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Kinetics and mechanism of dissolution of bayerite (γ-Al(OH)3) in HNO3-HF solutions at 298.2°K
Kinetics and Mechanism of Dissolution of Bayerite ('y-AI(OH)3) in HNO3-HF Solutions at 298.2°K K U R T PULFER,* P A U L W. SCHINDLER,* J O H N C. WESTALL,~" AND R O L F GRAUER~t *Department of lnorganic Chemistry, University of Bern, Bern, Switzerland; tDepartment of Chemistry, Oregon State University, Corvallis, Oregon, 97331; and ~Swiss Federal Institute of Reactor Research, Wiirenlingen, Switzerland Received July 19, 1983; accepted April 23, 1984 The rate of dissolution of bayerite ('r-Al(OHh) in H N O a - H F solutions of the constant ionic strength 1 M at 298.2°K is given by
R = S(k~[H+] + (k2CoK][n+]2[F-]3e+)(1+ (Ka])-J[H+]e_ + Ka~[n+]-'e+ + K][F-]e+ + KI[H+][F-] + K~[H+][F-]2e+)-') where kl = 1.5 (+0.3) × l0 -7 dm 3 sec-l m-E; k2 = l . l l (+0.1) × l0 II kg dm 12 m -2 sec -l mole-4; S = surface area (m2); Co = total concentration of reactive surface groups (=2.66 × 10-2 mole kg-l).
Ka], Kay, K], K~, and K~ as defined are equilibrium constants related to the adsorption of H+ and F- from the solution to the bayerite surface. Their numerical values were obtained from adsorption studies. The e+ = exp(F~b/RT) and e_ = exp(-F~/RT) account for the acting surface potential ~b which was calculated from the surface charge assuming a Helmholtz-type double layer. The results are discussed in terms of the stoichiometry of the precursor of the activated complex and possible reaction mechanisms. It is concluded that the present knowledge on the mechanisms of dissolution reaction of oxides and hydroxides is limited by the present ignorance of the surface structure and the structure of the electrical double layer. the mechanism of the reaction has so far not been provided. The present paper reports on a study of both the kinetics of dissolution of bayerite (3'-AI(OH)3) in H N O 3 - H F solutions and the adsorption of hydrogen ions and fluoride ions at the bayerite-solution interfaces. The combined results of these experimental studies lead to a mutually consistent model for both the surface complexation of bayerite in the presence of H + and F - and the mechanism of its dissolution in the above mentioned solvent.
INTRODUCTION
The rate of dissolution of metal oxides and hydroxides in noncomplexing acids (HC104, HNO3) is greatly enhanced by the addition of ligands such as fluoride (1-3), chloride (4-7), bromide (7), sulfate (4), thioglycolate (8), EDTA, and related aminocarboxylic acids (9). These effects of added ligands have generally been attributed to formation of surface complexes followed by release of the surface species (10). This assumption implies that the rate law of the dissolution reaction is related to the pertinent adsorption/desorption equilibria of both hydrogen ions and added ligands, i.e., to the stability constants of the pertinent surface complexes. This relationship that is an indispensable prerequisite for a deeper insight into
EXPERIMENTAL
Chemicals Bayerite was prepared from A1 strips (>99.99%) as described by Chesworth (l 1). BET surface area s = 3.0 m E g-l. 554
0021-9797/84 $3.00 Copyright© 1984by AcademicPress,lnc, All rightsof reproduction in any formreserved.
JournalofColloidandInterfaceScience,Vol. 101, No. 2, October 1984
DISSOLUTION KINETICS OF BAYERITE The concentration of the stock solution (prepared from analytical grade KF, Merck) was determined by analysis for K + (ion exchange on Dowex 50) and F - (spectrophotometrically by the Zr-Eriochrome Cyanine R method). Concentrations of HNO3 stock solutions (Titrisol, Merck) were controlled using KIO3 (analytical grade, Merck) as a primary standard. KOH solutions (Titrisol, Merck) were standardized against HNO3.
other, there was no necessity to measure [AI(III)] directly in order to determine the rate of dissolution:
d d/v. Ho --Hi)] R = ~ [ A I ( I I I ) ] V t = ~ / ' " - -3~-\- n o n ]
dt \
HF
where lit is the total volume of the solution and nON, ~iVare defined by the equations
Ionic Strength KNO3 (analytical grade, Merck) was used to maintain the ionic strength of the solutions close to 1.00 M.
Dissolution Experiments Small amounts of solutions SI ([H +] = Ho M, [K+] = (1.00 - Ho) M, [NO~] = 1.00 M) and $2 (IF-] = F0 M, [K+] = (1.00 + Fo) M, [NOel = 1.00 M) were added to Vo (usually 0.05) dm 3 of 1.00 M KNO3 to obtain solutions with selected initial values for [H ÷] = H~ and [F-] --- Fi. After addition of (usually) 500 mg of bayerite (equivalent to 6.4 × 10-3 mole of AI(OH)3) these initial concentrations of H ÷ and F- were maintained with the aid of two potentiostats each one consisting of the pertinent ion-selective electrode, a digital voltmeter (Orion 701 A), an Impulsomat (Metrohm E 614), and a Dosimat (Metrohm E 535). The volumes Vn and vv of the solutions S1 and $2 consumed by the dissolution reaction were recorded as a function of time. The suspensions were stirred at 600 rpm. Preliminary runs had shown that the rates of dissolution became independent on the rate of stirring at speed >400 rpm. In order to maintain (approximately) constant surface and particle size conditions, the fraction of bayerite allowed to dissolve was always less than 3.5%. From the primary data (Vn, VF, t) the rate of dissolution was obtained independently from the hydrogen ion balance and the fluoride ion balance. Since the values obtained by the two methods agreed well with each
555
m,~m[H+] -m ~on =
m 1 + E Xm[H+I - m + Z ¢~.[F-I" m
[2]
n
E nB,[F-]" nv =
" 1 + Z XmIH+I - m + E/3,[F-l" m
[3]
n
2g,, and/3, are the stability constants of the Al(III)hydroxo- and fluoro complexes: Ym = Bn
[AI(OH)~-m)+][H+lm [AI3+] [AIF(,3-'0+] [Ala+][F_],
Calculations of the chemical speciation in the system A13+-HzO-F - indicate that the concentrations of polynuclear hydroxo complexes can be neglected under the experimental conditions of this study.
Adsorption Measurements Adsorption-desorption equilibria of the hydrogen ions were investigated by potentiometric titration of A (usually 0.002) kg of bayerite suspended in V0 (usually 0.05) dm 3 of 1 M KNO3 with v dm 3 of either solution S1 or $3 ([OH-] = B0 M, [K +] = (1.00 + Bo) M, [NO~] = 1.00 M). The amounts {H+}a and {H+)d of adsorbed (desorbed) hydrogen ions were obtained from {H+)" =
vHo - (Vo + v)([H +] - Kw/[H+]) A [mole kg-t]
[4]
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
556
PULFER ET A U
vBo + (Vo + v)([H +1 - Kw/[H+]) {H+}~ =
A
[mole kg-'l.
