Chapter 5 Kinetics of Mineral Dissolutionepsc511.wustl.edu/Mineral_Dissolution_Kinetics.pdf · ·...

Chapter 5Kinetics of Mineral Dissolution

Susan L. Brantley

5.1 Introduction

5.1.1 Importance of Dissolution Reactions

The rates of mineral dissolution contribute to processes controlling soil fertility,porosity in aquifers and oil reservoirs, transport and sequestration of contaminantsand CO2, cycling of metals and formation of ore deposits, and many other geochem-ical characteristics and phenomena. For example, the weathering rates of Ca- andMg-silicates influence the concentrations of CO2 in the atmosphere over 105–106 ytimescales, impacting the global carbon cycle. Mineral dissolution thus influencesthe chemical and physical nature of our landscape as well as the quality and quantityof potable water and fertile soil available to sustain ecosystems. The rates of min-eral dissolution (Fig. 5.1) determine the lifetimes of minerals in soil environments.Especially since the 1970s, researchers have focused on measurement of mineraldissolution rates in order to promote quantitative prediction of the evolution of ourenvironment (Stumm, 1997). In this chapter, we discuss many of the concepts andmodels used to predict mineral dissolution rates for oxide, carbonate, and silicateminerals.

5.1.2 Steady-State Dissolution

In general, for dissolution of a mineral AυA BυB described by

AυABυB(S) → vAAqA(aq) + vBBqB

(aq), (5.1)

Pennsylvania State University, Center for Environmental Kinetics Analysis, Earth and Environ-mental Systems Institute, [email protected]

151

152 Susan L. Brantley

12108642pH

ApatiteForsteriteBasaltDiopsideAnorthiteAlbiteBiotiteHornblendeQuartzKaolinite

Fig. 5.1 Predicted dissolution rates as a function of pH derived from the fitting results describedin Table 6.3 in Chap. 6 and data compiled in the Appendix. Basalt rates were calculated from atemperature dependent model assuming T = 298K. Kaolinite rates were calculated using a rateconstant from published data (Huertas et al., 1999) as described in Chap. 6.

the rate of reaction, r′, is expressed (in mol mineral reacted per unit time per unitvolume) as

r′ = −d[AυABυB ]dt

=1

υA

d[Aaq]dt

=1

υB

d[Baq]dt

(5.2)

Here, [i] refers to the concentration of species i, νi is the stoichiometric coefficientof the reaction, t is time, and qi is the charge of the aqueous species. Here it isimportant to measure the total concentration of aqueous A and B, regardless ofspeciation, in order to determine the dissolution rate. For example, in analyzing thedissolution rate of gibbsite, the rate of release of all aqueous Al species must be

5 Kinetics of Mineral Dissolution 153

0 1000 2000 3000 4000 5000 6000

pH 5.6 crystalglass

Log

Disso

lution

Rat

e (m

oles

Si/cm

2 /s)

Time (hrs)

Fig. 5.2 Log dissolution rate (expressed as mol Si cm−2 s−1) as a function of reaction time mea-sured for albite crystal and glass in flow experiments (output pH = 5.6) at 25 C as previouslyreported (Hamilton et al., 2000). Rates, normalized using BET surface areas measured on pow-ders at the start of the experiment, decrease to a steady state rate after about 4,000 h. For clarity,only every fifth data point is shown. (Reprinted from Hamilton et al. 2000. With permission fromElsevier).

summed. The most common way to measure mineral dissolution is to measure therate of increase in concentration of solutes as a function of time as described byEq. (5.2); however, analysis of the rate of surface retreat (Dove and Platt, 1996)or rate of disappearance of mass can also be measured (see Chap. 3). If the rateof dissolution of a phase is limited by the interfacial reaction, then the rate of aheterogeneous reaction such as that given by Eq. (5.1) has generally been observedto depend upon the total or reactive mineral surface area. Most mineral dissolutionrates are therefore reported after normalization by the total mineral surface area asmeasured by geometric calculation or by the BET technique. Various approachesused to measure surface area-normalized dissolution rates are described in Chap. 1and will not be further discussed here.

Rates of release of solutes from minerals in water are often used to estimatethe dissolution rate using the initial rate method (Chap. 1). However, dissolutionrates often decrease from the initial value if measured over long periods of disso-lution duration (see for example Fig. 5.2). In addition, rates of dissolution of min-erals pre-weathered under field conditions are generally observed to be slower thanthose measured on laboratory-ground samples (White and Brantley, 2003). In fact,area-normalized release rates, r, of components are often observed to vary withtime according to the function, r = kt−0.5, giving rise to the term parabolic kinetics(Luce et al., 1972; Paces, 1973). Parabolic kinetics measured for silicate dissolu-tion have been attributed to the initial fast dissolution of fine particles or sites withhigh surface free energy (Holdren and Berner, 1979). Nonstoichiometric dissolu-tion (see next section) may also cause the dissolution rate to vary with time. Forexample, jadeite glass (NaAlSi2O6, Fig. 5.3) dissolved at pH 2 develops an Al- andNa-depleted surface layer that is thousands of Angstroms thick (Hamilton et al.,


0 1000 2000 3000 4000 5000 60000.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Al depletion depth

jadeite glasspH 2

unreacted100 hours648 hours1102 hours

Al/S

i sign

al int

ensity

rat

io

Depth (Å)

Fig. 5.3 Plots showing depth profiles of Al/Si ratios measured using secondary ion mass spectro-metric (SIMS) analysis of jadeite glass plates reacted in static pH 2 solution at 25 C for varyingdurations of time (Hamilton et al., 2001). Depletion of Al at the surface was attributed to nonstoi-chiometric surface leaching and creation of an Al-depleted surface layer. For modeling purposes,the authors have also indicated a nominal depth to which Al is depleted. See also discussion ofnonstoichiometric dissolution in Chap. 1. (Reprinted from Hamilton et al., 2001. With permissionfrom Elsevier).

