J. Elecrroanal. Chem.. 182 (1985) 141-156 Ekevier Sequoia S.A.. Lausanne - Printed in The Netherlands 141 ACIDIC AND REDUCTIVE DISSOLUTION OF MACNETYI’F iN AQUEOUS SULFURIC ACID SITE-BINDING MODEL AND EXPERIMENTAL RESULTS VlVIANNE I.E. BRUYkRE and MIGUEL A. BLESA l Depariamenro Quimico de Reactores, Comisibn Nacionol de Energio Afbmica, Aueniub dei tiberrodor 8250. 1429 Buenos Aires (Argenrina) (Received13h~March 1984; in revised form 22nd June 1984) ABSTRACT The open circuit dissolution of ionic metal oxjdes in mineral acids is modelled assuming that the rate is controlled by the transfer of metal ions in hydrolytic equilibrium with bulk metal ions, from the metal oxide surface to the Stem plane. The site-binding model of the double !ayer metal oxide/electrolyw soluticn is used IO obtain the pH dependence of surface and Stem potentials. The nature of the active sites is discussed and their surface concentration is assumed to be proportional to surface charge +_ Again, the site-binding model is used fo determine the pH dependence of oO. It is thus shown that the rate order in cH- is essentially defined by the potential dependence of the charge transfer process, ior oxides with points of zero charge near neutrality that dissolve in miId!y or strongly acidic solutions. The role of surface complexation is also discussed in terms of the site-binding mdel and the difficulties in inierpreting dissolution experiments under constant external appliezl potential are discussed in terms of the complexity of the semiconductor oxide/electrolyte solution interfacial region in magnetite. An experimental study of the open circuit dissolution of magnetite in sulfuric acid is presented and interpreted according to the proposed model. The reductive dissolution or magnetite is modelled by extension of the VaIverde-Wagner model of oxide dissolution. Experimental results are presented to demonstrate that the reductive dissolution rate of magnetite in ferrous containing solutions is conwolled by the rate of electron transfer from adsorbed Fe(I1) to Fe(Ill) surface states of magnetite. INTRODUCTION Currently, a large effort is being devoted to the development of adequate procedures for the chemical cleaning of steel surfaces that have developed an oxide layer by contact with water at high temperature and pressure. The nuclear industry requires such procedures in order to decontankate components and piping in the heat transfer circuit of nUclear power plants and also in order to clean steam * To whom all correspondence should be addressed_ 0022-0728/85/$03.30 0 1985 Ekevier Sequoia S_A.
Transcript
J. Elecrroanal. Chem.. 182 (1985) 141-156
Ekevier Sequoia S.A.. Lausanne - Printed in The Netherlands
141
ACIDIC AND REDUCTIVE DISSOLUTION OF MACNETYI’F iN AQUEOUS SULFURIC ACID
SITE-BINDING MODEL AND EXPERIMENTAL RESULTS
VlVIANNE I.E. BRUYkRE and MIGUEL A. BLESA l
Depariamenro Quimico de Reactores, Comisibn Nacionol de Energio Afbmica, Aueniub dei tiberrodor 8250.
1429 Buenos Aires (Argenrina)
(Received 13h~March 1984; in revised form 22nd June 1984)
ABSTRACT
The open circuit dissolution of ionic metal oxjdes in mineral acids is modelled assuming that the rate is controlled by the transfer of metal ions in hydrolytic equilibrium with bulk metal ions, from the metal
oxide surface to the Stem plane. The site-binding model of the double !ayer metal oxide/electrolyw
soluticn is used IO obtain the pH dependence of surface and Stem potentials. The nature of the active
sites is discussed and their surface concentration is assumed to be proportional to surface charge +_ Again, the site-binding model is used fo determine the pH dependence of oO. It is thus shown that the rate
order in cH- is essentially defined by the potential dependence of the charge transfer process, ior oxides
with points of zero charge near neutrality that dissolve in miId!y or strongly acidic solutions. The role of
surface complexation is also discussed in terms of the site-binding mdel and the difficulties in
inierpreting dissolution experiments under constant external appliezl potential are discussed in terms of
the complexity of the semiconductor oxide/electrolyte solution interfacial region in magnetite. An experimental study of the open circuit dissolution of magnetite in sulfuric acid is presented and
interpreted according to the proposed model. The reductive dissolution or magnetite is modelled by extension of the VaIverde-Wagner model of
oxide dissolution. Experimental results are presented to demonstrate that the reductive dissolution rate of magnetite in ferrous containing solutions is conwolled by the rate of electron transfer from adsorbed Fe(I1) to Fe(Ill) surface states of magnetite.
INTRODUCTION
Currently, a large effort is being devoted to the development of adequate procedures for the chemical cleaning of steel surfaces that have developed an oxide layer by contact with water at high temperature and pressure. The nuclear industry requires such procedures in order to decontankate components and piping in the heat transfer circuit of nUclear power plants and also in order to clean steam
* To whom all correspondence should be addressed_
0022-0728/85/$03.30 0 1985 Ekevier Sequoia S_A.
142
generators from the secondary side, thus preventing corrosion phenomena such as denting and wastage; fouling of heat exchange surfaces is another reason that makes the development of such chemical cleaning procedures urgent.