[5]
Measurements of the fluoride ion adsorption were carried out at constant values of log[H+]. They were restricted to concentrations where the rate of dissolution is small: A kg samples of bayerite were suspended in Vo dm 3 of solutions consisting preponderantly of 1 M KNO3 (and some HNO3 to obtain the selected value of log[H+]) and titrated with VF dm 3 of solution $2. After each addition of $2, the fluoride concentration in the solution (obtained potentiometrically) and vn, the volume of solution S1 required to maintain the selected hydrogen ion concentration were recorded. The amount of adsorbed fluoride is thus
cording to Brown (12). A Wilhelm-type salt bridge (13) was used to connect test solution and reference electrode. Under the prevailing experimental conditions, variations in the liquid-junction potential between the test solution and the salt bridge could be neglected. The emf of the cells are thus given by Ea = E °' +/ca log[H +]
Eb = E ° ' + kb logtF-] E °', /ca, E °', and kb were obtained from titrations of 1 M KNO3 with solutions S1 and $2, respectively.
Temperature Control Kinetic measurement and adsorption studies were carried out at 25.0 + 0. l °C. Auxiliary Constants
The evaluation of some of the above mentioned parameters requires a set of equilib{Z-}a = .4 rium constants related to the particular ionic [mole kg-l] [6] medium chosen for this study. Ka, the acid The amount of consumed hydrogen ions is dissociation constant of HF was taken from given by Smith and Martell (14). Kw was obtained from a potentiometric acid-base titration. v.Ho - ( Vo + VF + V.) Values for ,~1 and 3, were obtained from X ([H +1 - Kw/[H+]) potentiometric titrations of dilute (2.68 a { U +} = A X 10 -3 M) solutions of A I ( N O 3 ) 3 (in 1 M [mole kg -l] [71 KNO3) with solution $2 using both glassand fluoride-electrodes. The numerical values Electromotive Force Measurements (Table I) were calculated with the aid of The concentrations of hydrogen ions and FITEQL, a general nonlinear regression profluoride ions were obtained with the aid of the cells I)FF0 -- (Vo + VF -~ I;H)[F-]
TABLE I
RE/1 M KNO3//test solution/
Auxiliary Constants (298.2°K)
glass electrode
(a) Constant
1o8 constant (+2¢)
RE/1 M KNO3//test solution/ fluoride electrode
(b)
where RE is the reference electrode Ag, AgC1/0.01 M KCI in 1.00 M KNO3. Metrohm (EA 109) glass electrodes and Radiometer (1052 F) fluoride electrodes were used. Ag, AgCI electrodes were prepared acJournal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
,,~j ~z :~3 /81 /82 /83 /84
Kw Ka
-5.435 -10.28 - 16.08 6.158 11.19 14.99 15.75 -13.73 -2.96
(---0.005)
(---0.006) (+0.01) (___0.01) (+__0.01) (+-0.01)
557
DISSOLUTION KINETICS OF BAYERITE
Based on the radius of 0 2- e q u a l to 1.4 × 10-~° m and the specific surface area of the bayerite, the maximum number of surface OH- and OH2-groups for the sample of bayerite is calculated to be on the order of RESULTS AND DISCUSSION 6.4 × 10 -2 mole kg-~. Since the nature of The Structure of the Bayerite Surface the crystallographic planes exposed to the The bayerite surface contains both bridging solution was not known, it was not possible and terminal hydroxyl groups. From stoi- to evaluate the relative amounts of the indichiometric and structural reasons, it follows vidual species. Species III is, however, rethat the possible species on a neutral surface stricted to edges and corners; its abundance is thus comparatively small. With respect to are ligand exchange against F-, species II is H certainly more reactive than species I. For / OH / \O the subsequent discussion it will thus be (OH)5/2A1 Al(OH)5/2 (OH)4/2A1 assumed the the reactive bayerite surface is "~OH2 represented by the structure II. II
gram for chemical equilibrium problems developed by Westall (15). X2 and g"3 were taken from Baes and Messmer (16).
OH2
Adsorption and Desorption of Hydrogen lons
IjOH
(OH)2/2A1 ~
I
OH
The results of the acid-base titrations are shown in Fig. 1. Based on the foregoing considerations, adsorption and desorption of hydrogen ions are written as
OH2 II1
I
//OH27 + (OH)4/2AI~ [
OHz]
I
0"7
(OH)4/zAI~oH2] + H +
Ka] = {AI(OH)(OH2)}[H+] exp(-F~b/RT)
[mole dm -3]
{AI(OH2)~-}
I °Hl I (OH)4/2AI ~
OH2
0-7 (OH)4/2AI'---.OH]
Ka~ = {AI(OH)~ }[H +1 exp(-F¢/R T) {AI(OH)(OH2)} where ¢ is the acting surface potential and { } denotes surface concentrations (mole kg-~). Hence, the quantity q = ({H+}a - {H+}d) is given by q = {AI(OH2)~-} - {AI(OH)~} [mole kg -~] [10]
[8]
+ H+
[mole dm-3],
[9]
The total concentration Co of reactive surface hydroxyl groups is defined by Co = {AI(OH2)~-} + {AI(OH)(OH2)} + {AI(OH)~-} [mole kg -~]
[1 l]
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 198,1
558
P U L F E R ET AL.
-1og[H ÷]
lo. 9-
8-
76-
5-
4-
({.+}.-{.+}~). o l .
3-
1() -2
5 " 10 -3
()
- 5'.10 -3
k g -1 - 1'0 -2
FIG. 1. Acid-base titration of bayerite. The solid curve was calculated with the aid of Eq. [ 12] using the parameters given in Table II.
Combining the Eqs. [8]-[ 11] results in q = Co((Ka])-l[H+]e_ - Ka~[H+]-le+)
1 + (Ka])-l[H+]e_ + Ka~2[H+]-le+ [mole kg -~]
[12]
where e+ = exp(F~b/RT) and e_ = exp
(-F~/RT). In view of the high ionic strength, the capacitance of the electric double layer was approximated by a Helmholtz model: =
qF ~/~s
[v]
[ 131
where Xt is the specific double layer capacitance (F m-2). By means of a least-square treatment (15) it was attempted to find a unique set of constants (Co, Kay, Kay, ,,~) to relate the experimental data [q, [H+]) to the equilibrium model defined by the equations above. The resulting residual R = (q(~xp) - q(ca~c))2 was, however, practically independent of the value of ,,~ over a large range of •. The experimental data were thus combined with assumed values for ~ to obtain various sets for (Co, Kaj, Ka2). The constants obtained are presented in Table II. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
For the geometrical reasons mentioned above Co cannot exceed a value of approximately 0.03 mole. kg -~. On the other hand, measurements of the fluoride adsorption data suggest that Co is >10.02 mole. kg -1. Hence, the parameter values generated with ,,~ = 2.65 F m - : seem to be an acceptable set. The relatively high value for the effective double layer capacitance is in part due to the fact that charge at the bayerite-electrolyte interface is not located in well-defined planes, but is rather smeared out throughout the interface region. Figure 1 confirms the fair agreement of experimental and calculated curves. Further support is obtained from the comparisons
TABLE II Least-Square Treatment of the Acid-Base Titration X~ (F m -2)
log Ka]
log Ka~
Co
2.5 2.6 2.65 2.7 2.8
4.972 5.178 5.237 5.284 5.348
-8.352 -8.146 -8.087 -8.040 -7.976
0.05105 0.03097 0.02662 0.02360 0.01977
R
1.04 1.06 1.07 1.08 1.70
× X X × ×
10-6 10-6 10-6 10-6 10-6
DISSOLUTION KINETICS OF BAYERITE
i
(OH)a/2AI ~OH2_J
F o.] /(OH)4/2A1 L_ OH2
log Ka] = -5.24
+ H+
AI(OH2)4(OH)~- ~ AI(OH2)3(OH) ° + H + and
I.o.,.,,..o.1 ~OH2J
o.]
