Awrican Mineralogist Vol. 57, pp. 1163-1789 (1972) /

FREE ENERGIESOF FORMATION AND AQUEOUS SOLUBILITIESOF ALUMINUM HYDROXIDES AND OXIDE HYDROXIDES AT 25"C GnoncnA. P.e,nrs,Departntant of ApptiedEarth Scienaes,StanJord Uniu ersity, Stanl ord, Cal'it ornia I d305

AssrBAc{

comparison of the standard free energies of formation at 25'c of corundum, diaspore, boehmite, gibbsite, and bayerite estimated from carefully selected uq,ruor6 solubility data with those of calorimetric origin .permits selection of a set which is more consistent with stabilities observed in field and laboratory than the calorimetric set alone. The selection process involves acceptance of -378'2 and -1160 kcal per mole for AG'1 of aALo" and Al"* (aq) respectively and assignmentof -311'0 kcal per mole for the AG'1 of AI(OE); (aq)' Selected values for the solids are:

kcal/Mole

diaspore -219.5+ 0.5 boehmite -218.7+0.2 gibbsite -275.3+ 0.2 bayerite -274.6+ O.L Solubility-pE curves based on these asignments agree with independent solubility data only if it is assumed that slight supersaturation rezults during many experiments and leads, upon aging toward equilibrium, to precipitation of gibbsite or bayerite, depending on pE. One set of data which suggeststhis inter- pretation is discussed. Isrnopucrrow There is convincing evidencein phase equilibrium investigations that corundum is unsiable with respectto gibbsite in the presenceof of water aL25" and onebar pressure(Kennedy, 1959). Unfortunately, tabulated free energiesof formation (Wagmanet aI., L968,and Robie and Waldbaum, 1968) predict the opposite.During an attempt to find free energiesof formation with which to calculatesolubilities of the aluminum hydroxides,discovery of this discrepancyrevealed the need for critical appraisalof availabledata. It is the purposeof this paper to selectthe most reliable free energiesof formation available for the hydroxidesand oxide hydroxidesof aluminum. For the solids,this is done by critically reviewing the sourcesof tabulated free energiesof formation, which ale largely calorimetric, and. comparing them with independent data derived from solubility measurements.Derivation of free energiesfrom solubility data re- quired review of the free energiesof formation of Als-(aq) and 1163 1164 GEOBGE A. PARKS

Al(OH)n (aq). Followingselection of the freeenergies of formationof the mono-hydroxoeomplexes it is shorvnthat polymerichydroxo com- plexescan be ignoredat equilibrium and an attempt is madeto check the validity of the entire set of selectedfree energiesby comparing calculatedsolubility-pH curveswith an independentset of solubility data.

Teeur,ertD Fnpn Ewnncros ol' Fonnrerron oF THE Sor,rm Most tabulations of thermodynamic data rely heavily on U.S. Bureau of StandardsCireular 500,Selected Values of ChemicalTher- modgnamicProperties (Rossini et at., Lgb2) andOridation Potentials (Latimer, 7952). The Bureau of Standardsis updating Circular S00 and has releasedinterim tables, omitting references.Data for alu- minum appearin TechnicalNote 220-8 (Wagmanet cll.,1g68), one of the interim series.original referencescited for data attributed to Wagmanet aI. in the followingparagraphs were provided by Wagman in personal communicationsto the author (D. D. Wagman, 1g69, written communication). The u.s. Geologicalsurvey has arsorecently publisheda tabulation of thermodynamicdata (Robieand Waldbaum, 1968).The many publieationsof Pourbaixand his co-workers,col- lected in lhe Atlas of Electro-chemicalEqui.Iibria in Aqueou,ssolu- tions (Powbaix, 196G)comprise still anoiher exhaustivesource of thermodynamicdata. The original sourcesof free energiesof formation in thesetabula- tions have been examinedfor information useful in permitting selec- tion arnongdiffering estimates.

Corund,um,aAlzos The free energyof formation of corundumreported by Rossinief al. (1952) is -376.77 kcal/mole. The value given by Wagman et aI. (1968)is -378.2 kcal/mole.The latter is basedon heat capacities listedby Kelley and King (1901)and heatsof combustionof alumi- num reported by Roth, Wolf, and Fritz (1940), Snyder and Seltz (1945),Holley and Huber (1951),Schneider and Gattow (19b4),Mah (1957),and Kocherov,Gertman, and Geld (lgbg). The product of eombustionwas invariably identifiedby X-ray diffraction.Robie and Waldbaum (1968)report -378.082 -L 0.810on the basisof heat ca- pacity data attributed to Kelley and King (1961) and Furukawa et al. (7956)and the heat of formationreported by Mah (lgb7). The differencebetween 1g68 and 1g52estimates reflects new work. It requires revision of free energiesof formation of ail other sub- SOLT]BILITIES OF ALT]MINU M HYDROXIDES 1r65 stancesfor which corundum served as a referencematerial. This adjustmenthas beenmade where necessary in the paragraphsto follow.

Diaspore,aAIOOH Rossini et at. (1952) list data for a monohydratenot identifiedby name. The free energy of formation of diasporegiven by Wagman et al., (1968) is -220 kca!/mole. It is basedon an estimateof the enthalpy changeassociated with dehydrationderived from calibrated differential thermal analysis work (Foldvari-Vogl and Kiburszky, 1958)and on low temperatureheat capacitydata reportedfor diaspore by King and Weller (1961).Robie and Waldbaum (1968)list only the entropy of diaspore,citing King and Weller (1961) and Kelley andKing (1961). Fyfe and Hollander (1964) reporbthe free energyof formation of diasporeas -219.5 kcaf/mole.This estimateis basedon the tempera- ture at which diaspore and corundum coexist at equilibrium with liquid water and an estimateof the entropy neededto correctto 25'C' The estimatedprobable error from all sourcesis :t0'44 kcal/mole' Fyfe and Hollander took extremepains to insure equilibrium, but DTA methods are dynamic hence unlikely to produce equilibrium reaction products,thus -219.5 I 0.5 is probably the best estimate of the free energyof formation of diasporefrom thesesources.

Boehmite,YAIOOH The free energyof formation of boehmitegiven by Wagman et al' (1963) is -218.15 kcal/mole.It is basedon measurementsof the enthalpy changeassociated with its dehydrationreported by Calvet (1962),Foldvari-Vogl and Kiburszky (1953),Michel (1957b),and Eyraud et aL. (1955) and heat capacity data originally reportedby Shomateand Cook (1946). Robie and Waldbaum (1968) report -217.67:L 3.5 kcal,/mole,basing their selectionon Rossini et oZ' (1952) and the same heat capacity data. The heat of formation reported by Rossini et al., is a calculatedestimate for an AIOO'H which is not identifiedas boehmite. There are severalsources of uncertainty in the data for boehmite. Most important is ambiguity in identificationof the solid usedin the heat capacity ureasurementsby Shomateand Cook. The purity of boehmitesused in dehydration experimentsand the characterization of dehydrationproducts are also doubtful. Shomateand Cook (1946)used a monohydrateof correctchemical compositionbut reportedthat "X-ray examinationshowed . . . the 1166 GEONGEA. PARKS

monohydrate[to have] a structuresimilar to bayerite (AITOB.BH2O) differingfrom the latter principally in the intensitiesof rines.,,Neither they nor Rossiniet al. (1g52)identified the solid as boehmite.Beeause the x-ray diffraction patterns for bayerite and boehmite differ in the presenceor absenceof major lines as well as in relative intensities of lines, identificationof the solid as boehmiteis not justified on the basis of their data alone. Kelley and King (1g61) were the first to to usethe data of shomateand cook referringto the soridas boehmite.

