-vi t> -. if < the thermodynamics - part 2; the iron-water

Atomic 'Enemy of Canada Ijmil V1-V V' Jr

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THE THERMODYNAMICS

; ! AJ |LEVAT€D TEMPERAIIJRES ^

- PART 2; THE IRON-WATER S.VITEW

VIA-K DIGBY'O> MACDONALD, 'G.R, SKIERMAN and P. BUTLEF

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JWhiteshell Nuilear Research Establishment

Ptnawa, Manifoba

, c """ 1 r , ^"-Decemberr!972_J3^ : >„ ,.

THE THERMODYNAMICS OF METAL-WATER SYSTEMS AT ELEVATED TEMPERATURES

PART 2: THE IRON-WATER SYSTEM

by

Digby D. Macdonald*, G.R. Shierman** and P. Butlert

* Research Chemistry Branch** Assessment and Applied Mathematics Brancht Summer Student, May-September, 1971

Whiteshell Nuclear Research Establishment

Pinawa, Manitoba ROE 1LO

December, 1972

AECL-4137

CONTENTS

Page

1. INTRODUCTION 1

2. THEORY 1

2.1 POTENTIAL-pH RELATIONSHIPS 3

2.2 SOLUBILITY 4

3. INPUT DATA 5

4. DISCUSSION 7

5. SUMMARY AND CONCLUSIONS 12

6. REFERENCES 13

FIGURES 15

APPENDIX I CALCULATED THERMODYNAMIC FUNCTIONS FOR THEIRON-WATER SYSTEM AT 25, 60, 100, 150, 200,250 AND 300°C= 20

THE THERMODYNAMICS OF METAL-WATER SYSTEMS AT ELEVATED TEMPERATURES

PART 2: THE IRON-WATER SYSTEM

Digby D. Macdonald*, G.R. Shierman** and P. Butiert

* Research Chemistry Branch** Assessment and Applied Mathemetics Branchf Summer Student, May - September 1971

ABSTRACT

Free energies of formation for iron, iron oxides and ionic species

in solution are calculated at elevated temperatures by integrating free

energy functions over the range 25°C to 300°C. These data are used to

derive poteri£ial*-pH relationships for the iron-water system and to calculate

solubilities'0% iron, magnetite (FesO^) and haematite (a-Fe2O3) as a function

of pH at theSvarious temperatures considered.

Atomic Energy of Canada Limited

Whiteshell Nuclear Research Establishment

Pinawa, Manitoba ROE 1L0

December, 1972

AECL-4137

Thermodynamique des sySt'ë'ti.eg eaiu-iriétàl' aux températures élevées

Partife; Le système eau-» fer

par

Digby D. Macdonald, G..R. Shierman fit ^» Butler*

*Etudiant, été 1971

Résumé

Les énergies libres de formation pour le fer, les

oxydes de fer et les espèces ioniques en solution sont calculées

aux températures élevées en intégrant des fonctions d'énergie

libre de 25°C a. 300°C. Ces données sont utilisées pour établir

les relations potenciel-pH pour les systèmes eau-fer et pour

calculer les solubilités du fer, de la magnetite (Fe.,0.) et

l'hématite (a-Fe2O ) en fonction du pH aux diverses températures

considérées.

L'Energi-e Ajzômiaue du 1 Canada»: ;LimitéeEtablissement .de- Recherches Nucléaires de Whiteshell

Piiïawa ",;• Mani td tfa f\ OE ' IL 0 "-' -

Décembre fil9 7,21- -- J

- . - • - s AECL-4137

- 1 -

1. INTRODUCTION

deflrief the chemistry aaS corrosion behavior of iron

in water at elevalect temperatures1, detailed thermodynamic calculations for

reactiotts*between! Irdnp iron oxides, iron ions and water at temperatures to

300°C have? beetf made-. TheSe calculations: are presented in this report as

potential-pE relationships for a set of reactions intended to describe the

chemical interaction between iron and high temperature water. Also, the

solubilities of iron, magnetite (FeaO^) and haematite Co'-FeaOa) have been

calculated assuming certain ionic species are present in solution.