~ [(OH)4/2AI'~oHJ
559
log *K3 = -5.80
log Ka~ = -8.08
+ H+
log *K4 = -7.58
AI(OH2)3(OH) ° ~ Al(OH)4(aq)
that the ratio {F-}JA{H+}~ is somewhat larger than unity. This means that part of It was found that adsorption of fluoride the adsorbed fluoride ions are exchanged was strongly coupled with the consumption against hydroxyl groups whereas a (minor) of hydrogen ions. A closer inspection reveals part is exchanged against water molecules. The pertinent equilibria are thus
Adsorption of Fluoride Ions
I
OH ] I jOH](OH)4/2Al~ + F- ~ (OH)4/2AI'~F J OH2 K] =
[ o,j // (OH)4/2Al'~oH2
+ H20
{AI(OH)F- } exp(-F~/RT) {AI(OH)(OH2) }IF-]
jFj
[din 3 mole -t]
+ H + + F- "-- (OH)4/2AI~.. L OHz
+ H20
{AI(F)(OH2)} K~ = {AI(OH)(OH2)}[H+][F_ ]
[dm 6 mole-2]
(OH)4/zAI.. .OH2+
+ 2F- ~-
[151
+ 2H20
{A1 F¢} KS = {AI(OH)(OH2)}[H+][F_]2 exp{-F~/RT} The numerical values for the equilibrium constants as obtained from a least treatment (15) of the experimental data ([F-], [H+], {F-}a) are collected in Table III. The concentration of adsorbed fluoride is given by
[14]
[dm 9 mole-3].
[ 16]
{F-}a = (Co(K][F-le+ + K~[H+I[F-I + 2K~[H+][F-12e+))(1 + (Ka])-'[H+le+ Ka~[H+]-le+ + K][F-]e+ + K~[H+][F-1 + K~[H+][F-12e+) -1
[mole kg -~] [171
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
560
PULFER ET AL. TABLE III
Equilibrium Constants for the Adsorption of Fluoride (,,~6~ 2.65 F m -2, log Ka] =
5.237, log K ~ = -8.087)
log K] = 4.743 log K~ =
9.959
log K~ = 13.429
Figure 2 shows a reasonable agreement between experimental data and model curves.
Kinetics of Dissolution
Within the first series, Fi was kept constant and H~ was varied. In the second series H,was constant and F; was varied. The results (Figs. 6, 7) suggest that at high values for both Hi and F; the reactionis approximately first-order with respect to both [H ÷] and [F-]. Lowering Hi and Fi increases the order of the reaction with respect to both [H ÷] and [F-]. The series with constant Hi and variable Fi shows that at very low values of F; the rate R becomes independent of Fi. This suggests that a rate law for dissolution of bayerite in the presence Of fluoride can be written as the sum of two terms, one of which is related to kinetics when fluoride concentration is negligibly small:
(a) General. Typical experimental data are shown in Fig. 3. At first glance it seems that R = S(k,[H +] +f([H+], [F-])). [19] the quantity of dissolved AI(III) is a linear function of time. A closer examination reveals Formulation of the expression f([H+], [F-l) a slightly curved region close to the origin. in terms of concentrations and rate constants This region is partially attributed to the pres- is discussed in the following section, ence of small amounts (---6 × 10 . 6 mole or "~ 1%0) of material of enhanced reactivity. A similar observation has been reported by CorneU et al. (17). A further contribution may originate from the initial adsorption of H ÷ and F-. The dissolution rates to be dis2,0 cussed are based on data from the linear regions. (b) Effect of surface area. Figure 4 shows that the rate of dissolution is a linear function 2,5' of the sample size, i.e., the surface area. -log [F-]
(c) Dissolution in the absence of fluoride. The results of a series of measurements at log[H÷] > - 4 (Fig. 5) can be summarized by the equation R = k~. S. [H+];
k~ = 1.5 (+__0.3)
× l 0 -7
dm3.sec-! m -2,
2.0'
[18]
where S is the surface area of the sample. Measurements at lower H+-concentrations are extremely difficult since changes in vn and vv caused by the long-term drift of the potentiostats become more important than those caused by the dissolution process.
(d) Dissolution in the presence of fluoride. Two series of experiments were carded out. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
•
Io9 [H +] = - 6
2.5.
-log [F-]
FIG. 2. Adsorption of fluoride at the bayerite solution interface. The solid curves were calculated with Eq. [17] and the parameters given in Table III,
561
DISSOLUTION KINETICS OF BAYERITE 10 4. m o l
AI (Ill)
0 1.0
O 0
•
0
[]
•
D
o
e•
O O
[]
0.5 ¸ 0 0 oOo
00°
~D D
• •
D
DD
[]
i
D
[]
El
•
mm
O DD
171
•
•
•
•
5 "10 3
10 4
FIG. 3. Dissolution experiments: moles of AI(III) as a function o f time. Hi = 1.00 X X 10 4 M ( O ) , 7.53 × 10-5 M ( O ) , 4.62 × 10-5 M(Fq), 1.00 × 10-5 M(N).
Rate of Dissolution and Surface Speciation; Evaluation of the Rate Law and the Reaction Mechanism The dissolution mechanism can be viewed as a series of reactions at equilibrium followed by a single rate-controlling step involving an "activated species." The dissolution rate is then directly proportional to the concentration of the precursor of the activated species. It is thus the correspondence between equilibrium adsorption measurement and kinetic measurements in terms of plausible surface species that has to be examined. (a) Solutions without fluoride. The surface speciation is shown in Fig. 8. Within the range of the kinetic experiments, the change in log{Al(OH)(OH2)} and log{Al(OH2)~-}
sec l0 -4
M. F, = l. I4
with log[H +] is not very pronounced. In contrast R varies linearly with [H +] in this range. No meaningful correlation between R and {AI(OH2)~-} could be detected. The mechanism of dissolution consists presumably of steps that involve protonation of bridging OH- groups followed by concerted -
9
-
9.5
log
R
-10
108 R (tool • sec-1)
J -10.5
log surface
1
2
area
(m2)
3
FIG. 4. Effect of surface area upon the rate of dissolution.
-;.o
-;.~
[H*]
-;.o
FIG. 5, Rate of dissolution (in the absence of fluoride) as a function of [H+]. The solid line was obtained from Eq. [18] (S = 1.5 m2). Journal of Colloid and Interface Science, VoL 101, No. 2, October 1984
562 -7.
