Geoehimica el Cvsmwhimica Ada Vol. 53, pp. 327-341Copyright © 1989 Pergamon Press pic. Primed in U.S.A.

OOI6-7037/89/S3.00 4- .00

Co(II)-chloride and -bromide complexes in aqueous solutions up to 5 m Na^and 90°C:Spectrophotometric study and geological implications*

PUJING PAN ' and NICHOLAS J. SUSAK

Department of Geology, University of New Brunswick, Fredericton, New Brunswick, Canada, E3B 5A3

(Received May 31, 1988; accepted in revised form December 1, 1988)

Abstract—Absorption spectra of Co (II)-chloride and bromide complexes have been taken in the UV-visible-NIRregion, at temperatures from 25 to 90°C. The octahedral absorption bands have been resolved into components byfitting to Gaussian distribution functions, and the resolved bands have been assigned to ligand-neld transitions usingTanabe-Sugano diagrams. The ligand-field-splitting energies, 10 Dq, were obtained for both chloro- and bromo-cobaltouscomplexes. These data were then used to estimate the average chloro-ligation number at each temperature and thechloride concentrations.

At room temperatures and low halide concentrations, essentially only octahedral (6-fold) complexes exist. As thetemperature is raised or, especially, as the ligand concentration increases, the complexes undergo a transformationfrom an octahedral to a tetrahedral (4-fold) configuration. A combination of graphical and numerical methods hasbeen used to determine the stability constants. In the numerical treatment, activity considerations have been incorporatedthroughout. Based on these stability constants, the thermodynamic data, i.e. enthalpy, entropy and free energy changes,were calculated for all complexation reactions. It was found that the formation of both the first octahedral complexand the sole tetrahedral complex are endothermic. The favourable free energy changes for these reactions are due togains of entropy inasmuch as they are hard-hard interactions, showing an electrostatic bonding character. The tetrahedralcomplexes exhibit a greater degree of electrostatic bonding than the first octahedral complex. The other octahedralcomplexes are extremely weak and do not show typical hard-hard or soft-soft interactions. The octahedral-tetrahedraltransformation is strongly favoured by an increase in temperature or halide concentration or both. Thermodynamiccalculations suggest that higher halogenated octahedral complexes and, to a lesser extent, Co(H2O)i+ are selectivelyconverted to the tetrahedral complex, CoJfJ".

It is possible to factor total dissolved cobalt in a fluid into two terms, a free cobalt term and an enhancement termdue to chloride complexation. Investigation of each of the terms shows that under typical, low-temperature hydrothermalconditions (e.g. during the formation of red-bed type and Mississippi-Valley type deposits), several ppm cobalt canbe dissolved in natural fluids, provided that a sufficient source of cobalt is present. For major cobalt mineralization tooccur, environmental conditions which produce a high free cobalt term and very high salinities (>5 m at 90°C whichgive rise to large enhancement factors) are required, in addition to a sufficient source of cobalt.

aaAAb

BB

GHIKmnOh5TX10 Dq0fA

GLOSSARY OF SYMBOLS

Chemical activityIon size parameter in extended Debye-Hiickel equationDebye-Huckel limiting slope; optical absorbanceAngstromElectrostatic solvation and short-range interaction param-

etersDebye-Hiickel constantRacah-B term, in cm"1

Empirical constant used to extend Debye-Hiickel equationto higher ionic strengths

Free energy, in kj mol"'Enthalpy, in kJ mol"1

True ionic strengthEquilibrium constant; KelvinMolalityLigation numberOctahedralEntropy, in J mol"1 K"1

Temperature, K or °CHalogen (F~, CT and Br")Ligand-field-splitting energyAccumulative stability constantActivity coefficient; spectral band width at half heightIncremental change

* This paper was part of an invited presentation at the MERI con-ference.

1 Present address: Mineral Exploration Research Institute (MERI),C. P. 6079, Succursale "A", Montreal, Quebec, Canada H3C 3A7.Mailing address: Department of Geological Sciences, McGill Uni-versity, 3450 University Street, Montreal, Quebec, Canada H3A 2A7.

X Spectral wavelength; empirical constantv Wavenumber, in cm"'Superscripts:0 Standard state* Sum

Subscripts:

aq Aqueous speciesjj.t.n.m Components, species in solutiono),,-i.. .4 Denoting specifically tetrahedral complexes, For a reactionTr Complex configuration transition

INTRODUCTION

IT is GENERALLY accepted that metals are mobilized andtransported as complex ions in ore-forming environments.Because of its predominance in hydrothermal fluids, Cl~ isoften assumed to be the principal complexing ligand. Al-though some data are available on the stabilities of metal-chloride (and other ligand) complexes (e.g. HELGESON, 1969;BARNES, 1979; SEWARD, 1976, 1984), the data set is farfrom complete. Most of the work to date has focused on themore abundant metals (e.g. Fe, Cu, Pb, Zn, etc.); there arefew data available for the less abundant metals, such as Niand Co. Cobalt primarily forms hydrothermal deposits (e.g.in Central Africa Copper-belt and at Cobalt, Ontario). If weare to understand completely how and why hydrothermaldeposits occur, we must also investigate those conditions

327

328 P. Pan and N. J. Susak

where they do not form. Previous work by SUSAK andCRERAR (1985) indicates that the chloride complexes of thetransition metals Fe, Ni, Co and Cu all have two configu-rations, octahedral (6-fold) and tetrahedral (4-fold), over therange of conditions that yield hydrothermal deposits. It wasalso noted that most deposits appear to have formed underconditions where the tetrahedral complex predominates. Ifthis is true, how important is the coordination configuration

. to metal transport and deposition? Because of its spectralcharacteristics, cobalt is most suitable for establishing spec-trophotometric procedures. The investigation of its com-plexation with chloride in aqueous solutions may serve as agood example to begin to answer the question above.

Because of their very striking changes in colour and usesin the nuclear industry, the study of cobalt halide complexeshas attracted many chemists, as well as physicists (e.g. BALL-HAUSEN and JjeteGENSEN, 1955; LISTER and ROSENBLUM,1960; COTTON et al, 1961; KENNEDY and LISTER, 1966;LUDEMANN and FRANCK, 1967, 1968; ZELTMANN et al,1968; LUDEMANN and MAHON, 1969; BELOUSOV et al, 1972;KRAUO and LEHMANN, 1972; BLOKHIN et al, 1974; BJER-RUM et al, 1975; SKIBSTED and BJERRUM, 1978; SWADDLEand FABES, 1980; SUSAK and CRERAR, 1985; PAN and SU-SAK, 1985; SUSAK and PAN, 1988). Most of these studiesgive only a qualitative description of the complexation ofcobalt, primarily at room temperatures. Some authors(LISTER and ROSENBLUM, 1960; KENNEDY and LISTER,1966; ZELTMANN et al, 1968; BELOUSOV et al, 1972; BLO-KHIN etal, 1974; BJERRUM et al, 1975; SKIBSTED and BJER-RUM, 1978) have determined the stability constants, but thequality of their results is suspect, since there is little agreementamong these values (see Table 1). Most of these quantitativestudies only calculated the stoichiometric equilibrium con-stants in constant ionic strength solutions (LISTER and RO-SENBLUM, 1960; KENNEDY and LISTER, 1966; BELOUSOV etal, 1972), or in a few cases (ZELTMANN et al, 1968; BJER-RUM et al, 1975; SKIBSTED and BJERRUM, 1978) took ac-count of activity changes in only a semi-thermodynamicmanner (i.e. the activity coefficient for Cl~ was estimated byvarious methods, while assuming the others to be unity).Although it is recognized that over a wide range of temper-atures and ligand concentrations, both octahedral and tet-rahedral complexes coexist in solution, there have been noattempts to distinguish between them unambiguously whencalculating the stability constants.

In the present work, water has been considered as one ofthe ligands coordinating with Co (II), allowing us to calculatethe stability constants for both CoC\n(H2O)l~" andCoClm(H2O)4l™, respectively. Activity coefficients were in-corporated throughout the process. To examine the effect ofcobalt (II) complexing with ligands with different coordinatingpower, fluoride and bromide complexes of cobalt (II) werealso examined. Due to the low solubility of CoF2, cobaltousfluoride complexes could not be investigated spectrophoto-metrically. The work reported here is a preliminary reportof the low temperature behavior of this system. Studies athigher temperatures are currently in progress.