~<a i ji',; JiTnfermodynkmicjtcalculations' of the type described- here have been

-''•*'' •" ; d Iff all cases the results have been presented as: a

liagrams1 "-* ' -or electron activity (pe)-pH diagrams

andi are often restricted to condit'ibns which are unrealistic in practice

(e.g. all ionic activities equal to unity). In the present study, we report

tli& poteiiftit&i-pB eSqAiations f or; individwat reactions at 25, 60, 100, 150, 200,

250 and 300°C as well as free energies of formation for each species in the

system over the same temperature range. These data lead directly to potential-pH

diagrams of the typer previously3 mentionediL However, the electrochemist and

corrosion specialist, are likely to be interested in the response of individual

reactions to vary'iifeg conditions (e.g. pH, temperature, hydrogens-pressure and

ion activity). Since these responses are not always readily accommodated in

two-dimensional diagrams, we present the potential-pH relationships for the

iron-water system"in'this report in analytical form.

2. THEORY

The prediction of equilibrium phenomena in water-cooled nuclear

reactors requires"methods for calculating free energy changes for reactions

in aqueous systems at elevated temperatures . The calculations have been

performed byj computer, and full details "of the program used are given

elsewhere'6^.

_ 2. _

The free energy of a substance, for, which heat capacity data are

available, can be calculated as a function of temperature using equation [1]:

G°(T2D *>-• G^(%) - S (IitD 2 rtl - ^ ^ i " s # a r + I C°dT [1]• •; ,. ..-;: ., •.. :•.- • ,.• - ; • , . , . . . . . T l ... T l

where S°(Tx)-is the entropy of'the substance at temperature-T^., For i«any

'pure' substances (i.e:. solids, liquids and gases), heat capacities are

frequently'expressed as equation [2]s:

0° = A + BT + CT"2 [2]

and have been tabulated by Kelley and Wicks and Block . For ionic species,

where heat capacity data are not available, it has been shown f.;; that the free

energy 6fxfbrmat£oYiNcjf <an ion1 *ate temperature; T2u:can be calculated : from rthe ;,s;

free venergy|*bf afb'rmatibn" at temperature Ti arid the entropies of the, ion at, ,the

two temperatures' Jbfiiriterest'i using equation [31 >ii. , , ,i ,, >

- [T2SO'(T2) - T1S?(T1;)]--+ -—^[S0^)^0^) ] [3]

/

GrisS "and Cobble-: 4 have demonstrated Ithat reliable estimates of ionic entropies

at elevaitedfttemperatures can be made using" theirV'Gorrespondence, Principle': -

S°(T2) - a + bS-dx) [4]

where a and b are constants, unique for a given temperature and class of ion,

and S(Tx') and S(T2) are the entropies of the ion on the "absolute" scale

where the entropy of the hydrogen ion at 25°C is -20.93 J/K«mol (-5 ca-l/mol-oC).

Entropies of ions on the conventional scale S' S - (25'°;G) = 0 J/K-mol can beH+. -„.

transformed to the absolute scale using the equation [5] :

i '.- < -;' •

S(25°C) = S'(25°C) - 20.93 Z [5]

where Z is the ionic charge (including,sign)., Thus, "absolute" entropies

calculated using equations [4].and [5] are substituted into equation [3J

together with the free energy,rof formation of^the ion at 25°C, and the free

energy of formation at temperature T 2 is derived.

- 3 -

2.1 POTENTIAL-pH RELATIONSHIPS

Electrochemical processes ppcuring in aqueous systems can be

represented by the general half-cell reaction:

otA + 3H + ye~ = <5B + EH 20 [6]

The equilibrium reduction potential, referred to the standard hydrogen

electrode at the same temperature, is given by the Nernst equations

AG° RT .^ — —T! -Ln ['7]

The quantity AG° is the standard free energy change for the whole-cell reaction:

aA + (g - Y ) H + + * H2 = 6B + eH2O [8]

i.e. AG° = {5G; + efi^}. - {aG" + (3 - Y)G°+ + \ G°^} [9]

where G° is the standard free energy of formation of x at the temperature of

interest. Following normal procedure, we define -log a_. = pH and assign

a H ? 0 = ^ (i«e- dilute solutions). Thus, equation [7] transforms to equation

[10] which is then used to calculate the potential-pH relationship for any

given" reaction: "f l : •''" : ;'' j''^.-- :'' z'iy'*<;'< ;:;: . •: ' .-•

AG° 2.303 RT /., . ) 2.303 BRT

Potential-pH relationships for a set of reactions involving iron,

iron 2l®cles*a^ at'- temperatures to 300°C are

l r i / " :Dfetiafle|g''ai'8'feus'|lpnsf:-b| pbtential^pE' diagrams; for ;the,

iron-water system* atf^etevaSed tlinperatlres'have been presented by others' • ':-.^r,