may be uncertain by as much as a few percent.They are adequare, however,for ordinary heat balance calculations.,,Kennedy (lg5g) refers to low temperature heat capacity measurementsmade by Kelley and King on a boehmitehe suppliedbut there is no mentionof new measurementsin publicationsafter lgbg. Eyraud et al. (1955) reported 4 percent crystalline trihydrate in their boehmite. Eyraud et al. also point out that the dehydration product is, at least in some instances,a mixture of polymorphsof AlzOa.Since the other authors reporting dehydration did not repoft characterizationof the dehydration product, some doubt must be admitted about the phasepurity and identity of the oxide. In view of thesecriticisms, little or no confidencemay be placedin the validity of tabulated free energiesof formation of boehmite. Gibbsite,dAl(OH)s TIre free energy of formation of gibbsite given by Wagman et aI. (1968) is -273.35 kcalmole. It was selectedby considerationof heat

pacity and the heat of solutionin B0 percentNaoH solutionsprovided by Roth, Wirths, and Berendt (1942) and the heat of formation derived from HF solution calorimetry by Barany and Kelley (196l). 'Waldbaum The free energy of formation reported by Robie and (1968)is -273.486 -t 0.310kcal/mole. It is basedon the heat capacity data of shomateand cook (lg4o) and the heat of formation reported by Baranyand Kelley (1961). The free energy of formation reported by pourbaix (1g66) is -277.32 kca/mole. It is based on the solubility measurementsof SOLT]BILITIESOF ALUMINUM HYDROXIDES 1167

Fricke and Jucaitis (1930)and a freeenergy of formationof Al (OH) + . The free energyof formation of AI(OH)+ was derivedfrom the solu- bility of boehmite (Fricke and Meyering, 1933) and a free energy of formation of boehmite attributed to Latimer (1952). Latimer's soutcewas Rossiniet al. (1952),hence his flgure is invalid. This, to- gether with the high concentrationsof the solvents used by Fricke and Jucaitis (1930) and Fricke and Meyering (1933), which make activity corrections doubtful, unfortunately invalidates Pourbaix's estimateof the free energyof formation of gibbsite.

Bagerite,rAl(OH)s The free energyof formation of bayeriteis not reportedby'Wagman et al. (1968)nor by Robie and Waldbaum (1968).The value, -276.24 kcalr/mole,reported by Pourbaix (1966) is basedon solubility data with the samehistory as that describedfor gibbsite,hence is doubtful.

Fnnp ENnncrESoF FonnrerroNpnolr Sor,uprr,rrvDere Estimation of AGoyfor solidsfrom solubility data requiresthat the compositionof the solutionphase be known in detail and that the free energiesof formation of the dissolvedspecies be known. Al(III) solu- tions contain hydroxo-aluminum complexes.There is much contro- versy about which complexesare stable. Some authors find that their hydrolysis or solubility data are adequatelyrepresented by mono- nuclear complexesof the group AI(O}J)*"- with ra in the range 0 1 n ( 4. Someignore Al(OH)s (aq.); somedo not. Somefind it necessaryto assumethe existenceof polymeric complexes.Miceli and Stuer (1968) point out that the polymersare usually invoked in high ionic strengthsolutions containing a high concentrationof aluminum. Hem and Roberson(1967) and Smith (1969) found evidenceof poly- meric speciesin low ionic strengthsolutions containing no more than 13 ppm aluminum. Severalauthors decidedthat the polymers were unstableintermediates in the precipitation of solids and have found that their concentrationsdepend upon the conditions of mixing and rate of hydrolysis. (Hem and Roberson,1962; Frink and Sawhney, L967;Turner, 1968; Smith, 1969; W. Stumm, 1969,oral communica- tion.) If polymeric speciesare absentat equilibrium, the compositionof the solution can be least ambiguouslydefined in acid (pH ( 4) and basic (pH > 8.5) media where Al3* and AI(OH)+ predominate.We will seelater that ignoringpolymeric species is at least an acceptable approximation. 1168 GEORGEA. PARI6

To derive free energies of formation of the solids from solubility data we need the free energies of formation of Als* and AI(OH)4- and reliable solubility products for each solid.

The Free Energy ol Form,ati,on of AIs' (aq.)

The free energy of formation of Ala-(aq.) reported by Wagman et al. (1968) and by Robie and Waldbaum (1968) is -116.0 kcalmole. Robie and Waldbaum quote an earlier version of the Wagman et aL publication and assign an uncertainty of +0.300 kcal/mole. Wagman et 'o,2.based their selection on measurements of the potential of an aluminum electrode by Plumb (1s62), the solubilities of alums col- lected in Seidell and L,inke (1958), the solubility of an aluminum hydroxide quoted by Gayer, Thompson, and Zajicek (1958), and an earlier estimate by Latimer and Greensfelder (1g28). Latimer and Greensfelder based their estimate on the solubility of a well charac- terized cesium alum. unforiunately, there is reason to question much of this information. Plumb (1962) used 0.2 molar sulfate solutions or phosphate buffered systems in his electrochemical work and did not correct to zero ionic strength or correct for complexing. He reported a free energy of for- mation of AI3.(aq.) of -114.4 kcal/mole. Gayer et aI. (19:48) characterized the solid phase used in their work by chemical analysis and X-ray diffraction. It was a trihydrate but was not identified by name. The three major d-spacings they reported correspond most closely to bayerite. Since the free energy of forma- tion of bayerite is unknown or highly suspect in the sources quoted by Wagman et al. (1g68), the free energy of formation of Als. based on the data of Gayer et aI. mustralso be suspect. Latimer and Greensfelder (1g28) reported -116.9 kcal/mole for the free energy of formation of AlB.(aq.). Latimer (lg12) later reported -115.0, citing recalculation from the earlier work without further explanation. In view of this confusion, while I have chosen to use -116.00 kcalmole for the free energy of formation of AIB* in order to retain eonsistency with the NBS tabulations, an uncertainty of at ]east one kilocalorie per mole must be admitted.

The Free Energy of Fortnati.on of AI(OH);(aq.)

The free energy of formation of AI(OH); reported by W-agman et aL. (1968) is -310.2 kca/mole. It is based on experiments involving the hydrolysis of Al'.(aq.) and re-solution of the solid formed as SOLUBILITIES OF ALT.IMIN(] M HYDROXIDES 1169 reported by Oka (1938), Lacroix (1949), and Goto (1960), and on the solubility data of Gayer, Thompson, and Zajicek (1958). The free energy of formation of AlOz- reported by Pourbaix (1966) is -2W.71 kcal/mole, corresponding to -314.09 kcal/mole for Al (OH) + . This estimate is based on the solubilii,y of boehmite (Fricke and Meyering, 1933) and the free energy of formation of boehmite invalidated above. Latimer (1952) reports the free energy of formation of AlO2- and -255'2 H2AIOB- separately, giving -204.7 kcal /mole and kcal/mole respectively. These correspond to -318.08 and - 3f1.89 kca/mole for AI(OH)+. These estimates,too, are based on solubilities of hy- droxides which are not well characterized. nK*n, The equilibrium constants Ks6, Kru, and ,,8aa're defined as follows (Sillen and Martell, 1964):