EXPERIMENTAL

All chemicals used were Fisher certified or Fisher certified ACSgrade and were used as received without further purification. All

Table 1 Compilation from the literature

of stability constants of complexes

MCKH 0)' -.49(5M)°2 S -.51(2.8M)]

-3.54(.5-16M)°

-8. 1U.5-16M)C

-.32(5M)"-.024I3M)-.14(2M)C

-.177(2M)"-.77(.S-16M)°

.23(7M) f

-1.05{<5M)9

1.34UOM).60

-.15(7M) f

-3.74(<5M)9

.021

-6.05(.S-16M)"-.70I7M)

-5.28(<SM)9

-1.711

-1.70(7M)f

-4.51

1.43(10M)f

-6.62(<5M)9

2.57(10M)h

-2.09

-.72I3M)"

.03'

-i.ia'

M=Ni

.22(3M)-.17(2M)C

-.245(2M)"

-.8H3M)"-,12(2M)C

All data are presented as logJ3 and >at 25 C, terms inparentheses are ionic strengths in which the data were derived.a, ASHURST (1976); f, BELOUSOV et al. (1972);b, BLOKHIN et al. (1974); g, BJERRUM et al. (1975);c, KENNEDY and LISTER (1966); h, SKIBSTED and BJERRUM (1978);d, LISTER and ROSENBLUM (1960); i, This work;e, ZELTMANN et al. (1968); j, RAMAN (1976).

chloride and bromide solutions were made using NaCl or NaBr, re-spectively, except when very high chloride concentrations were de-sired. In these cases LiCl was used. All solutions were prepared usingdegassed, distilled-deionized water. Spectra were recorded with aVarian 2300 spectrophotometer equipped with a five-position ther-mostated cell holder and controlled by an Apple 11+ microcomputer(later replaced by a DEC PC350 microcomputer).

Temperature of the reference and sample cell was measured usinga type K thermocouple in contact with the appropriate cuvette andconnected to a Fisher Microscribe 4500 chart recorder. The temper-ature of the cells was controlled by an external circulating waterbath.Sample and reference cells remained within ±0.10°C of each otherafter an average equilibration time of 120 minutes. The ambienttemperature of the cell compartment was controlled to 25 ± 0.5 °Cby means of a second waterbath.

Cuvettes, 10 mm, square and constructed of UC-spectrosil or VC-infrasil, as appropriate, were filled with solution so that only onephase was present. When the temperature was raised, the excess so-lution resulting from thermal expansion was discarded. All solutionswere prepared on a molal basis to avoid corrections for concentrationchanges due to volume expansion. Solutions were analysed beforeand after each run by flame AAS and showed no significant changein cobalt concentration.

In the pH range of interest (pH 4-7), cobaltous hydrolysis is notdetectable (SWADDLE and FABES, 1980). Sample pH values wereadjusted within this range by adding HC1 or HBr. The pH was mea-sured, using a glass electrode and Ag-AgCl reference electrode, aftera fixed period of time because the pH varied with the reabsorptionof atmospheric CO: •

SPECTRA AND COORDINATION CHEMISTRY

Previous work (BALLHAUSEN, 1962, and referencestherein) indicates that the change in color of Co(II) halidecomplexes is a resuJt of a configuration CO/IVCM!

Chloride and bromide complexes of cobalt 329

differently coordinated complexes. At low temperatures andchloride concentrations, octahedral complexes form and thesolution is pink. When the temperature and/or the chlorideconcentration is increased, the fraction of tetrahedral com-plexes increases and the solution gradually becomes light blueto dark blue. This phenomenon may be interpreted in termsof ligand field theory.

Octahedral cobaltous complexes show two bands near8,000 cm"1 and 20,000 cm"1, respectively. The former israther weak, and the latter is an asymmetric band which isresponsible for the pink color. The asymmetry of the 20,000cm ~' band is caused by the overlap of two peaks, not by spin-orbit coupling or Jahn-Teller effects (cf. FIGGIS, 1967).ABRAGAM and PRYCE (1951) were the first to give the fol-lowing energy level scheme; their work and others (e.g.HOLMES and McCLURE, 1957) give rise to the following as-signments:

4T2g(F) «- 4Tlg(F) 8,000 cm-'

4A2g(F) *- 4Tlg(F) 19,000 cm"1

4T2g(P) *- 4Tlg(F) 21,000 cm-'.

All the other transitions involve different multiplicities,are thus strictly spin forbidden and are not observable inaqueous solutions. The UV-visible spectra were carefully andrepeatedly taken at different temperatures and metal-to-ligandratios. Selected data were then fitted to two Gaussian distri-bution functions by a modified computer program ORGLS(BUSING and LEVY, 1962) which uses an efficient nonlinear-least-squares (NLLSQ) method, and a subroutine CALC(SUSAK, 1982). These data are the principal basis for allcomputations and derivations carried out in this work.

When the assignment of ligand-field-transition bands isproperly made, and accurate data for the peak positions areobtained, the rf-orbital splitting energy of a ligand field, 10Dq, can be readily computed by employing the followingequations:

Table 2 Spectral data for octahedral cobaltous halide complexes

10

+ - V(9J? + 10 Dq)2 + 144J2 (2)

£ + 10Dq)2+ 144B2

10 Dq = Vi/i - 144fl2 - 9B

(3)

(4)

(5)

where i>i , i>2 and v3 are peak positions for bands near 8,000,19,000 and 21,000 cm"', respectively. Equations (1) to (3)are solutions to the Tanabe-Sugano matrices, and (4) and(5) are derived from (1) to (3) (cf. SUSAK, 1982). Since v{

and i»3 constrain the .B and 10 Dq values better and thereforeyield more consistent B_ and 10 Dq values, Eqn. (4) was usedto compute the B_ values. All spectral data, including _B and10 Dq values, are presented in Table 2. By comparing the

T Peak I Peak II Peak III°c ci ^ ^ S *2 rz c2Co-Cl complexes

25

50

90

Co-

25

50

90

.0000

.0387

.15031.6S62.9223.745

.0000

.0387

.57222. 1733.7734.840

.0000

.0387

.45051.6862.9223.745

8197 20478162 20928102 20388071 19378032 19038005 1935

8097 19948064 19378002 19357961 19597934 19057894 1868

7970 20887915 20237880 19747837 19877813 20257771 1951

.9396

.9455

.9623

.9737

.9819

.9840

.9499

.9511

.9685

.9883

.99641.010

1.0771.0781.0901. 1011.1191. 132

195501954019528194831941519362

194301942419382193001916419004

192731923919166190321887818816

284328402837282428042789

284728452833280927692723

282028092788

.090

.177

.253

.515

.771

.971

.404

.447

.612

.991

.554

.027

.332

.554

.7052731 5. 1802705 5.4912687 5.892

219972193321864217922172721659

218042178S21685216202155121442

216272154821476213762131021185

291628872881287528452825

295129612939291528622813

297529652919287728282808

C3

1.4591.4851.4911.6221.7411.841

1.7911.9071.9572.2172.7132.994

2.0682.2532.2812.6512.9113.007

RacahB

1001999998995993990

997995992990987982

990988985981978972

lODq

941593769310927592329200

930492679198315391219075

916291019062901389858937

3r complexes.0000.5000I. 0002.0003.0004.000

.0000

.50001.0002.0003.0004.000

.0000

. 50001.0002.0003.0004.000

8164 22088125 20488062 20628042 20258011 20497980 2112

8062 20487999 20297974 20827938 21217914 19057892 1868

7938 20887890 20237847 19747814 19877767 20257750 1951

.8931

.9014

.9035

.9324

.9438

.9706

.9011

.9066

.9138

.9365

.96541.020

1.0781.0901.1011. 1191.1401.130

196011959619S58195391951719502

195811958119561195311951619497

195451954119537195251949719467

vt wavenumber at the center of(cm ). E,inter-elec

extinction

344335103378333031913150

306631333030295128952865

296728742797275227042679

4.4284.4934.7264.9995.0265.227

4.6734.7864.9015.3215.5735.771

4.6774.8024.9975.3365.7876.062

a peak (cmcoefficient at v, Racah

219052184121740216932162121544

217112162521544214532141721353

214682140921327212242115221064

), r.