and are not repeated here. However, it should be noted that potential-pH

relationships occur only for reactions in which a change takes place in the

oxidation number of one of the components. Thus, processes*such astioii;^

hydxolysis and certain.solubility reactions are not affected;by galvanic

potential differences between phases. In contrast, corrosion involves

simultaneous anodic and cathodic processes, and the potential adopted

by the corroding metal will lie between the equilibrium potentials for

the anodic and :icathddicJ reaCtfbhs^ r Theory p Mdilcts fthat rthe cbrrosiori

potential is closest to the equiliDrium pbtential of the process with '

the higher exchange current density. Thus, a corrosion process which

is 'anodically1 controlled, i.e. the anodic reaction is rate limiting,

will have a corrosion potential close to the equilibrium potential for

the cathodic reaction and vice versa. It is evident, therefore, that if

the potential of a metal is known for a given set of conditions, then

the interpretation of the processes involved will be greatly aided by

potential-pH relationships of the type documented here.

2.2 SOLUBILITY

The dissolution of a solid (A) ,to prbduce ions in solution (B)

can be represented by equation [8]. Thus, at equilibrium:

V x6

AG° = H- RT In

where F is the partial pressure (strictly fugacity) of hydrogen in the

system. Expansion of the log term results in equation [12] for the dependence

of the activity of B of pH and hydrogen pressure:

l o g aB " "B " 2.303 RTS

The total solubility of A at a given pHT, temperature and ionic

strength is equal to the sum of ionic concentrations from the individual

reactions which contribute to the dissolution of the solid, i.e.:

- 5 -

where Yg is the activity coefficient for the ion B. For low ionic strength

media (<0.0Jm), the activity coefficient of an ion can be equated to unity

without significant error and the total solubility of A in mol/kg of solvent

is equal to the sum of ionic activities.

3. INPUT DATA

Numerical values for the free energy and entropy at 25°C and

the heat capacity for each substance considered are listed at the beginning

of the computer output in Appendix I. The free energies and entropies were

taken, whenever possible, from the recent NBS compilation . Heat capacities

were taken from the listings of Wicks and Block . Data not from these

sources are discussed below.

Free energy and entropy data for the hydrolysed Fe(III) species,

Fe(OH)2 , Fe2(0H)2 and Fe3(0H)V were calculated from the data of Arnek and

Schlyter . The free energy quoted in the NBS compilation for Fe(OH)

does not lead to the recently derived valuev 'of 10 " for the equilibrium

constant for the reaction:

Fe2+ + H2O S^FeCOH)"1" + H+ ^ ; [14];

We have assumed that the NBS value for the free energy of formation for

Fe + is correct and calculate the corresponding quantity for Fe(OH) using

equation [15]:

The entropies' listed are based on'the 'absolute scale' (sie!equatibh [5]).All thermodynamic data listed in Appendix I are given in terms of calories,i.e. in the same units as listed in refs. 7, 8 and 12. These values areeasily converted to the SI metric system by using the relationship1 cal. = 4.1868 J.

- 6 -

The value adopted for the free energy of formation for the, ferrate ion,

FeOi/", is due to Pourbaix^1^. However, the values used must be-regarded

as' a« crude1 «es tiinate ©hly T'•"•• '%r= • No-entropyjdata-are^fvailableîn. theA,:4, ,,,;;;V v ._ ..".:•..; .J>5-. :,' ..••.'.:... ' . l ; 2 — •-•' •

literature for the anionic species HFe02'J» F e02 u andiFeO^ s , The required ...

values were estimated using the empirical equation of Powell arid Connick[16]:

S°(25°C) = 182.1 - 194.7 (|z| - 0.28 n ) , J/K-mol [16]'',' - ' - ? ••_••• >:

where S°(25) is the entropy of the ion on the conventional scale, Z is the

ionic charge and n is the number of oxygen atoms not including those in

hydroxyl groups.