The state of the art in chemical cleaning and decontamination prescribes the use of acid chelating agents [1,2], reducing agents [3.4]. mixtures of both [5] and special autocatalytic mixtures including ferrous ion [6,7], which come under the special case of mixtures of reducing and complexing agents. Asp a part of our studies on the fundamentals underlying the processes of chemical decontamination, we are engaged in the study of the mechanisms of dissolution of magnetite and other iron oxides in aqueous solutions containing organic chelating acids, both with [8,9] or without [g-11] added ferrous ion. In this context, a critical review of the literature on the dissolution of magnetite by mineral acids was required, and this review suggested the need of a new study of the subject because of the many conflicting views and ambiguities in the available literature. In this paper we present a critical analysis of existing models, a model for the open circuit dissolution of existing models, a model for the open circuit dissolution of ionic oxides in mineral acids and the results of an experimental study of the (open circuit) dissolution of magnetite by sulfuric acid solutions in the temperature range 70-90°C. The influence of ferrous ion is also explored.
Dissolution of a crystalline solid is inherently anisotropic 112). Detailed analysis of the process requires knowledge, not only of the macroscopic dissolution rate, but also of the normal and lateral etch rates [13] and of the influence of additives and impurities on morphology and properties of etch pits [12-141 of high undersatura- tion. where massive dissolution is observed, and the process becomes essentially isotropic.
THE MODELS
Most of the analyses of the mechanism: of dissolution of metal oxides come from electrochemical studies that recognized the importance of applied potential. In the case of magnetite, Engell [15] showed that dissolution takes place under cathodic polarization with a well defiled maximum in the current/voltage profile at ca. 0.21 V (against SHE). This was later confirmed by Haruyama and Masarnura [16] and by Lecuire [17]. The basis of the interpretation was the assumption of rate control by the transfer of ions across the interface and the recognition of cations and anions as independent entities that at steady state should be transferred at the same rate. in a classic paper, Vermilyea [18] proposed a general mode1 in which the potential was essentially determined by the intrinsic rates of dissolution of anions and cations. For the dissolution of a hydroxide, when the rate is controlled by the removal of cations, he arrived at the expression:
R = tl+k,.+[n_k,._c,-/n+k, +]=+=+‘(=+=+ -=-‘-I
where R is the ra!e of dissolution, n, and )I__ are the surface concentrations cf cations and anions, k,, and k,_ are the intrinsic rate constants for transfer of
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cations and anions. The parameters a+ and a_ are the electrochemical transfer coefficients, and L + and z_ the charges of the transferred ions. Equation (1) gives and explicit dependence of rate on solution pH:
(a log R/apH) = -a+z+/(a+z+ -a-z_) (2)
In the more general case, the factor (n/v) expressing the ra!io of the stoichiomet- ric number of protons to the number actually involved in the dissolution step should be included [19].
(Cl log R/apH) = -(n/v)[a+z+/(a+z+ -a-z_)] (3)
The ideas of Vermilyea thus took into account the fact that oxides are not ideally polarizable electrodes, but rather they behave under certain conditions as ideally reversible electrodes, H+ and OH- being the potential determining ions 119,201. Even accepting the restricted case of a+ = a_ = 0.5, this model can accommodate any of a large number of fractional values for the order of reaction in protons, ranging from 0.50 to 1.33. Examples of the predictions of Vermilyea are gi\,en in Table 1. These ideas have beer. widely used in the litemture to :ationalize experimen- tal reaction orders in protons (see e.g. ref. 21).
The complexities of the double layer at the magnetite/aqueous solution interface are well known, and as Diggle pointed out [19]. only the potential drop between the solid surface and the Helmholtz plane is relevant for di.:solution; it was thus expected that the dependence of dissolution on applied potentii*l was not simple nor easy to interpret. This was confirmed by the experimental study of Allen et al. [22], who measured the rate of dissolution under conditions of constant applied potential. The complexity of ‘he double layer when perturbed by an applied external potential is best illustrated by the measurements of the differential capacitance [23j, these show the influence of semiconductor surface states. For an analysis of the influence of semiconductor electronic structure in the dissolution process. see refs. 19 and 24.
A very different approach to the problem was taken by Vaiverde and Wagner [25-271. These authors chose to make a thorough list of the possible factors influencing the rate, arriving at the following general equation for the dissolution of
magnetite, under conditions of rate control by caticn transfer:
R=xD r.~i.i.2Lj.2) exp$ ici.~,~~i.G4/R~) + ij
+CCk r.Yi.i.3Jh.j.3) exd a+;. 3)z+tj. 32’WRT) i j
(4)
which allows for the contribution to the overall rate of both di- and tri-valent metal ions placed in various types of kinks, each characterized by the number of bound complexing ions i and the number of available adjacent protons i_ Here l?, is the surface concentration of such kinks and Ic, is the relevant potential change. In cc)ngruent dissolution. the first and second terms on the r.h.s. must be related to the stoichiomettic ratio of both types of ions; if the interconversion of Fe(III) and Fe(II) is ruled out, this usually means that the second term only will dominate the dissolution_ We shall come back later to the case of reductive dissolution.
The pH dependence of the rate of dissolution is determined according to cqn. (4) by: (a), the pH dependence of the T,‘s; for this in some cases some type of equilibrium isotherm was assumed [18,28,29]; other authors have claimed that formation of the kink by proton att:ick can be rate determining 1301; (b), the pH dependence of z+ ; as shown in some of our previous work [9,31] and by other authors 132,331 the species on the surface of the oxide may vary with changing pH: (c) the pH dependence of I/J. This is discussed below, but it should be noted that Valverde and Wagner do not assume that 4 is solely determined by the intrinsic rate of phase transfer of metal cations and oxide anions.