2001) The development of this layer is attributed to faster leaching of Na and Al ascompared to Si: it can be shown that a parabolic release rate is predicted for diffu-sion of a component such as Na or Al across a thickening leached layer (Doremus,1983).

Given these difficulties, geochemists generally measure the rate of dissolution ofa mineral after many hours in order to determine the steady state rate. True steadystate kinetics may not be attainable however since the mineral surface continueschanging during dissolution (White and Brantley, 2003; Kohler et al., 2005). Steady-state dissolution, if it exists at all, would be expected to be characterized by a surfacewith a non-changing distribution of site energies and atoms. Figure 5.3 demonstratesthat the dissolution rate of jadeite glass might not attain steady state until more than1,100 h of dissolution. Nonstoichiometric dissolution is further discussed in the nextsection.

5.1.3 Stoichiometry of Dissolution

When a reaction rate is measured in a chemical reactor, the reaction is generally acomposite reaction rather than an elementary reaction (Chap. 1). Reflecting the na-ture of these complex mechanisms, many silicates are observed to release elements


into solution at different rates. If the ratio of release rates does not equal the sto-ichiometry of the starting mineral, such dissolution is called nonstoichiometric orincongruent dissolution. Nonstoichiometric dissolution may be caused by dissolu-tion of impurity phases or zones within the mineral, by precipitation of secondaryminerals, or by preferential leaching of elements from the mineral surface (as in-ferred for jadeite in Fig. 5.3).

The preferential leaching of elements from a dissolving surface is driven by dif-ferences in site energies for cations in the mineral structure. For example, leachingof cations to depths of several thousand A has been reported especially for the inosil-icate minerals (pyroxenes and amphiboles) and glasses as shown in Fig. 5.3 (Caseyand Cheney, 1993; Brantley and Chen, 1995; Hamilton et al., 2001). Cations in theM2 and M1 sites in pyroxenes and in the M4 sites in amphiboles are released prefer-entially due to differences in Madelung site energy (Schott and Berner, 1983, 1985;Brantley and Chen, 1995; Chen and Brantley, 1998).

For dissolving silicates, nonstoichiometric dissolution is especially pronouncedat lower pH and can be detected using surface-sensitive spectroscopies such as X-rayphotoelectron spectroscopy or secondary ion mass spectrometry (SIMS) (Chap. 3).Figure 5.3 shows how the Na/Si atomic ratio of the outer surface of albite crystal,measured by SIMS, changes during dissolution at pH 2 as a function of dissolutionduration. In contrast, alteration layers on feldspars such as albite are generally rela-tively thin. Thicker alteration layers can develop at pH < 3 on plagioclase feldsparsor on glasses of feldspar composition due to leaching of alkali, alkaline earth, and Alcations. Such layers can demonstrate the characteristics of amorphous silica whenanalyzed after dissolution (Casey et al., 1989; Hamilton et al., 2000, 2001).

The development of a leached layer on dissolving feldspar surfaces is influencedby the Al/Si ratio of the feldspar. Labradorite (Al/Si = 0.66–0.8) and bytown-ite (Al/Si = 0.8–0.9) crystals show much thicker altered layers when dissolvedat low pH than albite (Al/Si < 0.4), oligoclase (Al/Si = 0.4–0.5) and andesine(Al/Si = 0.5–0.66) crystals (Muir et al., 1990; Stillings and Brantley, 1995). Incontrast, dissolution of anorthite (Al/Si = 1.0) is almost stoichiometric at low pH(Amrhein and Suarez, 1992).

The mechanism underlying such observations has been investigated using manytechniques (see Sect. 5.2.2.1). For example, ab initio calculations of the optimizedgeometries of dissolving surface clusters (Hamilton et al., 2001) have been calcu-lated. As the Al/Si ratio is increased in the cluster, the average bond length of SiObonds within AlOSi linkages increases from 1.58 to 1.60 to 1.62 A, suggesting thathydrolysis of AlOSi bonds becomes easier. These theoretical results partially ex-plain why the dissolution rates of plagioclase feldspar increases with the Al/Si ratio,and why preferential leaching of Al occurs more readily at high Al/Si ratio. Insteadof formation by leaching, alteration layers on feldspars such as labradorite have alsobeen attributed to solution-precipitation (see Sect. 5.2.2.1).