The absolute accuracy of the data used in these calculations is

rj..difficult to; determine since the NBS thermodynamic data /have been

adjusted to-yielîinternal consistency. Howeyer, he values listed are

such that the experimental data from which they are derived may be recovered

with an accuracy equal to that of the original quantities. Also, the values

listed for any given substance satisfy; all known physical arid thermodynamic

relatipriships among yaripus properties, and the calcul&t^d va.lue for any

thermodynamiq qudntity .-for a reaction is. independent of the path chosen for

the.tevaluation. * ;

Equation [1] shows that, for solid substances, the uncertainty

in G°(T2) - C'CTj) depends upon the accuracy of S'î) and C°. For the sbiids

considered in this work (i.e. Fe, FesOij and a-Fe203), the entropies and heat

capacities are known to better than 1-2%. This uncertainty is small and the

accuracy of G°(T2) is most likely determined more by the error in G°(Ti) than

by the integration over the temperature range T\ to T2. For ionic species,

the uncertainty in G°(T2) - C O ^ ) is determined by the validity of the Criss

and Cobble correspondence principle. While no detailed analyses of the validity

of the Criss and Cobble extrapolation technique have been reported, comparison

between calculated and experimental electrode potentials for silver-silverhalide

cells at temperatures to 300°C indicate that the integrations are accurate to

better-than 5% ( 2 ).

- 7 -

The uncertainty in solubility due to error in AG° can be

determined using equation [12]. For an error in AGC of + 12.56 kJ/mol

(i.e. 3 Kcal/mol), log ag is uncertain to Hhl, i.e. an order of magnitude.

This latter figure is a reasonable-estimate of accuracy for the solubilities

calculated in' this wbrlc at 25°G. However, as discussed in the previous

paragraph, the integration ofAG° over the temperature range of interest

is accurate to a few percent. Hence, the uncertainty in the variation of

log an with temperature will also be of the order of a few percent.

4. DISCUSSION

In the present study, solubilities are calculated for iron and

magnetite '(F&3O4) underreducing; conditions (p = 0.101325 MN/m2, i.e.

1 atm) at temperatures to 300°C. Under these conditions Fe(III) ions are„ " • • • - • . . L ' - • . 2 +

unstable arid the dissolution reactions are considered to involve Fe ,+1 — 2— 7

Fe(OH) , HFeO2 and FeO2 . Due'to the lack of appropriate thermodynamic

data, it has not been possible to include Fe(0H>2 or large polymeric

(colloxdal)species which probably exist. These species probably determine

the level of ifbn in "solution" in the pH region where the solubility is

at a minimum. It should be noted that the reactions considered responsible

for the dissolution of iron and magnetite involve changes in the oxidation

number of the iron atoms present in the solid phase. Thus, the individual --

ionic activities, and therefore the total solubility, depend upon the partial

pressure of hydrogen. For partial"pressures other than 0.1 MN/m , the ionic

activities from the individual reactions which contribute to the total

solubility can be corrected by adding (Y/26) log p ^ to the values listed

in the computer-output (Appendix I). Alternatively, the desired hydrogen

pressure may be included in the input data and the necessary computations

will be "performed by the computer^6'. It is important to note that ionic

activities from the dissolution of magnetite increase with hydrogen pressure,

whereas the reverse is true for the dissolution of iron. The pressure at

- 8 -

which equal ionic activities occur, represents the condition for equilibrium

between iron and magnetite and is equal to 85 and 170 MN/m at 25°C and

300°C, respectively. At hydrogen partial pressures less than the above

figuresv the solubility ipfcironv isi alwaysf igreatet , than; the, solubility of .

magnetite^ 3//e>^n^gne£itei;is^ ,,- ;

iron. Gbnsequently-;ji. "the conversion; ofLirpn.'..to magnetite;,isa, spontaneous

process^ under theseHconditions,s and> mayj proceed either by direct oxidation,

of the metal or by consecutive dissolution and electrocrystallization

processes(e.g. reactions [22] and [10] respectively, as listed in the

computer output). Experimental evidence has been found for both mechanisms

in a recent study of. the electrochemistry of iron in 1M lithium hydroxide

solution at 200°C(l0).