216621302273265024722428

297829832931259325932572

300230302989290826492556

1.4931.4961.6141.6481.7511.867

1.6831.8912.1102.2462.4502.899

1.9502.0822.3682.5172.7433.011

Deak widthB in cm ' 1

997995992990987984

990988984980979976

981980977972970965

937693339263924192059170

926291939164912390969070

912390709022898389318910

at halfheights a measure of the

tronic repulsion.

chloro-complex data with those of bromo-complexes (Table2), it can be seen that the 10 Dq and Racah B_ values forchloro-complexes are higher than those for bromo-complexes,which indicates that Br~ is a weaker ligand than Cl~. Forboth Cl~ and Br~, the Racah B_ term decreases with bothincreasing temperature and increasing halide concentration.This suggests that there is an increase in covalent character(orbital overlap) for octahedral complexes with increasingtemperature and increasing ligation.

The rule of average environment (e.g. FIGGIS, 1967) statesthat 10 Dq of a mixed ligand complex is the weighted meanvalue of its end-member species. Thus, by comparing thecalculated 10 Dq values for the aqueous complexes with thoseof known crystalline Structures, the ligation numbers may beevaluated. The small number of spectrophotometric studiesof cobaltous bromide crystals (e.g. PAPPALARDO, 1959)makes any determination of ligation number for cobaltousbromide complexes somewhat ambiguous. Crystal spectralstudies such as those by LAWSON (1965), PAPPALARDO(1959) and GRINDSTAFF and FOGEL (1972), JOY and FOGEL(1975) are available for chloro-complexes, but most of theseare too discrepant to be useful. Since the data of PAPPALARDO(1959) and GRINDSTAFF and FOGEL (1972) are in relativeagreement, they were used. Because of an environmental ef-fect, the ligand field strength for aqueous complexes is strongerthan that of their crystal counterparts (PAPPALARDO, 1959).In Fig. 1 a straight line representing the relation between 10Dq and chloride ligation number for crystals was obtainedfollowing SUSAK (1982). Three other lines for aqueous com-plexes at temperatures 25, 50 and 90°C were drawn parallelto the crystal line. The relative positions of these parallellines were based on the 10 Dq values for Co(H20)6+ deter-

330 P. Pan and N. J. Susak

lODqCM'1

FIG. 1. Ligand-field-splitting energy (10 Dq) vs. chloride ligationnumber (n) for octahedral (6-fold) Co(II)-chloride crystals andaqueous complexes. Large symbols are for crystals and smaller onesfor aqueous complexes. 10 Dq for Co(H2O)6+ (crystal) was esti-mated by PAPPALARDO (1959). Data for CoCl2-4H2O andCoCl2 • 1H2O are from GRINDSTAFF and FOGEL (1972). A, for hexa-quo-cobaltous complex, determined in this work.

mined in this work at each temperature. Figures 2 and 3 werederived from Fig. 1. Figure 3 indicates the correlation of theligation number with chloride concentration and tempera-ture. Over the range of conditions investigated, the averageligation number shows an increase with increasing chlorideto a value less than 1.4. There is also a slight increase inligation number with temperature.

A similar treatment can also be applied to tetrahedralcomplexes. Roughly speaking, 10 Dq for a tetrahedral com-plex is —4/9 that of an octahedral complex with the same metaland ligands. Thus, tetrahedral absorption bands will movetowards considerably lower frequency. The following assign-ments are assumed after BALLHAUSEN and MRGENSEN(1955), BALLHAUSEN and LIEHR (1958), COTTON et al.(1961) and BALLHAUSEN (1962):

4T,(F) «- 4A2(F) 5,800 cm'1

4T,(P) «- 4A2(F) 15,000 cm'1

4T2(F) •«- 4A2(F) 3,500 cm~'.

25°C

90°C

FIG . 2. Ligand-field-splitting energy (10 Dq) of octahedral (6-fold)Co (II)-chloride complexes vs. chloride concentration at constanttemperature in aqueous solutions.

mcrFIG . 3. Average chlorine ligation number (n) determined from 10

Dq shifts of octahedral (6-fold) Co(II)-chloride complexes vs. chlorideconcentration in aqueous solutions. Note that at higher temperatures,(n) increases slightly.

The transition 4T(P) •*- 4A(F), which appears in the visiblered region and yields a blue color in the tetrahedral cobaltouscomplex solutions, was studied in this work. The other tran-sitions are in the NIR region, where water (as well as air andsilica) interferes seriously, and they cannot be measured undernormal experimental conditions. The visible band shows finestructure, which has not been resolved. It is likely that thefine structure is due to spin-orbit coupling (BIRD and DAY,1968), or less likely, vibronic coupling or thermal distortion.Because only one peak was studied, the tetrahedral (4-fold)ligand-field-splitting energy (10 Dq) could not be calculated,and hence, neither could the average ligation number. As weshall discuss later, only one tetrahedral complex apparentlyexists in solution. Hence, it is meaningless to discuss a changein ligation number with change of temperature and/or chlo-ride concentration.

STABILITY CONSTANTS

Over a wide range of temperature and ligand concentration,both the octahedral and tetrahedral complexes coexist (seeFig. 4). KRAUB and LEHMANN (1972) suggest that the ab-sorbance of Co (II) chloride solutions reaches a maximum,when chloride concentration approaches 11.5 m. Althoughwe find this not to be strictly the case, because the fractionof octahedral complexes is very small at high chloride con-centrations and high temperatures, there is little change inthe absorbance as Cl~ is increased (Fig. 5). On the otherhand, when chloride concentration is lower than 4.0 m at25 °C, the octahedral complexes are undoubtedly predomi-nant (Fig. 6). Similar remarks apply to bromo-cobaltouscomplexes (Figs. 7 and 8) at higher ligand concentrations.Therefore, the problem of obtaining stability constants maybe simplified by dividing the system into two parts in orderto obtain the stability constants for both octahedral and tet-rahedral complexes separately.

In theory, four tetrahedral cobaltous halide complexescould exist in solution. It has been reported (KRAuB and

Chloride and bromide complexes of cobalt 331

T=90°C

[Co2t]=O.OI94m

0 19500 23000 265OO 30000

WAVENUMBER

FIG. 4(a). Visible spectra of octahedral (6-fold) and tetrahedral(4-fold) Co(II)-chloride complexes at 90°C, in solutions of varyingchloride concentration. The line label indicates the chloride concen-tration. Note that tetrahedral peaks are located roughly in the rangeof 600-720 nm (16667-13889 cm~'). Note also that wavenumberis always in cm"1 throughout this report.

LEHMANN, 1972; SWADDLE and FABES, 1980) that only thetetrahalo-cobaltous complex, CoXl~ (X = Cl~, Br~) is im-portant. COTTON et al, (1961) found that the spectral bandsof cobaltous halide complexes in aqueous solution shifted tohigher energies compared to the bands for solid compoundsand cobaltous halide complexes in organic solvents of rela-tively low dielectric constant and coordinating power. Theyattributed the shifts to the existence of CoX3H2O~ (X = C\~,Br~, I~). CEIPIDOR et al (1980) show that cobalt(II)-chloridecomplexing reactions in acetone are exothermic, while theyare known to be endothermic in aqueous solutions (in agree-ment with the present work). This suggests that the solventeffect is important. The ligand field strength, the stabilityconstants, and the thermodynamic data derived in differentsolvent solutions may not be compared simply. The peakshifts observed by COTTON et al. (1961) could be attributedto the crystal-formation effect (PAPPALARDO, 1959) and thesolvent effects. LODEMANN and MAHON (1969) suspect thatthe difference in the extinction coefficients between the tet-

4.0

3.5

3.0

5 2.5

10

0.5

50 C[CoV.0075 m

7.0m

9.0m

10.0 mn.5 m12.0m12.5 m13.0m

135m

14.5m

18000 20000

Wavenumber

22000 24000

FIG. 5. Visible spectra of tetrahedral (4-fold) Co(II)-chloridecomplexes. Figures on the right are chloride concentrations. Notethat there is no peak shift with increasing chloride concentration.

rahedral complexes in aqueous solutions and non-aqueoussolutions may be attributed to halo-aquo complexes otherthan CoX$~. From the same laboratory, a 20 nm (446 cm"1)and a 40 nm (866 cm"1) peak shift at high temperatures (upto 500°C) was reported for chloro- and bromo-cobaltouscomplexes, respectively, due to the conversion fromCoX3H2O" to CoX2(H2O)% (X = Cl", Br") (LODEMANNand FRANCK, 1968). This shift was not observed in this work(cf. Figs. 5 and 7). In fact, the peaks remain in the samepositions over the entire temperature and ligand concentra-tion range studied, in agreement with KRAuC and LEHMANN(1972). Therefore, although we cannot totally rule out thepossibility of other tetrahedral cobaltous halide complexes athigher temperatures, there is little doubt that, under our ex-perimental conditions, only one tetrahedral halide complexpredominates in solution, i.e. CoX4". The work of manyother authors (BJERRUM et al, 1975; SKIBSTED and BJER-RUM, 1978; ZELTMANN et al, 1968; SMITHSON and WIL-LIAMS, 1958; SWADDLE and FABES, 1980) also supports thiscontention.