Al(oH),(s): Al'* + 3OH-iKso: (AI'.)(OH-)' (1) : :(Al(oH)'-) (2) AI(oH),(s)+ oH- Al(oH),-t K s+ (oH-)

Al(OH),(s)+ H,O : AI(OH),- * H*;*Kso : (AI(OH)'-)(H.) (3)

Al'* 4oH-: Al(oH),-p^ : l4l9l)="J-')(oH-). (4) + ; n+:!: so (Af Quantitiesin parenthesesare thermodynamicactivities. A free energyof formation of AI(OH)+ basedon the free energy of formation of Als* can be derived from B+. B4 may be determined directly through hydrolysis experiments involving undersaturated solutions.Such data are reported in Sill6n and Martell (1964) but none are derived from direct experiment.Sullivan and Singley (1968) report enoughdata in a set of hydrolysisexperiments to permit'esti- mation of Ba but they did not correctto zeroionic strengthand there is nearly an order of magnitude differencein equilibrium constants determined aL two dissolved aluminum concentrations.Dezelic, Bilinski, and Wolf (1971) report hydrolysis constantsat low ionic strength (<0.01 molar) but did not correctlo zeto ionic strength. Use of Ks6 and Ks+ to deriveFr requiresthat the identical solid be present during determinationof the two constants.If the solid is proclucedby hydrolysis of Al'* and subsequentlydissolved in more basic solutionsto yield Al(OH)+ or vice versa,this conditionis per- hapsmet. If Ksg is determinedby hydrolysisof Al3*solutions t"o yield a solid a.ndKsa by separatehydrolysis of AI(OH)4- solutions,also yielding a solid, the solids producedare not likely to be the same. I170 GEORGE A. PARKS

Different hydroxidesprecipitate from acidic than from basicsolutions (Schoenand Roberson,1g6g; Hem and Roberson,lg67; Hsu, 1g66; and Barnhisel and Rich, 19Gb).Among investigationsyielding Ks6 and Ksa and not usedby Wagmanet al.,Lhoseby Hem and Roberson (1967),Kittrick (1966)and Szatro,Csanyi and Kavai (195b)appear to involve a singlesolid. Free energiesof formation of Al(o'H)+ derived from thesesources and Wagman'sare summarizedin Table 1. Unfortunately, Hem and Roberson determinedKgo through hydrolysis experimentsyierding crystalline gibbsite after equilibration times exceedingeleven days while the experimentsyielding Ksa involved equilibrationtimes of one day or less.rnasmuch as they themselvesshowed that even after the longestaging times their gibbsitewas microcrystalrine,with a particle size small enoughto increasethe solubility, we have no guarantee that the solids involved in deriving Ks+ and Kga had the same free energyof formation.The investigationsof Szabo,Csanyi, and Kavai; Oka; L,acroix; and Goto involve hydrolysis experimentsbased on titrating or mixing Al3* solutionswith NaoH or KoH sorutionswith equilibrationtimes of a few hours.rt is doubtful that equilibriumwas attained in these experimentssince the techniquemay result in local high concentrationsof oH-, hence local premature precipitation of solidswhich equilibrateextremely slowly (Biedermannand schindler, 1967).Gayer, Thornpson, and Zajicek determinedKg6 and Ksa through study of the pH dependenceof the solubility of a pre-synthesized solid hydroxide. They do not describeprecautions taken to insure equilibrium but state that their method was similar to earlier work (Garrett and Heiks, 1941and Garrett, Vellenga,and Fontana, 1989) in which equilibrium was approachedfrom under and oversaturation and with equilibration times of 20 days or more. The"more recent

of Fomtlotr of A1(OE);

^c: (Ar(ou)l) Source (ca1/nole

E@ and Roberso! (1957)

Xtttrtck (1955) -311.03

cafe, Thonpsoo and Zaltcek (1948) -310.61

Szabo, Csaayl, 6il Ravat (1955) -3r2,06

Lacrotx (1949)

oka (1938) -372.46 SOLUBILITIESOF ALUMINUM HYDBOXIDES 1171 solubility investigations of Kittrick and Hem and Roberson demon- strate that equilibration requiresmonths to years. With these arguments in mind, it is not difficult to understandthe wide variation in the free energiessummarized in Table 1. The in- vestigationleast subject to criticismis Kittrick's, hencethe free ener5/ of formationof A1(OH)r is probably closestto -311.02 (basedon AGol for Al3* of -116 kca/mole). Kittrick estimatesa probable error of :t0.07 kcaVmole. It is certainly not justified to claim sig- nificancebeyond -311,0 :L 0.1. BecauseAGol for AI(OH)+- is based on AG"7 for Al3*to which we have assigneda probableuncertainty of :t l kcal/mole, AGol for Al(OH)a- is also uncertain to at least 1 kca/mole in spite of the much smallerexperimental probable error.

SelectedSolubility Prodztctsand Deriued"Free Energies of Formatian Sillen and Martell (1964)record a long list of estimatesof Kso and Kga. Choosing,from these and a few more recent papers,investiga- tions in which the solid phaseis well characterized,the solutionionic strength very low or correctedLo zero, corrections for hydrolysis are small, and in which specificefforb was taken to insure equilibrium, leavesfew sourcesof data suitable for estimationof free energiesof formation of aluminum oxide hydrates. Kittrick (1966), Hem and Roberson(1967), and Frink and Peech(1962) report Ks6, and Russell et al. (1956) reporb Ks+. The equilibrium constantsand free energies of formation derived from them and the free energiesof forrnation of Al3* and AI(OH); are listed in Table 2. The solubility product chosenby Feitknechtand Schindler(1963) for amorphousAl(OH)s is includedfor comparison. The very painstaking work of Reesmanand Keller (1968) and Reesman,Pickett, and Keller (1969) has not beenused because their solidswere not pure, singlephase materials. Their work will be used to judge selectedfree energiesof formation,however.

Snr,ncmowoF THE Fnpo Ennncv on FonlrerroN oF rnn Sor,ros Gibbsi,te One estimate of AGlo for gibbsite derived from solubility data is very close to the calorimetric value quoted earlier, near -273 kcal/ mole. Two estimatesfrom solubility data, one from Kso and one from Ksa are close to -275 kcal,/mole. Both pairs include experimentsof quite different histories and the close agreementwithin one pair if consideredalone would be persuasiveevidence of the validity of the estimate. However, gibbsite must be more stable than corundum in lt72 GEORGEA. PARKS

soUd Solid Partlcle Slze solublltty Ploduct Ac;, Kcal/uo1e

IoC KSo= -33.5 fraB and feecn (lrDl, clbbslteb 0.05 Dlcron 1o8 KSo - -34.06 + .09 Klrtrlck (1955) Glbbelteb 1oc Kso = -33.98 1 .0I -275.34+ .OL (lrtrtck (1966) 1or Kso - -32.65 + 0,3 -213.34+ O.4 E@ & bberoor (1957) clbbstted Iog*KS4 - -15.27 -275.L + O.l Russeu et al, (1955) -d log*(S4 - -14.82 -274.6 + O.7 Rueseu et dl. (1955) Iog*KS4--13,96+0.2 -213,4 + O.3 He E Roberson (1957) 1og{s4 - -15,27 -218.7,+ 0.1 Bu6se11 et ar, (1955) e, A1(0s)3 IoC KSo= -31.2 -27r.34 Feltknecht e Schldre! (1963)