The charge cc and potential #c on the surface of non-dissolving ionic metal oxides immersed in electrolytic solutions is determined by the extent of adsorption.of H’ and OH- [2$34]. At present there are models avaiIab!e that give a rather detailed picture of this interface. In particular, the site-binding model [34-381 offers the picture given in Fig. 1; the model involves three planes: the surface plane and the inner and outer Helmholtz planes. These are identified by the subscripts zero, /3 and d respectively. The corresponding potentials +a, ‘Ls and $J~, and charges a,, up and ad, as well as the capacity C, of the innermost layer can be determined experimen- tally [37-401 from acid-base titration data. Surface ionization equilibria (eqns. 5-8) are described by equilibrium constants that are also obtained from acid-base titration data. In the case of magnetite all this information is available in the temperature range 25-80°C. For our purposes, the important quantities are the potentials #,, and Gs, and the surface charge a,.
-Fe-OH: = -Fe-OH + H’
-Fe-OH = -Fe-O- + H+
K‘E’ (5) K in1
a2 (6)
-Fe-OH+ z . . .NO, = -Fe-OH + H+ + NO; *K& (7)
-Fe-OH + K+ = -Fe-O- . . . K+ + H’ *Kin: K’ (8)
Profiles of I/J,, and #LB (including also $d) vs. pH are shown in Fig. 2; the slope
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i i i
Fig. 1. Schematic representation of the metal oxide-solution interface according IO the site-binding model. I,L represents potential. The Three planes defined by the subscripts zero. J3 and dare the surface and inner and outer Helmholtz planes respectively. C, and C, are the capacities for the inner and outer region of the compact layer.
-50 -
-100 -
-150
Fig. 2. pH dependence of & (- ). +B (- - -). and I/J~ (-- - .-) for magnetit: in aqueous KNO, (0.1 mol dm-‘) at 80 “C (from ref. 41). For the meaning of symbols, refer to Fig. 1.
(i!I$,/apH) is less than (59 T/298) mV/pH unit, the deviation becoming increas- ingly important with increasing temperature. The extent of the deviation is given by the site-binding model [42] as:
(4” - q/p: )= -(RT/ZF) ln(6+/8_) (9)
or
where O+ and 8_ are the fractions of -Fe-OH; and -Fe-O- surface sites respectively. According to eqn. (10) (see also Fig. i), /3 is close to unity and roughly independent of pH. Experimental evidence shows that Go is related to pH through eqn. (11). where pH, is the pH of the point of zero charge of the oxide (6.00 for magnetite at 80°C [41]):
$0 = 2.3( PRT/F)(pH, - PHI (11)
We shall take the view that in the rate determining step ions are transferred from the zero plane to the P-plane, i.e. across the potential difference 4” - z,L~. Using the nomenclature y = 1 - ( IJ~/+IJ/,), we can write:
G/o - $,r = ~.~(PYRT/F)(PH, - PHI (12)
Both j3 and y can be calculated from the site-binding model; typically (see Fig. 2) y - 0.6, p - 0.8 for the experimental conditions of the dissolution experiments [41].
Next, we shall write for the concentration of active protonated kinks:
r, = {-Fe-OH;} + {-Fe-OH: . ..X-} (13)
or
$.= (e,,/F)= (c,/F)&-Gfi) (14)
These are the site-binding model equations for the concentration of protonated sites in the surface; in writing eqns. (13) and (14) there are some assumptions that must be mentioned. First, only one type of surface site is assumed to be involved in dissolution (or more correctly, two types of sites with identical reactivity); second, either all protonated sites are considered reactive or a certain constant (albeit unknown) fraction of the total number of protonated sites participates in the reaction. This latter assumption seems more reasonable.
Valverde and Wagner’s equation (4) is therefore simplified to:
R=k(C,/F)($,,-#P) expa+Z+F(#U-#,p)/RT (15)
From eqns. (12) and (15) the pH dependence of R is
- (a log R/apH) = o+z+Py +(pH, - PHI-’ (16)
The first term in the r.h.s. of eqn. (16) represents the electrochemical nature of the ion transfer process, and for dissolution conditions such as (pH,-pH) is large, it
147
dominates the pH dependence of the rate of dissolution. By using experimental or model values for /I and y, it provides a!,=+ and hence I, if the value for the transfer coefficient can be assumed to be 0.5. The second term arises from the pH depen- dence of the concentration of pro!onated sites on the surface and it should be important for oxides with low pH, values. Equation (16) can hard]]. be considered as predictive, although data for the dissolution of silica and other oxides with low pH,‘s may yield a useful test for its validity. It is however consistent with current models of the metal oxide/water interface and with experimental results for open circuit dissolution. Under conditions of applied external potential. the system can be considered neither ideally reversible nor ideally polarizable. and thus the interpre- ?ation is not easy; complex couplings are expected, as experimentally found by Allen et al. [22]_
Equation (16) (as well as eqn. 4) assumes cation transfer control. It is convenient to show that -at least for open circuit conditions in iron oxide systems-this must be the case. When compared with the time scale of dissolution. protonation-depro- tonation equilibria on the oxide surface are fast. For silica, some of these processes have been measured by Ikeda et al. [43]. who found the following expressions for the forward and reverse rate constants for the equilibrium analogous to eqn. (5):
k, = 46 exp( F#,/2RT) s-’ (17)
k-j = 2.9 X lo4 exp( -F#,/2RT) M-‘s-’ (18)
which represent fast processes for ]$e] < 200 mV. Water exchange on Fe(III) is also a fast process. In Table 2 we show some results
from the literature which illustrate this point. It must be concluded therefore that “bare” surface Fe(II1) ions will not exist as such, but will be essentially equilibrated
