Mineralogist
Awrican
Vol. 57, pp. 1163-1789 (1972)
/
FREE ENERGIESOF FORMATION AND AQUEOUS
SOLUBILITIESOF ALUMINUM HYDROXIDES AND
OXIDE HYDROXIDES AT 25"C
StanJord
GnoncnA. P.e,nrs,Departntantof ApptiedEarth Scienaes,
I
ornia
al'it
ord,
C
Uniuersity,Stanl
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
- 2 1 9 . 5+ 0 . 5
-218.7+0.2
- 2 7 5 . 3+ 0 . 2
- 2 7 4 . 6+ O . L
diaspore
boehmite
gibbsite
bayerite
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 interpretation is discussed.
Isrnopucrrow
There is convincing evidencein phase equilibrium investigations
that corundum is unsiable with respectto gibbsite in the presenceof
of water aL25" and one bar 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 calculatesolubilitiesof
the aluminum hydroxides,discoveryof this discrepancyrevealedthe
need for critical appraisalof available data. 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
Derivation of free energiesfrom solubility data remeasurements.
quired review of the free energiesof formation of Als-(aq) and
1163
1164
GEOBGE A. PARKS
Al(OH)n (aq). Followingselectionof the freeenergies
of formationof
the mono-hydroxoeomplexes
it is shorvnthat polymerichydroxo complexescan be ignoredat equilibrium and an attempt is made to 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,SelectedValuesof ChemicalThermodgnamicProperties(Rossiniet at., Lgb2) and Oridation Potentials
(Latimer, 7952). The Bureau of Standardsis updating Circular S00
and has releasedinterim tables, omitting references.Data for aluminum appearin TechnicalNote 220-8 (Wagmanet cll.,1g68),one of
the interim series.original referencescited for data attributed to
Wagmanet aI. in the following paragraphswereprovidedby Wagman
in personal communicationsto the author (D. D. Wagman, 1g69,
written communication)
. The u.s. Geologicalsurvey has arsorecently
publisheda tabulation of thermodynamicdata (Robie and Waldbaum,
1968).The many publieationsof Pourbaix and his co-workers,collected in lhe Atlas of Electro-chemicalEqui.Iibriain Aqueou,ssolutions (Powbaix, 196G)comprisestill anoiher exhaustivesource of
thermodynamicdata.
The original sourcesof free energiesof formation in thesetabulations have been examinedfor information useful in permitting selection arnongdifferingestimates.
Corund,um,
aAlzos
The free energyof formation of corundumreportedby 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
listed by Kelley and King (1901)and heatsof combustionof aluminum 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 capacity data attributed to Kelley and King (1961) and Furukawa
et al. (7956)and the heat of formationreportedby Mah (lgb7).
The differencebetween1g68and 1g52estimatesreflectsnew work.
It requires revision of free energiesof formation of ail other sub-
SOLT]BILITIES OF ALT]MINU M HYDROXIDES
1r65
stances for which corundum served as a referencematerial. This
in the paragraphsto follow.
adjustmenthas beenmadewherenecessary
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 changeassociatedwith 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 temperature at which diaspore and corundum coexist at equilibrium with
liquid water and an estimateof the entropy neededto correctto 25'C'
The estimatedprobableerror 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'
of the
(1963) is -218.15 kcal/mole. It is basedon measurements
enthalpy changeassociatedwith its dehydration reported 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,basingtheir 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 severalsourcesof uncertainty in the data for boehmite.
Most important is ambiguity in identificationof the solid usedin the
by Shomateand Cook. The purity of
heat capacity ureasurements
experimentsand the characterization
in
dehydration
used
boehmites
products
are
also
doubtful.
of dehydration
(1946)
a monohydrateof correctchemical
used
and
Cook
Shomate
reported
that
but
composition
"X-ray examinationshowed. . . the
1166
GEONGEA. PARKS
monohydrate[to have] a structuresimilar to bayerite (AITOB.BH2O)
differing from the latter principally in the intensitiesof rines.,,Neither
they nor Rossiniet al. (1g52)identifiedthe 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 polymorphs of
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).
The free energy of formation reported by Robie and 'Waldbaum
(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 freeenergyof formationof Al (OH) + .
The free energyof formation of AI(OH)+ was derivedfrom the solubility of boehmite (Fricke and Meyering, 1933) and a free energy
of formation of boehmite attributed to Latimer (1952). Latimer's
soutcewas Rossini et al. (1952),hencehis flgure is invalid. This, together 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,henceis doubtful.