•-<>„--. The solubility of magnetite at Q.I MN/m2 partial pressure ofhydr°.8§ftr^

d?at|va^ o f

pHT in Figure,1. ^Atfeach temperature the,solubilitypassesthrough a

minimum,aar;a function of .pH^ f o the leftj0 the minimum the predominant

soluble sgecies, are r,the cations .Fe2*.and ,?e (OH^t, whereas to the right 'of

the minimum.,the anions HFeQ2~ and |eO22~ prevail.

w si e'contributions that the individual ions make to the solubility

of magnetite at 25°C and-3gO°C and at.Q.l MN/m2 partial pressure of hydrogen

a^lptted In Figure,?. At,;25°G the predominant .species at pH <9.5 is

Fe , whereas in the region pH 9.5 to 10.7 Fe(0H)+ predominates. In more

alkaline solution HFeO2" is,the major product. The ion FeO22" becomes

important only at very high PH values (>14.45). On increasing the'temperature

to 3006C, the principal change which occurs is the large increase in stability

of the anions HFeOz~ and FeO22" and the greatly increased pH range of

predominance of the hydrolysed cation Fe(0H)+. The increased stability of ,

HFeO2 has been noted previously(1);. and becomes important in the corrosion •

of iron in lithium hydroxide solutions at elevated temperatures(10).

7 T h e P H T a t whlc*» the minimum solubility occurs is plotted as a '

function of^emperature in Figure 3, together with the PH T values adopted by

10 and 10 ' mol/kg hydroxide (e.g. LiOH) solutions assuming that pH

- 9 -

changes arise from the variation of K alone. The plots show that the

pHT of minimum solubility parallels the plL of the hydroxide solutions

and are nearly coincident with the values adopted by the 10 mol/kg 0H~

solution up to 250°C. At 300°C the minimum solubility occurs somewhat

lower arid coincides with the pHT calculated for a lo"** mol/kg hydroxide

solution. Experience .has shown that corrosion in boilers at 250 - 300°C

is minimized by adjusting the room temperature pH of the solution to 10

to 10.5. This is precisely the pH of minimum solubility of magnetite as

calculated here.

Sweeton and Baes^ have recently published a detailed study of

the solubility of magnetite in dilute acid and base solutions at temperatures

between 50°C and 300°C. The solubilities calculated in our work agree

reasonably well with the data of Sweeton and Baes. For instance at 300°C

in neutral water ti-ei pH^ = 5.6) j the calculated value is 0.6 x 10~7

mol/kg, whereas the value obtained experimentally varies between 0.7 x 10

and 1.5 x 10 mol/kg. This level of agreement is maintained in acid

solutions but not in dilute alkali solutions. Thus, in a 10""* mol/kg

hydroxide solution at 300?C, Sweetoh and Baes find [Fe] = 1 x 10~

mol/kg whereas the calculated value is 0.4 x 10 mol/kg. However, the

experimental data are not well defined in the alkaline region, and it is

difficult to determine if the difference is really significant. The

difference could be due to the existence of colloidal or neutral (Fe(0H)2)

iron species. These would contribute to the measured solubility but, because

of a lack of data, they could not be included in the calculated values. ,

Another apparent difference between the experimental and calculated] values

lies in the position of minimum solubility. Thus, the calculated minimum

occurs at [0H*~] = 10~ " mol/kg to 10 mol/kg, whereas the experimentally

observed minimum appears to lie closer to neutral pH_. However^ considerable

scatter exists in the experimental data in this region of pH and ;the? discrepancy

between the calculated and experimental positions of minimum solubility may_;

not be real.' It should be noted that no measurements of pH^ were made in the

experimental studies referred to above. The comparison discussed above is

based on the assumption that the change in pH with temperature arises .from

variations in K alone.. In view of the complex hydrolytic phenomena which .

- 10 -

are knowri to occur in solutions containing iron ions and oxides, this

assumption may not be valid arid this is especially so for poorly buffered

solutions, e.g. pure water.

