Atomic Energy of Canada Limited3
THE THERMODYNAMICS OF METAL-WATER SYSTEMS
AT ELEVATED TEMPERATURES
PART 3: THE COBALT-WATER SYSTEM
by
DIGBY
D. MACDONALD, G R SHERMAN and P BUTLER
Whit»sl»*M Nucl«or Research E*tabH»hment
Pinawa, ManHobo
r 1972.
'
.
THE THERMODYNAMICS OF METAL-WATER SYSTEMS AT ELEVATED TEMPERATURES
PART 3: THE COBALT-WATER SYSTEM
by
Digby D. Macdonaid*, G.R. Shiermaii** and P. B u t i e r t
*
**
t
Research Chemistry Branch
Assessineat and Applied Mathematics Branch
Summer Student, May-September, 1971
Whiteshell Nuclear Research Establishment
Pinawa, Manitoba ROE 1LO
December, 1972
AECL-A138
THE THERMODYNAMICS OF METAL-WATER SYSTEMS AT ELEVATED TEMPERATURES
PART 3: THE COBALT-WATER SYSTEM
by
Digby D. Macdonald*, G.R. Shiermdi** and P. Butlert
*
**
t
Research Chemistry Branch
Assessment and Applied Mathematics Branch
Summer Student, May-September 1971
ABSTRACT
Free energies of formation for cobalt, cobalt 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 potential-pH relationships for the cobalt-water system and to calculate
solubilities of cobalt and cobalt oxide (CoO) as a function of pH at the
various temperatures considered.
The potential-pH relationships predict an
expanded region of corrosion in alkaline solutions at elevated temperatures.
This prediction is consistent with the increased stabilitv of the anion,
HCo0 2 , at higher temperatures.
The solubility calculations predict that
transport of Co by differential solubility occurs from the hotter to the
colder regions of n non-isothermal system for pH 2 5 > 10.
reverse occurs.
At pH 2 5
=
9 the
For CoO at 250°C < T < 300°C transport is predicted to occur
from the hotter to the colder regions at p H 2 5 > 10.
At p H 2 5 = 9 transport
occurs in the reverse direction over the entire temperature range.
Atomic Energy of Canada Limited
Whiteshell Nuclear Research Establishment
Pinawa, Manitoba ROE 1L0
December, 1972
AECL-4138
Thermodynamique des systèmes eau-métal
aux températures élevées
Troisième P a r t i e ;
Système eau-cobalt
par
Digby D. Macdonald, G.R. Shierman et P. Butler*
*etudiant, été 1971
Résume
Les énergies libres de formation pour le cobalt,
les oxydes de cobalt et les espèces ioniques en solution
sont calculées a des températures élevées en intégrant les
fonctions d'énergie libre dans l'intervalle allant de
25°C a 300°C.
Ces données sont utilisées pour obtenir
les relations potentlLei-pH pour le système ëau-cobait et
pour calculer les solubilités du cobalt et de l'oxyde
de cobalt (GoO) en fonction du pH aux diverses températures
considérées.
Les relations potentiel-pH prédisent une
région étendue de corrosion, dans les solutions alcalines,
aux températures élevées.
Cette prédiction coïncide avec
la stabilité accrue de l'anion, HCo0 2 , aux hautes
températures.
Les calculs de solubilité prédisent que le
traasporE de Co par solubilité différentielle va des régions
chaudes aux régions froides d'un système non-isothermique
pour p H 2 5 > 10.
A p H 2 5 = 9 le contraire ce produit.
Pour
CoO à 250°C < T < 300°C on prévoit que le transport ira
aussi des régions chaudes aux régions" froides pour P H 25
>
^®'
A pH-- = 9 le transport se produit en sens inverse dans tout
l'intervalle de températures.
L'Energie Atomique du Canada, Limitée
Etablissement de Recherches Nucléaires de Whiteshell
Pinawa, Manitoba, ROE 1L0
,;
Décembre 1972
3
AECL-4138
CONTENTS
Page
1.
INTRODUCTION
1
2.
THEORY
1
2.1
POTENTIAL-pH RELATIONSHIPS
3
2.2
SOLUBILITY
4
3.
INPUT DATA
4
4.
RESULTS AND DISCUSSION
7
4.1
POTENTIAL-pH RELATIONSHIPS
7
4.2
SOLUBILITY
10
5.
SUMMARY AND CONCLUSIONS-
13
6.
REFERENCES
14
FIGURES
16
APPENDIX I CALCULATED THERMODYNAMIC FUNCTIONS FOR THE COBALT-WATER
SYSTEM AT 298, 333, 373, 423, 473, 523, AND 573K
T\,-''-->f
•• v i ' - . ' V
•;'•-"•..«'-
•:.
':
•-.•
• ' • - ' • •
;
'
h':'
25
- 1-
1. INTRODUCTION
As part of a program to study the chemistry and corrosion
behaviour of metals in water at elevated temperatures we report detailed
thermodynamic calculations for reactions betweeu cobalt, cobalt oxides,
cobalt ions and water at 25, 60, 100, 1505 200, 250, and 300°C. Previous
studies of this type have been reported
series for the copper-water
and iron-water
including two in the present
systems.