In cases where the octahedral complexes are dominant,the problem becomes more complicated. No polynuclearcomplexes have been reported for solutions of low metal

K>.om, soc

K>.0 m, 25°C

18000 20000

Wavenumber

FIG. 4(b). Visible spectra of octahedral (6-fold) and tetrahedral(4-fold) Co(II)-bromide complexes in 10 m NaBr solutions and at25° and 50°C. Peaks from 13000-17000 cm"1 represent tetrahedralspecies.

19400 22600 23600

VWVENUMBER

FIG. 6. Visible spectra of octahedral (6-fold) Co(II)-chloridecomplexes. The line label indicates the concentration of Co (II).

332 P. Pan and N. J. Susak

---------- 14.7 m

---------- 13.7 m

------- 13.3 m

------ 13.0 m

125 m

1t7m

10.0m

18000 20000

Wavenumber

22000 24000 28000

FIG. 7. Visible spectra of tetrahedral (4-fold) Co(H)-bromidecomplexes at 90°C. Figures on the right are bromide concentrations.Note that there is no peak shift with increasing bromide concentration.

concentrations, but, in theory, six monomeric octahedralcomplexes may exist in solutions simultaneously. However,the highly charged complexes (e.g. +3, +4) are probably notstable, especially at elevated temperatures. Many other au-thors ( LISTER and ROSENBLUM, 1960, and references therein;ZELTMANN et al, 1968; BELOUSOV et a!., 1972; KRAuC andLEHMANN, 1972; BJERRUM et al., 1975; SKIBSTED andBJERRUM, 1978; SWADDLE and FABES, 1980) suggest thatover a wide range of temperature and ligand concentration,the ligation number of cobaltous complexes does not exceedfour, and the predominant complexes are thought to beCoJr(H2O)5 and CoX2(H2O)t No complex with ligationnumber 5 or 6 has been reported. Also, because n as calculatedfrom the 10 Dq shift is low, we feel that it is reasonable toconsider only the first four octahedral complexes in ourmodel.

Graphical approach to stability constants

As a rule, numerical methods for stability constant cal-culation require first guesses. Poor first guesses may lead tounreasonable results or a divergence of iterations. Good firstguesses must be based on a correct understanding of the sys-tem in question, and should be obtained experimentally. Since

there is not a single data set available in the literature whichis suitable for our purpose, we made a great effort to derivethese data experimentally prior to our final numerical treat-ments.

For the sole tetrahedral complex, CoX\' , the continuousvariation method (Job's method; JOB, 1928) was employedto evaluate the stability constants (for details, see PAN, 1988).Because the assumption that only a single tetrahedral complexis present is not strictly valid, it is possible that the results(see Table 3) might involve relatively large errors (within anorder of magnitude ) .

For octahedral cobaltous halide complexes, the only spec-trophotometric method that may be used to work out thefour stability constants is the corresponding solutions method( BJERRUM , 1 944 ) . This method only applies to systems wherecomplexes are moderately strong and differ appreciably fromeach other (RossoTTi and ROSSOTTI, 1961). In our case,complexes have similar ligand field strengths, and their spectraoverlap considerably. As a result, the experimental resultsare badly scattered (PAN, 1988). Therefore, both the resultsobtained by the corresponding solutions method (see Table3) and by Job's method may not be particularly accurate.However, they serve adequately as the first guesses requiredby the subsequent numerical treatments. Nevertheless, theresults of the corresponding solutions method are comparableto some of the previous works (LISTER and ROSENBLUM,1960; KENNEDY and LISTER, 1966; BELOUSOV et al, 1972;BLOKHIN et al., 1974; SKIBSTED and BJERRUM, 1978).

Activity relationships

In the graphical methods, we used concentrations ratherthan activities for all calculations. However, in the solutionswe studied, the salinities ranged up to 1 5.0 m LiCl (see PAN,1988) and the temperatures ranged from room temperatureto 90°C. Hence, the activities might deviate considerably fromtheir concentrations. Therefore, activity coefficients have tobe evaluated. For reactions

Co(H2O)0+ + nX~ = CoXn(H2O)2

6-"n + nH2O (6)

Co(H2O)f + mX

(m + 2)H20 (7)

10-

0.9-

0.8-

0.7

\ 0.8

2 0.5

3CU

O3-

0.2

0.1

OJOH

20600 24600 28600

Wavenumber

32500 36500 40500

FIG. 8. UV-visible spectra of octahedral (6-fold) Co(II)-bromidecomplexes. The line label indicates the bromide concentration. Thepeak near 33500 cm"' is one of the charge-transfer peaks.

Table 3 Stability constants for Co(II) hallde complexes

log*, logs, log?, logs.

Co-Cl

25°C

50°C

30°C

Co-Br

25°C

50°C

90°C

g

complex

0.97

<es

0.

f

60

0.63

0. 67

g f

-0.65 0.02

0.07

0. 15

s f

-0.68 -1.71

-1.62

-1.50

g f

-2.9 -4.51

-4.41

-4.23

logf

i

-5.2

-4.7

-3.9

f

-2.09

-1.72

-1.41

complexes

0.59

0.54

0.77

-.

-,

-

03

.02

.01

-.64 -1.18

-.45 -1.17

-.67 -1.13

-1.1 -3.28

-1.1 -3.25

-.64 -3.21

-2.3 -6.45

-2.2 -6.41

-2.4 -6.36

-5.3

-4.9

-3.9

-3.74

-3.40

-2.98

g: Graphical results; f: Final results. Stability constants are In the

order of CoXt O)*, CoX H , CoX O}". CoX^r^OjJ" and CoX^~. The

same order hereinafter. The standard deviations for the final results are

in the range of ±0.05.

Chloride and bromide complexes of cobalt 333

we have

ft-'

^^ (8):+-v1-

(Co(H20)t+][X-]" 7Co(H20)i+7A-

(9)

Because, in concentrated halide solutions, the activity ofwater will deviate considerably from unity, and because wateris considered to be one of the ligands as well as the solvent,it is apparent that an accurate estimate of the activity of wateris necessary to derive the stability constants. Using the ex-tended Debye-Hiickel equation in conjunction with theGibbs-Duhem equation, without introducing any new pa-rameters, the following equation may be derived ( ROBINSONand STOKES, 1965, Ch. 9; WOOD, 1975, 1976):

In

where

(10)

*)-21n(l

and A and B are the conventional Debye-Hiickel parameters,/is the true ionic strength as denned by HELGESON (1969),a is the ion size parameter, and B' is the deviation function.Note that this equation does not take account of the effectsof the cobalt aqueous species on water activity, which is con-sidered negligible and within the accuracy of the method,due to the relatively low concentration of total Co(II) (<0.05m) compared to the total concentration of ions in solution.

To calculate the activities of A" and all complexed species,the following approximation was employed (HELGESON etal, 1981):

log 7, =-AZjf!

-iog(l + 0.0180153m*)

1.66027 X 105Z?f | - 1) 7

(11)where bnaX is the electrostatic solvation parameter for NaJST,

- is the short-ranf;e interaction parameter between Na+

and X~, rej is the effective electrostatic radius of the rthaqueous species, and rn* is the sum of molalities of all ionsin solution, which may be treated as m* = I. HELGESON etal. (1981) pointed out that Eqn. (11) should afford close ap-proximation of individual ion activity coefficients over a widerange of concentrations, temperatures and pressures. All pa-

rameters in Eqns. (10) and (11) were either taken from WOOD(1976) and HELGESON et al. (1981) or approximated usingHELGESON et al. 's (1981) method (cf. PAN, 1988).