Fnnp ENnncrESoF FonnrerroNpnolr Sor,uprr,rrvDere
Estimation of AGoyfor solids from solubility data requiresthat the
compositionof the solutionphasebe known in detail and that the free
energiesof formation of the dissolvedspeciesbe known. Al(III) solutions contain hydroxo-aluminum complexes.There is much controversy about which complexesare stable. Someauthors find that their
hydrolysis or solubility data are adequatelyrepresentedby mononuclear complexesof the group AI(O}J)*"- with ra in the range
0 1 n ( 4. SomeignoreAl(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 strengthsolutionscontaininga high concentrationof aluminum.
Hem and Roberson(1967) and Smith (1969) found evidenceof polymeric speciesin low ionic strengthsolutionscontainingno more than
13 ppm aluminum. Several authors decidedthat the polymers were
unstable intermediatesin 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 communication.)
If polymeric speciesare absent at equilibrium, the compositionof
the solution can be least ambiguouslydefinedin acid (pH ( 4) and
basic (pH > 8.5) media where Al3* and AI(OH)+ predominate.We
will seelater that ignoring polymericspeciesis 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)4and 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 collected 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 characterized 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 formation 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 formation 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
H2AIOB- separately, giving -204.7 kcal /mole and -255'2 kcal/mole
respectively. These correspond to -318.08 and - 3f1.89 kca/mole
for AI(OH)+. These estimates,too, are based on solubilities of hydroxides which are not well characterized.
nK*n, and
The equilibrium constants Ks6, Kru,
,,8aa're defined as
follows (Sillen and Martell, 1964):
: Al'* + 3OH-iKso: (AI'.)(OH-)'
Al(oH),(s)
(1)
AI(oH),(s)+ oH- : Al(oH),-t K s+:(Al(oH)'-)
(oH-)
(2)
Al(OH),(s)+ H,O : AI(OH),- * H*;*Kso : (AI(OH)'-)(H.)
(3)
l4l9l)="J')(oH-).
Al'* + 4oH-: Al(oH),; p^: +:!:
n so (Af
(4)
are thermodynamicactivities.
Quantitiesin parentheses
A free energy of 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 hydrolysis experimentsto permit'estimation of Ba but they did not correctto zero ionic 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 derive Fr requiresthat the identical solid be
present during determination of the two constants.If the solid is
proclucedby hydrolysis of Al'* and subsequentlydissolvedin more
basic solutionsto yield Al(OH)+ or vice versa,this conditionis perhaps met. If Ksg is determinedby hydrolysisof Al3*solutionst"oyield
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 hydroxidesprecipitatefrom 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 Wagman et 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 determined Kgo through hydrolysis experimentsyierding
crystalline gibbsite after equilibration times exceedingeleven days
while the experimentsyielding Ksa involved equilibrationtimes of one
day or less.rnasmuchas they themselvesshowedthat 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 experimentssincethe techniquemay result in local
high concentrationsof oH-, hence local premature precipitation of
solidswhich equilibrateextremelyslowly (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 describeprecautionstaken to insure
equilibrium but state that their method was similar to earlier work
(Garrett and Heiks, 1941 and 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
E@ and Roberso!
Xtttrtck
cafe,
-311.03
(1955)
Thonpsoo and Zaltcek
Szabo, Csaayl,
Lacrotx
(ca1/nole
(1957)
6il
(1948)
Ravat (1955)
-310.61
-3r2,06
(1949)
oka (1938)
-372.46
SOLUBILITIESOF ALUMINUM HYDBOXIDES
1171
solubility investigations of Kittrick and Hem and Roberson demonstrate that equilibration requiresmonths to years.
With these arguments in mind, it is not difficult to understandthe
wide variation in the free energiessummarizedin Table 1. The investigationleastsubjectto criticism is 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 significancebeyond -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 smallerexperimentalprobableerror.