The calculated data include free energies of the various
components of the cobalt/water system as well as standard free energy
changes and potential -pH relationships for a number of reactions which
are proposed to describe the chemical interaction between cobalt and
water in high temperature systems. The standard free energy changes are
further used to calculate solubilities of Co and CoO as a function of
pH and temperature.
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 technique employed here
has been previously described and full details of the computer program used
to perform the computations are given elsewhere
The free energy of a substance, for which heat capacity data are
available, can be calculated as a function of temperature using equation [1]:
T2 - TX - T2 ff \^j dT + Jf2 C°dT [1]
where S°(T1) is the entropy of the substance at temperature
For many pure substances heat capacities are frequently expressed as
equation [2]:
C° = A + BT + GT
"P
and fuhcMons 6F t h i s type have^been tabulated ^ K e l l e y : land^icfcsiandv u
Block (9) v
F&r-ibnic species involution^ •fbr-whichHeat^ capacityidatai are
not generally available^ i t n a s ^ W f n o w t i M ^ ^ t h a t the free energy a t ;
temperature-Tz6ah be calculate^using&iquatldn-[33: - '
G°(T Z )
where S
0
-
-
!
= G
^ ^ and S'(Ti) are the Absolute' entropies of the ion at temperatures
T 2 and T x , respectively. Criss and Cobbl 6 ( l l ^ 2 ) have demonstrated that
reliable estimates of ionic entropies at elevated temperatures can be made J
using their 'correspondence principle':
S°(TZ) =
vhere a and b a r e constants which are unique for a given temperature and
class of ion. The 'absolute' entropies at 25°C are based qn the scale where
the entropy of the hydrogen ion is -2MS£j/Kimcl (i.e. -5 cal mol deg ) .
Entropies of ions on the conventional scale S 0 '
can
[s o ' H+ (25°C) = 0 J/K-molJ
be transformed (ll ' 12) to the absolute scale using equation t5]:
S°X25°C) =-S°.'(25°C) - 20.93 Z, J/K'iaol
[5]
where Z is the ionic^charge including sign. - Thus,, 'absolute1 entropies
calculated using equations [4] and [5],are substituted into equation. [3]
together with the free energy of formation of the ion at 25°C and the free
energy at temperature T2 is derived. .
_
-r
- 3 -
2.1
•
POTENTlAL-pH RELATIONSHIPS
Electrochemical.processes which occur in aqueous systems can be
rep res ented r ?by sa?combination gof,half-cell reactions of the following general
form:
t
. . ,.
. •;
.. ...
aA + 3H+ +* ye" =
6B + e H2O :
[6]
The equilibrium reduction potential referred to the standard hydrogen electrode
at the same temperature is given by equation [7]:
(a J
B JV
AG° RT.,
E
T
[7]
where the quantity AG° is the standard free energy change for the whole cell
reaction:'"'•'•.*'•"•''"""" lj"' " ^''["
'
'""."'
aA + (g-Y)H + + X H 2
6B + eH20
[8]
2
i.e.,
G° is the standard free energy of formation of component x at the temperature
of interest. For dilute solutions a ^
=
1, and by definition -log afl+ =
i.e." the pH of the solution at temperature T.
pH T
Thus, equation [7] transforms
into equation [10] which is then used to calculate the potential-pH relationship
for any given reaction:
'Potential-pH relationships for reactions between cobalt, cobalt
oxides and ions in aqueous solution at elevated temperatures are listed in *
Appendix I.
- 4 -
2.2
SOLUBILITY
dissolutionM a solid f(A)
a given typ^CS) can W
AG°
=
presented by equation [8h
At equilibrium:
[11]
-RTln
<*H+>
where p H
tti produce ions involution of
CP
H2:
is the partial pressure of hydrogen in the system.
Expansion of
2
equation [ll] results in the following expression for the dependence of the
activity of B on P H T and the pressure of hydrogen in the system, p ^ i
The total solubility of A is equal to the sum of ionic concentrations from
the individual reaction^ which contribute to the dissolution of the solid,
i . e . ;
•,
.•
S
•
=
-
•
-
•
•
'
.
E(aB/YB)
B
[13]
where Y B is the activity coefficient of ion••>/ in^ow-ioni%strength solutions
(<0.01ra) the activity coefficients can be equated to unity
13
, and the total
solubility is approximated by equation [14]:
S
=
S afi
[14]
3. INPUT DATA
Free energies of formation and entropies at 25°C for Co, CoO,
2+
C03O1,, Co ,.HCo0i, OH", H 2 , 0 2 , and H 2 0 were taken from the recent NBS
compilations of thermodynamic data^11*'15 and are listed in Appendix I .
All entropies are based on the absolute scale. The thermodynamic data
listed in Appendix I aTe expressed in units of calories. These data may be
converted to the SI metric systpm using the relationship 1 cal = 4.1868 J.
- 5 -
Free energies for H at temperatures to 300 °C have been calculated in a
previous report in this series
and the same values are used here. Heat
capacities of the pure substances have been taken directly from the
(8)
(9)
compilations ofVKelley
and Wicks and Block
. The hydroxide, Co(0H)2
has not been considered in this report since heat capacity data over the
temperature range of interest are not available for this compound. It
should be noted, however, that Co(0H) 2 is thermodynamically Stable with
respect to CoO in hydrothermal systems at temperatures less than ^220°C
.