'"• The solubility^of magnetite-in a number' 'of; hydroxide .solutions

and as a function of'temperature at Oil MN/m^ partial -pressure'sof hydrogen

is plotted in Figure 4. these values have been calculated assuming that

pH_, depends only on K (iwe. it is not altered by other hydrolysis

equilibria). At temperatures less than 200°C, the solubility increases

with temperature in all solutions. At higher temperatures, the solubility

is predicted to increase with temperature for hydroxide concentrations

greater than 10 mol/kg but decrease for more dilute solutions. At—k —

10 mol/kg-OH , the solubility of magnetite is predicted to be very

nearly independent of temperature-at T > 2Q0°C. Thesevjpredictions are;.

in; agreement witihithe iexperimental data of/ Sweeton arid Baesf ift> .The .

solubility-temperature relationships demonstrate that changes in,the pH

of the solution can not only•> affect the amount of ?.Fe30itjcrhich-is transferred

across a*:temperature^ gradient^ but also the direction. Thus, in a water-

cooled nuclear reactor with a coolant pH(25°C) of less than 10v transfer

of magnetite via solubility phenomena should occur from: the colder to the

hotter1 regions, eig; from the boiler to the fuel.-i<. Itti more alkaline solutions

(i.e. pH25>l0), 7the reverse is predicted to occurs i.e. transport occurs

frofflthe hotter to the colder regions. At pH25=10, there is very little

driving force for the transport of ¥es0k by differential solubility. The

above predictions are in keeping with experience where it is found that

fouling of fuel elements occurs at pH25<10."

- 1.

As previously mentioned,'the solubility of magnetite depends

upon the pressure of hydrogen in the system as shown by equation [12].

This dependence is shown graphically in' Figure 5 where the solubility of .

magnetite in a 10 mol/kg hydroxide solution at 25°C and 300°C is plotted, ,

as a function of partial pressure of hydrogen. The solubility is seen to .,,-

increase with" hydrogen pressure, as expected, since the dissolution reaction,

results in a reduction of the oxidation number of ions, i.e. from 2.67 for

Fe30i, to 2 for Fe , Fe(OH) and HFe02~. The dependence of solubility on,.

-.11 -

l o g PH 2 ± S d e t e r m l n e d by t h e coefficient Cy/26)(see equation [12]) which

for magnetite is numerically equal to 0.333. Thus, the solubility of

magnetite changes one order of magnitude for every three orders of magnitude

change in pressure of hydrogen in the system.

The equilibrium oxygen pressure for equation [17]:

4Fe30it + 02 = 6Fe203 [17]

can be calculated from the data listed in Appendix I and is found to be

lO"53-50 and ID"23'95 N M 2 (i.e. lO"68'50 and ICf28"95 atm) at 25° and

300°G, respectively. At oxygen partial pressures greater than these values,

Fe (III) species are stable and the total iron in solution will be determined

by the dissolution of haematite (a-Fe2O3) to produce Fe (III) ions. Four

Fe (III) species were considered, viz, Fe3+, Fe(0H)2+, Fe2(0H)2't+ and

Fe3(0H)it . The Fe(OH)2 was not considered since the work of Arnek and

Schlyter shows this species contributes little to the hydrolysis of3+

Fe at 25°C and was not included in their calculation of stability constants.

Since the thermodynamic data used in this report are derived directly from

the work of Arnek and Schlyter, we have adopted the same hydrolysis scheme

in describing the Fe (III) system at elevated temperatures. No anionic

Fe (III) species are considered because of a lack of data. Consequently,

the calculated solubility of a-Fe2O3 does not show an increase with pH in

alkaline solutions. Furthermore, no change in oxidation number of Fe occurs

on--dissolution of a-Fe2O3 to give Fie (III) species in solution. Thus, if

oxygen is used to maintain the mild oxidizing conditions in the systeai, the

solubility of,a-Fe203 will be independent of the partial pressure of the

gas. , Finallyt it is of interest to note that the solubility of Fe30ir, under

mild reducing conditions (e.g. 0.1 MN/m2 of hydrogen), is orders of magnitude

greater than the solubility of Fe203 under mild oxidizing conditions at the

same pH. Thus, if oxygen is injected into a system which has first equilibrated

in the preseli4e:of h^drogenV precipitation of haematite from solution will

occur; This;phenomenon;smay have important implications for the operation

and eleari-up of water-cooled nuclear reactors.

- 12 -

5. SUMMARY AND CONCLUSIONS

• • •

(1) Thermodynamic calculations" of! equilibrium phenomenavin:? the :,•v•:•• >:;

iron-water system at temperatures to 300?C have, been made by integrating

free energy functions over the-temperature range ofoLnterest. ;

(2) The solubility of magnetite at all temperatures to 300°C is

found to pass through a minimum as a function of pH. At 25°G the minimum

occurs at pH * 10.5 but shifts to pHT *••?• at 3Q0?C. Over the temperature,

range 25°C to 300°G, the pH_ of minimum solubility roughly parallels the

change in acidity of the solution due to variation of K w with temperature.