'solld PleclPltated fr@ E(oH); solutlon slrh co2 at 95o, sashd ln 4N Ec1 and Hzo, drled ar tlooc. Idertlfled by PetlograPhlc Dethods. Equiltbratlou floD both ssb- and superssturatton for 30 day6 or Eo!e. Xso correcEd to zero lonlc stleqth.

b (herclal gtbbsltes ldentlfled by x-ray dlfflactlo! 6nd DTA. ro! o.o5 Dtcron @cerlat equlublared fr@ both sub- ad suPersatu?at1on for st le6st 267 da]/s, 50 Dlcronuterial equilibrated floE eupelsaruratton only,

" sotra tu E Product of hydrolysle floE d11ute pelchlolate solurloE6 ar 25o, ldeDtlfi€d by x-!ay dtfflacrlon and clyltal bolphology. Equlllbratlon tlDe etwm to 135 days. KSo correcred ro zero ionlc srrength. d *fr4 *" detemlnd as a funcElol of t@pe!.ture and Naof, concentlatlon rhen colrecred to zero lonic stleryth. Xavetlte was Prducd by CO2 acldtftcatlon of an at@iute solur{on and idenrifled by X-ray dtfflactlon. The prob- able errols a€elsnd to flee enersles r€flect oily the Dtntuu@ plobable error ln Ac:([(oH);) hetrce ale eintu@s. e product or hydtolysl€ lu dilute baslc perchlolate soluttoDs ar 25oc. rdentlfld by x-ray dlffractlon. Equtltbla- tlod ttue oue day or 1ess. *Ks4 collecred ro zero lodic srrengrh.

liquid water at one bar pressure (Kennedy, 1959), hence the free energy of formation of gibbsite must be more negative that -224 kcal/mole if that of corundum is -378.2 kca/mole. Kittrick (1966) observed that his free energv of formation for gibbsite was more negative than earlier estimates and considered differences in pari,icle size and crystallinity among the solids involved in explanation. Observing a barely significant particle size effect in his solubility work, he attributed the discrepancy to differences in crystallinity between his gibbsite and those used in earlier investiga- tions which yielded less negative values of AGt". The difference in AGy" between material of two different particle sizes is related to pafticle size through the surface free energy as follows (Schindler et a1.,1965):

^n 2 Mal I 1\ ALT:;- - --, op d2 dr/

2 Mal AG: if d, ({ d, 3 pd" where M : formula weight of solid p : density of solid f : mean surface free energy SOLT]BILITIES OF ALU MINU M HY DROXIDES tt73

d : characteristic particle dimension, d, ) d, d : a shape factor, the ratio of particle surface area to particle volume multiplied by d. For gibbsite crystals in the form of thin hexagonal plates as observed by Hem and Roberson (1967), a is about 14. Ideally, at equilibrium, there should be only one particle size present. In most real systems there is a particle size distribution and the minimum size present at apparent equilibrium determines the solubility, hence the apparent free energy of formation. The surface free energies of oxides in equilibrium with their saturated aqueous solutions range from -l2O erg/cm' for a hydrated silica gel (Adamson, 1960) to 890 + 240 ergf crn"for CuO (Schindler et al.,1965). A mean surface free energy of 100 ergf cmt is consistent with the small apparent particle size effect observed by Kittrick. However, his particle size estimates were made before equilibration and the possibility of grain growth during the experiment must be admitted. If grain growth did occur, his results would be consistent with a larger f. Hem and Roberson (1967) describe a single 0.04 micron hexagonal plate observed in an electron micrograph of gibbsite from an equilibrium system. This is neither a maximum nor a minimum particle size, judging from the published micrograph. The two kilocalorie difference between their AGlo for gibbsite and Kittrick's can be attributed to a particle size effect if 7 is about f 100 erg/cm'. If the minimum particle size present were 0.01 micron, r- would have to be about 270 ergf cm2. The assumptions needed to attribute the difference between the maximum and minimum AGlo listed in Table 2 for gibbsite to a particle size effect are not unreasonable. Admitting the probability that dif- ferencesin particle size and crystallinity are responsible for the differ- ences in free energies of formation observed dictates selection of the most negative estimate as closestto the true value for well crystallized, large particles. On this basis, -27534 kcal/niole, with a probable error of perhaps +0.2 kcal/mole is the free energy of formation of gibbsite. This assignment requires the assumption that the gibbsite used by Barany and Kelley (19'61) be poorly crystalline or very fine grained (-.05 micron) and that the gibbsite used by Russell ef oZ. (1955) be well crystallized and relatively coarse grained (>0.5 micron). None of the gibbsite used by Barany and Kelley is available today (E. G. King, written communication, 1970), so a direct check of particle size is impossible. It was prepared by G. C. Kennedy but no records of the preparation are available (G. C. Kennedy, written com- munication, 1970). The gibbsite was synthetic, probably prepared by II74 GEONGEA. PARKS

hydrothermal alteration of synthetic bayerite, hence, probably very fine grained (G. C. Kennedy,written communication,1970). The work of Russell et al. (1955) involved concentratedNaOH solutions,high temperatures,and equilibrationtimes up to two months, thus the probability that grain growth would occur is higher than in Kittrick's investigations.Unfortunately no parbiclesize measurements were reported. The work of Reesmanand Keller (1968)and Reesman,Pickett, and Keller (1969) lends credenceto the selectedAGol for gibbsite.They originally reporteda AG"ybased ultimately on acceptanceof the AGol for boehmitelisted by Rossiniet aI. (1952).Using their data and the selectedAGol for Al(OH+ (Table5), to avoidthe discrediteddata for boehmite,yields -275.9 kcal/mole for AGoTof gibbsite,in goodagree- ment with the value selectedhere. Bayerite Of the two estimatesof the free energy of formation of bayerite in Table 2, the more negativeis probably to be preferred,again because the solid phaseresulting in the less negativeestimate was probably microcrystalline,having beenproduced by low ternperaturehydrolysis. On this basis,the free energy of formation of bayerite is -274.6 ! 0.1kca/mole. Diaspore No solubility data for diaspore,reliable by the criteria applied,are available. The selectedfree energy of formation remains -219.5 ,! 0.5kca/mole. Revision of the free energy of formation of diasporereported by Reesmanand Keller (1968) to reflectthe seleetedfree energyof for- mation of Al(OH)a (Table4) yields -218.2 kcal/molefor the AGoy of diaspore.In view of this result the.uncertainty in the free energy of formation of diasporemay be as mueh as one kilocalorieper mole. Boehmite Having rejectedcalorimetric estimates of the free energyof forma- tion of boehmite,only the one estimate based on solubility data remains. The free energy of formation of boehmite,on this basis, should be -218.7 + 0.1 kcaVmole.However, boehmite is considered metastablewith respectto the other oxide hydrates (Kennedy,1959), so that its free energy of formation should be less negative than -218.6 kca/mole. For this reason,the probableerror associatedwith the free energyof formation of boehmiteis probably at least =0.2. SOLABIIJITIESOF ALUMINUM HYDROXIDES II75

Reversingthe calculationsof Reesman,Pickett, and Keller (1969) andusing the selectedfree energy of formationof Al(OH)r (Table4) yields an estimateof AGoyfor boehmite,-2173 kcal/mole. In view of this result, the uncertainty in the free energy of formation of boehmitemay be as much as one kilocalorie per mole. Summmry Selectedfree energiesof formation of the solids are collectedin Table 3. Except for corundum,the probable uncertaintiesindicated are minimums,reflecting only experimentalreproducibility, and not the much larger probableuncertainty introducedthrough use of AGol of Al3*. The free energiesof formation of Al3* and AI(OH); upon which the data in Table 3 are basedare collectedwith the free energies of formation of the monohydroxocomplexes in Table 4.