2-r
A number of studies of the hydrolysis of Co have been
reported
. Only the monomer, Co(OH) , is well established in dilute
3+
solutions (<0.01m) although polymeric hydrolysis products such as Co2(0H)
and Cog(OH) g have been suggested, particularly for more concentrated cobalt
solutions
. The accepted value for the formation constant for the first
-9 81
hydrolysis product ( 3 n ) is 10 , " ~ and the free energy of formation, and
the entropy for this species, at 25°C were calculated using equation [14]
and [15], respectively.
G
°Co(0H)+ " G 'to*+ G°H20 ~G V -R T l n 3 ^
lU]
S
°Co(OH.)+ =S V *+S °H 2P ~S V " AS °
where AS0 i s the change in entropy for the hydrolysis reaction and was
(19)
calculated from the data of Bolzan and Arvia
' . We assumed that the
cbr^ie^onaervce^ (pri&cipl&coef flcientsi (see equation [41) :f or cations .also^,
ap£ly;-;£o -siLml^e'litpJ^j^^^cidsqtSi such ^ali , Co{OH); •,-,.,, The^validity of;y this , , L
assOTp^onlhjask&t^^
of 5releyant .data... jNo hydVrolysed
'iM| u iill5|| ? ihS i ; Ie.^v?-AisO;, ? ll ? M
f reef eneirgy and:entrbpyV:.katav
%M^I||ISSl|le|p3lSe|eo||#) ,fft#|k);s%4es,,: i^e ., Cozpa^and.CoO^,
''•'^^^^^^^G^s^^^W^^^W^^^-^^^
sllUlfgu&y§Sl^t|^t§the^^
considered.Je^e..^^,.^,.
^ ^ ^ - - i ^ s ^ l . ^ kiA
- 6 -
No entropy data are available in the literature for the anionic
cobalt species, HCo02~.
The entropy has been estimated using the empirical
equation of Connick and Powell
-
:
;
"I
" ' '
182.1-194.7 (|z| -0.28n); J/K-mol
[16]'
where Z is the ionic charge and n the number o* oxygen atoms excluding those
contained in hydroxyl groups.
The absolute accuracy of the data used in these calculations is
difficult to 4etermine since the NBS thermodynamic data^
adjusted to yield internal consistency.
' ^have been
However, the values listed are
5
such that the'experimental data from which they are derived may be recovered
with'kn4 accuracy ei^vial-'to that5 ofs the original quantities. Also, the values
liste'd'iorl!any-ugiyen substance satisfy all known physical and thermodynamic
relationships?Jamongsvariotife-properties, and the calculated value for any
thermodynamic quantity for a reaction is independent of the path chosen
for the evaluation.
Equation [1] shows that for solid substances the uncertainty
in G°(T2) - G'dj) depends upon the accuracy of -8.° (Jf) and C°, For the
solids considered in this work (i.e. Co, (2030^), the entropies and heat
capacities are known to better than 1 to 2%. This uncertainty is- small,
and the accuracy of CCT^) is most likely determined more by the error in
G°(Ti) than by the integration over the temperature range Ti to T^.
For
ionic species the uncertainty in G°(T2) - G°(Tj) 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-silver halide cells at" temperatures to 300°C indicates
that the'integrations'are accurate to better than 5%
.
•i
The uncertainty in solubility due to error in AG° can be determined
using equation [12]. For an error in AG° of + 12.56 kJ/mol (i.e. 3 kcal/mol)
log afi is uncertain to + 1, i.e. an order of magnitude. This latter figure
is a reasonable estimate of accuracy for the solubilities calculated in this
- 7 -
work at'25°C. However, as discussed in the previous paragraph, the
integration of AG° over the temperature range of interest is accurate
to a few percent. Hence, that uncertainty in the variation of log a
,
-- - .
g
with temperature will also be of,the order of a few percent.
Free energies of the various species considered above have been
calculated to 300°C using equations [1] and [3] and ar*- listed in Appendix I.
Also listed are standard free energy changes for a set of reactions which
is used here to describe the interaction of cobalt with water at elevated
temperatures.
4. RESULTS AND DISCUSSION
4.1
POTENT!AL-pH RELATIONSHIPS
Potential-pH relationships for the cobalt-water system at
25 and 300°C are plotted in Figures 1 and 2, respectively.
The equilibrium
relationships are plotted for ionic activities and gas partial pressures
equal to 10~ and 0.101325 MN/m2 (i.e. 1 atm). These values are in the
range of interest for practical systems, e.g. water—cooled nuclear reactors.
The diagrams identify three regions'of corrosion behavior for
cobalt metal in aqueous systems. The immune region corresponds to the
conditiors wherein cobalt metal is thermodynamicallystable, and is- bounded ,
by reactions 13-1, lO^I and 15-1 . Under these conditions oxidation of cobalt
to form Co" , CoO and'HCo02' is thermodynamically impossible. (The passiveregions' correspond to areas of stability of the solid oxidation products,
CoO and C03O4,
The theoretical regions of corrosionoccur under conditions,
of thermodynamic stability of the ions, Co
and HCo0 2 . U n d e r these
conditions solid oxidation products (e,g. CoO and Co30^) are not stable.
13-1 designates reaction.13, Appendix I. The Roman numerals are
omitted in Figures 1 and 2.
- 8 -
However, these oxides may exist as metastable products in these regions at
potentials more anodic than the equilibrium values determined by extrapolation
of reactions 10-1 and 12-1 into the theoretical regions of corrosion.