(3) -UrnThe solubility ofmagnetite ±s,predictedv^q;increase;fbyj-one»

order ofc-Magnitude if dr \eyery 'three brdersy of^magnitude dMcriedsie-iiitfthe ;

h y d r o g e n p f e s s u r e i n t h e s y s t e m . ' =i" ' '' ! "!'"'; '•••'•"••-. ;1/' '•'•*- ;;•; -: l!-:

(4) V > -Soiubility-pH relationships predict that', l

range 250°C:£o SO^C and at pH25<i0, magnetite is 'transport edi-fr;om the

colder to the hotter zorie by differential solubility. At pH2§>i0;the^reverse

i s p r e d i c t e d t o o c c u r . • " - J '• •..•..•••.. s o -, -. .*•;•-. :%c,.\- -•-..,., /^\^.{

(5)•.""'•.','•."• "•. In the presence df oxygen, the conversion of iron (II) -species

to iron (III) species is thermodynamically possible and the stable oxide of

iron is haematite., The solubility of haematite is predicted to be much less

than the solubility of magnetite at 0.1_MN/m?- (i.e'. 1 aim) partial pressure

of hydrogen. "Thus, if oxygen isJinjected"into a system which has first - '

equilibrated in the presence of hydrogen, precipitation of haematite .from v

solution will occur. ' '- ^ '• ' '' • >

a ' "

- 13 -

6. REFERENCES

1. 1 Herbert E; Townsend, Jr., Potential-pS Diagrams at ElevatedTemperature for the.System Iron-Water-, Corrosion Science,& i 3 5 ^ (19703. . •"•".'•

2. D.b. Macdonald arid F. Butler, The Thermodynamics of the Aluminum-. , ;,,. , Watep, System at Elevated Te/mperatitres, accepted for publication

in Corrosion Science.

3. , D. ,Lewis, The Theoretical Studies of Aqueous Systems Above 25°C.; >2. The Iron-Water System3 Aktiebolaget Atomenergie, Report

AE-432, (1971)

4. R.G» Robins, The Application of Potential-pH Diagrams to thePrediction of Reactions in Pressure Rydrothermal Processes.WSL Report LR80(MST), U.K. Ministry of Technology, (1968).

5. [ ' RiL-, Gowan and R.W. Staehle;, The Thermodynamics and Electrode: Kinetic pehavibur of Nickel in Acid Solution in the Temperature" Rangey 25°, to:300°C.3:Journal of Electrochemical Society,

557V 118-68^' (1971).

6. D.D. Macdonald, G.R. Shierman and P. Butler, The Thermodynamicsof Metal-Water.Systems at Elevated Temperatures. 1. The Waterand Copper-Water^1'Systemst Atomic Energy of Canada Limited,AECL-4136, (1972).

7. K.K. Kelley, Contributions to the Data on Theo±'siical Metallurgy.XIII. High Temperature Heat-content, Heat-capacity, and EntropyData for the Elements and Inorganic Compound, Washington, U.S.Department of Interior, Bureau of Mines, Bulletin 584, (1960).

8. Charles E. Wicks and F.E. Block, Thermodynamic Properties of 65Elements: Their Oxides, HaHdes, Carbides, andMitrides,Washington, U.S. Government Printing Office, D'.S. Bureau ofMines Bulletin 605, (1963).

9. ' Cecil M. Criss and: J.W. Gobble, The Thermodynamics Properties ofHigh Temperature Aqueous Solutions. IV. Entropies of the ionsup "to 200° and the Correspondence Principle, Journal of theAmerican Chemical Society, 8£: 5385-5390, (1964).

10. D.D. Macdonald and D. Owen, The Electrochemistry of Iron inIM Lithium Hydroxidr Solution at 22° Cand 200°C. submitted toJ. Electrochem. Soc, (1972).

11. ' 'R. Arnek and K. Schlyter, Thermochemical studies of HydrolyticReactions.- VII. A Recalculation of Calorimeter Data on Irpn(III)Hydrolysis,- Acta CHem. Scand., 22_: 1327-30,' (1968).