with -Fe-OH: species, such as depicted in equilibrium (5). Because of the character of oxide ion as a constituent of the solvent, there is no transfer of free anions; they are transferred bound to the cation. This is true both for inert and labile M-O bonds. In the latter case, oxygen interchanges with the solvent easily, but such interchange is essentially in equilibrium and net transfer takes place only associated with metal cation transfer. This has been dramatically shown in the case of MgO, where the initial rate is first order in Mg’+ concentration in bulk; the r.d.s. is considered to be the transfer of H,O and this is accelerated by the availability of
TABLE 2
Species 7/S Reference
Fe(H?O):+ 6.0x lo-’ 44
Fe(OH)(H,O);- 1.5 x 1o-6 45
FedOH)4(HzO)?,’ 5.8x10-7 46
u-0x0 oligomer 3.9x1o-8 46
148
Mg”+ in the Stern plane (47). This analysis leads to the conclusion that even in a disintegrating interface the potential is not determined by the excess of cations over anions, but rather by the acid-base properties of the surface cations. .The critical parameter z + is determined therefore by the extent of hydrolysis of transferred Fe(III), e.g. F(H,O)i’, Fe(OH)(H,O)g+ or Fe(OH),(H20)f_ As we shah see, experimental data in our system suggest that the transferred species is essentially equilibrated with bulk solution. The dissolution of LX-Al,O, in oxalic acid presents a term proportional to CL- [28] and this seems to corroborate the above idea.
The identification of transferred species as Fe(H,O)z’ requires that k in eqn. (15) be given the meaning of a kinetic constant times a (very small) pre-equilibrium constanl, and that the activation energy associated with k be interpreted as including the corresponding equilibrium enthalpy changes.
The above model, though applied to magnetite, is in fact based on the analysis of the transfer of one relevant cation only. Thus, it requires further elaboration for the case of magnetite, which can be represented as [Fe(IIi)],[Fe(III)F~Ii)]~O~ (A and B denote octahedral and tetrahedral holes in the cubic close packing of oxide ions). Valverde [27] considered two possibilities: (a) that the overall rate be governed by the rate of release of the more labile species (Fe(I1) in this case); because of extensive disruption of the lattice during this event, the less labile species would simulta- neously be transferred; (b) that the overall rate be governed by the rate of release of the less labile species. There is compelling evidence that magnetite dissolution is governed by the release of Fe(III), this explains for instance the electrochemical data [15-191, the reductive dissolution data [3,4,8,9,48-511, and some properties of the
passive oxide on iron and its alloys [52-S]. The experimental results of Valverde [26] showed that the redox potential of the solution affects the rate of dissolution of magnetite and he interpreted this result in terms of changes in the ratio [Fe(III)]/[Fe(II)J in the surface; however, he also noticed a dependence on the overall concentration of the redox buffer, as was the case for the cou3le V(IV)/V(III).
The idea of a surface composition and potential determined by the solution potential was also used by Gorichev et al. [56,57] and by Malysheva et al. [58] to describe the dissolution of magnetite in describe the dissolution of magnetite in the presence of the Fe(II)/Fe(III) couple. According to Gorichev et al.
R = ka~~?a~~~~,U;~i:l, (19)
and this rate law was interpreted as indicative of 2 potential determined by the redox
potential in solution, i.e. through equilibration of surface and solution potentiai through a fast exchange current. In the dissolution of magnetite by ferrous ions in the presence of several complexing agents, we have found a rate that is first order in the concentration of the electroactive species, viz Fe(&O,)z- or Fe(NTA)- [6,59-611. In these cases, the rate of electron transfer across the interface becomes limiting, rather than the rate of cation transfer. In terms of Valverde and Wagner’s
equation (4), if kr.+ci.j.2J =+ kr.yi.J.3) the rate becomes controlled by the removal of Fe(II1) because I?c(i.i.2, falls to a very low steady state value. When interconversion of FelIJI) and Fe(II) is taken into account, the two parallel reactions scheme implicit in
eqn. (4) must be modified to:
- Fe(rI)k’.Y=BFe(Ir)(aq)
ik,
-Fe(III)Br.:%e(III)(aq)
The reduction of surface F4III) is a heterogeneous electron transfer process ant. involves a reductant placed in the Stem plane; this process can be treated in terms 0, Marcus’ theory [62-641. Provided there is an adequate Gibbs energy change in this process, the reverse oxidation of surface Fe(II) ought not to be important and all ferrous ions formed will be essentiahy released into solution. Furthermore, the required activation of solvation and coordination modes [65] suggests that the Fe(I1) originated in the electron transfer process will be highly activated and therefore easily released into solution. Allen et al. have forwarded experimental evidence that indeed Fe(H) from Fe(II1) reduction is more easily transferred than constitutive Fe(I1) [49]. The rate of dissolution is:
R = &-I&.j.3)Ld.l3 (2Ij
where L.p represents the concentration of reductant in the fi plane. This reductive process dominates the dissolution of magnetite in the presence of chelating agents that stabilize the 3+ oxidation state of iron, and are discussed in detail elsewhere [59-61,641. At present there is no experimental evidence that such a pathway is operative in the dissolution in minera! acids. The form of eqn. (21) suggests that this pathway should iead to a first order dependence on Fe(II), because adsorption of Fe(II) in acidic media is an unfavorable process [9], and I?,, B is a first order function of bulk Fe(I1) concentration under all reasonable conditions.