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,investigathe solutionionic
tions in which the solid phaseis well characterized,
strength very low or correctedLo zero, correctionsfor hydrolysis are
small, and in which specificefforbwas 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 becausetheir
solids were not pure, singlephasematerials.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 persuasiveevidenceof the validity of the
estimate. However, gibbsite must be more stable than corundum in
lt72
GEORGEA. PARKS
soUd
Solid
clbbslteb
Partlcle
0.05
Slze
solublltty
Dlcron
Glbbelteb
clbbstted
-d
e,
A1(0s)3
'solld
PleclPltated
lonlc
Ac;,
E(oH);
fraB
(lrDl,
and feecn
Klrtrlck
(1955)
(lrtrtck
(1966)
log*(S4 - -14.82
-275.34 + .OL
- 2 1 3 . 3 4+ O . 4
-275.L + O.l
-274.6 + O.7
Iog*KS4--13,96+0.2
1og{s4 - -15,27
IoC KSo= -31.2
-213,4 + O.3
- 2 1 8 . 7 ,+ 0 . 1
-27r.34
He
solutlon
Equiltbratlou
Kcal/uo1e
slrh
floD
co2 at
both
ssb-
95o, sashd
for
(1957)
Russeu
et al,
(1955)
Rueseu
et dl.
(1955)
E Roberson
(1957)
Bu6se11 et ar,
(1955)
Feltknecht
4N Ec1 and Hzo,
ln
and superssturatton
E@ & bberoor
drled
ar tlooc.
30 day6 or Eo!e.
(1963)
e Schldre!
Idertlfled
Xso correcEd
by
to
zero
both
sub-
stleqth.
b (herclal
ad
fr@
Dethods.
PetlograPhlc
Ploduct
IoC KSo= -33.5
1o8 KSo - -34.06 + .09
1oc Kso = -33.98 1 .0I
1or Kso - -32.65 + 0,3
Iog*KS4 - -15.27
gtbbsltes
suPersatu?at1on
" sotra
tu E Product
clyltal
d *fr4
*"
Xavetlte
able
tlod
by x-ray
le6st
hydrolysle
Equlllbratlon
detemlnd
as a funcElol
errols
a€elsnd
or hydtolysl€
ttue
of
st
bolphology.
was Prducd
e product
ldentlfled
for
dlfflactlo!
267 da]/s,
floE
d11ute
tlDe
of
lu
enersles
dilute
oue day or 1ess.
baslc
pelchlolate
etwm
to
t@pe!.ture
by CO2 acldtftcatlon
to flee
r€flect
of
ro!
o.o5 Dtcron
equilibrated
solurloE6
135 days.
ar 25o,
KSo correcred
and Naof, concentlatlon
an at@iute
oily
perchlolate
*Ks4 collecred
6nd DTA.
50 Dlcronuterial
solur{on
soluttoDs
ar
ro zero
25oc.
by x-!ay
ionlc
rhen colrecred
error
rdentlfld
ln
equlublared
eupelsaruratton
ldeDtlfi€d
and idenrifled
the Dtntuu@ plobable
ro zero lodic
@cerlat
floE
fr@
only,
dtfflacrlon
and
srrength.
to
zero
by X-ray
Ac:([(oH);)
by x-ray
lonic
stleryth.
dtfflactlon.
hetrce ale
dlffractlon.
The probeintu@s.
Equtltbla-
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 investigations 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
ALT:;-
AG:
2 Mal
op
2 Mal
3 pd"
where
M :
p :
f :
formula weight of solid
density of solid
mean surface free energy
I - - ,1 \
-
d2
if
dr/
d, ({ d,
SOLT]BILITIES OF ALU MINU M HY DROXIDES
d :
d :
tt73
characteristic particle dimension, 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 differencesin particle size and crystallinity are responsible for the differences 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 communication, 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 equilibrationtimesup to two months,
thus the probability that grain growth would occur is higher than in
Kittrick's investigations.Unfortunately no parbiclesizemeasurements
were reported.
The work of Reesmanand Keller (1968)and Reesman,Pickett, and
Keller (1969) lends credenceto the selectedAGol for gibbsite.They
originally reporteda AG"ybasedultimately on acceptance
of the AGol
for boehmitelisted by Rossiniet aI. (1952).Using their data and the
selected
AGol for Al(OH+ (Table5), to avoidthe discredited
data for
boehmite,yields -275.9 kcal/mole for AGoTof gibbsite,in goodagreement 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 phase resulting in the less negativeestimate was probably
microcrystalline,having beenproducedby low ternperaturehydrolysis.
On this basis,the free energy of formation of bayerite is -274.6 !
