis and do notindicate which species actually form on a bareiron electrode polarized in the passive domain:the two-dimensional (surface) species S ads (Fe

a three-dimensional (bulk) oxide. If the kineticsof adsorption of sulfur on bare iron is more rapidthan the kinetics of formation of oxide layers oniron, a sulfur monolayer may form on iron andprevent or delay passivation of the iron. Detri-mental effects of sulfur on the corrosion resis-tance of iron are then expected, even underpH conditions where a classic diagram predictspassivity. The diagrams (Fig. 19, 20) also predictthat sulfur is likely to adsorb in part of the do-main of anodic dissolution of iron; this is im-portant because dissolution enhanced by ad-sorbed sulfur is experimentally observed in theactivity domains of nickel- and iron-base alloys(Ref 33, 34). Even if the metal is not thermo-

dynamically stable and dissolves, a sulfur mono-layer may adsorb on the fresh surface, which iscontinuously produced, and increase the kineticsof dissolution.

Thus, the E -pH diagrams presented hershowing the domains of thermodynamic stabilityof adsorbed layers on metals, provide a basis forassessing the risk of corrosion of metals or alloysinduced by species adsorbed from aqueous so-lutions.

ACKNOWLEDGMENT

Portions of this article have been adaptedfromD.L. Piron, Potential versus pH (Pourbaix) Di-

agrams, Corrosion, Vol 13, Metals Handboo9th ed., ASM International, 1987, p 24–28.

REFERENCES

1. M. Pourbaix, Thermodynamique des Solu-tions Aqueuses Diluees, Potentiel D’oxydo-Reduction (resume de conference), BSoc. Chim. Belgique, Vol 48, Dec 1938

2. M. Pourbaix, Thermodynamics of Dilu Aqueous Solutions, Arnold Publication1949

with pH, the ratios hS /(1 hS hO) and hO(1hS hO) depend both on hS (or hO) and pH.

Therefore, the E -pH relations calculated for sul-fur adsorption from HS (Eq 69, 70) and oxygenadsorption from water (Eq 63, 64), for given val-ues of hS and hO , give nonstraight lines (Fig. 20).These lines become vertical at the pH valueswhere the water coverage becomes innitesimal,that is, the coverage hS hO reaches unity (fullmonolayer of coadsorbed sulfur and oxygen). Atthese pHs, the line for a given sulfur coverage,hS, meets the line for the complementary oxygencoverage hO 1 hS, and they merge with thevertical line plotted for the corresponding ratiohO / hS (Fig. 20).

In the stability domains of thiosulfates, the E -pH relations for the replacement reaction be-tween adsorbed sulfur and oxygen give straightlines for a xed ratio hO / hS (Eq 72, 73, 75, 76).A simplication occurs here, because the watercoverage θH O2

1 hO hS is negligible inthe domain of thiosulfates (that can be checkedby associating Eq 57 and 58 or 60 and 61 with63 and 64 and calculating θH O2 at the anodic limit

of the suldes domains), so hO in Eq 72, 73, 75,and 76 can be approximated by 1 hS. Then,straight lines are obtained for given values of hS,which delimit the respective stabil ity domains of adsorbed sulfur and oxygen (Fig. 19, 20).

The diagrams (Fig. 19, 20) allow the predic-tion of the E -pH conditions in which sulfur isadsorbed on an iron surface from suldes orfrom thiosulfates dissolved in water (Ref 40).

The main features are the following: when thepotential is increased, adsorbed water moleculesare replaced by sulfur atoms adsorbed by elec-trooxidation of suldes. Similarly, when the po-tential is decreased, adsorbed oxygen atoms (orhydroxyl groups) are replaced, totally or par-tially, by sulfur atoms adsorbed by electro-reduction of thiosulfates. The replacement takesplace within a very narrow range of potential( 0.06 V at 25 C; 0.11 V at 300 C). At 300C, the stability domain of adsorbed sulfur alone

is limited at high pH by the domain of coad-sorption S ads Oads (Ref 40).

The two-dimensional reactions involving ox-ygen (hydroxyl) and sulfur adsorbed on bare ironsurfaces are of a different nature than the reac-tions involving the three-dimensional (bulk) Fe-O(OH) or iron-sulfur compounds. Hence, the di-agrams developed here (Fig. 19, 20) are differentfrom the classic E -pH diagrams of the iron-sul-fur-water system (Fig. 13, 18). However, super-imposition of the two types of diagrams is usefulto discuss in more detail the possible effects of an adsorbed sulfur layer on the corrosion behav-

ior of iron. At room temperature, the domain of stability of the adsorbed sulfur monolayer in-cludes the stability domains of the bulk metalsuldes and Fe 3O4 and overlaps the domains of metallic iron (immunity domain) of Fe 2 (activ-ity domain), and Fe 2O3 (Fig. 19). Sulfur adsorp-tion is then expected for E -pH conditions whereiron suldes are not thermodynamically stable,which reects the excess of stability of the two-

Fig. 20 E -pH diagram for the system of sulfur, oxygen, and water adsorbed on iron at 300 C (573.15 K) in the casewhere the thiosulfates are the only oxidized forms of sulfur. The stability domains are limited by the dotted

lines for the water system, dashed lines for the sulfur-water system, and thin solid lines for the iron-sulfur-water systemand thick solid lines for the adsorbed species system. hS and hO are the relative surface coverages of adsorbed sulfur andoxygen, respectively. m S 10 4 mol/kg, m Fe 10 6 mol/kg




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SELECTED REFERENCES

● C.M. Chen, K. Aral, and G.J. Theus, “Com-puter Calculated Potential pH Diagrams to300 C,” Vol 1, 2, and 3, EPRI NP-3137, Pro-

ject 1167-2, Electric Power Research Insti-tute, June 1983

● R.P. Frankenthal and J. Kruger, Ed., Equilib-rium Diagrams/Localized Corrosion, Proceedings of an International Symposium to Honor Marcel Pourbaix on His Eightieth Birthday, Vol 84–89, The ElectrochemicalSociety, 1984, p 611

e ph diagram

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