Sor,unrr,rrr-pH Cunvns ANDTHE Accunecy on Snr,ncrnoFnnn Exoncrns on Fonlre.rrom Somesolubility data have not beenused in selectionof free energies of formation of the solids. These data are largely in the pH range in which hydroxoaluminumcomplexes are important.Comparison with solubility data calculatedfrom selectedfree energiesof formation of the solidsrequires selection of free energiesof formationof both mono- nuclearand polymerichydroxoaluminum complexes and demonstration that polymeric speciesare not significantat equilibrium. Th,e Free Energies of Fornuafinn of Hgdroroaluminum Compleres All estimatesof the free energyof formation of the hydroxo com- plexesare derived from stability constants.In selectingthe data fot' this purpose,experiments involving solids were rejected unlessthe data availablein a singlepaper permitted derivationof stability con- stants independentof the propertiesof the solid. If Ksz alone was reported,for example,it was not used.If Ks2 and Kse were reported the data were acceptedand used to derive Fz, thus permitting calcu- lation of a LG"7for Al(OH)z* independentof the identity of the solid phase.

M,onorruclear Co mpler e s Estimatesof log *K1, correspondingto the reaction, Al"*+HrO:AIOH'*+H* rangefrom -4.49 to -5.9 (Sillenand Martell,1964; Holmeset aI., 1968; Sullivan and Singley, 1968; and Nazarenko and Nevskaya, 1176 GEOEGE A. PARKS

TABLE 3

of A1ul.n6

a Species Ac: (25oc) kcaumole

-378.2 d A12O3 , corundum + 0.3 -219.5 o A1O0II , aliaspore + 0.5

"y A10OH , boetmire -218.7+ 0.2 -275,3 o AI(OH)3 , glbbsite + O.2 -274.6 Y A1(oH)3 , bayerlte + O.L

a The uncertainty in Ac! tot bayerite and glbbsite nay be larger

than one kilocalorie owing to the undertaitrty ia the Acf, of e13+.

The uncertainty in Ac! for boehmiEe and diasPore nay be larger

thail one kllocalorie since the one available independent esti-

nate of Ac! in each case is about one kilocalorie less negative t Ehan the selected value (see Text).

of ltononucler Bydroxoal@lnu (III) c@p1ses at 25oc

Free Elergy of Fo@tlon . ^a * Coopld roc-n o 298 kcal/oo1e

t+ A10It-' +8.99+ .04

A1(ou)- +19.3+ 0.1 -2L7.5

A1(0u)a(aq) +25.8+ 0.1 -zo).J

A1(OU); +32,7+ O,L -311.0 + 0.1

a The reactloo correEpondl.Dg to Fn ls Irs+ron--Alloull+ SOLUBILITIES OF ALUMINUM H''DROXIDES tt77

1969).Among the estimatesat 25'C and zeroionic strength,the most reliable,by thesecriteria: attainmentof equilibrium,absence of com- plexinganions, awareness of the possibilityof polymer formation,etc., are thoseby Frink and Peech(196.3), Raupach (1963), and Schofield and Taylor (1954).The averageof log *K1 &mongthese estimates is -5.01 and the rangeis only * 0.04. The formation constantof the dihydroxocomplex, Bz, corresponds to the reacbion,

At'*+2OH-:AI(OH),*

Severalinvestigators report data from which 92 can be derived.The values of log p2 obtained from work with estimatedionic strengths below 0.01 molar are 19.36 :L 0.1 (Gayer, Thompson, and Zajicek, 1958),L7.72 !.0.3 (Sullivanand Singley,1968), and 19.19(Dezelic, Bilinski, and Wolf, L971).Work by Nazarenkoand Nevskaya (1969) was done at 0.1 molar ionic strength.All of these investigationsin- volved solids and relatively short equilibrationtimes. Agreementbe- tween the work of Gayer et al. involving approachto equilibrium from subsaturationand that of Dezelicet al. which involved approach to equilibrium from supersaturationis perhapssufficient grounds for assumingequilibrium was actually attained and for selectingthe -+ averageof the two results,19.3 0.1 as the preferredvalue of log Fz. Sillen and Martell (1964)report one estimateof ps and two others can be calculatedfrom the data of Dezelic et aI. (7971) and Nava- renko and Nevskaya (1969). Again omitting the data Nazarenkoand Nevskaya obtained at 0.1 m ionic strength,the averagevalue of log Bs in dilute solutionsis * 26.8 I 0.1. Formation constantsand correspondingfree energiesof formation of the mononuclearcomplexes are summarizedin Table 4. The ranges indicated for log p" in Table 4 are rangesonly, not probable€ffors. No attempt has been made to estimate probable error in the free energiesof formation.

PotymericCom,pleres: A wide variety of hydroxoaluminumcomplexes containing more than one aluminum atom have beenproposed. Aveston (1965)reviewed the subjectin 1965.In most investigationsyielding equilibrium constants, the authors have pointed out that their resultscould probably be ex- plained equally well by somecomplex other than the one they chose, or by a seriesof complexes.We have seenthat polymeric complexes may not be present at equilibrium. They are probably present in 1178 GEONGE A. PANKS

TABLE 5

Conplex Tdp. *B loe oc -qn Ar (oH)3'-q Medlm Inve6tlgatot Source (Note l)

25 0.12Ba(No3) -8.06 Taucherre (1948) Stllen & l,IarEell (1964) 2 25 0.60nBa(No3) -s.24 Iaucherle (L948) 2 25 +0 (entMa (1955)

25 +0 -6.27 Kubota (1956)

25 bNaC104 -7.07 + 0,06 Aveston (196s) Aveston (1965)

A15 (ofl)i; 40 2ilac104 -47 .00 Brosset (1954) si11en & Matteu (1964)

lr-rosrll 50 3dac104 -48.8 Biedemann (1962)

A113(0H);l 50 3dac104 -97.6 Biedemann (1962)

A1r3(oH)ii 25 lNac104 -104.5 + 0.06 Aveston (1965) Aveston (1965)

Nole 1: *B : nArk + quro + nH+ qn A1n(oH)3n-q supersaturatedsolutions, however, and provisionalstability constants have beenderived. These are collectedin Table 5. For illustrative purposesonly I have selected: log *9r,, : -Z .7 log *prt,r : -48.8 log *0rr,r, : -104.5 Evidencefor polymericanionic complexes has beenreported (Plumb and Swaine,1964), but not coryoboratedin more recentwork (Yoshio et al., 1970). No data are readily available from which to estimate stabilities. Sor,usrr,mv-pH Cunvns At any pH, the solubility of an aluminum oxide or hydroxide,S, is definedby the equation s: (1) f [Al(oH)"'-']+? ]nu[Al-(oH)"3--"] Bracketedquantities are concentrations.The activities of the various complexesmay be derived from the activity of Al3*,the appropriate cumulative complexstability constants,S, and Kgo. Thus, for mono- nuclear complexes,and a generalizedsolid phase, + (3- ??)H+: Al(orr)"s-"* (3 * (2) *x"o".rno i- ")y,o SOLUBILITIES OF ALAMINUM HYDROXIDES r179