In summary, the present model uses Wagner and Valverde’s approach as given by eqn. (4) for the dissolution of a metal oxide and assumes that only one type of kink needs to be recognized. This kink, in the case of magnetite corresponds to a surface Fe(II1) ion; direct transfer may take place as Fe(H,O)i+ or complexed species such as FeSOl. The potential 4 in eqn. (4) is identified as $,-, - $J~; this magnitude, and
also r,,i.j.3) are calculated using the site-binding treatment of the interface on the basis of acid-base titration data. Fe(II1) in the kink may also be reduced by a reductant adsorbed in the inner Hehnholtz plane and later transferred as Fe(H,O)i+. When the reductant is Fe(II), the electron transfer from the IHP to the surface kink may be rate determining, giving rise to a dissolution rate that is first order in Fe(I1).
In what foJ.Iows we shall present the experimental results for the dissolution of magnetite in sulfuric acid solutions, including ferrous-containing solutions, in order to test the ideas put forward above. It must be emphasized that, because of the scarcity of experimental information, considering the complexity of the problem, it should not be expected that experimental data unambiguously prove the proposed mechanism; the results should however be consistent with it, and this is demon- strated below.
150
EXPERIMENTAL
Magnetite was prepared following the technique described previously [66], and
characterized by chemical analyses, X-ray diffraction, Moessbauer spectroscopy, scanning electron microscopy and specific surface area measurements by N, adsorp- tion at low temperature and calculations through the BET equation. All kinetic runs were performed with the same batch; it was composed of cube-octahedral particles
with edges ca. 0.15 pm in length. No other oxides were present. For further details,
see refs. 66 and 67. Kinetic runs were carried out in a thermostated jacketed glass vessel provided
with a Teflon stopper which allowed sampling, stirring, N, bubbling and tempera- ture measurement. Temperature was controlled to +O.l?C. Stirring (either magnetic or mechanical) maintained a dissolution regime that was independent of stirring rate, i.e., dissolution was not diffusion controlled. In a typical run, 50 m8, magnetite were suspended in water under continuous stirring and N,bubbling. After 30 min equilibration, dissolution was started by adding an aqueous sulfuric acid solution of appropriate concentration to yield the desired acidity and a total final volume of 150 cm3. Aliquots (0.50 or 1.00 cm)) were withdrawn periodically, and immediately quenched by pouring them into a large amount of water at room temperature. The suspension thus formed was immediately filtered through cellulose nitrate mem- branes (pore size 0.1 urn) and iron was determined spectrophotometrically by the o-phenanthroline method [68], using hydroxylamine as reducing agent. Occasionally ferrous and total iron were independently measured and the results showed in every case congruent dissolution. Initial rates R, in moles dissolved per unit area and per
second were obtained by least squares fitting of the initial (linear) part of the plot cf dissolved iron as a function of time.
Similar procedures were used to determine the rate of dissolution in the presence
of ferrous ion. This was added as solid Fe(NH,),(SO,), - 6 H,O just before sulfuric acid addition. In some experiments, KzSO, was also added to obtain solutions of identical pH but varying sulfate total concentration.
All reagents were analytical grade, or better, and water was tridistilied, twice from
a quartz apparatus.
RESULTS AND DISCUSSION
Magnetite completely dissolves in the sulfuric acid so!utions under the conditions of our experiments. In spite of the use of the same batch of magnetite for all the expc.riments, the shape of the dissolution profiles (dissolved Fe vs. tune) were not identical. Gorichev et al. [69] have discussed the problem of separating geometrical factors from factors influencing the intrinsic reactivity in the analysis of conversion/time curves. Comparison of rate constants is meaningful only if the sequerlce of stages (nucleation, growth of nuclei, contracting geometry) remains unchanged in the whole set of experiments. This is approximately true for our system, except for a short initial acceleratoty period in some experiments. Compari-
sons are therefore made on rates of dissolution. measured as the maximum slope of the .dissolved iron/time profile; this was usually the initial slope, but in the cases noted above it was measured after the acceleratory period. This procedure is
equivalent to accepting the contracting sphere.geometry laws and, in fact. plots of 1 - (1 -f)‘/’ vs. I wsle linear except for the noted periods (/ is the fraction of magnetite dissolved at time i). All rates are therefore expressed as amount of iron transferred to (constant volume) solution per unit surface area and time; control
experiments showed that cFLinrr/cF,..,,, was 2: 1 throughout the dissolution without any indication of incongruent di:;solution; rates are expressed accordingly in terms of total dissolved iron. Analysis of activity data for concentrated sulfuric acid solutions 1701 shows that H,SO, molality and uH. are proportional in the studied range and thus there is no need to account for deviations from idenlity. unless
absolute values of k are to be determined. Figure 3 shows the dependence of the initial rate of dissolution on the molality of
sulfuric acid at 70. 80 and 90cC. The curves can be recast in the form
log R = log R, + ilog nzH,sl,4 (22)
E.xcept for the data at the higher acidities and temperatures (dashed part of the uppei curve in Fig. 3), good straight lines are obtained in the plots of log R vs. log
‘)!Ii,SO,* the slopes yielding the apparent order in protons as 0.83. 0.83 and 0.79 for 7Q. 80 and 90°C respectively The contribution to these numbers from CY+Z+~Y is obtained in Fig. 4, where log [ R/(pH, - pH)] is plotted vs. pH, - pH. The values for pH, at each temperature were taken (directly or by interpolation or extrapola-
tion) from the data in ref. 41. The figures obtained from the slope of Fig. 4 are 0.80. 0.75 and 0.72 for 70. 80 and 90°C respectively. These values are easily rationalized assuming H + = 3. with the approximate valze a,.fiy = 0.25. The small change with
Fig. 3. Inilial rate of dissolution of magnetite in aqueous sulfuric acid r:s a function of acid molalicy at 70
(0). 80 (e) and 9Cl (s) “C.