P U L F E R ET AL. log
R
R = S(k,[H +] + (k2CoK~1[H+I2[F-]3e+) × (1 + (Ka~)-~[H+]e_ + Ka~[H+]-te+ + K][F-]e+ + K~[H+][F -]
- 8-
+ K~[H+][F-]2e+) -l)
[mole sec -1]
[21]
Least-square treatment of the data leads to a value of k2 = 1.11 (_+0.1) × l0 II
-9
[kg dm 12 m -2 sec -l mole-l]. The Figs. 6 and 7 show the fair agreement between calculated and observed R-values. Equation [21] can also be used to evaluate the equilibrium constants K~, K~, and K~ from the kinetic data. The values obtained (log K] = 4.6, log *K~ = 9.8, log K~ = 13.1)
-10, [ F - ] = 1.83 x 10 - 4
-11 - 6
log
R
- log [H÷I
FIG. 6. Rate of dissolution at [F-]i = 1.83 × 10-4 as a function of [H÷]. The solid curve was calculated with Eq. [21] with the parameters collected in the Tables II and IlL
opening of A1-O bonds. Although the data do not reveal the details of the mechanism, it would be consistent with the data if the precursor to the activated species was formed by addition of one proton to the AI(OH2)~ species. (b) Solutions with H + and F-. The surface speciation is shown in Fig. 9. At first glance there is no obvious connection between dissolution rate a n d surface speciation. A closer inspection reveals a good correlation between the dissolution rate (corrected for dissolution in the absence of fluoride) and the concentration of the surface species {AI(OH)F-}:
=
-8
.
-9'
-10
-log
[~-]
i
R' = R - k1S[H +]
4
= k2S{AI(OH)F-}[H+]E[F-] 2.
[20]
Upon substitution of the expression for {AI(OH)F-}, the complete rate law can thus be written as Journal of Colloid and Interface Science,
-7
Vol. 101, No. 2, O c t o b e r 1984
5
6
FIG. 7. Rate of dissolution at [H+]i = 1.00 × 10 -4 M as a function of [F-]. At low values of [F-] the solid curve (Eq. [21]) approaches a value of log R = - 1 0 . 6 5 that corresponds to the dissolution rate in the absence of fluoride (Eq. [18], S = 1.5 m2).
563
DISSOLUTION KINETICS OF BAYERITE ~'-17 ._¢
AI(OH)(OH2)
u) 2¢D o
AI(OH2) +
,-%-3 AI(OH) 2
-4"
dissolution
-5"
i
|
-2.8
|
-3.2
-3.6
studies
i
i
-4.0
-4.4 log I'H+]
FlG. 8. Chemical speciation at the bayerite solution interface in the absence of fluoride.
are in reasonable agreement with those given in Table III. On the basis of the foregoing data, the composition of the precursor of the activated species can be written as (OH)2/2F:/2A1 × (OH)F- or (OH)3/2(F)I/2AIF~-. The paramount factor is the replacement of a critical
AI F(0H 2)
number of bridging OH--groups by fluoride which has almost no bridging properties. A possible mechanism of the dissolution process (Fig. 10) can be described as follows. Two bridging OH--groups are replaced by fluoride; it is plausible that this replacement is already favored by foregoing substitution of the terminal water molecule by fluoride. The final ratedetermining step is a concerted opening of the remaining two A1-O bonds. The departing
.(o. ul ~-4F-5
H -4
-5
OH
H
l slow
-6
log [F-] -
•~
F F ~
AIF(0H2)
~-~
-
I fF1 OH
.1
I rapid AI(OH)F~
~ -4
~AIIOH)(OH2) rapid equilibration in solution
log [H ÷] FIG. 9. Chemical speciation at the bayerite solution interface in the presence of fluoride.
..(o.).
7:'/
FIG. 10. Suggested mechanism of dissolution of bayerite in aqueous HNOa-HF solutions. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
564
PULFER ET AL.
species is presumably the fourfold coordinated AI(OH)F3 that equilibratesrapidly in solution to form AI(OH)m(F)n(OH)I~-.~--~+. CONCLUSIONS
T h e rate law (Eq. [21]) contains constants, chemical potential (concentration) terms, and electrostatic potential terms. The occurrence of the electrostatic term is a logical consequence of the fact that the dissolution reaction involves charged species and a charged surface. Any attempt to formulate the rate law o f such a reaction without explicit inclusion of the electrostatic term involves the assumption that the variation in this term over the range of experimental conditions is negligible. Earlier work, in which the validity of this assumption was not examined, must be looked upon with some reserve. Although the present paper results in a consistent model for both adsorption equilibria and dissolution kinetics, this consistency is based on at least partially arbitrary assumptions regarding the structure of the bayerite surface and the magnitude of the double layer capacitance. It should be remembered that the acid-base properties of the bayeritesolution interface can be equally well fitted by a comparatively broad range of interfacial capacitance values (and associated values for K a y , K a y , and Co), i.e., the analysis of the acid-base titration curve does not reveal a unique value for a Helmholtz double layer capacitance. (Moreover, as shown by Westall and Hohl (18), acid-base titrations of oxide surfaces do not even permit to discriminate between diffuse and planar double layers.) The same conclusion applies for studies on the adsorption of metal ions and anions. On the other harid, a good fit of the observed dissolution rates with the aid of Eq. [21] is restricted to a range of ,,~ = 2.65 + 0.05. A favorable interpretation o f this aspect would result in the conclusion that although adsorption studies with oxides and hydroxides do not reveal the structure of the electrical double layer, the additional information is available from kinetic studies. A less favorable interpretation would emphasize Journal of Colloid and Inte(face Science, Vol. 101, No. 2. October 1984
the dependence o f the postulated reaction mechanism on partially arbitrary assumptions and predict that an improved knowledge of both surface structure and electrical double layer will modify our models of dissolution mechanisms. The present authors_ believe that the latter perspective may be closer to reality than the former. ACKNOWLEDGMENTS The authors are indebted to Professor W. Schneider (ETH Ziirich) for valuable discussions. Part of the work was done during a stay of P.W.S. at Gunma University, Kiryu (Japan). P.W.S. is indebted to ProfessorH. Akaiwa for his generous hospitality and for valuable advice. The work was financially supported by the Swiss National Science Foundation. REFERENCES 1. Shying, M. E., Florence, T. M., and Carswell, D. J., J. Inorg. Nucl. Chem. 32, 3493 (1970); 34, 1665 (1972). 2. Barney,G. S., J. Inorg. Nucl, Chem. 39, 1665 (1977). 3. Kline, W. E., and Fogler, H. S., J. Colloid Interface Sci. 82, 93 (1981). 4. Packter, A., and Dhillon, H. S., J. Chem. Soc. (A) 2588 (1969). 5. Cornell, R. M., Posner, A. M., and Quirk, J. P., J. Inorg. Nucl, Chem. 38, 563 (1976). 6. Valverde, N., Ber. Bunsenges. Phys. Chem. 80, 333 (1976). 7. Jones, C. F., Segall, R. L., Smart, R. St, C., and Turner, P. S., J. Chem. Soc. Faraday 1 74, 1615 (1978). 8. Baumgartner, E., Blesa, M. A., and Maroto, A. J. G., J. Chem, Soc. Dalton 1649 (1982). 9. Chang, H.-Ch., and Matijevi6, E., J. Colloid Interface Sci. 92, 479 (1983). 10. Grauer, R., and Stumm, W., Colloid Polym. Sci. 260, 959 (1982). 11. Chesworth, W., Nature Phys. Sci. 230, 65 (1971). 12. Brown, A. C., J. Amer. Chem. Soc. 56, 646 (1934). 13. Forsling, W., Hietanen, S., and Sill6n, L. G., Acta Chem. Scand. 6, 901 (1952). 14. Smith, R. M., and Martell, A. E., "Critical Stability Constants, Volume 4: Inorganic Complexes." Plenum, New York/London, 1976. '. 15. Westall, J. C., "FITEQL, A Computer Program for Determination of Chemical Equilibrium Constants from Experimental Data," Report 82-01, Chemistry Department, Oregon State University, Corvallis, 1982. 16. Baes, Ch. F., and Messmer, R. E., "The Hydrolysis of Cations." Wiley, New York, 1976. 17. Cornell, R. M., Posner, A. M., and Quirk, J. P., Soil Sci. Soc. Amer. Proc. 38, 377 (1974). 18. Westall, J. C., and Hohi, H., Adv. Colloid Interface Sci. 12, 265 (1980).