*Kso:S#F#i *K.o:ffi (3)

AI'* + nIJ2o : AI(OH)"'" I nIJ* (4) _ {Al(oH)"'-"}{H*1" *QPn - (D.,l {Af.} *Kro : *Fn*Kro (6) Quantitiesin bracesare activities. For polymericcomplexes ; -} {Af '11*r, so- : -ffi;ira=;ili-{Al.(oH)"t'-"} : *A*r. so: (7) 1H- l'- *Fn-: {Al-(oHLj--"}{H.}" (8) {Al'*}- *Ksn- : *Bo^*Kso^ (9) Combination of equations (1), (6), and (9) yields a relationship among S, uKro and the u,B'sif activities and concentrationsare assumedto be identical: *g**K.o[H*](3-D) s : I + ffi*9,**K"o^[rf+]taz-d (10) ] ? The influenceof polymericcomplexes on the shapeof solubility curves can be seenif *Kso is brought outsidethe sums,insofar as possible, t - *r..[P *8,[H*]"-"',* (11) + +;**Fo^*Kro@-1)[H+]3u-al The solubilitiesof many oxidesand hydroxidesare high in solutionsof extremepH and minimum at someintermediate pH. The [H-] corte- spondingto the minimum may be found by differentiatingequation (11)to obtain(12).

ds *K*tP (3 - n)*B^lFJ*f<2-") d[H"] + - q)*Po^*K*ot--1)[H*1(3m-q-r)](12) lm(zm At the solubility minimum the derivativeis equalto zeroand equation (12) may be ,solvedfor [H*]-6 or pHMS, the pH correspondingto minimum solubility. Equations (11) and (12) provide tests for the presenceor absence of polymeric speciesin concentrationssufficient to affect solubility. The relative contributions of individual polymeric complexesto S L180 GEORGEA. PARKS

xKge, dependson see equation (11), hencethe shape of the log,gpH *Kse curve depends on or upon the solubility itself. The relative con- tributions of individual monomeric complexes do not depend oo *Ks6, hence the shape of the log *9-pH curve is independent of *Ksa or solubility if polymers are absent. This second observation means that all solubility curves should coincide if normalized with respect to concentration. Should polymers be the predominant dissolved species at any pH, the slope of the log S-pH curve, 3m - e, will exceed 3.0. This is il- lustrated in Figure 1. The pHMS should be the same for all solids if polymers are absent since, in equation 12, Kso is absent from terms corresponding to monomeric species.The pHMS should be different for each solid if polymers are present. Raupach (1963) has published solubilities of several aluminum oxides over a wide pH range. All of these data are plotted in Figure 2 af.ter normalization at pH 4.5 Lo 5 for all solids. Ignoring the calcu- lated curve in the figure, and within the scatter inherent in each set, most of these data can be said to fall on a single curve for 6 ( pH < 8, to include no portions with slope greater than 3, and to have a single, common minimum. Within the accuracy of the experimental data, polymeric complexesmay be consideredabsent. Accuracy of C,alatlated Solubikty-pH Curues A solubility-pH curve calculated with the free energiesin Tables 3 and 4, assuming the same ionic strength used by Raupach (1g63), is

J

pH Frc. 1. Change in slope of solubility-pll curves caused by the polymeric com- plex AI"(OH)#*. (A. polymer absent; B. polymer present. Curves drawn for a microcrystalline A1(OH)" with aG", - -224.84 kcallmole). SOLUBILITIES OF ALA MINU M HY DROXIDES 1181

(D 0 () -l at

L o '5 -1 oL i .9 -1 o L c 6-4 c o o = .sf E 3 . qeot o E-o o BAUXITE !t (l) a GIBBSITE -l o + DIASPORE an o .9 BOEHMITEPPT E ctt -8 o J 4567891o pH

Fra. 2. Experimental and calculated variation of the solubilities of aluminum hydroxides and oxide hydroxides with pH. (Experimental data at 20' in 0O1 m KrSO from Raupach, 1963.The solid curve was calculated from the selected 25o free energy data corrected to 0.03ionic strength.) compared with his data for all minerals in Figure 2. The data and calculated curye are normalized at pH 4.5. In the vicinity of minimum solubility, the total concentration of- dissolved aluminum is a few parts per million. Accidental contamination of the analyzed solution by colloidal solidsmust result in a high analysis;the incrementwill be particularly damagingnear the minimum solubility. If all observed data were high with respectto the calculatedcurve this might explain the discrepancy.If observeddata were low with respectto the calcu- lated curve, the AGol chosenfor Al(OH)g(aq) would be suspect.As it is the data support neither possibility but perhaps indicate a large probableerror in the free energyof formation of Al(OH)g(aq). The experimental solubility is high with respect to the calculated 1182 GEORGEA. PARKS curve on the basic branch in all cases.There are two possibleex- planationsof the discrepancybetween calculated and observedsolu- bilities when Al(OH)e- predominatesin solution. The free energy of formation of Al(OH)+- upon which the calculationis based,-311.0 kca/mole, may be wrong; perhapsthe true value is nearerthe more negative end of the wide range of estimatesavailable. If the free enersr is changedin this direction, however,the discrepanciesbe- tween estimatesof the free energyof formation of gibbsitebased on Kg6 and those basedon Kga and betweenestimates based on solu- bility data in generaland thoseof calorimetricorigin are increased. Study of the experimentaldetails reported by Raupach (1963) revealsan alternateexplanation of the discrepancybetween calculated and observedsolubility. Of the four sampleshe studied,gibbsite and diasporealone are pure with respectto other phases.For gibbsite,he recordedthe changesin pH and dissolvedaluminum concentration which occurredas the system evolvedtoward equilibrium. The data are plotted separatelyin Figure 3. Somepoints selectedas representa- tive of equilibrium representsolutions which at one time in their his- tory containeda higher concentrationof dissolvedaluminum than was found at apparent equilibrium. Aluminum must have precipitated from thesesolutions. We have alreadyseen that the solidsprecipitated by hydrolysis are different in acidic than in basic media.If this dif- ferencepersists in spite of possiblenucleation by the originally in- tendedsolid and if the precipitatedmaterial reachesa meta-equilib- rium state more rapidly than the original solid, the compositionof the solution may be determinedby the precipitatedmaterial rather than by the intendedsolid. On the assumptionthat somethingof this sort happens,we should expectto find that a systemin which the concentrationof dissolved aluminum increasesthroughout the experimentwill end up at an aluminumconcentration characteristic of the most solublesolid present among relatively stable solids,or at a lower concentrationif insuf- ficient time has been allowed. In a system which evolves toward equilibrium in such a way that the concentration of dissolved alu- minum decreasesat any stage the solubility observedat apparent equilibrium will probably be that characteristicof a microcrystalline gibbsit€if the solutionis acidic or of bayerite if the solutionis basic. These argumentsassume that true equilibrium among solids is not attained,but that precipitatedsolids do reacha meta-equilibriumstate with respectto the solution phasein a matter of a few days or per- haps weeks.Can we expect a precipitatedhydrous oxide to reach a meta-stable equilibrium with respect to a solution phase? Ilem and SOLABILITIES OF ALUMINU M HYDROXIDES ll83

-l

.?