As discussed in Sect. 5.1.2, many silicates dissolve nonstoichiometrically at firstbut eventually show steady state dissolution that is stoichiometric. For minerals thatnever show stoichiometric dissolution, the determination of reaction rate dependsupon which component released to solution is used in the rate equation. Due to


preferential release of cations such as Na, K, Ca, and Mg from silicates duringdissolution, for example, dissolution rates are usually calculated from the observedSi release. Here, we report silicate dissolution rates based upon Si release, but wegenerally normalize by the stoichiometry of the mineral and report as mol mineralper unit (initial) surface area per unit time. It is important to note that dissolutionrates reported on this basis depend upon both the formula unit and the monitoredsolute (Chap. 1).

5.2 Mechanisms of Dissolution

5.2.1 Interface Versus Transport Control

5.2.1.1 Carbonate Dissolution Mechanism

Dissolution rates of highly soluble and highly insoluble minerals tend to be rel-atively fast and slow, respectively. Dissolution of highly soluble minerals there-fore have a greater likelihood of becoming transport-limited as compared to low-solubility minerals which are likely to be interface-limited. Experimentalists oftentest for transport control of dissolution of minerals by varying the agitation or re-cycle rate of the reactor (Rosso and Rimstidt, 2000). One mineral that has beeninvestigated in the laboratory under both transport and interface limitation is calcite.The relative importance of interface versus transport control during calcite disso-lution varies with pH (Plummer et al., 1978). Here we review the classic model ofPlummer et al. but the reader is also referred to more recent surface complexationmodels for carbonate dissolution (Pokrovsky and Schott, 2000).

Plummer et al. suggested that the following reactions occur in parallel duringcarbonate dissolution under ambient conditions:

CaCO3(s) +H+(aq) = Ca2+

(aq) +HCO−3(aq) (5.3)

CaCO3(s) +H2CO3(aq) = Ca2+(aq) +2HCO−

3(aq) (5.4)

CaCO3(s) +H2O(aq) = Ca2+(aq) +HCO−

3(aq) +OH−(aq) (5.5)

Here, H2CO∗3 represents the sum of H2CO3(aq) and CO2(aq). Rates of these reactions

(r, mol cm−2 s−1) were posited by Plummer et al. to be described by the followingequations where k1, k2, and k3 are rate constants and ai refers to the activity of therelevant species:

r = k1aH+ (5.6a)

r = k2aH2CO∗3

(5.6b)

r = k3aH2O (5.6c)


−1 0 1 2 3 4 5 6 7 8 9 10 11 12

−7

−6

−5

−4

−3

−2

−1

0

0 atm

Extrap. to 0 atm

10−2 - 10−3 atm

0-10−3.5 atm

0 atm

0 atm

1-10−6atm

log

Rat

e (m

ol c

alci

te m

−2s−1

)

pH

Shiraki et al. (2000)Chou et al. (1989)Plummer et al. (1978)Sjoberg (1978)Schott et al. (1989)Rickard and Sjoberg (1983)Busenberg and Plummer (1986)Sjoberg and Rickard (1984)Alkattan et al. (2002)

Transport-control

Interface-control

Fig. 5.4 Calcite dissolution rates measured at 298K and various CO2 partial pressures. At lowpH, rates are transport controlled and are not dependent upon CO2 partial pressures, whereas atpH > 3.5, dissolution becomes interface-controlled (see text). For pH > 5.5, the precipitationreaction also contributes significantly to the overall rate (Plummer et al., 1978). All data frompublished values (Plummer et al., 1978; Sjoberg, 1978; Rickard and Sjoberg, 1983; Sjoberg andRickard, 1984; Busenberg and Plummer, 1986; Chou et al., 1989; ?; Shiraki et al., 2000; Alkattanet al., 2002). (Figure compiled by A. Zimmerman).

These reactions occur in parallel and the fastest reaction should therefore be rate-controlling (Chap. 1). However, at any pH, transport and interface reactions mustoccur consecutively, and for these steps, the slowest reaction must be rate-limiting.Two regions of dissolution were distinguished based on pH and PCO2 : for pH < 3.5,dissolution is controlled by transport while for pH > 3.5 the interfacial reaction isslower than transport and the rate is interface-controlled (Fig. 5.4). Above pH 5.5,the precipitation reaction was also observed to be significant. Consistent with theseobservations, in the low-pH region where the reaction is dominated by Eq. (5.3),calcite dissolution is characterized by a very low activation energy consistent withtransport control (see Sect. 5.4.1).

In region 1, where dissolution is fast enough that transport limits the rate, theconcentration of dissolution products in the solution layer around the dissolvingcalcite (the boundary layer) approaches the equilibrium concentration (see Chaps. 1and 3). In contrast, in region 2, where transport does not limit the rate, diffu-sion across the boundary layer is fast compared to the rate of the interface re-action and the concentration of solutes in the layer is equal to the bulk concen-tration (and this value is lower than the equilibrium value). Hence dissolutionin the higher pH region is more dependent upon solution chemistry and PCO2

(Fig. 5.4).