152
temperature may reflect the decrease in By upon increasing temperature [41). The difference between n (see eqn. 22) and a,~+/37 are more important at 9o°C, probably because the lower acidities employed at higher temperatures make the second term in eqn. (16) more important.
The activation energy associated with the rate constant k in kqn. (15) can be obtained from Fig. 4, from the extrapolated values of log[R/(pH, - pH)] to pH, - pH = 0. In order to do this, corrections were introduced to take into account the dependence of the capacity C, on temperature [41], and the log T term arising from eqn. (12). The results are shown in Fig. 5; this gives the value E, = 136 kJ mol-‘. As stated above, this figure certainly includes enthalpy terms for protonation equilibria, as well as the kinetic activation energy proper.
The dependence of the rate of dissolution on temperature is dependent on
- 9 l log. R/ mol t-r? S’
pH.-pH
I 5.0
I I P&-P”
5.5 6.0
Fig. 4. Plot of log( R/(pHo -pH)) as a funclion of pE I0 -pH at 70 (A), 80 (I) and 90 (a) “C.
L lo3 T/K’ , 1 2.75 2.80 2.85 2.90
J
Fig. 5. Plot of lo& R/(pH, - pH)) extrapolated to pH, - pH = 0 as a function of T-l.
153
solution pH. This is predicted by our model and is confirmed by the experimental data, which indicate increasing activation energy with increasing pH in the range O-l. Our model predicts
E”pp = E= -’ 2.3RT - 2.3R a log c, AH,, + AH,,
U a(l/T) +-- ~(PH, - pH) (23)
Although this equation cannot be demonstrated quantitatively, the qualitative agree- ment is satisfactory in view of the approximations involved. The enthalpy terms in eqn. (23) correspond to equilibria (5) and (6).
Our data in the pH range O-l yield an average value EZPP = 71 kJ mol-‘, and this compared reasonably well with the value reported by Sidhu et ai. for the dissolution of magnetite in 0.5 A4 HCI at 25 “C [71]; these authors report 79.4 kJ mol-‘. We
shall not ana$ze the value of ths preexponential term, as this magnitude cannot be analyzed unless the actual relation between the number of active sites and u,, is kncwn and corrections for hydrogen ion activity are introduced, even then the resulting magnitude is sensitive to details in the surface structure and morphology that change from sample to sample [72].
The rise in the rate/acid molality curve at 00 OC and acidities higher than 1 M is obvious in Fig. 3 and represents the onset of a new phenomenon, probably the influence of anion complexation on the rate. The model postulated above includes implicitly the influence of anions according to the site-binding model: &he charge o, is determined by both -Fe-OH: and -Fe-OH: . _ .X- sites, the latter being by far the more abundant at high ionic strengths [73]. There is however a second possible type of interaction, the chemisorption, which is best described as an anion exchange process between -OH surface groups and the anions, eqn. (24):
-Fe-OH + H+ + HSO; = -Fe-SO,H + H,O (24)
This type of interaction has been well documenttid for compiexing anions (see ref. 9 and references therein) and can also take place for comIAexing inorganic anions [32,33j. The rise in the curve of rate vs. acid modality is indicative of the involvement of surface complexes of sulfate with iron( which are likely to be transferled more easily than fully aquated Fe(III). Similar involvement of surface chloride complexes has been postulated by other authors 130,741.
In the presence of Fe(H), dissolution at 70 “C in 1 m or 1.5 m sulfuric acid is accelerated, as shown in Fig. 6. These data are consistent with a rate law of the. type:
R’ = R + k’cFe(,,) (24)
where R is the rate of dissolution in the absence of Fe(H), as discussed above. The first order dependence of the second pathway is at variance with Gorichev’s results [56,57], and agrees wirh our own results on the ferrous ion assisted dissolution of magnetite in oxalic ;?I. ethylenediaminetetraacetic [9], and nitrilotriacetic [59] acids. Gorichev’s interpretation requires that the rate be proportional to [cFti,,~/cFe(,n~]u~; our own data suggest that the rate of electron transfer determines the rate of dissolution and this is in agreement with the results of Allen et al. [49], who even
154
10’ R/mbl ni2S’ 1.1 -
1.0 -
0.9 -
0.8 -
0.4tr 10
3 C&&mol dni3
o’30 1 2 3 4 5 6 7 8
Fig. 6. Rate of dissolutton of magnetite in aqueous sulluric acid (1.00 m) at 70°C for various concentrations of added Fe(l1).
suggest that the Fe(II) Ions formed in the surface by electron transfer are + a highly reactive state, thereby breaking the remaining bonds with the crystal lattice more easily than structural Fe(!Ij. Even in the absence of added Fe(lI), this reductive pathway is certainly of importance in the later stages of dissolution [8,71]. Marcus’s theory of electron transfer [62-651 easily rationalizes this idea; the site receiving the electron would correspond to a surface state of the semiconductor with an apprecia- ble degree of solvent and coordinating sphere polarization [75]. A more detailed study of this heterogeneous charge-transfer mediated dissolution of semiconductor oxides is under way.