R = S(k~[H+] + (k2CoK][n+]2[F-]3e+)(1+ (Ka])-J[H+]e_ + Ka~[n+]-'e+ + K][F-]e+ + KI[H+][F-] + K~[H+][F-]2e+)-') where kl = 1.5 (+0.3) × l0 -7 dm 3 sec-l m-E; k2 = l . l l (+0.1) × l0 II kg dm 12 m -2 sec -l mole-4; S = surface area (m2); Co = total concentration of reactive surface groups (=2.66 × 10-2 mole kg-l).
Ka], Kay, K], K~, and K~ as defined are equilibrium constants related to the adsorption of H+ and F- from the solution to the bayerite surface. Their numerical values were obtained from adsorption studies. The e+ = exp(F~b/RT) and e_ = exp(-F~/RT) account for the acting surface potential ~b which was calculated from the surface charge assuming a Helmholtz-type double layer. The results are discussed in terms of the stoichiometry of the precursor of the activated complex and possible reaction mechanisms. It is concluded that the present knowledge on the mechanisms of dissolution reaction of oxides and hydroxides is limited by the present ignorance of the surface structure and the structure of the electrical double layer. the mechanism of the reaction has so far not been provided. The present paper reports on a study of both the kinetics of dissolution of bayerite (3'-AI(OH)3) in H N O 3 - H F solutions and the adsorption of hydrogen ions and fluoride ions at the bayerite-solution interfaces. The combined results of these experimental studies lead to a mutually consistent model for both the surface complexation of bayerite in the presence of H + and F - and the mechanism of its dissolution in the above mentioned solvent.
INTRODUCTION
The rate of dissolution of metal oxides and hydroxides in noncomplexing acids (HC104, HNO3) is greatly enhanced by the addition of ligands such as fluoride (1-3), chloride (4-7), bromide (7), sulfate (4), thioglycolate (8), EDTA, and related aminocarboxylic acids (9). These effects of added ligands have generally been attributed to formation of surface complexes followed by release of the surface species (10). This assumption implies that the rate law of the dissolution reaction is related to the pertinent adsorption/desorption equilibria of both hydrogen ions and added ligands, i.e., to the stability constants of the pertinent surface complexes. This relationship that is an indispensable prerequisite for a deeper insight into
EXPERIMENTAL
Chemicals Bayerite was prepared from A1 strips (>99.99%) as described by Chesworth (l 1). BET surface area s = 3.0 m E g-l. 554
0021-9797/84 $3.00 Copyright© 1984by AcademicPress,lnc, All rightsof reproduction in any formreserved.
JournalofColloidandInterfaceScience,Vol. 101, No. 2, October 1984
DISSOLUTION KINETICS OF BAYERITE The concentration of the stock solution (prepared from analytical grade KF, Merck) was determined by analysis for K + (ion exchange on Dowex 50) and F - (spectrophotometrically by the Zr-Eriochrome Cyanine R method). Concentrations of HNO3 stock solutions (Titrisol, Merck) were controlled using KIO3 (analytical grade, Merck) as a primary standard. KOH solutions (Titrisol, Merck) were standardized against HNO3.
other, there was no necessity to measure [AI(III)] directly in order to determine the rate of dissolution:
d d/v. Ho --Hi)] R = ~ [ A I ( I I I ) ] V t = ~ / ' " - -3~-\- n o n ]
dt \
HF
where lit is the total volume of the solution and nON, ~iVare defined by the equations
Ionic Strength KNO3 (analytical grade, Merck) was used to maintain the ionic strength of the solutions close to 1.00 M.
Dissolution Experiments Small amounts of solutions SI ([H +] = Ho M, [K+] = (1.00 - Ho) M, [NO~] = 1.00 M) and $2 (IF-] = F0 M, [K+] = (1.00 + Fo) M, [NOel = 1.00 M) were added to Vo (usually 0.05) dm 3 of 1.00 M KNO3 to obtain solutions with selected initial values for [H ÷] = H~ and [F-] --- Fi. After addition of (usually) 500 mg of bayerite (equivalent to 6.4 × 10-3 mole of AI(OH)3) these initial concentrations of H ÷ and F- were maintained with the aid of two potentiostats each one consisting of the pertinent ion-selective electrode, a digital voltmeter (Orion 701 A), an Impulsomat (Metrohm E 614), and a Dosimat (Metrohm E 535). The volumes Vn and vv of the solutions S1 and $2 consumed by the dissolution reaction were recorded as a function of time. The suspensions were stirred at 600 rpm. Preliminary runs had shown that the rates of dissolution became independent on the rate of stirring at speed >400 rpm. In order to maintain (approximately) constant surface and particle size conditions, the fraction of bayerite allowed to dissolve was always less than 3.5%. From the primary data (Vn, VF, t) the rate of dissolution was obtained independently from the hydrogen ion balance and the fluoride ion balance. Since the values obtained by the two methods agreed well with each
555
m,~m[H+] -m ~on =
m 1 + E Xm[H+I - m + Z ¢~.[F-I" m
[2]
n
E nB,[F-]" nv =
" 1 + Z XmIH+I - m + E/3,[F-l" m
[3]
n
2g,, and/3, are the stability constants of the Al(III)hydroxo- and fluoro complexes: Ym = Bn
[AI(OH)~-m)+][H+lm [AI3+] [AIF(,3-'0+] [Ala+][F_],
Calculations of the chemical speciation in the system A13+-HzO-F - indicate that the concentrations of polynuclear hydroxo complexes can be neglected under the experimental conditions of this study.
Adsorption Measurements Adsorption-desorption equilibria of the hydrogen ions were investigated by potentiometric titration of A (usually 0.002) kg of bayerite suspended in V0 (usually 0.05) dm 3 of 1 M KNO3 with v dm 3 of either solution S1 or $3 ([OH-] = B0 M, [K +] = (1.00 + Bo) M, [NO~] = 1.00 M). The amounts {H+}a and {H+)d of adsorbed (desorbed) hydrogen ions were obtained from {H+)" =
vHo - (Vo + v)([H +] - Kw/[H+]) A [mole kg-t]
[4]
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
556
PULFER ET A U
vBo + (Vo + v)([H +1 - Kw/[H+]) {H+}~ =
A
[mole kg-'l.
[5]
Measurements of the fluoride ion adsorption were carried out at constant values of log[H+]. They were restricted to concentrations where the rate of dissolution is small: A kg samples of bayerite were suspended in Vo dm 3 of solutions consisting preponderantly of 1 M KNO3 (and some HNO3 to obtain the selected value of log[H+]) and titrated with VF dm 3 of solution $2. After each addition of $2, the fluoride concentration in the solution (obtained potentiometrically) and vn, the volume of solution S1 required to maintain the selected hydrogen ion concentration were recorded. The amount of adsorbed fluoride is thus
cording to Brown (12). A Wilhelm-type salt bridge (13) was used to connect test solution and reference electrode. Under the prevailing experimental conditions, variations in the liquid-junction potential between the test solution and the salt bridge could be neglected. The emf of the cells are thus given by Ea = E °' +/ca log[H +]
Eb = E ° ' + kb logtF-] E °', /ca, E °', and kb were obtained from titrations of 1 M KNO3 with solutions S1 and $2, respectively.