Numerical refinement of stability constants

Basically, graphical methods only apply to simple systems.For systems such as those considered here, which involve fiveor more complexes, most of the graphical methods fail toyield accurate results. It is possible to compute the equilibriumconcentrations of species in a multicomponent system ofmetals and ligands using multiple-linear-regression or othernumerical methods (McBRYDE, 1974; LEGtjETT, 1977,1985). In the present work, a modified version of SQUAD(LEGGETT et al, 1983; LEGGETT, 1985) and a subroutineGAMMAS, written by Pan, were used for this purpose. Forthe system described by Eqns. (6) and (7), the absorbanceat the fcth wavelength of the ith solution is

= 2 /Sn[Co(H20)?+],[^-]?[H20]

X 7co(H2o)r,.7™-,«7£iA-m(H2o)i::,,7S^o,l2)<(m) (12)

where tkn and e*m) are the extinction coefficients at the fcth

wavelength for the species CoXn(H2O)t,Z" and CoXm-(H2O)4l™, respectively; /?„ and 0(m) were defined in Eqns.(8)and(9).The original version of SQUAD searches for the"best" set of apparent stability constants which will describethe supplied total concentrations of metals and ligands andabsorbance. Then, based on the current f?s, extinction coef-ficients are calculated. The subroutine GAMMAS incorpo-rates the activity considerations described above into SQUADto give true stability constants. The process is an iterativeone. In the first cycle, based on the "first guess" £Ts derivedgraphically and activity coefficients set equal to unity, con-centrations of each complex, free cobalt and ligand ion arecalculated. Then, based on these current concentrations, allactivity coefficients are obtained, and are subsequently usedin mass balance equations. Next, the process begins again,using the corrected ^s and activity coefficients. When thecorrections for (?s are less than 0.0001, convergence is con-sidered to have been achieved. A FORTRAN programSQTEST was written to generate artificial data sets to testthe validity of the program. Both the original program andthe one modified with activity coefficient considerations weretested in this manner. Both algorithms resulted in a good fitto the synthetic data.

Stability constants of cobaltous chloride and bromidecomplexes computed by SQUAD are presented in Table 3.These stability constants differ greatly from those obtainedby graphical methods (Table 3). One reason for this is veryapparent: in the graphical methods, concentrations have beenused; in the numerical computations, activities have beenused. Another reason may be the fact that the assumptions

334 P. Pan and N. J. Susak

made in employing the graphical methods are not strictlyvalid.

The results obtained with the numerical method dependheavily on the number of parameters to be estimated, andthe initial input data. If all parameters but one are fixed ar-bitrarily, the single parameter obtained by converged com-putation will be mathematically rational, but may be non-sense chemically. Furthermore, because the spectra of dif-ferent complexes overlap severely, our data sets are often ill-conditioned. One or two stability constants have to be fixedfor a particular run in order to derive the other stability con-stants by converged computation. This process is repeatedusing systematically different fixed data to obtain the "best"data set, giving the smallest standard deviations. In such cases,previous knowledge (from graphical and other methods) ofthe system in question is necessary.

Another point that should be mentioned here is the effectof activity correction on the stability constants of complexes.Changes up to two orders of magnitude have been observedin stability constants, depending on whether or not activitycorrections are taken into account. In Eqns. (10) and (11),activities are dependent on re and a values, for many of whichthere are no reliable data available. It was observed that upto about 4.5 m salinity, a 1 A change in re and a did notcause significant changes in activities (<15%) and causedonly minor adjustments in stability constants. However, athigher salinities, the same change gave rise to much largervariations in activities (for higher-charged species, e.g. Co2+,more than an order of magnitude).

In SQUAD, the "standard deviation in the absorbancedata", ovfcta, provides an overall measure of the fit of a modelto a data set. According to LEGGETT (1985), experience hasshown that <rdata > about 0.01 is indicative of a poor fit. Ourfits have <7<jata in the range 10~4-10~2 which are acceptableto excellent. By assuming only three octahedral and one tet-rahedral complex in our model, slightly better fits could beobtained and the resultant changes in the stability constantsare within 10%. This suggests that the fourth octahedral com-plex is not important relative to the others (see Figs. 9 and10), and the stability constants for this complex listed inTable 3 are known with less confidence. If we assume morethan four octahedral complexes in solutions, convergence

FIG. 9. Distribution of all Co(II)-chloride complexes in aqueoussolutions at 25, 50 and 90°C. The biaquotetrachloro complex is notshown on the diagram, due to its low abundance

FIG. 10. Distribution of all Co (II )-bromide complexes in aqueoussolutions at 25, 50 and 90°C. The proportion of the biaquotetrabromocomplex is too low to be shown on this diagram.

can not be achieved. The failure to converge occurs whetherwe treat /35 and 06 as fixed or varying parameters, which sup-ports the assumption made before that complexes with li-gation number greater than 4 may be ignored.

Stability constants for Fe(II), Co (II) and Ni(II) chlorideand bromide complexes from different sources are compiledin Table 1. Since the data are rather discrepant, it is hard tomake a proper judgement about the quality of a data set byeach individual laboratory. However, as indicated in Table1, all the stability constants but our own are apparent onesderived in constant ionic strength solutions (some are cor-rected for Cl~ activities to some extent, as discussed above).With activity corrections and the statistically rigorous treat-ment employed, our final data (presented in Table 3) are themost reasonable ones to date.

According to ROSSOTTI (1961), successive stepwise for-mation constants of a series of mononuclear complexes withN identical ligands usually decrease in magnitude, andlog Kn/Kn+t are usually approximately equal. This statementwas expressed by an equation by VAN PANTHALEON VANECK( 195 3) as follows

log Kn = log Kt - 2\(n - 1) (13)

where X is an empirical constant for each specific system andn is the ligation number.

Since this principle has been well documented theoreticallyby considering statistical factors, steric relations, and cou-lombic interaction, and experimentally for some systems(ROSSOTTI, 1961, and references therein), it may be used asa measure to check the validity of the stability constants ob-tained in this work. The successive stepwise formation con-stants for the octahedral complexes are calculated and listedin Table 4. In Fig. 11, the successive stepwise formation con-stants at 25°C are plotted vs. (n - 1) for both systems westudied (data at higher temperatures may also be used, butthey almost completely overlap with the 25°C data). All thedata points are reasonably close to the two linear regressionlines which have slightly different slopes, supporting the va-lidity of our stability constants.

Based on the stability constants computed by the numericalmethod, the species distributions can be used to calculate nfor the octahedral complexes. Comparing Figs. 3 and 12, it

Chloride and bromide complexes of cobalt 335

Table 4 Successive stepwlse stability constants

for octahedral complexes

Co-Cl complexes

2S°C

50°C

90°C

logK,

0.60

0.63

0.67

log*,

-.58

-.56

-.52

'°gK3

-1.72

-1.69

-1.65

logK4

-2.81

-2.79

-2.74

Co-Br complexes

25°C -0.03 -1.15 -2.07 -3.17

BO°C -0.02 -1.14 -2.08 -3.17

90°C -0.01 -1.13 -2.07 -3.15

Complex order Is the same as In Table 3.

can be seen that n as estimated from 10 Dq shifts is in generalagreement with the n calculated from the stability constants.However, as temperature increases, the change in averageligation number is not as apparent as indicated by Fig. 3.This is due primarily to two factors. First, all the crystal spectraare taken at room temperature. The lines on Fig. 1 at highertemperatures may not have the same slope as that of crystalsat room temperature. Second, the linear relationship of therule of average environment does not completely describethe shift of 10 Dq with increasing chloride ligation number.Although the data are badly scattered, consideration of allavailable crystal data (cf. Fig. 2 of SUSAK and CRERAR, 1985)suggests a curvilinear relationship of 10 Dq and n.