Whether
or not passivation of ttie metal by a mefcastab'le oxide (or hydroxide) actually
occurs in practice is determined by the kinetics of the system and cannot
be inferred from the present data.
Temperature is seen to have a marked effect on the potential-pH
relationships for the cobalt-water system.
The principal effect of temperature
is the shift of the equilibrium relationships to lower pH T values and potentials
and results in an expanded region of corrosion in alkaline solutions.
Part
of the shift to lower pH T values arises from the temperature varistion of
K
—2
as illustrated by the pEL values for a 10
designated (a) in Figures 1 and.2.
mol/kg hydroxide solution
However,""the1-data-show that reaction
6-1 shifts to lower pH_ values with temperature than can be accounted for
by variation of K
alone. This observation is consistent with the more
favourable formation of HCo02
from CoO at high temperatures.
Similar
arguments can be used in discussing the effect of temperature on the formation
of HC0O2
(i.e. pH_
_2
from cobalt metal. Thus, in a 10 mol/kg hydroxide solution
=
(a) ) the equilibrium potential for reaction 15-1 at 25°C is
-0.58V. At 300°C, however, the equilibrium potential is shifted to -1.07V,
i.e. the formation of HG0O2
from cobalt metal becomes thermodynamically
easier with increasing temperature.
In acid solutions the anodic process in the corrosion of cobalt
2+
is the formation of Co , i.e. reaction 13-1. The equilibrium potential for
this reaction at 25°C and for an activity of Co
equal to 10
is -0.46V.
At 300°C the potential is more negative(-0.61V), although the. shift is not
nearly as large as for the-equilibrium between HCoOg- and cobalt metal. Thus,
cathodic protection of cobalt metal in both rcid and'alkaline systems becomes
thermodynamically more difficult with increasing temperature and especially
so for alkalir-e systems.
The principal use of potential-pH diagrams lies in rationalizing
metallic corrosion with known chemical reactions. Tha electrochemical theory
of metallic corrosion postulates simultaneous anodic and cathodic reactions
- 9 -
occurring at the metal surface. On open-circuit the anodic and cathodic
partial currents are equal and the metal adopts a potential (E
corrosion potential) which satisfies this condition.
, the
Electrochemical theory
shows that E v_. lies between, the equilibrium potentials for the anodic (E°)
and cathodic (E°) processes and is closest to the equilibrium potential of
the reaction with the higher exchange current density.
Since the overall
corrosion reaction is thermodynamically possible only if the equilibrium
reduction potential for the anodic process is more negative than that for
the cathodic reaction, then the corrosion potential must satisfy the following
inequality:
E <E
l corr < EC
™
In hydrogen.,.rich systems (e.g. at 0.1 MN/m2 (i»l atm) partial
pressure of H2) the cathodic partial reaction in the corrosion of cobalt
is the evolution of hydrogen:
2H + + 2e~ =
H2
[18]
The equilibrium condition for the above reaction
in Figures 1 and 2.
is represented by reaction 19
At 25°C (Figure 1) inequality [17] is satisfied only at
pH < 7.5. At higher pH values none of the reactions considered here can act
as anodic processes under the conditions stated and cobalt will not corrode
to produce any of the oxidation products considered.
cobalt can corrode tojfonn Co
At pH < 7.5, however,
and the corrosion potential will lie within
the region defined^by, reactions 13-1* and 19-1. At 300°C corrosion is also
possible in alkaline solutions, and E __ will have a value within the region
r
•
•-••::.
. . - - • . . •.-•.
-
.
corr
defined by reactions 15-1 and 19-1. The increased thermodynamic tendency
for Co to corrode in alkaline systems at elevated temperatures is a further
manifestation of the increased stability of HC0O2 .
In oxygen rich systems the reduction of oxygen:
0 2 + AH + + 4e~ =
2H2O
- 10 -
can act as the cathodic reaction in the overall corrosion process and the
equilibrium potential' for- therreaction-— is given, as ret. .ion 20 in
Figures 1 and 2 f P O 2
=
O.i lOf/m? 'frlatm)j
corrosion of cobalt to produce. Co
2+
. The data show that
+
, Go(OH) , CoO and HCo02" is possible
at both 25 ar.d 30Q°C. Also, oxidation of Cob to 00364 is possible under the
conditions stated and corrosion films formed on cobalt metal in oxygen
rich systems will likely contain both CoO and
4.2
SOLUBILITY
The solubilities of Co and CoO as a function of pH T at temperatures
to 300°C and at a partial pressure of hydrogen of 0.1 MN/m2'^ 1 atm) are
plotted in Figures 3 and 4, respectively.
In both cases the solubility
passes through a minimum as a function of pH . To the left of the minimum
2+
+
the predominant soluble species are the cations Co
and Co(OH) whereas to
the right the anion HCo02~ dominates. The contributions that these ions
moke to the solubility of CoO at 25°C and 300°C are plotted in Figure 5.
The principal influence of temperature is to shift the equilibrium concentrations
of the various ions to lower pH
values. The shift is much greater than can
be accounted for by the variation of K
and indicates that the ion HCo0 2
becomes increasingly stable with temperature'. This is well illustrated by
evaluating the ratio [ HCo02~ ] / ([Co2+] + [Co(OH)+]) for CoO in a hydroxide
—•'3
'
~
~"
solution (say 10
mol/kg) at the two temperatures nf interest.
is found to be 0.91 at 25°C, but increases to 2500 at 300°C.