ACKNOWLEDGEMENTS
To. A.E. Regazzoni for helpful discussions. To SUBCYT for partial support. V.I.E.B. is a Fellow of the Comision de Investigaciones Cientificas de la Provincia de Buenos Aires; M.A.B. is a member of Consejo National de Investigaciones Cientificas y Tecnicas.
REFERENCES
J.W. Ayres (Ed.), Decontamination of Nuclear Reactors and Equipment. The Roland Press Co., New York, 1970. M.M. Osterhout (Ed.), Decontamination and Decommissioning of Nuclear Facilities, Plenum Press, New York, 1979. G. Bradbuty, M.G. Se@. T. Swan, G.C.W. Cotnfey and D.J. Ferrett. Nucl. Energy, 20 (1981) 403. M.5. Segal and T. Swan. Water Chemistry of Nuclear Reactor Systems, 3, British Nuclear Energy Scciety. London, 1983. p. 187. Ri. Clark. A.P. Johnson and RA. Shaw in Canadian Nuclear Association and American Nuclear Society (Eds.), Decontamination of Nuclear Facilities. VoL 2, 1982, p. 3-61.
155
6 M.A. Blesa and A.J.G. Maroto in Canadian Nuclear Association and American Nuclear Socirly
(Eds.). Decontamination of Nuclear Facilities. Keynote Addresses. 1982. 7 M.A. Blesa and A.J.G. Maroto, Argentine Patent 227. 255 (1982). 8 E.C. Baumgarmer. M.A. Blesa. H.A. Marinovich and A.J.G. Maroto. Inorg. Chem.. 22 (1983) 2224. 9 M.A. Blesa. E.B. Borghi. A.J.G. hlaroto and A.E. Regazzoni, J. Colloid Interface Sri., 98 (1984) 295.
10 E.H. Rueda, M.A. Bless and R.L. Grassi. Third Argentine Congress of Physical Chemistry, La Plats, Argentina. 1983.
11 EC. Baumgartner. M.A. Bless and AJ.G. hlaroto. J. Chem. Sot. Dalton Trans.. (1982) 1649. 12 N. Cabrera in J.H. De Boer (Ed.), Reactivity of So!ids. Elscvier. Amsterdam, 1961. p. 345. 13 K. Sangwal, J. hlater. Sci., 15 (1980) 237. 14 K Sangwal, 5. Mater. Sci., 17 (1982) 3598. 15 H.J. Engell, Z. Phys. Chem. N.F., 7 (1956) 158. 16 S. Haruyama and K. Masamura. Corros. Sci., 18 (1973) 263. 17 J.M. Lecuire. Ph. D. Thesis, University of Nancy 1. Nancy, France. 19i4. 18 D.A. Vermilyea. J. Eleztrochem. Sot., 113 (1966) 1067. 19 J.W. Diggle in J.W. i)iggle (Ed.). Oxides and Oxide Layers, Vol. 2, Marcel Dekker. New York. 1973.
p. 281. 20 Y.G. Berube and P.L. de Bruyn. J. Colloid Interface Sci., 27.(1968) 305. 21 RL. Segall. R&C. Smarr and P.S. Turner. J. Chem. Sot. Faraday Trans. 1, 74 (:978) 2907. 22 P.D. Allen, N.A. Harnpson and G.J. Bignold, Surf. Technol. 12 (1982) 199. 23 P.D. Alien, N.A. Hampson and G.J. Bignold. Surf. Technol. 9 (1979) 395. 24 C.F. Jones. R.L. SegaB. R.St.C. Smart and P.S. Turner. J. Chem. Sot. Faraday Trans. 1. 74 (1978)
1615. 25 N. Valverde and C. Wagner. Ber. Bunsenges. Phys. Chem., 80 (1976) 330. 26 N. Valverde, Ber. Bunsenges. Phys. Chem.. 80 (1976) 333. 27 N. Valverde, Ber. Bunsenges. Phys. Chem., 81 (1977) 380. 28 R. Grauer and W. Stumm. Colloid Polym. Sci.. 260 (1982) 959. 29 W. Stumm, G. Furrer and B. Kunz, Croar. Chem. Acta, in press. 30 RM. Cornell, A.M. Posner and J.P. Quirk J. Inorg. Nucl. Chem.. 38 (1976) 563.
31 M.A. Bless A-I-G. Maroto and A.E Regazzoni. J. CoUoid Interhce !&i.. 99 (1984: 32.
32 J.A. Davis and J.O. Leckie in EA_ Jenne (Ed.), Chemical Modeling in Aqueous Systems, (ACS Symp. Ser. 93). American Chemical Society, 1979, p. 299.
33 W. Stumm. R. Kummert and L. SigA Croat_ Chem. Acla. 53 (1980) 291. 34 RO. James and G.A. Parks in E Matijevic (Ed.). Surface and Colloid Science. Vol. 12. Plenum Press,
New York, 1982, Ch. 2. 35 D.E. Yams, S. Levine a?d T.W. Healy. J. Chem. Sot. Faraday Trans. I. 70 (1974) 1807. 36 G.R. Wiese, R.O. James, D.E. Yates and T.W. Healy in J.O’M Bockris (Ed.), international Review of
Science, Physics and Chemistry Series 2, Vol. 6, Bultetworths, London, 1976.