From Fig. 9, it may be seen that at temperatures 25 to90°C, salinities up to 4 m, Co(H2O)i+, CoCl(H2O)£ andCoQ2(H2O)4 are predominant. As they diminish in concen-

3-

2

1-

-2

-3

-4

-5

x Co-Cl complexes

Y Co-Br complexes

—r3

( n - 1 )FIG. 11. Successive step-wise formation constant of cobaltous

chloride and bromide complexes vs. (n — 1). The two lines are derivedby linear regression, with X = 0.568 for chloride complexes and X= 0.477 for bromide complexes (cf. Eqn. (13)).

IJ0.6-

0:0-1

90'C

0 1 2 3 4 S 6 7 8

m (Nad)

FIG. 12. Average Cl-ligation number of octahedral Co-Q complexesvs. Cl~ concentration at 25,50 and 90°C, calculated using the complexstability constants obtained in this work.

tration at higher salinities, CoClJ gradually gains impor-tance, and eventually becomes the sole predominant species.CoCl3(H2O) J may be important only at lower temperaturesand extremely high salinities, and CoCLt(H2O)i~ neverexists to an appreciable extent. Increase of temperature greatlyfavours the formation of CoClJ" as it becomes predominantat much lower salinity (about 4.3 m) at 90°C with respectto that (about 6.2 m) at 25°C. As the trend continues, wemay expect that at hydrothermal conditions (150-350°C,about 1 ma-), the principal complex of cobalt(II) isCoClJ" (probably plus other tetrahedral Co-Cl complexes;see discussions below). In a surface environment, free co-baltous ions and CoCl(H2O)5 are the principal species.

As for the speciation of bromo-cobaltous complexes (Fig.10), the general picture is similar to those of cobaltous chlo-ride complexes. The most striking difference is that the te-trabromocobaltous complex, CoBrJ", becomes predomi-nant in solutions at much higher concentrations of ligand(bromide) and/or higher temperatures compared with thetetrachlorocobaltous complex. The free cobaltous species, orthe aquo-cobaltous complex, is the principal species over amuch wider range of ligand concentration, which directlysuggests that bromo-cobaltous complexes are much weakerthan chloro-cobaltous ones.

It is predicted that the tetrahedral bromo cobaltous com-plex may be of little significance in geological environments,because bromide concentrations in natural waters and hy-drothermal fluids are so low that, even at elevated temper-atures, octahedral complexes are predominant.

THERMODYNAMIC RELATIONS

The thermodynamic parameters A#? and AS? may beestimated from the temperature dependence of the stabilityconstant. However, with only three data points at 25, 50and 90°C, respectively, such functions may not be well con-strained. Nevertheless, as the experiments cover a relativelysmall range of temperature, it is likely that over this rangeof temperature, AfY? and AS? are more or less constant. Soit may be adequate to assume

\nK =AS?R RT

(14)

336 P. Pan and N. J. Susak

where AT is the successive stepwise equilibrium constant. BothAS? and A#? may be obtained using a linear regressionmethod. The thermodynamic properties for chloro- andbromo-cobaltous complex formations are listed in Table 5.

Figure 13 shows the fit of Eqn. (14) to our data. Althoughwith only three points the validity of our derived A/f? andAS? might be questioned, there is a good agreement betweenour value and the calorimetrically determined value of KEN-NEDY and LISTER (1966) for the first stepwise reaction. Theavailable thermodynamic data for cobalt complexes aresummarized in Table 6. There is no general agreement amongany of the published values other than that mentioned above.The free energies and entropies in particular show large vari-ations amongst various laboratories and methods. However,all the A(/? and AS? have been determined from equilibriumconstants in solutions of different ionic strengths.

The thermodynamics of complexation of a soft donor X~(Cl ~, Br ~) and a fairly hard acceptor Co2+ is not as predictableas the typical hard-hard or soft-soft cases (AHRLAND, 1968,1972, 1973). The first-step octahedral complex and the tet-rahedral complex formations are like typical hard-hard in-teractions, with both positive entropy and enthalpy of reac-tion. The replacement of water by a halogen in complexes isendothermic, and releases water molecules into the bulk so-lution, resulting in an overall increase of entropy. The restof the successive complexations are not like the typical hard-hard case or soft-soft case. The successive bonding betweenCo2+ and X~ is weaker and reflects a more covalent nature.This is shown by the small increase in A//? and supportedby the decrease in the Racah B_ term. The Br~ ion complexesshow similar behavior with an even greater covalent character,as typified by the very small A//?.

The AS? for the stepwise reactions other than the first step

Table 5 Therraodynamlc data for

cobaltous halide complex formations

Co-Cl complex formations

25°C -3.4

50°C -3.9

90°C -4.6

AH°kJ mol"1

3.3

3.5

3.6

9.8

10. S

11.5

16.0

17.2

19.0

2.21.2 2.331.03 2.21.4

AS°J mol"1 K

18.71.3 -3.81.5 -25.51.9 -46+1

(4)

11.9

10.6

9.8

22+3

33+9

12.0

12.9

14.4

18.1

19.6

21.9

21.3

21.0

20.7

Co-Br complex formations

AG° IcJ mol"1

r25°C 0.2 6.6

50°C 0. 1 7. 1

90°C 0.1 7.8

AH° kJ mol"'

0.71.1 0.8+.1

AS° J mol"1 K"1

r1.913 -19.31.5 -37.81.8 -58.21.3 9.51.6

Free energy changes calculated using AG° = -RTlnK. deviations are

within 10.4, changes of enthalpy and entropy were evaluated from

equation (14). The second line enthalpy and entropy values are

errors.

0.7+.2 0.771.09 24.2i.2

a 1st complex

A 3d complex

o 2nd complex

* 4th complex Tetra complex

3.0 3.2

1000/T

FIG. 13. Stability constants (In K) of Co (II) -chloride complexesvs. temperature (1/7") for derivation of A#? and AS? of complexformations. The first to fourth complexes refer to octahedral com-plexes with 1 to 4 chloride ligand(s).

all show increasingly more negative values. The trends aresimilar for both anions with the change in AS? between suc-cessive steps of -22 J mol"1 K'1 for Cl~ and -19 J mol~'K~' for Br". The negative AS? and positive Atf? for n > 1indicate that the higher halogenated octahedral complexesare unstable with respect to the mono-halide complex; thus,they are very weak. These complexes can exist only at rela-tively high halide concentrations at temperatures low enoughthat the octahedral site preference energy (OSPE) can stabilizethe octahedral coordination. OSPE decreases with increasingtemperature. Assuming the same trends in AS? continue athigher temperatures than in this study, the dominant speciesof octahedral complexes at higher temperatures should beCoCl(H2O)f and possibly Co(H2O)?+.

There must be a significant temperature dependence ofA/f ? and AS?. A linear extrapolation to higher (300°C) tem-peratures of the stability constants presented here does notsignificantly alter the speciation shown in Figs. 9 and 10. Onthe other hand, the results of SWADDLE and FABES (1980),SUSAK and CRERAR (1985), LODEMANN and FRANCK (1968)and SUSAK (1982) all show the predominance of the tetra-

Table 6 Compilation of thermodynamic data

for Co(II) halide complexes

CoCKH 0)*2 5

CoCl*"

CoBrfH 0)*2 B

AG°r

kJ mol"

2.3"

.79"

4.25--3.43'1.6f

46.5-

11.9°

4.1'

.67b

.176'

AH°

kJ mol"1

3.8°

2.2b

4.2C

12"2.14'Of

71. 5"

21.5'

9.2"

.59b

.743'

AS"

J molV1

4°

4.6"

26"18. 7e

-5.4f

84"

32.7'

IS*

-.29"1.88'

These free energy terms are calculated from enthalpy and

entropy terms. All data are at 2S°C.

a, BLOKHIN et al. (1974);b, KENNEDY and LISTER (1966);c, LISTER and ROSENBLUM (1960);

d. ZELTMANN et al. (1968);e. This work;f. AHURST (1976).

Chloride and bromide complexes of cobalt 337

hedral species at high temperatures, even at low halide con-centrations.