Fig. 5.5 Photomicrographs showing successive dissolution of the same area of a cleaved surfaceof unstrained calcite at 25 C after (a) 0, (b) 0.5, (c) 1.5, (d) 3, (e) 11, and (f) 17.5 h total dis-solution time. Surface ledges imaged in (a) have almost completely disappeared in (d) due tostep retreat and pitting. Examples of pits growing both horizontally (getting wider) and vertically(getting deeper) are prevalent on the surface. Many small pits nucleate and grow throughout thedissolution period until they are annihilated by intersection with other pits or by surface retreat:these pits deepen for awhile but eventually become flat-bottomed. In contrast, at least one largepoint-bottomed pit (upper right) grows deeper throughout the dissolution period. The large pit isinferred to be dissolving along a dislocation. These photographs are from run UC25-1 (MacIn-nis and Brantley, 1992). (Reprinted from MacInnis and Brantley, 1992. With permission fromElsevier).

5.2.1.2 Etch Pits

Transport or interface limitation during dissolution of minerals such as calcite can beinferred based upon the morphology of the dissolving surface of the mineral (e.g.,Fig. 5.5); however, to understand this concept requires a better conceptual under-standing of surface features related to dissolution (see also Chap. 3). In general,


dissolution can be conceptualized as the sum of i) the horizontal movement ofatomic-scale steps defining incomplete surface layers (step retreat) and ii) removalof atoms by drilling into the mineral (2D or pit nucleation). For example, surfacesteps imaged in Fig. 5.5a represent many atomic steps that have bunched into visiblemacrosteps. Over the time evolution in this figure, these steps move by step retreatand disappear. The figure also shows many pits that nucleate, grow, and intersect.Etch pits generally nucleate at both perfect surface sites and at defect outcrops.Such defects can be 0-dimensional (point defects), 1-dimensional (line defects), or2-dimensional (planar defects). Pits nucleated at 0-dimensional defects become flat-bottomed quickly because the defect is etched away, but new pits can nucleate ho-mogeneously on the surface (Fig. 5.5). However, Fig. 5.5 also shows that pits thatform at line defects continue to deepen along the dislocation line (MacInnis andBrantley, 1992). (Where dislocations jog or loop back to the surface, dislocationpits may terminate, but in general dislocation pits continue deepening as long as thedislocation line is present). The term homogeneous nucleation is used to describenucleation of vacancy islands—pits at perfect surface (Dove et al., 2005) — and dis-location etching is used to describe formation of etch pits at line defects. The largestpit imaged on the calcite in Fig. 5.5f shows the pointed bottom that is characteristicof dislocation etching.

Regardless of the type of pit, when dissolution occurs near equilibrium, nucle-ation of pits is not energetically favored. Under these conditions, dissolution occursas steps sweep across the crystal surface, but new steps can only nucleate at crys-tal edges. Surfaces become smoother rather than more pitted and edges becomerounded. However, further from equilibrium, the large strain field around a disloca-tion can cause nucleation of an etch pit at a dislocation outcrop, so steps originatein parallel from both crystal edges and dislocation etch pits — the crystal thereforedissolves faster further from equilibrium. Even more removed from equilibrium, nu-cleation can occur due to the strain associated with impurities or point defects andeventually at the highest degree of undersaturation, homogeneous nucleation occurseverywhere. Steps nucleated at crystal edges, at dislocation etch pits, at impurityetch pits, at point defects, and at perfect surface thus dominate from small to largeundersaturations respectively because i) the rates of reaction at these sites differs,and ii) the relative number of these sites varies. Of course, close to equilibrium,steps only form at edges, but as the undersaturation increases, step retreat occursfrom all the sites in parallel.

Such conceptual models for dissolution were outgrowths of crystal growth theo-ries known as Burton Cabrera Frank (or BCF) models (Burton et al., 1951; Cabreraet al., 1954; Cabrera and Levine, 1956). The BCF models quantify the values ofthe critical concentrations that define where pitting occurs at defects. For example,consider a pit that nucleates at a dislocation intersecting the surface of a crystal ofcomposition A dissolving to A(aq). Assuming the pit consists of a cylindrical hole ofradius ε and depth a, then the free energy of formation of this small pit is composedof volume, surface, and elastic strain energy terms respectively:

∆Gdislocation =πε2aRT ln([A]/[Aeq])

V+2πεaγ − aτb2

4πln

(εεo

)(5.7)


Here, τ is an energy factor related to the dislocation, b is the Burger’s vector de-scribing the dislocation, εo is the dislocation core radius, V is molar volume, [Aeq]is the equilibrium concentration of A in solution, and γ is the energy of the crystal-water interface. The cylindrical pit geometry is chosen for simplicity. This equationshows that opening of a pit on a crystal surface is a competition between the firstand last terms which decrease the free energy (notice that ln[A]/[Aeq] is a negativevalue if the solution is undersaturated) and the second term which increases the freeenergy due to creation of surface area. Pit nucleation theory is thus similar to crystalnucleation theory (see Chap. 7).

Without a dislocation outcrop, the third term does not appear in Eq. (5.7) and anactivation barrier therefore always slows down pit opening. Such pits only format relatively high undersaturation because of this activation barrier. In contrast,it can be shown that there is no activation barrier to pit opening at a disloca-tion when [A] < [Acrit ], the critical aqueous concentration value (Brantley et al.,1986a; Blum and Lasaga, 1987). The critical concentration of A(aq), [Acrit ], can becalculated:

[Acrit ] = [Aeq]exp

(−2π2γ2VRT τb2

)(5.8)

Above this concentration, an activation barrier exists and etch pits do not sponta-neously open up at dislocations with Burgers vector b.