Temperature Control Kinetic measurement and adsorption studies were carried out at 25.0 + 0. l °C. Auxiliary Constants
The evaluation of some of the above mentioned parameters requires a set of equilib{Z-}a = .4 rium constants related to the particular ionic [mole kg-l] [6] medium chosen for this study. Ka, the acid The amount of consumed hydrogen ions is dissociation constant of HF was taken from given by Smith and Martell (14). Kw was obtained from a potentiometric acid-base titration. v.Ho - ( Vo + VF + V.) Values for ,~1 and 3, were obtained from X ([H +1 - Kw/[H+]) potentiometric titrations of dilute (2.68 a { U +} = A X 10 -3 M) solutions of A I ( N O 3 ) 3 (in 1 M [mole kg -l] [71 KNO3) with solution $2 using both glassand fluoride-electrodes. The numerical values Electromotive Force Measurements (Table I) were calculated with the aid of The concentrations of hydrogen ions and FITEQL, a general nonlinear regression profluoride ions were obtained with the aid of the cells I)FF0 -- (Vo + VF -~ I;H)[F-]
TABLE I
RE/1 M KNO3//test solution/
Auxiliary Constants (298.2°K)
glass electrode
(a) Constant
1o8 constant (+2¢)
RE/1 M KNO3//test solution/ fluoride electrode
(b)
where RE is the reference electrode Ag, AgC1/0.01 M KCI in 1.00 M KNO3. Metrohm (EA 109) glass electrodes and Radiometer (1052 F) fluoride electrodes were used. Ag, AgCI electrodes were prepared acJournal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
,,~j ~z :~3 /81 /82 /83 /84
Kw Ka
-5.435 -10.28 - 16.08 6.158 11.19 14.99 15.75 -13.73 -2.96
(---0.005)
(---0.006) (+0.01) (___0.01) (+__0.01) (+-0.01)
557
DISSOLUTION KINETICS OF BAYERITE
Based on the radius of 0 2- e q u a l to 1.4 × 10-~° m and the specific surface area of the bayerite, the maximum number of surface OH- and OH2-groups for the sample of bayerite is calculated to be on the order of RESULTS AND DISCUSSION 6.4 × 10 -2 mole kg-~. Since the nature of The Structure of the Bayerite Surface the crystallographic planes exposed to the The bayerite surface contains both bridging solution was not known, it was not possible and terminal hydroxyl groups. From stoi- to evaluate the relative amounts of the indichiometric and structural reasons, it follows vidual species. Species III is, however, rethat the possible species on a neutral surface stricted to edges and corners; its abundance is thus comparatively small. With respect to are ligand exchange against F-, species II is H certainly more reactive than species I. For / OH / \O the subsequent discussion it will thus be (OH)5/2A1 Al(OH)5/2 (OH)4/2A1 assumed the the reactive bayerite surface is "~OH2 represented by the structure II. II
gram for chemical equilibrium problems developed by Westall (15). X2 and g"3 were taken from Baes and Messmer (16).
OH2
Adsorption and Desorption of Hydrogen lons
IjOH
(OH)2/2A1 ~
I
OH
The results of the acid-base titrations are shown in Fig. 1. Based on the foregoing considerations, adsorption and desorption of hydrogen ions are written as
OH2 II1
I
//OH27 + (OH)4/2AI~ [
OHz]
I
0"7
(OH)4/zAI~oH2] + H +
Ka] = {AI(OH)(OH2)}[H+] exp(-F~b/RT)
[mole dm -3]
{AI(OH2)~-}
I °Hl I (OH)4/2AI ~
OH2
0-7 (OH)4/2AI'---.OH]
Ka~ = {AI(OH)~ }[H +1 exp(-F¢/R T) {AI(OH)(OH2)} where ¢ is the acting surface potential and { } denotes surface concentrations (mole kg-~). Hence, the quantity q = ({H+}a - {H+}d) is given by q = {AI(OH2)~-} - {AI(OH)~} [mole kg -~] [10]
[8]
+ H+
[mole dm-3],
[9]
The total concentration Co of reactive surface hydroxyl groups is defined by Co = {AI(OH2)~-} + {AI(OH)(OH2)} + {AI(OH)~-} [mole kg -~]
[1 l]
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 198,1
558
P U L F E R ET AL.
-1og[H ÷]
lo. 9-
8-
76-
5-
4-
({.+}.-{.+}~). o l .
3-
1() -2
5 " 10 -3
()
- 5'.10 -3
k g -1 - 1'0 -2
FIG. 1. Acid-base titration of bayerite. The solid curve was calculated with the aid of Eq. [ 12] using the parameters given in Table II.
Combining the Eqs. [8]-[ 11] results in q = Co((Ka])-l[H+]e_ - Ka~[H+]-le+)
1 + (Ka])-l[H+]e_ + Ka~2[H+]-le+ [mole kg -~]
[12]
where e+ = exp(F~b/RT) and e_ = exp
(-F~/RT). In view of the high ionic strength, the capacitance of the electric double layer was approximated by a Helmholtz model: =
qF ~/~s
[v]
[ 131
where Xt is the specific double layer capacitance (F m-2). By means of a least-square treatment (15) it was attempted to find a unique set of constants (Co, Kay, Kay, ,,~) to relate the experimental data [q, [H+]) to the equilibrium model defined by the equations above. The resulting residual R = (q(~xp) - q(ca~c))2 was, however, practically independent of the value of ,,~ over a large range of •. The experimental data were thus combined with assumed values for ~ to obtain various sets for (Co, Kaj, Ka2). The constants obtained are presented in Table II. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
For the geometrical reasons mentioned above Co cannot exceed a value of approximately 0.03 mole. kg -~. On the other hand, measurements of the fluoride adsorption data suggest that Co is >10.02 mole. kg -1. Hence, the parameter values generated with ,,~ = 2.65 F m - : seem to be an acceptable set. The relatively high value for the effective double layer capacitance is in part due to the fact that charge at the bayerite-electrolyte interface is not located in well-defined planes, but is rather smeared out throughout the interface region. Figure 1 confirms the fair agreement of experimental and calculated curves. Further support is obtained from the comparisons
TABLE II Least-Square Treatment of the Acid-Base Titration X~ (F m -2)
log Ka]
log Ka~
Co
2.5 2.6 2.65 2.7 2.8
4.972 5.178 5.237 5.284 5.348
-8.352 -8.146 -8.087 -8.040 -7.976
0.05105 0.03097 0.02662 0.02360 0.01977
R
1.04 1.06 1.07 1.08 1.70
× X X × ×
10-6 10-6 10-6 10-6 10-6
DISSOLUTION KINETICS OF BAYERITE
i
(OH)a/2AI ~OH2_J
F o.] /(OH)4/2A1 L_ OH2
log Ka] = -5.24
+ H+
AI(OH2)4(OH)~- ~ AI(OH2)3(OH) ° + H + and
I.o.,.,,..o.1 ~OH2J
o.]