The ratio
At all temperatures to 300°C and at 0.1MN/m?- (^ 1 atm) partial
pressure of l.ydrogen the data plotted in Figures 3 and 4 show that the
solubility of cobalt metal is less than that of CoO. Thus, under these
conditions cobalt metal is thennodynamically stable and the conversion of CoO
to Co is a spontaneous process. This may occur by direct solid state reduction
or,by dissolution/electrocrystallization processes.
However, the solubility
of Co is dependent on the pressure of hydrogen in the system (Figure 6 ) ,
since the overall dissolution reaction involves a change in oxidation state
- 11 -
of cobalt from 0 to +2. On the other hand, the dissolution of CoO to form
Co(II) ions in solution dees not involve a change in oxidation state and the
solubility of this oxide will be independent of the pressure of hydrogen in
the "system. Equation [12] shows that the dependence of solubility on
hydrogen pressure is determined by the coefficient (y/26), which, for the
2+
+
—
dissolution of Co to produce Co ,. Co (OH) and HC0O2 , is numerically equal
to -1.0. Thus, the solubility of cobalt decreases by one order of magnitude
for every order of magnitude increase in the pressure of hydrogen in the
system.
The hydrogen pressure at which the solubility of Co is equal to
that of CoO defines the condition for equilibrium between these two solids.
* Q7
The equilibrium partial pressures of hydrogen at 25°C and 300°C are 10°'
4 ft ?
2
and 10 " N/m respectively, as shown by the intersections of the solubility /
lpg.-p_ lines for Co and CoO in Figure 6. At hydrogen pressures greater than
these values ....cobalt..metal is stable but at lower pressures the oxide is
thermodynamically stable.
The concentration of hydrogen In the heat transport systems of
CANDU PHW's is normally maintained at 4.5 x 10~ mol/kg OvLOcckg" ) . This
concentration corresponds to partial pressures of 10 ' and 10 " N/m
25 and 300°C, respectively
at
. Therefore, at 25°C, the partial pressure
of hydrogen in the system (p ) is greater than the equilibrium partial
pressure (p
) for the C0/C0O reaction a-d cobalt metal is the thermodynamically
stable solid.
At 300°C, however, p
form CoO. At. 237°C p
between.Co agd Cop.
=
p
< p
and cobalt metal will oxidize to
which corresponds to a state of equilibrium
It is clear from the above discussion that the chemical
i-denti-ty of: cobalt^ ,(i.e. metal, or oxide) in a PHW reactor can be affected by
Varying .both the. temperature and hydrogen pressure in the system. This may
have important implications concerning the movement of
60
Co in PHW reactor
heat transport systems and is discussed in detail elsewhere
The pH
values at which minimum solubility occurs for cobalt and
cobalt oxide are plotted as a function of temperature in Figure 7. These
data show that the minimum solubility is shifted to lower pTL values with
increasing temperature. The pH T values adopted by ib
and 10
mol/kg
6
hydroxide solutions (i.e. pH 11 and 10 at ?.5 C) are also plotted in Figure 7
assuming that changes in pH with temperature can be attributed to K^ alone.
- 12 -
The plots demonstrate that the pH
of minimum solubility decreases more
rapidly with temperature than does K . This is consistent with the increased
stability of the anion, HCo02~, at the higher temperatures as discussed
previously.
The data predict that miiiimi'-ra solubility of Co and CoO at
300°C occurs at pH T
-
6.6.
This pH corresponds to a 25°C value of ^9.6,
close to the value maintained in CANDU PHW's.
60
Thus, if the transport of
Co in PHW heat transport systems is related to the solubility of Co and
CoO the problem may be minimized by maintaining the coolant at
The solubility of Co and CoO in various hydroxide solution?
at temperatures to 300°C and at 0.1 MN/m2 (^ 1 atm) partial pressure of
hydrogen are plotted in Figures 8 and 9, respectively.
concentrations represent PH25 values of 12(10
The hydroxide
mol/kg OH ) to 9(10
which are in the range of interest for PHW reactor operation.
mol/kg OH )
The data
plotted in Figure 8 for cobalt metal show that except in the least alkaline
solution the solubility is predicted to increase over the entire temperature
range. In 10
mol/kg hydroxide solution, however, the solubility passes
through a maximum at 1"v200°C. Thus, transport by differential sbluTbiiity at
200°C < T < 300°C can occur from the hot to the cold regions at pH2'5 > 10
and in the reverse direction at pH25
=
9.
-3
Figure 9 show that at T < 250"C, and in 10
The data for GoO plotted in
••
solutions, the solubility increases with temperature.
10
-2
mol/fcg and 10
•
mol/kg hydroxide
In 10
mol/kg and
mol/kg hydroxide solutions, however, the solubility decreasesover this
temperature range and continues to decrease in the 10
solution for temperatures to 300 °C.
In the 10
-10
mol/kg hydroxide
mol/kg hydroxide "
solutions at 25Q°C < T < 300°C the solubility increases with temperature.
Thus, in the temperature range 250-300°C, transport by differential solubility
can occur as described above for cobalt metal, i.e. from the hot to the cold
region at p^s** 10 and in the reverse direction at pH25
=
9.