0.1 kca/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 formation of Al(OH)a (Table 4) 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 rejectedcalorimetricestimatesof the free energyof formation 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,boehmiteis 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)
and usingthe selected
freeenergyof 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 monohydroxocomplexesin Table 4.
Sor,unrr,rrr-pH Cunvns ANDTHE Accunecy on Snr,ncrnoFnnn
Exoncrns on Fonlre.rrom
Somesolubility data have not beenusedin selectionof free energies
of formation of the solids. These data are largely in the pH range
in which hydroxoaluminumcomplexesare important. Comparisonwith
solubility data calculatedfrom selectedfree energiesof formation of
the solidsrequiresselectionof free energiesof formation of both mononuclearand polymerichydroxoaluminumcomplexesand demonstration
that polymeric speciesare not significant at equilibrium.
Th,e Free Energies of Fornuafinn of Hgdroroaluminum Compleres
All estimatesof the free energy of formation of the hydroxo complexesare derived from stability constants.In selectingthe data fot'
this purpose,experimentsinvolving solids were rejected unless the
data availablein a singlepaper permitted derivation of stability constants 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 calculation of a LG"7 for Al(OH)z* independentof the identity of the solid
phase.
M,onorrucle
ar Compleres
Estimatesof log *K1, corresponding
to the reaction,
Al"*+HrO:AIOH'*+H*
range from -4.49 to -5.9 (Sillen and Martell,1964; Holmeset aI.,
1968; Sullivan and Singley, 1968; and Nazarenko and Nevskaya,
GEOEGE A. PARKS
1176
TABLE 3
of A1ul.n6
a
Ac: (25oc) kcaumole
Species
a
d A12O3
, corundum
- 3 7 8 . 2+ 0 . 3
o A1O0II
, aliaspore
- 2 1 9 . 5+ 0 . 5
"y A10OH
, boetmire
- 2 1 8 . 7+ 0 . 2
o AI(OH)3
, glbbsite
- 2 7 5 , 3+ O . 2
Y A1(oH)3
, bayerlte
- 2 7 4 . 6+ O . L
The
than
The
uncertainty
one
uncertainty
thail
one
nate
of
Ehan
the
Ac!
in
Ac!
in
kllocalorie
Ac!
t
in
selected
of ltononucler
tot
to
for
case
value
the
the
one
about
is
(see
glbbsite
ia
undertaitrty
boehmiEe
since
each
and
bayerite
owing
kilocalorie
and
diasPore
available
one
nay
be
the
Acf,
nay
be
a
of
estinegative
less
Text).
Bydroxoal@lnu
(III)
c@p1ses
.
^a
r o c- n o
at
25oc
of Fo@tlon
*
298
kcal/oo1e
t+
A10It-'
+8.99+ .04
A1(ou)-
+19.3+ 0.1
- 2 L 7. 5
A1(0u)a(aq)
+ 2 5 . 8+ 0 . 1
-zo).J
A1(OU);
+ 3 2 , 7+ O , L
-311.0 + 0.1
The reactloo
correEpondl.Dg
to
Irs+ron--Alloull+
e13+.
larger
independent
kilocalorie
Free Elergy
Coopld
larger
Fn ls
SOLUBILITIES OF ALUMINUM H''DROXIDES
tt77
1969).Among the estimatesat 25'C and zero ionic strength,the most
reliable,by thesecriteria: attainment of equilibrium,absenceof complexinganions,awarenessof the possibility of polymer formation,etc.,
are thoseby Frink and Peech(196.3),
Raupach(1963),and Schofield
and Taylor (1954).The averageof log *K1 &mongtheseestimatesis
-5.01 and the rangeis only * 0.04.
The formation constantof the dihydroxocomplex,Bz,corresponds
to
the reacbion,
At'*+2OH-:AI(OH),*
Severalinvestigatorsreport 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 investigationsinvolved solids and relatively short equilibration times. Agreementbetween the work of Gayer et al. involving approach to equilibrium
from subsaturationand that of Dezelicet al. which involved approach
to equilibrium from supersaturationis perhapssufficientgroundsfor
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 Navarenko 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 mononuclearcomplexesare 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.