The rate law and rate mechanism describing dissolution of a mineral thereforechanges as a function of concentration: for [A] [Acrit ], step retreat occurs fromvacancy islands, impurities, dislocation etch pits, and crystal edges; for [A] < [Acrit ],step retreat occurs from dislocation etch pits and crystal edges; and for [Acrit ] <[A] < [A]eq, step retreat occurs only from crystal edges. Rate models such as thosedescribed in Sect. 5.5.2 attempt to describe how different surface sites dominatedissolution under different values of undersaturation, but this complexity is difficultto capture in one equation.

As mentioned at the beginning of this section, the distribution of etch pit size onthe dissolving surface yields information about the dissolution (and deformation)history for calcite or other crystals (Schott et al., 1989a; MacInnis and Brantley,1992, 1993). The observation of etch pits on a mineral surface indicates that thecrystal experienced far-from-equilibrium dissolution. For example, the surface ofthe dissolved calcite crystal in Fig. 5.5 documents the characteristic features of asurface dissolved far enough from equilibrium where both homogeneous nucleationand dislocation pitting occurred in parallel. Such observations are characteristic ofinterface-controlled dissolution. In contrast, when a mineral such as calcite dissolvesunder transport control it becomes rounded because only the high-energy surfacesites dissolve in the near-equilibrium conditions within the boundary layer (Berner,1978). Furthermore, the effects of dislocations on rate suggest that dissolution ratesshould increase when defect densities on calcite increase above 107 cm−2: indeed,rate enhancements of 2–3 have been observed for highly strained as compared tounstrained calcite crystals (Schott et al., 1989a). Consistent with these observations,


pre-treatment of crystals by etching or roughening the surface causes a transientincrease in the observed dissolution rate (MacInnis and Brantley, 1992; Beig andLuttge, 2006). Many of the geochemical implications of these phenomena were firstdiscussed for calcite (see references above) and for silicates in the 1980s (Brantleyet al., 1986a, b).

5.2.2 Silicate and Oxide Dissolution Mechanisms

5.2.2.1 Alteration of Silicate Surface

Transport-controlled dissolution can either refer to slow transport through the fluidboundary layer as discussed for carbonates in the previous section, or through an al-teration layer on the mineral surface (e.g., Sect. 5.1.3). Such alteration layers growon many dissolving silicates where the rate of Si release is less than release of othercations (e.g., Fig. 5.3). After long durations, the rate of diffusion of leaching cationsthrough such a layer and the rate of release of Si to solution eventually becomes sto-ichiometric for many silicates (Schweda, 1990; Stillings and Brantley, 1995; Tayloret al., 2000b). For some silicates such as hornblende, however, even after long dis-solution periods the alteration layer may never reach steady-state (Mogk and Locke,1988).

The mechanism of formation of alteration layers on silicates has most commonlybeen attributed to simple leaching accompanied by surface condensation and re-construction reactions (Brantley, 2004). For example, 6-coordinate Al, observedon the dissolving albite surface despite the fact that bulk albite only contains 4-coordinate Al, was attributed to reconstructive reactions occurring within a layerformed by leaching (Tsomaia et al., 2003). However in cases such as labradoritedissolved at low pH, the sharp interface between surface layer and bulk mineralmay not be consistent with simple diffusion across a leached layer, but rather maydocument dissolution, reprecipitation, and reconstruction (Hellmann et al., 2003).According to this solution-precipitation hypothesis, reprecipitation reactions occurwell below solubility limits for secondary phases. Regardless of whether dissolu-tion is followed by precipitation, hydrolysis of bridging oxygens generally reducesthe connectedness of network atoms (Fig. 5.7) from 4 (Q4) to 3 (Q3) to 2 (Q2) to 1(Q1) before hydrolysis releases the atom to solution (Hellmann et al., 1990; Brantleyand Stillings, 1997; Hamilton et al., 2001; Tsomaia et al., 2003). In this notation,tetrahedral sites, noted as Qi sites, have 4, 3, 2, or 1 bridging oxygen (= i). Theconnectedness, or number of bridging oxygens around the tetrahedrally coordinatedatom, increases with the relative polymerization of the silicate. A distribution of Qsites must characterize the layer regardless of whether the layer forms by solution-precipitation or by leaching. Interestingly, for some silicates, silica polymers maybe released directly to solution before connectedness is reduced to 1 (Dietzel, 2000;Weissbart and Rimstidt, 2000).


5.2.2.2 Surface Complexation Models

Rates of oxide dissolution (Fig. 5.1) are generally observed to be affected by the pro-ton concentration of the reacting solution and are often described by the followingempirical equation:

r = kHanH+ + kOHam

OH− (5.9)

where kH and kOH are the rate constants for proton- and hydroxyl-promoted dissolu-tion respectively, ai is the activity of species i in solution, and n and m are sometimesreferred to as the partial orders of reaction. These partial orders vary as a function ofmineral composition. Some authors include a third rate term in Eq. (5.9) describingdissolution as a function of the rate constant for reaction with H2O, kH2O, at neu-trally charged surface sites, ≡ SiOH(= kH2O[≡ SOH]). While values of n vary formany minerals (Fig. 5.1), some researchers have suggested that m equals 0.3 for allaluminosilicates (Brady, 1991).