Few experimental measurements of the solubility of Co and CoO in
hydrothermal systems have been reported.
(22}
However, some data have been
1
-'
/ •
' >
recently obtained by Tewariv 'for the solubility of CoO in hydroxide
solutions at temperatures to 300°C. These experimental results show that
-it
at pH25
=
10 (i.e. 10
—
•
„
mol/kg OH ) the solubility decreases with increasing
temperature which is in qualitative agreement with the calculated solubility
behaviour reported in this study.
- 13 -
5. SUMMARY AND CONCLUSIONS
(1)
Potential-pH relationships for the cobalt-water system at
elevated temperatures (25°C to 300°C) and solubilities of Co and CoO as a
function of pH_ over the same temperature range have been calculated by
integrating free energy functions for the various components of the system.
(2)
The equilibrium partial pressures for the reduction of CoO to
Co are calculated to be 10°* S7 atm and lo"*"82 N/m2 at 25°C and 300°C,
respectively.
These data show that if the concentration of hydrogen in the
—if
system is maintained at 4.5 x 10
_X
mol/kg (VLOecKg
) then cobalt metal
is thermodynamically stable at T<237°C but CoO is stable at higher temperatures.
(3)
The solubility of Co and Cob passes through a minimum as a
function of pH T at temperatures to 300°C. The minimum solubility occurs
at pH
=
11. and 6.-6 at 25 °C and 300°C respectively, i.e. the pH^, at
which the minimum occurs shifts to lower values with increasing temperature.
The shift is greater than can be accounted for by variation of K w alone
and is consistent with increased stability of the anion, HC0O2 , at elevated
temperatures.
(4)
In the temperatur? range 250°C to 300°C, transport of cobalt via
differential solubility at pH^s > 10 can occur from the hotter to the colder
regions of a hydrothermal system.
At pH£5
=
9 the calculations predict
that transport occurs in the reverse direction, i.e. from the colder to the
hotter regions.
- 14 -
6. REFERENCES
!.
Herbert E. Townsend, Jr., PotenUal-pB diagrams at Elevated
Temperature for the System Iron-Water, Corrosion'Science,
10_: 343-58 (19- ^ •
2.
D. Lewis, Theoretical Studies of Aqueous Systems Above 25°C.
1. Funcamental Concepts fgr Equilibrium Diagrams and Some
General Features of the Water System. Aktiebolaget Atomenergie,
Sweden, Report AE-431 (1971).
: ,
3.
D. Lewis, The Theoretical Studies of Aqueous Systems Above 25°C.
2. The iron-Water System, Aktiebdlaget Atomenergie, Report
AE-432 (1971).
4.
R . G . Robins, The Application of Potential-pH Diagrams to the
Prediction of Reactions in Pressure Hydrothermal Processes.
U.K. Ministry of Technolopy, W.S.L. Report LR80(MST) (1968).
5.
R . L . Cowan and R.W. Staehle, The Thermodynamics and Electrode
Kinstic Behaviour of Nickel in Acid Solution in the- Temperature
Range 25° to 300°C, Journal of Electrochemical Society,
557: 118-68 (1971).
6.
D.D. Macdonald, G.R. Shiermari and P. 'Butler, The Thermodynamics*
of Mptal-Water Systems at Elevated Temperatures. 1. The Water
and Copper-Water System, Atomic Energy of Canada Limited, AECL4136 (1972).
7.
D.D. Macdonald, G.R. Shierman and P. Butler, The Thermodyn-->mics
of Metal-Water Systems at Elevated Temperatures. 2. Iron-Water
System. Atomic Energy of Canada Limited, AECL-4137 (1972)..
8.
9.
10.
'
'
K.TC. Ke'lley,' Contributions to the Data on Theoretical Metallurgy.
-XITI., Mgh Temperature. Beat-content, - Beat-capacity, and Entropy
Data for the Elements and Inorganic Compo-md3 Washington, U.S,
Department of Interior, Bureau of Mines, Bulletin 584 (I960).
Charles E. Wicks and F.E. Block, Thermodynamic Properties of
65 Elements: Their Oxides, Balides, Carbides, and Nitrides,
Washington, U.S. Department of Interior, Bureau of Mines,
Bulletin 605 (1963) .
D.D. Macdonald and P. Butler, The Thermodynamics of the AluminumWater System at Elevated Temperatures, accepted for publication
in Corrosion Science.
- 15 -
11.
•
Cecil M. Criss and J.W. Cobble, The Thermodynamic Properties of
High Temperature Aqueous Solutions. V. The Calculation of Ionic
\:.Heqt Capacities up to 200°. Entropies and Heat Capacities Above
200°, Journal of the American Chemical Society, J36_: 5390-3 (1964).
12.
Cecil M. Criss and J.W. Cobble, The Thermodynamia Properties of
High Temperature Aqueous Solutions. IV. Entropies of the Ions
up to 200° and the Correspondence Principle3 Journal of the American
Chemical Society, 86_: 5385-90 (1964).
13.
J.W. Cobble, The Thermodynamia Properties of High Temperature
Aqueous Solutions. VI. Applications of Efitropy Correspondence
to Thermodynamics and Kinetics, Journal of the American Chemical
Society, 86_: 5394-5401 (1964).
14.