The transition from octahedral to tetrahedral complexeshas been studied by a number of workers. KRAuB and LEH-MANN (1972) felt that the change might occur from thediaquo-tetrachloro-complex and estimated a A//TY of 46 kJmol~l. SCAIFE and WOOD (1967) suggested the same octa-hedral complex and estimated M/Tr to be 49 kJ mol"1.SWADDLE and FABES (1980) suggested that the tetraaquo-dichloro complex converts to the tetrahedral complex at el-evated temperatures with a &H°, of 62 kJ mol~'. We feelthat the transition involves all species in solution to variousdegrees depending on the temperature and chloride condi-tions. Table 7 presents A//rr and A5jr calculated from ourstability data for each octahedral complex. Notice that theA//Tr shows a range of values that vary linearly with thechloride number of the octahedral complex. There is a largediscrepancy with previously published results, primarily be-cause the previous determinations were made from series ofsolutions of varying ionic strengths without correction foractivity coefficients. The more significant trend is that bothCl~ and Br~ show a minimum in AS^r at the monohalidecomplex, suggesting that the higher halogenated octahedralcomplexes and, to a lesser extent, free Co(H2O)6+ are some-what selectively converted to the tetrahedral configuration.Because of the large positive entropies of transition, increasingtemperature should favor the formation of the tetrahedralcomplex. That is, at high temperatures (and hence in lowdielectric fluids) the predominant species should be CoXl~and CoX(H2O)s (where octahedral complexes are still sta-ble). These are also the species with the hard-hard type be-havior characteristic of low dielectric fluids. The decrease inthe dielectric strength may also result in the formation ofCoXm(H2O)l~% (m < 4) complexes as reported by others(LODEMANNandFRANCK, 1967, 1968), but their existencecannot be evaluated from this study.

GEOLOGICAL IMPLICATIONS

The abundance of cobalt in the Earth's crust is about halfthat of copper, but cobalt mineralization is far more rarethan that of copper. There must be some specific constraintson the mobilization and transport of cobalt which are rarelyfulfilled effectively. Because cobalt has always been mined asa by-product of the ores of other metals (e.g. Cu, Pb, Zn, Ag,Ni, U), there has been little work dealing specifically withcobalt mineralization.

Table 7 Thermodynamic data for octahedral totetrahedral conversions

Co(H20)=*

CoX(H20)*

CoX2(H20)°

CoX3(H20)"

CoX (H O)2"4 2 2

AH°

kJ mol"1

21.5

19.4

17.2

14.8

12.6

X-C1

AS°

32.7

14.0

17.8

42.9

89.4

AH°

kJ mol"1

24.2

23.4

22.6

21.9

20.8

X=Br

AS°Tr

J mol" K"1

9.54

7.58

26.9

64.8

122.0

Errors are as follows: for Cl-complex conversions, 4H° are

3-4 KJ mol"'. AS°r are 9-12 J mol"1; for Br-complex conversions,

AHTr are about °-5 KJ mol"1. AS0 are 0.5-2 J mol

Sam-l

2SC

Oh Complexes

Td Complex

Total Term

Oh Complexes

Td Complex

Total Term

0 1 2 3 4 5 6 7

m (Nad)

FIG. 14. Cobalt solubility enhancement term vs. chloride concen-tration. When chloride concentration is less than 3 m, the enhance-ment term remains low, and shows little variance with temperature;when chloride concentration is greater than 3 m, the enhancementterm increases rapidly with increasing temperature and chloride con-centration, due mainly to the effect of the tetrahedral complex.

The total concentration of cobalt (2 Co) is the sum of theconcentrations of all species in the solution. From the stabilityconstants and the definition of activity (a/ = 7,m,-) we canderive the following equation:

2 Co = [Co(H20)i+] 1 + 24 /UCT]

"]4 TCI ~

[H20]6 (15)

That is, we can factor the total cobalt concentration into twoterms: a free cobalt term which reflects environmental pa-rameters and the solubility controlling mineral, and an en-hancement factor due to the chloride complexes. Figure 14shows a plot of the enhancement term. Note that the en-hancement term will vary somewhat with 2 Co, since 2 Cowill affect the ionic strength and, hence, the activity coeffi-cients in the enhancement term. However, when 2 Cochanges from 20 ppm to 2000 ppm, the change in enhance-ment factor is about 1% at 4 m salinity.

At low salinities, where the octahedral complexes predom-inate, the enhancement factor is small and shows little vari-ation with temperature (2.4 at 1.0 m NaCl and 19.4 at 3.0m and 90°C). When the octahedral complex predominates,the 2 Co depends primarily on the free cobalt term. Coolingor, to a lesser extent, dilution of the solution will not yieldsignificant mineralization unless they have a large effect onthe free cobalt term.

At 25 °C the octahedral complexes predominate up to halitesaturation. The enhancement term increases to severalhundred due to the increased stability of the higher chlorideoctahedral complexes. As the temperature rises at high salin-ities, the tetrahedral complex becomes more important untilit carries the largest fraction of dissolved cobalt. The en-hancement term then increases to the order of 102 to 103.Thus, highly saline solutions can carry large amounts of cobaltin solution even at relatively low temperatures. Cooling ordilution of the fluid will destabilize the tetrahedral complex,

338 P. Pan and N. J. Susak

resulting in large changes in the enhancement term. Thus,significant quantities of cobalt may precipitate even if thefree cobalt term does not change greatly.

Although our numerical data are limited to 90°C, we canmake some predictions about the behavior of cobalt chloridecomplexes at higher temperatures based on earlier qualitativestudies up to 600°C. LODEMANN and FRANCK (1967, 1968)and SUSAK and CRERAR (1985) show that low chloride ( < 1 .0m) octahedral peaks exist up to 200°-300°C and a significanttetrahedral peak is also present. At higher temperatures orchloride concentrations only tetrahedral peaks are observed.Thus, the steep rise in the enhancement term should shift tolower salinities as temperature increases. Because the con-version to the tetrahedral configuration tends to leaveCoCl(H2O)? as the octahedral complex, and because it isthis complex that dominates at low temperatures and salin-ities, the enhancement term may not show large increases athigher temperatures and low salinities. Since increasing pres-sure favors the formation of the octahedral complexes, pres-sure increases accompanying the temperature increasesshould moderate the magnitude of the shift in the enhance-ment term somewhat. LODEMANN and FRANCK (1967, 1968)and LUDEMANN and MAHON (1969) have interpreted thetemperature dependence of the tetrahedral band as indicatingthe dechlorination of CoCl4~ via

m(H20) = CoCl4-m(H20) (16)

A more recent study by SWADDLE and FABES ( 1 980 ) suggeststhat this reaction only occurs at low chloride concentrationsand that, in the range of 2.0-5.0 MNaCl, CoCl4~ is the onlytetrahedral complex. If these low chloride complexes do existat high-temperatures then the slope of the enhancement curveshould decrease, since the power dependence on the activityof chloride should decrease. The enhancement term is prob-ably less than 1000 for most geologically reasonable temper-atures and salinities, which would suggest that the major limiton the occurrence of cobalt mineralization is the constrainton the free cobalt term.

The world's primary cobalt ores are the red-bed stratiformcopper deposits of the Central African Copperbelt in Zaireand Zambia (ANNELS and SIMMONDS, 1984). Red-bedstratiform deposits in other parts of the globe also containcobalt (GUSTAFSON and WILLIAMS , 1 98 1 ) . In general, thosedeposits that show cobalt mineralization are associated withevaporite sequences, which provide chloride and sulfur. Fluidinclusion studies (PiRMOLiN, 1970) and isotopic temperaturedeterminations (GUSTAFSON and WILLIAMS, 1981) indicatethat the temperature for main stage mineralization is slightlyover or close to 100°C.

The Mississippi- Valley type (MVT) deposits of the South-east Missouri Lead District also show hydrothermal cobaltand nickel mineralization (SNYDER and GERDEMANN, 1968;ROGERS and DAVIS, 1977; KISVARSANYI, 1977; JESSEY,1981). These deposits are better constrained with respect totemperature and salinity. ROEDDER (1977) found homoge-nization temperatures between 82° and 137°C for fluid in-clusions in sphalerite. He also reported (ROEDDER, 1979)salinities of 15 to 20% (3-4.3 m) or more for these deposits.The salinities and temperatures of MVT deposits would sug-gest enhancement terms up to 1000 or higher, so that there

is no problem in transporting cobalt provided sufficient cobaltis available and reactive in the source rock.