- 14 -

12. Donald D. Wagman, Selected Values of Chemiaal ThermodynamicProperties, Washington, U.S. Department of Commerce, NationalBureau of Standards, National Bureau of Standards TechnicalNote

13. F.H. Sweeton and C.F. Baes, Jr., Sotiibility of' Magnetite, andHydrolysis of Ferrous ion in AqueouW Solutions at ElevatedTemperatures3 J. Chem. Thermodynamics, 2_: 479-500, (1970).

14. Marcel Pourbaix, Atlas of Electrochemical Equilibria, LinaqueousSolutions, Pergamon Press, London, 644 p. (1964).

15. Rpbert. E.. Connick and Richard E- Powell, The' Entropy of AqueousOxy-ariions, Journal of Chemical Physics, 2^: 2206-7, (1953).

- 15 -

O 25 °CV f 0°C• ipo°c• i 50 °C• 200 °C ,A 25O"?c/

300»C

10

PH.T

, FIGURE 1: THE INFLUENCE OF pHT ON THE CALCULATED SOLUBILITYOF MAGNETITE-AT TEMPERATURES BETWEEN 25°C AND 300°C AND AT,- 0.101325 MN/m2 (1 atm) PARTIAL PRESSURE OF HYDROGEN.

THE HORIZONTAL DASHED LINE CORRESPONDSTO A CONCENTRATION OF 1 ppb.

- 16 -

10 -

12

FIGURE 2: THE CONTRIBUTIONS OF VARIOUS IONS TO THE SOLUBILITY OF MAGNETITEAT 25°C (SOLID,LINES) AND 300°C (DASHED LINES) AS ,A FUNCTION OF pH-,-.

- 17 -

O

10

©MINIMUM SOLUBILITY OF Fe30<.

# id"4 rhol/kg OH" SOLUTION

• IO"3Smol/kg 0H~ SOLUTION

100 200T(°C)

300

FIGURE 3: VARIATION OF THE pHT OF "MINIMUM SOLUBILITY OF MAGNETITE-1 AS A FUNCTION OF TEMPERATURE BETWEEN 25°C AND 300°C.

- 18 -

10

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o

10.-8

10-9

T

100

0"6Q I0"6 mol/kg OH

• I0"3 mol/kg 0H~

(9 I0'2 itiol/kg'OH"

200 300

FIGURE 4.: THE EFFECT OF TEMPERATURE ON THE SOLUBILITY; OF MAGNETITE AT0.1 MN/m2'(i.e. 1; atm) HYDROGEN PRESSURE-AND AT VARIOUS

CONCENTRATIONS.OF HYDROXIDE IONS IN SOLUTION.

FIGURE 5: THE EFFECT OF HYDROGEN PRESSURE ON THE SOLUBILITY OF MAGNETITEAT 25°C AND 300°C AND AT A HYDROXIDE JON CONCENTRATION OF lO"1* moi/kg.

- 20 -

APPENDIX I

CALCULATED THERMODYNAMIC FUNCTIONS FOR THE IRON-WATER SYSTEM AT

25, 60, 100, 150, 200, 250 AND 300°C.

- 21 -

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PH( 0,0)( 2,5)( 5,0)( 7,5)(10,0)(12,5)(15,13)(17,5)

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f. PH( 0,5)( 3,0)( S,5)( 8,8>(10,5)(13,2)t(15,5)(18,0)

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PH(•1.0)( 1 . 5 )( * . t l i( 6,9)( 9,?)(11.5)(14,0)116.5)

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REACTION * 14

PH(-1.0)( 1.5)( 4,0)

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ACTIVITY FE3+ VS, PH

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REACTION # 15

PH(.1,?)( 1,9)( 4,0)I ,6,5)I 9,0)

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REACTION * 17

PH(-1.1')( 1.9)

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ACTIVITY FE2(0H>2 VS, PH

PH A PH(.0,5) 0.22700&E.13 ( 0,0)( 2,0) 0.227006E.23 I 2,5)

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REACTION * 1»

PH'•342348E.20

ACTIVITY FE3(0H)4 VS, PH

PH A( - 0 , 5 ) '• 0.10B26I9E.22

PH0,342348E'2Si

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-vi t> -. if < the thermodynamics - part 2; the iron-water

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