Donald D. Wagman, Selected Values of chemical Thermodynamic
Properties, Washington, U.S. Department of Commerce, National
Bureau of Standards Technical Note 270-4 (1969).
15.
] Donaljd^i*Wagman j Selected Values of Chemical Thermodynamic
; Properties,Washington, U.S. Department of Commerce, National
Bureau of -Standards Technical Note 270-3 (1968).
F
16.
- Ach&aza,rPorrOs'ion of Metal Surfaces Partially Immersed in
, SaZt'SSSutions. ^Corrosion on the Edge of Immersion, Rendiconti
Del Seminario Delia Facolta Di Scienze Delia Universita Di
Cagliari* 29': 46-^51 (1959).
, M.P:. Collados, F. Brito and R. Diaz Cadavieco, Hydrolysis of
^Cobalt (II) in 1.5M(Ba, Co) (CIO.) „ at 25°, An. Real. Soc. Esi
Fis. Quim., Ser. B, 63.: 7-8, 834-5 (1967).
17.
18.
,
19.
J. Shankar and B.C. de Souza, Hydrolysis of Co and Ni Ions,
Australian Journal of Chemistry, 16_: 1119-22 (1963).
, Jorge A. Bolzan and A.J. Arvia, Hydrolytic Equilibriums of
' Metallic Ions. I. The Hydrolysis of Co(II) Ion in Na ClO^
Solution, Electrochimica Acta, r7_: 589-99 J1962).
20.
Robert E. Connick and Richard E. Powell, Ths Entropy of Aqueous
Xoy-anions, Journal of Chemical Physics, 21: 2206-7 (1953).
21.
D'.D. Macdonald'and T.E. Rummery, The Thermodynamics of Metal
Oxides in Water-cooled Nuclear Reactors, AECL-4140 (1972).
22.
.
~ ,P.H. ^Tewari, Private Communication. ,
•• •••,-
- 16 -
2.0-
-2.0
'
PHT
FIGURE 1:. POTENTIAL-pH DIAGRAM FOR THE COBALT-WATER SYSTEM AT 25°C.
IONIC 6ACTIVITIES AND GAS 2 PARTIAL PRESSURES ARE EQUAL TO
lO" AND 0.101325 MN/m (i.e. 1 atm) RESPECTIVELY.
- 17 -
FIGUREr 2: POTENTIAL^ DIAGRAM FOR THE COBALT-WATER SYSTEM AT 300°C.
< IONIC eACTIVITIES AND GAS 2PARTIAL PRESSURES ARE EQUAL TO
10" AND 0:101325 MN/m (i.e. 1 attn) RESPECTIVELY.
- 18 -
O 23 °C
• 60 °C
A IOO°C
•
IS0°C
V EOO°C
T 250°C
a
300°c
14
FIGURE 3 : THE INFLUENCE OF p H T ON THE CALCULATED SOLUBILITY OF COBALT
AT TEMPERATURES BETWEEN 25°C AND 300°C "AND AT O . l M N / m 2 ^ 1 attn)
PARTIAL PRESSURE OF HYDROGEN.
- 19 -
10
10 -s
o
£
1
o1
o
10 -6
101
-2
pH T
10
14
FIGURE 4 : THE INFLUENCE OF pH T ON THE CALCULATED SOLUBILITY
OF COBALT OXIDE (CoO) AT TEMPERATURES BETWEEN 25°C AND 300°C.
- 20
-
PH T
FIGURE 5: THE CONTRIBUTIONS OF VARIOUS IONS TO THE SOLUBILITY
OF CoO AT 25°C (SOLID LINE).AND 300°C (DASHED LINE).
- 21 -
yi
i
1
1
—r
\
\
\
\
10
-5
\
00,300*0
\
\
\
10
-6
\ _
CoO,25°C
=i
\
\
o
\
o
. O.
\
10
-7
\
V
CoO, 300°C —
\
\
\
10
\
-8
,Co,25°C
\
\
,
log
\
PH ( N / m 2 )
FIGURE 6: THE DEPENDENCE OF THE SOLUBILITY OF Co AND CoO ON THE PRESSURE
OF HYDROGEN IN A 10-" mol/kg HYDROXIDE SOLUTION AT
25°C (SOLID LINE) AND 300°C (DASHED LINE).
- 22 -
© PH T of minimum solubility of Co ond CoO
« pH T of IO" 3 molAg OH" solution
O pH T of IQ- 4 mol/kfl
200
100
OH" soiution
300
, T t°C)
FIGURE 7: VARIATION OF THE pH, OF MINIMUM .SOLUBILITY OF Co AN? CoO
AS A FUNCTION OF TEMPERATURE BETWEEN 25°C AND 300°C.
- 23
10
-
-7
10
o
e
o
o
10.-9
10
T(9C)
300
FIGURE 8: THE. INFLUENCE OF TEMPERATURE
ON THE CALCULATED,SOLUBILITY,OF Co
IN HYDROXIDE SOLUTIONS'-AT O.lMN/m 2 ^ 1 atm) PARTIAL PRESSURE OF HYDROGEN.