To understand all the constraints which control the cobaltmineralization under conditions under which the red-bed typeand MVT deposits were formed, the free-cobalt term needsto be evaluated. Table 8 lists all the available thermodynamicdata for cobalt minerals and other related species, and thechemical reactions which may constrain free cobalt in fluids.Note that not all cobalt minerals and corresponding reactionsare included, and some relatively more important mineralsmay be absent (e.g. CuCo2S4), due to the lack of thermo-dynamic data. Although free cobalt exists in aqueous solutionsas Co(H2O)i+, tabulated thermodynamic data are availableonly for COgq . Since most other methods of measurementcannot distinguish coordinated water from bulk water, thesetwo species are treated as being equivalent in the followingdiscussion.

Figure 15 is a fo2 - aca^ diagram at 400 K and along theboundary of SO 5" - H2S ( I S = 0. 1 1 m) with different pHcontours. Note that not all the solid phases are stable simul-taneously in solutions. It may be noticed that at pH = 6.5,when log f02 < -28, CoCO3 will replace Co3O4, whenlog fo2 < -45, Co3S4 will replace CoCO3, and when log 2

< -46, Co3S4 will be replaced by CoS2. The diagram wasconstructed using GHCOJ = 4.4 X 10~4 m, and at slightly basicsolutions (pH = 6.5), the upper limit of free cobalt is con-strained by cobalt carbonate. This is in agreement withHAYNES and BLOOM (1987a). However, when CHCOJ< 10"3 4 m, the upper limit of free cobalt will be constrainedby CoO, which is higher than that constrained by carbonate.The effect of pH on the free cobalt term is significant, es-pecially at higher oxygen fugacities. At the same <ZHCOJ (4.4X 10"4 m), when pH = 7.5, the upper limit of free cobalt isconstrained by CoO. A pH change from 7.5 to 5.5 correspondsto a free cobalt change from 10~62 to 10~37.

At pH = 6.5, in the presence of sulfides, a typical valuefor free cobalt activity in fluids may be taken as 10~6'5 m,

Table 8 Thermodynamic data used in free cobalt calculation

4H°f,28

S'

J mor'K'

f ,298

-!„-!

HS*

-237.94 S2.97-58.2 -113.-891.19 102.51

-153.13 69.04

-358.99 184.51

-712.9° 97."

-20.627 205.8

-285.83 69.95

-691.99 91.20

0. 205.IS

-909.27 20.00

Reactions considered

CoO + 2H* = Co2* + H20

Co304 + 6H* = 3Co2* + 3H20 + -i-02

CoS + 2H* + H 0 = Co2* + 2H S + -i-02 2 2 2 2

Co S + 6H* + H 0 = 3Co + 4H S + -^-O3 t 2 2 2 2

CoCO + H* = Co + HCO"

H S + 20 SO2" + 2H*

a, ROBIE et al. (1978);b, MILLS (1974);

UAGMAN et al. (1969);HAYNES and BLOOM (1987a).

Chloride and bromide complexes of cobalt 339

-20

-30

oo»

°

-40

-50

1 — -f~ 1 \ 1

-o Vo

. Y°~'•."• Yu>

\

Coaq ; :

i ;

:

-^^s~^~_Pyrite

1 1 1 1

1 \ 1 1 1

Co3O4

CoC03

\ Co3O4

\ Co304

\ Co o \CoCO3

\Sr-*

CoCOa c*co3

CoO

~

i-J;---

•.:.-:-:^COiSi-.:: .:•:.-... - ,-,,,:,,-

• • c o s 2

i i i i

-50

-40

-30

-20

-10

-6 -4

'aq

-2

FIG. 15. Logarithmic oxygen fugacity W. free cobalt activity dia-gram. The thermodynamic data and sources are listed in Table 9,free energy changes at 400 K are calculated assuming constantA//? and AS?. This diagram is constructed along the boundary ofSOj- - H2S. Activities of 2 S and HCOj are adapted from HAYNESand BLOOM (1987a) as 0.11 m and 4.4 X 10~4 m, respectively. Notethat a pH of 6.5 is slightly basic at 400 K (101.85°C).

which multiplied by a typical enhancement factor of 100 (at90°C, 4.2 m salinity) can yield about 3 ppm total cobalt influids. This amount of cobalt may adequately account forthe widespread appearance of cobalt in stratiform depositsas a trace metal. To form an economically valuable cobalt-bearing deposit, a minimum of 10 ppm of cobalt in fluidsmay be needed (as for the other base metals, see BARNES,1979), which may be achieved at higher salinities (at 90°C,5.75 m Cl~, the enhancement term approximately equals500) or by a free cobalt term of 10~55 or higher at very fa-vorable conditions (e.g. at CoCO3 region, or more acidic pH).

It should be pointed out that in the discussions above,sufficient cobalt in the source region and equilibrium havebeen assumed. However, the amount of cobalt in fluids largelydepends on the availability of cobalt in source rocks. HAYNESand BLOOM (1987a,b) show that cobalt concentrations inlow temperature metal-transporting waters derived from ba-salt (gabbro) can be several times higher than that derivedfrom granite. It is suspected that in low temperature hydro-thermal fluids (around 100°C), depending on the rates ofchemical reactions, the fluid/rock ratio, the flow rate of thefluid (permeability of rocks and pressure gradient), and thetraveling distance of the flowing fluid, the amount of dissolvedcobalt in a period of time is variable, and equilibrium may

never be reached. Thus, kinetics add further constraints tocobalt mineralization.

CONCLUSIONS

Spectrophotometric determinations of the stability con-stants for aqueous cobalt halides show a range of octahedrallycoordinated species of the form CoA^^O)^" (0 < n < 4)and a tetrahedral coordinated CoXt~ for chloride and bro-mide solutions up to 90°C. CoJ(H2O)s and CoXl~ arestrong complexes, showing small positive enthalpies and largepositive entropies. The other octahedral complexes areweaker, having positive enthalpies and negative entropies and,hence, are not energetically favoured with respect to themonohalide penta-aquo complex. The formation of the higherhalogenated octahedral complexes is due to the mass-actioneffect of increasing halide concentration. The chloro-com-plexes are stronger than the corresponding bromide com-plexes, which show a greater covalent component in theirbonding.

There is no sharp transition between the two configurationsas all species are in equilibrium. The transformation to thetetrahedral complex is driven by the entropy change of thereaction and is thus favoured at higher temperatures. Al-though the transformation is not restricted until after a par-ticular octahedral complex has formed, a comparison of thestepwise transformation reactions suggests that the relativeorder of conversion is CoCl4(H2O)2~ > CoCl3(H2O)J> Co(H20)i+ > CoCl2(H20)S > CoCl(H20)J. Thus, theaverage chloride ligation number for the octahedral com-plexes in equilibrium with the tetrahedral complex at highertemperatures should be low. Bromide shows a similarorder, except that hexaaquo cobalt is more stable thanCoBr2(H2O)S to the coordination transformation. Previousdeterminations of the enthalpy of the transformation are sig-nificantly greater than reported here, due to their neglect ofactivity coefficient corrections.

The rule of average environments provides a reasonableestimate of the average ligation number from the 10 Dq termat low temperatures. At higher temperatures, it tends to over-estimate the average ligation number, particularly at highsalinities. This may be due to a non-constant temperaturedependence of 10 Dq for H2O and Cl~ or to a nonlinearmixing of 10 Dq values in mixed-ligand complexes. A majorlimitation of estimating ligation numbers from 10 Dq is thelack of adequate determinations of 10 Dq for solids of knownstructure.

The total dissolved cobalt in a fluid may be factored intotwo terms, i.e. a free cobalt term and an enhancement termdue to chloride complexation. Investigation of these two termsunder typical hydrothermal conditions in which sediment-hosted stratiform deposits were formed, shows that severalppm cobalt can be transported, provided that a sufficientcobalt source is present. However, to form an economicallyimportant cobalt deposit, environmental conditions whichproduce a high free cobalt term and very high salinities (>5m at 90°C) are required.

Acknowledgements—This research has been supported by NSERCand the University of New Brunswick Research Fund. Thanks go toD. J. Leggett (DOW Chemical, Texas Division) for sending us a copy

340 P. Pan and N. J. Susak

of original SQUAD. Critical reviews by S. M. Richardson and twoanonymous reviewers are sincerely acknowledged. Special thanks aredue to Scott Wood, for his extremely thorough comments and varioushelp.

Editorial handling: S. A. Wood

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