:J o L C _A (DT BAYERITE (J GIBBSITE o BOEHMITE o cw l .= E-A f, E E o o a a ! -o or o J 4 7 9 ro pH

Frc. 3. Detailed comparison of experimental and calculated solubilities of gibbsite (data after Raupach,1963). Fine lines trace the evolution of solution composition toward the final state. Heavy lines are solubility curves calculated from the selected 25" free energy data and are corrected to an ionic strength of 0.03.Raupach's data were obtained zt2O"C in 0.01.m KoSO+.

Roberson (1967) report the data on apparent solubilities of young precipitatesplotted in Figure 4. The fact that the solubility of their oneday old bayeritechanges linearly with pH in the basicrange lends confidenceto the suppositionthat accidentalcontamination by solid hydrolysis products may lead to behavior expectedof true equilibrium systems. Look again at Figure 3. In the range of pH ( 7, most apparent' equilibriumpoints have evolvedupward only. In this range,calculated and observeddata agreewell for gibbsite.The concentrationof dis- solved aluminum decreaseswith time on the basic branch of the solubility curve equilibrating closer to the calculated curve for bay- 1184 GEONGEA. PARKS

o o E

c o o c q, o E 8-+ oo o o + E + 5 od c E & a oo 5-5 a o t E & + .E' oa c) +*+ . ++ o-A f o 1C microcrystolline boyerite ct o gibbsile cn o J tl pH

Frc. 4. Experimental pE dependence of ttre solubility of precipitated eibbsiie and bayerite (from Ifem and Roberson, 1967). erite. Unfortunately, the data are inconclusive.They will permit the interpretation proposed but agreement is not sufficiently consistent to be convincing.Direct observationof the bayerite proposedwould obviouslyhelp a great deal,but has not beenreported.

Concr,usroNs Recommendedfree energiesof formation of the solids are given in Table 3 and of the hydroxo-complexesin Table 4. Judging from Kennedy's (1959) review of phaseequilibrium data and evidencein natural occurrences,gibbsite is more stable than bayerite,boehmite has only a metastableexistence, and corundumis unstable with respectto hydrates in the presenceof water al' 25"C and one bar pressure.The recommendedfree energiesof formation, with the exceptionof that for boehmite,are consistentwith thesere- quirements.The free energiesof formation show that diaspore is the most stable hydrate under these conditions.The metastability of boehmite with respect to all other hydrates is not confirmed by the free energy selectedand for this reasonit must still be considered 80 LU BI LI TIES OF ALII M I NT]M H YD ROXI D E8 1185 doubtful.It hasnot beenpossible to reconcilethe selectedfree energies in detail with the one independentset of solubility data involving carefully characterizedsolids, Raupach's, without unverified reinter- pretation.The interpretativemodel proposed does not call for startling assumptions,however. The entire selectionprocess underscores the pessimisticview that, as usual, more work is needed.It ir,lsooffers repeatedreminders of the absolutenecessity of careful characterizationof the solid phasesafter equilibrationby techniquescapable of detectingtrace phaseimpurities and measuringparticle size. In any system in which metastableor microcrystallinesolids are possible,they must be expecteduntil proven absent.We can probably predict no more than a lower limit of solu- bility. Use of solubility in phaseidentification appears unwise unless a variety of evidenceis providedin proof that the solid is well crystal- lized in large particlesand is at equilibrium with the solution.

Acrrrrowr,spcMor.rts

Many of my students have endured repeated discussions of this topic. They deserve thanks for their patience and ideas. Tevfik Utine, John Baca, and Robert Railey helped with caleulations and computer programming. I am in- debted to J. D. Hem of the U.s. Geologicalsurvey; ProfessorsK. B. Krauskopf,

Division of Earth Sciences.Grant GA 1451.

RpnnnrNcns

Anenrsory,A. W. (1960) Physi,cal Chemistra o! Surfaces.Interscience Publishers. New York. Avnsrow, JonN (1965) Hydrolysis of the aluminum ion: ultracentrifugation and acidity measurements. Clt'ern, Soc. J. lLondon'J, 1965, 443U443- Benenv, RoNer,o,ext K. K. Ksr,r,nv (1961) Heats and free energies of formation Inuest' of gibbsite, kaolinite, halloysite, and {ickite. US. Bur. Mi'nes Rep' 5825. BenNnrsnr,, R. L, eur C. L Rrcr (1965) Gibbsite, bayerite, and norstrandite formation as affected by anions, pH, and mineral surfaces' Proc, Soi'I' Sci" Soc.Amer.29,53L-5M. Bmnrnltewx, G., ewo P. ScRrNtr,rn (1967) On the solubility product of precipi- tated iron (III) hydroxide. Acta. Chem. Scand,.1r,73L-740. Cer,vnr, E. (f962) Emploi du microcalorimetre differentiel et a compensation par effet peltier en analyse thermique difierentielle quantit'ative. J. Chim. Ph'ys' 59,319-323. 1186 GEORGEA. PARKS

Doznr,rc, E[., I[. BnrrvsKr, AND R. II. E. Wor,n (1g21) precipitation and hy- drolysis of metallic ions--IV. Studies on the solubility of aluminum hydrox- ide in aqueoussolution. J. Inorg. Nucl, Chem.33, Zgl-98. Exnegr, C., R. Goror.r, Y. Tnerunouzn,T. H. Tnn, eNn M. pnnrrnn (lgb5) Decomposition of ALO" Hydrates by differential enthalpy analysis. C.rB. Acad. Sci. (Paris).24o,8624. [in French; Chem. Abstr. So,8810d (1956)]. FnrtrNucrrr, W., exo P. Scnrxor,un (I%B) Sotubititg Constants o! Metat Ox,td,es, Metal Hgdroxides, and Metal Hgd,roxide salts. Butterworths scientific press. London. For,nvenr-Vocr,,M., eNo B. Kr,rsuRszrv (lgb8) An attempt to determine the heats of dissociationof minerals.Acta. Geol. Acad. Sci. Hungarg.5, 192-196 lin French ; Chem. Abstr. 52, l1}l}g (l95g) ] . Fnrcr