- 24 -
©
0
#
Q
I0"5 mol/kg
\b~4 mol/kg
1OFS mol/kg
IO-2mol/Hg
OH
OH
OH
OH
10
100 '
T(°C)
200
300
FIGURE 9: THE 'INFLUENCE OF TEMPERATURE ON THE CALCULATED"SOLUBILITY
OF CoO IN HYDROXIDE SOLUTIONS. '
- *
- 25 -
APPENDIX I
CALCULATED THERMODYNAMIC FUNCTIONS FOR THE COBALT-WATER SYSTEM AT
2 9 8 , 3 3 3 , 3 7 3 , 4 2 3 , 4 7 3 , 5 2 3 , '-NO 573K
iMlllM'i
I '
SPECIES
H*
H2 '
02
M2O
CO '1
COO I
C0304
co**
COtOHl*
HC002«
CO***
TYPE
FREE ENERGY 25C
SOLUBLE
ENTROPY 25C
CP» il)
0,00000flE*00
0,000000E*00
0,3180«aE*02
tff0(l0000E*00 0,490030E*02
•0,566870E*09
B,16T108E*(!2
0,000CI00E*00
0,7ia000E*ei
•U,5l2eB0E*05
0.126600E*CI2<
.tf,i85B0BE«06
0.2490OBE*92
•0,130000E*05 •0,370000E*02
•B.563000E*09 •0.327000e*e'2
•0,S2970BE*09
0,150000E*B12
0,320»00E*09 •>0,88000«E*CI2
CASEOUS
CASEOUS
SOLUBLE
SOL 10
SOLID
SOLID
SOLUBLE
SOLUBLE
SOLUBLE
SOLUBLE
CP< |2)
•
0,6528WE*01
0,7i*0«0E*01
0 t 1799SBE»02
0,4740«0E*01
0,1194i)0E*02
0,3Pia4aBE*02
B',7B0I»00E»03
t»a100000E»02
B,4)3Oi)00£:*00
0,400B00E»B2
0,204000E«02
M,l7aa0BE.01
CP( ,3)
ACTIVITY
0.100B0BE-05
a,120«)0BE*tf5
0,1BBB00£*01
-0,40tiBBBE*05
H,100BBBE*01
0,000B0f»E*DI« , B,a0Bkl0BE*m
0,000U00E*00
B,lBt)BBBE«01
B,40BBB0E«BS
0,1B0B00E*01
.0,572k)00E*06
B.100000E*0i,
B,100B0BE.:B5
0.100000E-0S
B,lB0BBBE.Iil5
U.1BB0BBE.05
TREE EMER6Y VS', TEMPERATURE
.1 ,
2
H*
H2
3
4
02
H2O
9 '
6
CO
COQ
CO3C4
CO**
Cn(OH)*
7
B
9
.10
11
,CO***
DEG KELVIN
423
298
333
373
0,«)PiBfi0aE*0(>
0|000^00E*00
0,030000E*00
0',566B7S!E*05
0,0ti000BE*00
fl,512000E*05
0,18900tlE*06
B,13BH0flE*B5
0.56380HE*05
0,829700E*05
0,320000E«05
0i'l29S00E*03
•0 I 11B991E*04
"0il72906E*04
•0iS73079E*B9
•0,263i32E*03
-B,516680E*05
•0ilB9917E*06
-0.116B42E*05
•0,552312E*05
•0i833S60E*0S
0 ( 349399E*05
B,134330E*B3
•0,240075E*04
•0 a 373717E*04
•0,588974E*05
-0,S91i44E*03
-»,522594E*05
-0,187106E*06
•0il07368E*05
• 0i5«3*12£*i)5
•0,B349B7E*0S
Bi378734E*05
473
>B,790000E*02
•0i62E000E*03
«0,406064E*04
-B,576151E*04
«0,629075E*04
»0,888791E*34
•0i591927E*BS
•0,603»45E*a5
•0il03BS7E*B4 , -0,152407E*04
-0i530741E*B5
•0,539636E*05
•0ilB879lE*06
•0,190683E*06
>0i986110E*04
•0,946302E*04
•0i936446E*05
«0,534B79E*05
-0,83B479E*B5
•0,82B455E*05
B,408736E*k)5
0,431860E*05
REACTIONS
II
KCO**
1 *
KH20
->
21
KCO**
> *
2IH20
31
KCO(OU)*
) *
41
KC00
) *
1<H*
) «
KCOtOH)*
->
3<H*
i *
KHC002-
)
KH20
->
2<H*
) *
11HC002"
)
2CH*
->
HC0$*
) *
1CH20
)
sr
KC00
> • 1<H*
->
i(CO(OH)*
)
61
1CC0C
) *
->
KH*
J • KHC002*
KH20
)
- *> •
71
KC0304
) * 6(H*
) *
KH2
)
..-.......—,>
3<C0**
) + 4IH20
81
1CC0304
) * 3(H*
) *
KH2
)
..........-..>
3(C0(0H)*
t *
KH20
91
KC0304
) * 1IH2
) « 2(H2C
)
....
3IH*
) *
i(HCQ02«
...-•>
523
573
-0il44400E**04
-0,749915E*B4
-B,116Z45E*B5
-0,6165H7E*05
.B,204467E*04
^0iS4?203E405
«0•192767E*06
-0,99566iE*a4
.0,242B6BE*B4
•'0l'92;70i5E*0'4
•0!B04744E*05
B,44BB05E*05
•0i630796^*09
•0i^597»6t**4
•0,5593e0E*05
»0il9SB3iE*B4
•B,1B1332F.*B5
-B,543486E*05
-Bi795623E*05
0.457243E*a5
- 27 -
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