Potymeric Com,pleres:
A wide variety of hydroxoaluminumcomplexescontainingmorethan
one aluminum atom have beenproposed.Aveston (1965)reviewedthe
subjectin 1965.In most investigationsyielding equilibrium constants,
the authors have pointed out that their results could probably be explained equally well by somecomplexother 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
Ar (oH)3'-q
Tdp.
oc
*B
loe- q n
(Note l)
Medlm
Source
Inve6tlgatot
25
0.12Ba(No3)
2
-8.06
Taucherre
(1948)
25
0.60nBa(No3)
2
-s.24
Iaucherle
(L948)
25
+0
25
+0
(entMa
-6.27
Kubota
Stllen
& l,IarEell
(1955)
(1956)
25
bNaC104
-7.07 + 0,06
Aveston
(196s)
Aveston (1965)
A15 (ofl)i;
40
2ilac104
-47.00
Brosset
(1954)
si11en & Matteu
lr-rosrll
50
3dac104
-48.8
Biedemann
A113(0H);l
50
3dac104
-97.6
Biedemann
A1r3(oH)ii
25
lNac104
Nole 1: *B
qn
:
nArk
-104.5 + 0.06
+ quro
Aveston
(1964)
(1964)
(1962)
(1962)
(1965)
Aveston (1965)
A1n(oH)3n-q + nH+
supersaturatedsolutions,however,and provisionalstability constants
have beenderived.Theseare collectedin Table 5.
For illustrative purposesonly I have selected:
log *9r,, : -Z .7
log *prt,r : -48.8
log *0rr,r, : -104.5
Evidencefor polymericanioniccomplexes
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:
f [Al(oH)"'-']+? ]nu[Al-(oH)"3--"]
(1)
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 mononuclear complexes,and a generalizedsolid phase,
: Al(orr)"s-"
(3 - ??)H+
* (3 * i*x"o".rno +
")y,o
(2)
SOLUBILITIES OF ALAMINUM HYDROXIDES
r179
*Kso:S#F#i *K.o:ffi
(3)
AI'* + nIJ2o : AI(OH)"'" I
(4)
nIJ*
_ {Al(oH)"'-"}{H*1"
*Q
Pn -
(D.,l
{Af.}
*Kro :
(6)
*Fn*Kro
Quantitiesin bracesare activities.
For polymeric complexes
;
{Al.(oH)"t'-"} :
so- : -ffi;ira=;ili-
*'11
r,
**A
r.
*Fn-: {Al-(oHLj--"}{H.}"
{Al'*}*Ksn- : *Bo^*Kso^
-}
{Af
so:
1H- l'-
(7)
(8)
(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)
+
ffi*9,**K"o^[rf+]taz-d (10)
] ?
The influenceof polymericcomplexeson the shapeof solubility curves
can be seenif *Kso is brought outsidethe sums,insofar as possible,
s :
I
(11)
t - *r..[P *8,[H*]"-"',
* +
+;**Fo^*Kro@-1)[H+]3u-al
The solubilitiesof many oxidesand hydroxidesare high in solutionsof
extremepH and minimum at someintermediatepH. The [H-] cortespondingto the minimum may be found by differentiatingequation
(11)to obtain(12).
ds
d[H"]
*K*tP (3 - n)*B^lFJ*f<2-")
- 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 concentrationssufficientto affect solubility.
The relative contributions of individual polymeric complexesto S
+
L180
GEORGEA. PARKS
dependson xKge, see equation (11), hence the shape of the log,gpH
curve depends on *Kse or upon the solubility itself. The relative contributions 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 illustrated 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 calculated 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 energies in 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 complex 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
(D
0
()
at
1181
-l
L
o
'5
-1
L
o
i
.9
o
L
-1
c
6-4
c
o
o
=
f
.s
E
.
3
E-o
a
(l)
.9
o
o BAUXITE
!t
o
an
qeot
-l
GIBBSITE
DIASPORE
o B O E H M I T EP P T
+
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 normalizedat 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 calculated 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 possibleexplanationsof the discrepancybetweencalculatedand observedsolubilities 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 discrepanciesbetween estimatesof the free energyof formation of gibbsitebasedon
Kg6 and those based on Kga and betweenestimatesbased on solubility data in generaland thoseof calorimetricorigin are increased.