Knr,r,nr, K. K., ewn E. G. KrNo (1961) Contributions to the data on theoretical metallurgy XIY. Entropies of the elements and inorganic compounds' U,S' Bur. Mi.nes BulI. sgz. KoNNnrv, G. C. (1959) Phase relations in the system ALOi, at high temperatures and pressures.Arner. Jour. Sci.2s7,563-573. 'W. KrNo, E. G., eNr W. Wnr,mn (1961) Low temperature heat capacities and entropies at 298.15"K of diaspore, kaolinite, dickite, and hallovsite. U.S' Bur' M ines.R ept, I naest. 5810, Kttrntcr, J. A, (1966) The free energy of formation of gibbsite and AI(OH); from solubility measurements. Proc. Soil Sci. Soc. Amer,30' 595-598. - (1969) Soil minerals in the ALO-SiO;-E"O svstem an{ theory of their formation. Clags Clag Mineral. t7, 157-167. Kocunnov, P' V., Yu. M. Gnnrrvrer*r'r,eNn P' V. Gnln, (1959) Heats of formation of the alloys of calcium and aluminum. Zhur. Neorg. Khim. 4, 1106, [in Russian; Chem. Abstr. 54,7492i (1960) l. LecRorx, S. (1949) Etude de quelques complexes et composes peu solubles des ions A18*,Gat*, Ins. Ann. Chi,m.4,5-83. Larrrvrnn, W. M. (1952) Oxid'ation Potentials. 2nd ed. Prentice-Eall, Englewood Cliffs, N.J. -, ero B. S. Gnnnwsnnr,nnn,(1928) The heat capacity and entropy of cesium alum from 18" to 300' C absolute. The entropy of aluminum ion. The po- Soc' tential of the aluminum electrode from thermal data. "I. Amer' Chem' so,2202-2213. Men, A. D. (1957) Eeats of formation of ALO,, MoOs, and MoOz. I. Phgs' Chem.67,1572-3. Mrcnr,r, J., ar.rp J. Srunn (1968) Ligand penetration rates into metal ion co- ordination spheres.Aluminum (III), gallium (III), and indium (III) sul- fates.J. Amer. Chem. Soc.90,69674972. Mrcuer,, M. (1957a) A calorimetric study of the thermal decomposition of the trihydrates of Al. C..R.Acail. Sci'.Paris.244,73-4 [in French; Chem. Abstr. s1,6310d(1957)1. - (1957b)A calorimetric study of ALo" monohvdrate. C.R. Acad'- Sci. Pari's. 24+,5954 [in French ; cltem. abstr. 5r, tl027b ( 1957)] . Nezennwro, V. A., eNn E' M' Novsreva (1969) Spectrophotometric determina- tion of the constants of mononuclear hydrolysis of aluminum ions. Russ. ./' Inorg. Chem. 14,1696-1699. Ora, Y. (1938) The fundamental reactions in analytical chemistry. I. Reactions of caustic soda with metallic ions. J. Chem. Soc. Japan. 59' 971-1013 [in Japanesel. Pr,urr.n, R. C. (1962) Oxide coated electrodes. I. Aluminum in asid solutions' J. Phgs. C hem. 66,86G70. exo J' W. SwerNn, Jn. (1964) Oxide-coatedelectrodes' II. Aluminum in alkaline solutions and the nature of the aluminate ion. J. Phas. Chem.68, 2057-2064. Pounn,rrx, M. (1966) Atlas ol Electrocheminal Equi,lbri,a In Aqueous Solutions. Pergamon Press,New York. Rawecn, M. (1963) Solubility of simple aluminium compounds expected in soils, I. Eydroxides and oxyhydroxtdes. Awtral. J. Soil Res. l, %4-35. R^nnsnrAw,A. L., aNo W. D. Knr,r,nn (1968) Aqueous solubility studies of high alumina and clay minerals. Amer. M'i,neral.53,929-942 1188 GEONGEA. PARKS

-t E. E. Prcrnrr, AND W. D. Knr,r,nn (1969) Aluminum ions in aqueous solutions.Amer. J . Sci,267,99-ll3. Rourn, R. A., ,rxn D. R. Waugauu (1968) Thermodynamic properties of minerals and related substancesat 298.15"K (25O'C) and one atmosphere (1.018bars) pressure and at high temperatures. US. GeoI. Suru. BuIl. tzsg. Rossrwr, F. D., D. D. Weouex, W. If. EveNs, S. Lnvrxu, eNr I. Jernp, (1952) Selected values of chemical thermodynamie properties. US. Nat. Bur. of Stand,.Circ. SOo. Rmn, W. A., G. Wrnrus, AND II. Bnnnwm (1g42) Beitrag zur Themocheimie des Aluminium s. T. Z . E leclctro chem. 48,26+-2.62 . V. Wor,r, er.ro O. Fnrrz (1g40) The heat of formation of aluminum oxide (corundum) and lanthanum oide. Z. Elecktrochem. 46,42-45 [in German; chem. Abstr.34,1905 (1940)1. Russer,r,, A. S., J. D. Eowenos, eNo C. D. Teyr,on (198b) Solubility and density of hydrated aluminas in NaOE solutions. Trans. Amer. Inst. Min. Met. . Ens.2o3,112&-1128. Scnrnnr,nn, P., E[. Ar,rnaus, F. Hornn, .lrvo W. Mrrnrn (1g65) Loslichkeitspro- dukte von Metalloxiden und Hydroxiden 10. Loslichkeitsprodukte von Zin- koxyd, Kupferhydroxid und Kupferoxid in Abhangigkeit von Teilchengrosse und molarer Oberflache. Ein Beitrag zur Thermodynamik von Grenzflachen fest-flussig.Helu. Chim. Act. 48,lzO4-lZlE. ScnNnmnn, A., arn G. Gamow (1954) The heat of formation of aluminum oxides.Z. Anorg. Chem.277,4l-48 lin German; Chem. Abistr.4916715a (1e55)I . Scnonrv,R., eNo C. E. RosunsoN (1970) Structures of aluminum hydroxide and geochemicalimplications. Am er. M ineral. Ss, 4g-77 . Scnorrnr,n, R. K., aNo A. W. Teyr,on (lg54) The hydrolysis of aluminium salt solutions. Chem Soc. llondonl J. rss4. 444H448. Scuwrnre, If. E., ervn G. Zrncr,nn (1g58) Thermochemical investigation of the dehvdration of gibbsite with the aid of dvnamic differential carorimetry. z. Anorg. Chem. 298,42-50 lin German; Chem. Abstr.53, 8292h (1959)]. Snmnr,r,,A., rNo W. F. LrNno (79ffi) Solubiliti,es ol Inorganic and, Metal Organic Compound,s.D. Van Norstrand, New York. snouarn, c. H., arn o. A. coor (1946) Low-temperature heat capacities and high temperature heat contents of ALO".H,O. J. Amer.,Chem. Soc. ag. 2t4o-2t42. Snr,nw, L. G., enn A. E. Menrnr,l (1964) Stabi,ti,tyConstants of Metal lon Com_ plexes.Chern. Soc.(London) Spec.pub.17. Sir.rrrn, Ross W. (1969) The State ol At (m) in Aqueous Solutiom and, Ad,sorp- tion of Hydrolysis Products on ALO". PhD thesis, Department of Mineral Engineering, Stanford University. S*vnun, P. E., ewn I[. Srr,rz (1g45) T'he heat of formation of ALO". J. Amer. Chetn. 9oc.62,683-5. Sur,r,rverv,J. H., ervo J. E. Srncr,pv (196g) Reactions of metal ions in dilute aqueous solution; hydrolysis of aluminum. J. Amer. Water Works: z4ssoc. 60, 1280-1287. Szmo, Z. G., L. J. Cse*rr, er.rnM. Kever (lgbb) Bestimmung der Loslichkeits- produkte von Metallhydroxydniederschlagen I. Uber die Reaktion des Aluminum-ions mit dem Hydroxyl-Ion. Z. Arwl. Chemie. 146, 4Ol-414 SOLUBILITIES OF ALUMINUM HYDROXIDES 1189

Tunr,wn, R. C. (1968) Conditions in solution during the formation of gibbsite in dilute Al salt solutions: I. Theoretical treatment of the formation of mono- and poll'truclear hydroxyaluminum ions, precipitation and crystallization curves representing the titration of AICL with a base. Soil Sci'. Lo6,29l-296. WecnAN, D. D., W. I[. Evans, V. B. Panron, I. Ilar,ow, S. M. Blrrnv, eNo R' II. Scrrurtu (1968) Selected values of chemical theimodynamic properties' U.S. Nat. Bur. Stand. Tech.Note 27F3. Yosnro, M., H. Werr, N. IsrrrsesHr (1970 Determination of the composition of aluminate ions in sodium hydroxide solution by ion exchange. J. Inarg, N ucl. C hem. 32, 1365-1373.

Manuscript receiued,,December 16, 1969; acceTttedlor publicati'on, March, 31, 1 0'to