Stumm and coworkers (Furrer and Stumm, 1983, 1986; Stumm and Furrer, 1987;Wieland et al., 1988) first suggested that the pH effect can be explained by thefact that sorption of protons on an oxide surface polarizes the metal-oxygen bonds,weakening the bonding with the underlying lattice (see also Chap. 4). According tothis model, if [≡ SOH+

2 ], and [≡ SO−] represent the concentration of positively andnegatively charged surface complexes, respectively, then the dissolution rate, r, insolutions without reactive ligands can be predicted from these surface site concen-trations (Fig. 5.6):

r = kH [≡ SOH+2 ]q1+ = kOH [≡ SO−]q2 (5.10)

where q1 and q2 are constants. Consistent with this model, the rate of dissolutionof most oxides is slowest in solutions at the pH of the pristine point of zero charge(pHppzc) where the net concentration of charged sites equals zero (compare Fig. 5.1).These workers and others (Guy and Schott, 1989; Schott, 1990; Ludwig and Casey,1996) suggested that q1 corresponds to the number of protonation steps required torelease a cation from the surface as the connectedness of this central metal is reducedto 0 (see for example Fig. 5.7). More simply, the value of q1 represents the oxidationnumber of the metal: e.g., q1 = 2(BeO),= 3(δ−Al2O3),= 3(α− Fe2O3) and =4(SiO2).

In general, application of this model to mixed oxides such as feldspar has beendifficult. Proton sorption has been measured on feldspars and attributed to both Aland Si protonation for pH < 3 and to Al protonation between pH 3 and 7. Consis-tent with a value for q1 equal to the oxidation number of the metal being protonated,a value of q1 = 3 was reported for albite and a similar value reported for anor-thite (Amrhein and Suarez, 1988; Schott, 1990). However, a value of q1 = 1 wasalso reported for albite as exemplified in Fig. 5.6. Specifically, the logarithm of thesurface charge of albite under acid conditions, log[≡ SOH+

2 ], was observed to beproportional to loga0.52

H+ as shown in Fig. 5.6a (Blum and Lasaga, 1988; Blum andLasaga, 1991). Because the rate of albite dissolution at low pH fit to Eq. (5.9) also


Fig. 5.6 (a) Logarithm of the change in surface charge (∆ Surface charge) as a function of pHduring titration of an albite slurry (Blum and Lasaga, 1991). ∆ Surface charge is interpreted as theconcentration of protonated surface sites, [≡SOH+

2 ], for pH < 7 and deprotonated surface sites,[≡SO−], for pH > 7. (b) The logarithm of the dissolution rate of albite as measured previously(Chou and Wollast, 1985) and replotted by Blum and Lasaga. Blum and Lasaga argued that thesimilar slopes indicated in (a) and (b) were evidence suggesting that protonation of the surfacewas a precursor step to dissolution for subneutral pH while deprotonation of the surface was a pre-cursor step for dissolution above neutral pH. They inferred that q1 and q2 were unity in Eq. (5.10).(Reprinted from Blum and Lasaga 1991. With permission from Elsevier).

yields n =∼0.5 (Fig. 5.6b), Blum and Lasaga proposed that q1 = 1 for dissolutionof albite at 25 C. These workers argued similarly that above pH 7 the increase inalbite dissolution rate was due to the increase in density of deprotonated surface Alsites (compare Fig. 5.6a and 5.6b for pH > 7). Above pH 7, other researchers haveattributed negative charge on feldspar surfaces to deprotonation of Si (Brady andWalther, 1992).


Fig. 5.7 For silicates, the number of bridging oxygens (the connectivity or connectedness) of Siatoms in the altered surface layer must decrease from 4 (tetrahedrally coordinated — Q4 — sites)to 3 (Q3 sites) to 2 (Q2) to 1 (Q1) to 0 in order to release Si into solution as shown. Although weare emphasizing here the distribution of these sites within an altered surface layer, Q3,Q2, and Q1

sites when outcropping on the silicate surface could be conceptualized as perfect surface, step, andadatom sites respectively (see also Fig. 3.7). The number of protonation steps required to hydrolyzethe central cation in an oxide as the cation is depolymerized has been related to the value of n in Eq.(5.9). Where Al replaces Si in the lattice, Al-O bonds may be attacked first by hydronium ions, andAl may be released to solution faster than Si, leaving behind a Si-rich altered layer (not shown).Back-reactions may also occur to build an altered surface layer and some authors interpret thealtered surface layer as forming by dissolution-precipitation instead of leaching. (Figure courtesyof N. Tsomaia).

Despite the satisfyingly simple observations shown in Fig. 5.6, it is not gener-ally possible to explain the value of q1 in terms of an activated complex (Casey andLudwig, 1996) and inconsistencies arise when comparing minerals treated differ-ently (Schott, 1990). The proton-promoted surface complexation model appears in-adequate to explain dissolution of mixed oxides such as feldspars where protonationand deprotonation reactions are difficult to measure and interpret (Brantley and Still-ings, 1996, 1997). Furthermore, ab initio calculations do not show that protonationof either silanols or aluminols promotes dissolution. In fact, ab initio calculationsdocument that protonation of terminal ≡ SiOH and ≡ AlOH groups strengthensrather than weakens the bonds connecting these groups to the underlying mineral(Kubicki et al., 1996). Nonetheless, equations such as Eqs. (5.9) and (5.10) areoften used to provide a conceptual framework for predicting dissolution behaviorand the lowest dissolution rates are often observed at the pHppzc of a mineral (seeFig. 5.1).