Study of the experimentaldetails reported by Raupach (1963)
revealsan alternateexplanationof the discrepancybetweencalculated
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 representative of equilibrium representsolutionswhich at one time in their history containeda higher concentrationof dissolvedaluminumthan was
found at apparent equilibrium. Aluminum must have precipitated
from thesesolutions.We have already seenthat the solidsprecipitated
by hydrolysis are different in acidic than in basic media. If this differencepersistsin spite of possiblenucleation by the originally intendedsolid and if the precipitatedmaterial reachesa meta-equilibrium state more rapidly than the original solid, the compositionof
the solution may be determinedby the precipitated material 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
aluminumconcentrationcharacteristicof the most solublesolid present
among relatively stable solids,or at a lower concentrationif insufficient time has been allowed. In a system which evolves toward
equilibrium in such a way that the concentration of dissolved aluminum decreasesat any stage the solubility observedat apparent
equilibrium will probably be that characteristicof a microcrystalline
gibbsit€if the solution is acidic or of bayerite if the solutionis basic.
These argumentsassumethat true equilibrium among solids is not
attained,but that precipitatedsolidsdo reacha meta-equilibriumstate
with respectto the solution phasein a matter of a few days or perhaps weeks.Can we expect a precipitatedhydrous oxide to reach a
meta-stable equilibrium with respect to a solution phase? Ilem and
ll83
SOLABILITIES OF ALUMINU M HY DROXIDES
-l
.?
:J
o
L
BAYERITE
C
_A
(DT
(J
GIBBSITE
BOEHMITE
o
o
cw
l
.=
E-A
f,
E
E
o
o
a
a
!
or
-o
o
J
4
7
pH
9
ro
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'sdata 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
one day old bayeritechangeslinearly with pH in the basicrangelends
confidenceto the suppositionthat accidentalcontaminationby 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 dissolved aluminum decreaseswith time on the basic branch of the
solubility curve equilibrating closer to the calculated curve for bay-
GEONGEA. PARKS
1184
o
o
E
c
o
o
c
q,
o
E
8-+
oo
o
E
5
c
E
5-5
E
.E'
c)
o-A
o
1C
ct
o
a
a
oa
&
o
+
+
oo
o
&
f
m i c r o c r y s ltloi n e
gibbsile
od
t
+
+*+
. ++
boyerite
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
in Table 4.
Table 3 and of the hydroxo-complexes
Judging from Kennedy's (1959) review of phase equilibrium data
and evidencein natural occurrences,gibbsite is more stable than
bayerite,boehmitehas 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 theserequirements.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 has not beenpossibleto reconcilethe selectedfree energies
in detail with the one independentset of solubility data involving
carefully characterizedsolids,Raupach's,without unverified reinterpretation.The interpretativemodelproposeddoesnot call for startling
assumptions,
however.
The entire selectionprocessunderscoresthe pessimisticview that,
as usual, more work is needed.It ir,lsooffers repeatedremindersof the
absolutenecessityof careful characterizationof the solid phasesafter
equilibrationby techniquescapableof detectingtrace phaseimpurities
and measuringparticle size. In any system in which metastableor
microcrystallinesolidsare possible,they must be expecteduntil proven
absent.We can probably predict no more than a lower limit of solubility. Use of solubility in phaseidentification appearsunwiseunless
a variety of evidenceis providedin proof that the solid is well crystallized in large particles and 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 indebted 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, 443U443Benenv, RoNer,o,ext K. K. Ksr,r,nv (1961) Heats and free energies of formation
of gibbsite, kaolinite, halloysite, and {ickite. US. Bur. Mi'nes Rep' Inuest'
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 precipitated 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 hydrolysis of metallic ions--IV. Studies on the solubility of aluminum hydroxide 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<n, v. R., em P. Jucarrrs (1980) untersuchen iiber die Gleichgewichte in
den Systemen ALO-NapO-E O und AlrO-KrO-HrO. Z. Anorg. AIIgem. Chem.
19r, l2g-149.
ewo K. Mnynnrwc (1933) Zur alterung junger Aluminiumhydroxydgele.
Z . Anorg. Allgem. Chem. 214,269-224.
Fnrcrn, R., aru E[. Snvnnrx (lg3z) Uber die Zersetzungsdrucke kristallisierter
hydroxide, insbesondere von Aluminium und Beryllium. Z. Anorg. Chem.
205,287-308.
Fmwr, C. R., ero M. Poncrr (1962) The solubility of gibbsite in aqueous solutions and soil extracts. Soil Sci. Soc.Amer. Proc.26, B4A+42.
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Manuscript receiued,,December 16, 1969; acceTttedlor publicati'on, March, 31,
1 0'to