~ [(OH)4/2AI'~oHJ
559
log *K3 = -5.80
log Ka~ = -8.08
+ H+
log *K4 = -7.58
AI(OH2)3(OH) ° ~ Al(OH)4(aq)
that the ratio {F-}JA{H+}~ is somewhat larger than unity. This means that part of It was found that adsorption of fluoride the adsorbed fluoride ions are exchanged was strongly coupled with the consumption against hydroxyl groups whereas a (minor) of hydrogen ions. A closer inspection reveals part is exchanged against water molecules. The pertinent equilibria are thus
Adsorption of Fluoride Ions
I
OH ] I jOH](OH)4/2Al~ + F- ~ (OH)4/2AI'~F J OH2 K] =
[ o,j // (OH)4/2Al'~oH2
+ H20
{AI(OH)F- } exp(-F~/RT) {AI(OH)(OH2) }IF-]
jFj
[din 3 mole -t]
+ H + + F- "-- (OH)4/2AI~.. L OHz
+ H20
{AI(F)(OH2)} K~ = {AI(OH)(OH2)}[H+][F_ ]
[dm 6 mole-2]
(OH)4/zAI.. .OH2+
+ 2F- ~-
[151
+ 2H20
{A1 F¢} KS = {AI(OH)(OH2)}[H+][F_]2 exp{-F~/RT} The numerical values for the equilibrium constants as obtained from a least treatment (15) of the experimental data ([F-], [H+], {F-}a) are collected in Table III. The concentration of adsorbed fluoride is given by
[14]
[dm 9 mole-3].
[ 16]
{F-}a = (Co(K][F-le+ + K~[H+I[F-I + 2K~[H+][F-12e+))(1 + (Ka])-'[H+le+ Ka~[H+]-le+ + K][F-]e+ + K~[H+][F-1 + K~[H+][F-12e+) -1
[mole kg -~] [171
Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
560
PULFER ET AL. TABLE III
Equilibrium Constants for the Adsorption of Fluoride (,,~6~ 2.65 F m -2, log Ka] =
5.237, log K ~ = -8.087)
log K] = 4.743 log K~ =
9.959
log K~ = 13.429
Figure 2 shows a reasonable agreement between experimental data and model curves.
Kinetics of Dissolution
Within the first series, Fi was kept constant and H~ was varied. In the second series H,was constant and F; was varied. The results (Figs. 6, 7) suggest that at high values for both Hi and F; the reactionis approximately first-order with respect to both [H ÷] and [F-]. Lowering Hi and Fi increases the order of the reaction with respect to both [H ÷] and [F-]. The series with constant Hi and variable Fi shows that at very low values of F; the rate R becomes independent of Fi. This suggests that a rate law for dissolution of bayerite in the presence Of fluoride can be written as the sum of two terms, one of which is related to kinetics when fluoride concentration is negligibly small:
(a) General. Typical experimental data are shown in Fig. 3. At first glance it seems that R = S(k,[H +] +f([H+], [F-])). [19] the quantity of dissolved AI(III) is a linear function of time. A closer examination reveals Formulation of the expression f([H+], [F-l) a slightly curved region close to the origin. in terms of concentrations and rate constants This region is partially attributed to the pres- is discussed in the following section, ence of small amounts (---6 × 10 . 6 mole or "~ 1%0) of material of enhanced reactivity. A similar observation has been reported by CorneU et al. (17). A further contribution may originate from the initial adsorption of H ÷ and F-. The dissolution rates to be dis2,0 cussed are based on data from the linear regions. (b) Effect of surface area. Figure 4 shows that the rate of dissolution is a linear function 2,5' of the sample size, i.e., the surface area. -log [F-]
(c) Dissolution in the absence of fluoride. The results of a series of measurements at log[H÷] > - 4 (Fig. 5) can be summarized by the equation R = k~. S. [H+];
k~ = 1.5 (+__0.3)
× l 0 -7
dm3.sec-! m -2,
2.0'
[18]
where S is the surface area of the sample. Measurements at lower H+-concentrations are extremely difficult since changes in vn and vv caused by the long-term drift of the potentiostats become more important than those caused by the dissolution process.
(d) Dissolution in the presence of fluoride. Two series of experiments were carded out. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
•
Io9 [H +] = - 6
2.5.
-log [F-]
FIG. 2. Adsorption of fluoride at the bayerite solution interface. The solid curves were calculated with Eq. [17] and the parameters given in Table III,
561
DISSOLUTION KINETICS OF BAYERITE 10 4. m o l
AI (Ill)
0 1.0
O 0
•
0
[]
•
D
o
e•
O O
[]
0.5 ¸ 0 0 oOo
00°
~D D
• •
D
DD
[]
i
D
[]
El
•
mm
O DD
171
•
•
•
•
5 "10 3
10 4
FIG. 3. Dissolution experiments: moles of AI(III) as a function o f time. Hi = 1.00 X X 10 4 M ( O ) , 7.53 × 10-5 M ( O ) , 4.62 × 10-5 M(Fq), 1.00 × 10-5 M(N).
Rate of Dissolution and Surface Speciation; Evaluation of the Rate Law and the Reaction Mechanism The dissolution mechanism can be viewed as a series of reactions at equilibrium followed by a single rate-controlling step involving an "activated species." The dissolution rate is then directly proportional to the concentration of the precursor of the activated species. It is thus the correspondence between equilibrium adsorption measurement and kinetic measurements in terms of plausible surface species that has to be examined. (a) Solutions without fluoride. The surface speciation is shown in Fig. 8. Within the range of the kinetic experiments, the change in log{Al(OH)(OH2)} and log{Al(OH2)~-}
sec l0 -4
M. F, = l. I4
with log[H +] is not very pronounced. In contrast R varies linearly with [H +] in this range. No meaningful correlation between R and {AI(OH2)~-} could be detected. The mechanism of dissolution consists presumably of steps that involve protonation of bridging OH- groups followed by concerted -
9
-
9.5
log
R
-10
108 R (tool • sec-1)
J -10.5
log surface
1
2
area
(m2)
3
FIG. 4. Effect of surface area upon the rate of dissolution.
-;.o
-;.~
[H*]
-;.o
FIG. 5, Rate of dissolution (in the absence of fluoride) as a function of [H+]. The solid line was obtained from Eq. [18] (S = 1.5 m2). Journal of Colloid and Interface Science, VoL 101, No. 2, October 1984
562 -7.
P U L F E R ET AL. log
R
R = S(k,[H +] + (k2CoK~1[H+I2[F-]3e+) × (1 + (Ka~)-~[H+]e_ + Ka~[H+]-te+ + K][F-]e+ + K~[H+][F -]
- 8-
+ K~[H+][F-]2e+) -l)
[mole sec -1]
[21]
Least-square treatment of the data leads to a value of k2 = 1.11 (_+0.1) × l0 II
-9
[kg dm 12 m -2 sec -l mole-l]. The Figs. 6 and 7 show the fair agreement between calculated and observed R-values. Equation [21] can also be used to evaluate the equilibrium constants K~, K~, and K~ from the kinetic data. The values obtained (log K] = 4.6, log *K~ = 9.8, log K~ = 13.1)
-10, [ F - ] = 1.83 x 10 - 4
-11 - 6
log
R
- log [H÷I
FIG. 6. Rate of dissolution at [F-]i = 1.83 × 10-4 as a function of [H÷]. The solid curve was calculated with Eq. [21] with the parameters collected in the Tables II and IlL
opening of A1-O bonds. Although the data do not reveal the details of the mechanism, it would be consistent with the data if the precursor to the activated species was formed by addition of one proton to the AI(OH2)~ species. (b) Solutions with H + and F-. The surface speciation is shown in Fig. 9. At first glance there is no obvious connection between dissolution rate a n d surface speciation. A closer inspection reveals a good correlation between the dissolution rate (corrected for dissolution in the absence of fluoride) and the concentration of the surface species {AI(OH)F-}:
=
-8
.