37 J.A. Davis, R.O. Jamesand J.O. Leckie. J. Colloid Interface Sci. 63 (1978) 480. 38 RO. James, J.A. Davis and J.O. Leckie. J. Colloid Interface Sci., 65 (1978) 311. 39 W. Smit and C.L.M. Holten. 5. Colloid Interface Sci.. 78 (1980) 1. 40 A.E Reg-ni, Ph. D. Thesis, University of Tucum&, Argentina, 1984 41 M.A. Bless. N.M. Figliolia, A.J.G. Mar010 and A.E. Regazzoni. J. Colloid laterface Sci., in press. 42 S. Levine and A.L. Smith. Discuss. Faraday Sot., 52 (1971) 290. 43 T. Ikeda, S. Sasaki. K Hachiya T. Yasunaga &rd Z.A. Schelly, J. Phys. Chem., 86 (1982) 3861. 44 E. Mentasti, E. Pelizzetti and G. Saini. J. Chem Sot. Dalton Trans.. (1974) 1944. 45 D.W. Margerum, G.R Cayley. DC. Weatherbum and G.J. Pagenkopf. in A.E. hfarrell (Ed.),
Coordination Chemistry, Vol. 2, (American Chemical Society Monograph 174). Am. Chem. Sot., 1978, p. 1.
46 H.W. Dodgen. G. Lin and J.P. Hunt, Inorg. Chem.. 20 (1981) 1002. 47 C.F. Jones. RL. See _,a!!, P_St.C. Smart and P.S. Turner, Proc. R. Sot. London ser. A, 374 (1981) 141. 48 M.G. Segal and RM. Sellers , J. Chem. Sot. Faraday Trans. 1. 78 (1982) 1149.
156
49 G.C. Allen. R.M. Sellers and P.M. Tucker. Philos. Man. B. 48 (1983) L5.
50 51 52
53 54 55 56 57
58
59
60
61 62
63
64
65 66 67
68 69
D.W. Shoesmith, T.E. Xumm cry, W. Lee and D.G. Owen. Power In-d. Res.. 1 (1981) 43. D.W. Shoesmith. W. Lee and D.G. Owen. Power Ind. Res., 1 (1981) 253.- A.M. Sukhotin, EA. Gankin and A.1. Kentov. Zashch. Met. (EngI. Trami.). 11 (1975) 156. and
references therein. M. Nagayama and M. Cohen, J. EIectrochem. Sot., 119 (1972) 139. J.L. Ord and D-l. De Smet. J. Electrochem. Sot., 123 (1976) 1876. A.hl. Sukhotin and D. Reies lola. Elektrokhimiya (EngI. Transl.). 18 (1982) 723. I.G. Gorichev and N.A. Kipriyanov. Zh. Prikl. Khim. Moscow (Engl. Transl.). 52 (1979) 473. IS. Mikbal’chencko. I.G. Gorichev, V.F. Gorsheneva and N.A. Kipriyanov, Russ. J. Appl. Chem. (Bngl. Transl). 54 (1981) 651. T.V. Malysheva, AS. Afanas’ev. V.V. Shevchenko. E.M. Chudnovskii aad E.N. Bloshchinskaya.
Zashch. Met. (Engl. Transl.). 11 (1975) 323. M. del V. HidaIgo, EC. Baumgartner and MA. Bless, Third Argentine Congress of Physical Chemistry. La Plata Argentina 1983.
E.C. Baumgartner. MA. Bless. H.A. Marinovich and AJ.G. Maroto. Th?d Argentine Congress of Physical Chemistry, La Plata, Argentina, 1983. MA Bless. E.B. Borghi and A.E Regazzoni, unpublished results.
RA. Marcus, J. Phys. Chem., 43 (1965) 679. W.L. Reynolds and R.W. Lumry, Mechanism of Electron Transfer. The Ronald Press Co.. New York. 1966. M.A. Blesa. Third Argentine Congress of Physical Chemistry, La Plata, Argentina, 1983. N. Sutin. Act. Chem. Res.. 15 (1982) 275. A.E. Regazzoni. GA_ Urrutia. MA. Blesa and AJ.G. Maroto, J. Inorg. Nucl. Chem., 43 (1981) 1489. h1.A. Bless. AJ.G. Maro~o, S.1. Passaggio, F. Labenski and C. Saragovi-Badler. Radial. Phys. Chem.. 11 (1978) 321.
A.I. Vogel, Quantitative Inorganic Analysis (3rd Edn.), Longmans, London, 1961. p. 787. I.G. Gorichev. N.A. Kiptiyanov, S.K. Vainman and N.P. Shevelev. Russ. J. Appl. Chem. (En& Transl.), 54 (1981) 43.
70 W.L. Gardner. R.E. Mitchell and J.W. Cobble, J. Phys. Chem.. 73 (1969) 2021. 71 P.S. Sidhu. RJ. Gilkes, RM. Cornell, A.M. Posner and J.P. Quirk, Clays Clay htiner., 29 (1981) 269. 72 ME. Shying. J. Inorg. Nucl. Chem.. 37 (1975) 2339. 73 A.E. Regazzoni, M.A. Bless and A.J.G. Maroto, J. Colloid Interface Sci.. 91 (1983) 560. 74 V.S. Surana and I.H. Warren, Inst. Min. Metall. Trans. Sect. C. 79 (1969) 133. 75 W. Schmickler, J. Electroartal. Chem.. 137 (1982) 189.