5.2.2.3 The Effect of Dissolved Cations and Anions

Recognizing that simple proton-promoted surface complexation models may be in-adequate to describe the complex mechanism underlying mixed oxide dissolution,several research groups have proposed surface sorption or leaching models that in-corporate the effects of cations other than protons (Oelkers et al., 1994; Hellmann,1995; Oelkers and Schott, 1995; Brantley and Stillings, 1996, 1997; Pokrovsky andSchott, 2000). The model of Oelkers and Schott, which assumes that the dissolvedconcentration of cations other than protons must also be included in the rate modelin order to predict dissolution, has been successfully applied to the widest range ofminerals (Oelkers, 2001b).

For many pyroxenes, amphiboles, and feldspars, leaching of alkali, alkaline earth,or other cations leaves Si tetrahedra that are still connected to the lattice by bridgingoxygens as shown in Fig. 5.7. For these minerals, the Oelkers and Schott modelpredicts that the dissolution rate varies with the activity of the leached cation insolution. In contrast, for other minerals, complete leaching of cations such as Caand Al (anorthite) or Mg (forsterite) leaves Si tetrahedra that do not contain bridgingoxygens (connectedness = 0). According to this model, minerals such as anorthiteand forsterite therefore dissolve according to a proton-promoted mechanism and arenot affected by the concentration of cations leached into solution.

A general kinetic rate equation for far-from-equilibrium dissolution of silicatescontaining cation Mi (Oelkers and Gislason, 2001) has been proposed assuming thata precursor species controls dissolution:

r = ki

∏i=1,i =k

⎡⎢⎢⎣

Ki

(a

νiH+

aνiMi

)s

(1+Ki

(a

νiH+

aνiMi

)s)⎤⎥⎥⎦ (5.11)

Here k is the rate constant, and Ki is the equilibrium constant describing the ex-change reaction between protons and the metal cation Mi at the surface that formsthe precursor species. The parameters νi and s are stoichiometric coefficients forspecies appearing in the formation reaction for the precursor in the rate-limitingstep. For this model, two endmember rate conditions may be considered. When theterm Ki(a

νiH+/aνi

Mi)s is small, significant Mi remains in the surface layer, and the

denominator becomes unity. This simplified rate equation predicts the rate will beaffected by the dissolved concentration of Mi during dissolution: for example, thisequation successfully described dissolution of basalt glass (25 C, pH 3), kaolinite(pH 2, 150 C), enstatite (70 C, pH 2), and muscovite (150 C, pH 2). In contrast,for forsterite (25 C, pH 2), and for anorthite (60 C, pH 2.5), Kia

νiH+/aνi

Mi)s is large,

and dissolution rates become independent of Mg2+ (forsterite) and Al3+ (anorthite).Consistent with this model, Fig. 5.8 (top) documents how dissolved Al concentra-tions have been observed to affect the dissolution rate of a mineral such as muscovitebut not that of anorthite (bottom).


Fig. 5.8 Logarithm of thedissolution rate of muscovite(top) and anorthite (bottom)under acid conditions. As pre-dicted theoretically (Oelkers,2001b), no dependence ondissolved Al3+ is observedfor anorthite, but a strongdependence is observed formuscovite. Oelkers arguesthat dissolution of muscoviteis dependent upon the sur-face concentration of anAl-deficient surface species,but that anorthite dissolutionis not dependent upon sucha species (see Sect. 5.2.2.3).(Reprinted from Oelkers,2001b. With permission fromElsevier).

−14.5

−14

−13.5

−5.5 −4.5 −3.5

log a Al3+

log (a Al3+)

LOG

(r/

(mol

/cm

2/s

ec)

−12

−11

−10

−6 −5.5 −5 −4.5 −4

log

(r/(

mol

/cm

2/s

ec))

The model yielding Eq. (5.11) provides a conceptual framework to predictthe rate of mineral dissolution as a function of dissolved cation concentrationwhen the cation is released to solution from the dissolving phase. The modelis also consistent with the observation that addition of aqueous Al3+ as a back-ground salt does not affect dissolution of forsterite but does inhibit dissolutionof albite (Chen and Brantley, 1997; Chen and Brantley, 2000) and quartz (Dove,1995). Other researchers have proposed similar models for the effect of back-ground electrolytes by modeling cation sorption by Langmuir or competitive Lang-muir isotherms. Such Langmuir models implicitly assume ideal sorption of ionsonto identical surface sites without interaction of sorbate molecules with eachother. These models yield rate equations that are not dissimilar from Eq. (5.11)in form.