-9'
-10
-log
[~-]
i
R' = R - k1S[H +]
4
= k2S{AI(OH)F-}[H+]E[F-] 2.
[20]
Upon substitution of the expression for {AI(OH)F-}, the complete rate law can thus be written as Journal of Colloid and Interface Science,
-7
Vol. 101, No. 2, O c t o b e r 1984
5
6
FIG. 7. Rate of dissolution at [H+]i = 1.00 × 10 -4 M as a function of [F-]. At low values of [F-] the solid curve (Eq. [21]) approaches a value of log R = - 1 0 . 6 5 that corresponds to the dissolution rate in the absence of fluoride (Eq. [18], S = 1.5 m2).
563
DISSOLUTION KINETICS OF BAYERITE ~'-17 ._¢
AI(OH)(OH2)
u) 2¢D o
AI(OH2) +
,-%-3 AI(OH) 2
-4"
dissolution
-5"
i
|
-2.8
|
-3.2
-3.6
studies
i
i
-4.0
-4.4 log I'H+]
FlG. 8. Chemical speciation at the bayerite solution interface in the absence of fluoride.
are in reasonable agreement with those given in Table III. On the basis of the foregoing data, the composition of the precursor of the activated species can be written as (OH)2/2F:/2A1 × (OH)F- or (OH)3/2(F)I/2AIF~-. The paramount factor is the replacement of a critical
AI F(0H 2)
number of bridging OH--groups by fluoride which has almost no bridging properties. A possible mechanism of the dissolution process (Fig. 10) can be described as follows. Two bridging OH--groups are replaced by fluoride; it is plausible that this replacement is already favored by foregoing substitution of the terminal water molecule by fluoride. The final ratedetermining step is a concerted opening of the remaining two A1-O bonds. The departing
.(o. ul ~-4F-5
H -4
-5
OH
H
l slow
-6
log [F-] -
•~
F F ~
AIF(0H2)
~-~
-
I fF1 OH
.1
I rapid AI(OH)F~
~ -4
~AIIOH)(OH2) rapid equilibration in solution
log [H ÷] FIG. 9. Chemical speciation at the bayerite solution interface in the presence of fluoride.
..(o.).
7:'/
FIG. 10. Suggested mechanism of dissolution of bayerite in aqueous HNOa-HF solutions. Journal of Colloid and Interface Science, Vol. 101, No. 2, October 1984
564
PULFER ET AL.
species is presumably the fourfold coordinated AI(OH)F3 that equilibratesrapidly in solution to form AI(OH)m(F)n(OH)I~-.~--~+. CONCLUSIONS
T h e rate law (Eq. [21]) contains constants, chemical potential (concentration) terms, and electrostatic potential terms. The occurrence of the electrostatic term is a logical consequence of the fact that the dissolution reaction involves charged species and a charged surface. Any attempt to formulate the rate law o f such a reaction without explicit inclusion of the electrostatic term involves the assumption that the variation in this term over the range of experimental conditions is negligible. Earlier work, in which the validity of this assumption was not examined, must be looked upon with some reserve. Although the present paper results in a consistent model for both adsorption equilibria and dissolution kinetics, this consistency is based on at least partially arbitrary assumptions regarding the structure of the bayerite surface and the magnitude of the double layer capacitance. It should be remembered that the acid-base properties of the bayeritesolution interface can be equally well fitted by a comparatively broad range of interfacial capacitance values (and associated values for K a y , K a y , and Co), i.e., the analysis of the acid-base titration curve does not reveal a unique value for a Helmholtz double layer capacitance. (Moreover, as shown by Westall and Hohl (18), acid-base titrations of oxide surfaces do not even permit to discriminate between diffuse and planar double layers.) The same conclusion applies for studies on the adsorption of metal ions and anions. On the other harid, a good fit of the observed dissolution rates with the aid of Eq. [21] is restricted to a range of ,,~ = 2.65 + 0.05. A favorable interpretation o f this aspect would result in the conclusion that although adsorption studies with oxides and hydroxides do not reveal the structure of the electrical double layer, the additional information is available from kinetic studies. A less favorable interpretation would emphasize Journal of Colloid and Inte(face Science, Vol. 101, No. 2. October 1984
the dependence o f the postulated reaction mechanism on partially arbitrary assumptions and predict that an improved knowledge of both surface structure and electrical double layer will modify our models of dissolution mechanisms. The present authors_ believe that the latter perspective may be closer to reality than the former. ACKNOWLEDGMENTS The authors are indebted to Professor W. Schneider (ETH Ziirich) for valuable discussions. Part of the work was done during a stay of P.W.S. at Gunma University, Kiryu (Japan). P.W.S. is indebted to ProfessorH. Akaiwa for his generous hospitality and for valuable advice. The work was financially supported by the Swiss National Science Foundation. REFERENCES 1. Shying, M. E., Florence, T. M., and Carswell, D. J., J. Inorg. Nucl. Chem. 32, 3493 (1970); 34, 1665 (1972). 2. Barney,G. S., J. Inorg. Nucl, Chem. 39, 1665 (1977). 3. Kline, W. E., and Fogler, H. S., J. Colloid Interface Sci. 82, 93 (1981). 4. Packter, A., and Dhillon, H. S., J. Chem. Soc. (A) 2588 (1969). 5. Cornell, R. M., Posner, A. M., and Quirk, J. P., J. Inorg. Nucl, Chem. 38, 563 (1976). 6. Valverde, N., Ber. Bunsenges. Phys. Chem. 80, 333 (1976). 7. Jones, C. F., Segall, R. L., Smart, R. St, C., and Turner, P. S., J. Chem. Soc. Faraday 1 74, 1615 (1978). 8. Baumgartner, E., Blesa, M. A., and Maroto, A. J. G., J. Chem, Soc. Dalton 1649 (1982). 9. Chang, H.-Ch., and Matijevi6, E., J. Colloid Interface Sci. 92, 479 (1983). 10. Grauer, R., and Stumm, W., Colloid Polym. Sci. 260, 959 (1982). 11. Chesworth, W., Nature Phys. Sci. 230, 65 (1971). 12. Brown, A. C., J. Amer. Chem. Soc. 56, 646 (1934). 13. Forsling, W., Hietanen, S., and Sill6n, L. G., Acta Chem. Scand. 6, 901 (1952). 14. Smith, R. M., and Martell, A. E., "Critical Stability Constants, Volume 4: Inorganic Complexes." Plenum, New York/London, 1976. '. 15. Westall, J. C., "FITEQL, A Computer Program for Determination of Chemical Equilibrium Constants from Experimental Data," Report 82-01, Chemistry Department, Oregon State University, Corvallis, 1982. 16. Baes, Ch. F., and Messmer, R. E., "The Hydrolysis of Cations." Wiley, New York, 1976. 17. Cornell, R. M., Posner, A. M., and Quirk, J. P., Soil Sci. Soc. Amer. Proc. 38, 377 (1974). 18. Westall, J. C., and Hohi, H., Adv. Colloid Interface Sci. 12, 265 (1980).