For example, background electrolytes in solution generally decrease the rate ofdissolution of feldspars (Sjoberg, 1989; Nesbitt et al., 1991; Stillings and Brantley,1995). Feldspar dissolution in acidic solution far-from-equilibrium was thereforerelated to competitive adsorption of H+ and other cations on the surface of feldspar(Stillings and Brantley, 1995):

r = k

⎡⎣ Kads

H aH+

1+KadsH aH+ +∑

iKads

MiaMi

⎤⎦ (5.12)


where k is the apparent rate constant, Mi refers to adsorbing cations, and KadsH and

KadsMi

refer to the equilibrium constants for adsorption of H+ and Mi on reactive sites.Such a rate equation can be derived if one assumes that dissolution is a function ofthe sorbed proton density, and if this site density can be described by a competitiveadsorption Langmuir model (Laidler, 1987).

In contrast to the feldspars, alkali or alkaline earth cations at low concentrationsin solution increase the dissolution rate of quartz and amorphous silica by factorsup to 100x in low and high temperature solutions. This effect has been attributedto cationic effects on the solvent at the mineral-water interface (Dove and Crerar,1990; Bennett, 1991; Gratz and Bird, 1993; Dove, 1994, 1995; Dove and Nix, 1997;Icenhower and Dove, 2000). Recently, a model has been proposed to explain whysalt solutions accelerate quartz dissolution but inhibit feldspar dissolution (Doveet al., 2005).

Although the effects of cationic solutes on mineral dissolution have been inves-tigated intensively as described above, many fewer researchers have investigatedthe effects of inorganic anions. Anions that form binuclear surface complexes suchas phosphate, borate, and arsenate inhibit oxide dissolution probably because theyform bi- or multinuclear inner-sphere surface complexes. Stumm and coworkershave suggested that release or removal of such complexes is energetically un-favorable, inhibiting proton-or ligand-promoted dissolution (Biber et al., 1994;Stumm, 1997).

5.2.2.4 Effect of CO2 on Dissolution

The increase in concentration of carbon dioxide in the atmosphere has led to manyproposals to pump the gas into aquifers or through mineral media to promote min-eral dissolution and precipitation reactions that can sequester the gas. The rates ofmineral reaction as a function of CO2 concentration are thus of current interest. Forexample, the dissolution of forsterite and precipitation of magnesite has been ex-plored in the context of deep saline aquifer storage (Giammar et al., 2005). For thisand several other studies, the effect of CO2 on dissolution has been attributed not toa direct effect, but to the indirect effect on pH. The indirect effect of CO2 on disso-lution can be predicted using Eqs. (5.9)–(5.12). In contrast, some researchers havereported that adsorption of inorganic carbon species to surfaces can affect dissolu-tion behavior for Fe oxides and Ca or Mg silicates (Wogelius and Walther, 1991;Bruno et al., 1992; Xie, 1994; Malmstrom and Banwart, 1997; Berg and Banwart,2000; Pokrovsky and Schott, 2000; Golubev et al., 2005). However, even under al-kaline conditions, silicate dissolution rates show only a negligible or at best weakdependence on PCO2 when pH is held constant. For example, the release of Ca andMg from diopside during dissolution decreased only slightly or not at all for PCO2 >atmospheric (Knauss et al., 1993) and the dissolution rates of augite and anorthiteat pH 4 did not vary measurably as a function of PCO2 (Brady and Carroll, 1994).


1 2 3 4 5 6 7 8

EDTA

DFO-D1

DFO-B and/or oxalate

proton-promoted

Log

rate

(m

ol F

e/m

2 /s)

pH

oxalateaHa

HQS

Calculated rate of FeO dissolution

1 2 3 4 5 6 7 8−14

−13

−12

−11

−10

−9

−8

−7

−6

−5

−4

3,4DHBascorbate/citrateascorbate/oxalate

ascorbatecatecholgallic acid

H2S

hydroquinoneoxalate/Fe2+

pyrogallolresorcinol

cysteineHQS

HQS+humusphotoreduction

log

rate

(m

ol F

e/m

2 /s)

pH

Calculated FeO dissolution rate

Goethite/hematite dissolution rate


Dissolution rates of volcanic soils at low pH were similarly negligibly affected byvariations in PCO2 (Stephens and Hering, 2004).

5.2.2.5 Ligand-Promoted Dissolution

The effect of mM concentrations of organic anions on dissolution rates is less than afactor of ∼10 for ortho- and inosilicates (Wogelius and Walther, 1991; Brantley andChen, 1995) and less than a factor of ∼15 for feldspars (Drever and Stillings, 1997).These effects are pH- and ligand-dependent (Wogelius and Walther, 1991; Welchand Ullman, 1996). When organic ligands are present in lower concentrations thatare more similar to those observed in soil solutions, the effect of these ligands ondissolution rates of silicates are less than a factor of ∼5 (van Hees et al., 2002).Perhaps because these effects are relatively small and are affected by both mineraland solution composition, reports of anionic effects have not always been consistent.

In contrast to silicates, the effects of organic ligands on Fe oxide dissolutionare better understood. For example, goethite dissolution (Fig. 5.9a) is generally

Fig. 5.9 (a) Compilation of initial rates of proton- and ligand-promoted dissolution of Fe oxidesfrom published sources summarized previously (Brantley et al., 2006). Proton-promoted dissolu-tion of goethite () and hematite (+) are plotted as a function of pH for non-reductive conditions.The dotted line shows the equation, log (Rate) = −10.98− 0.43pH, and represents a linear fit tocombined dissolution rates measured for goethite without ligands added and for goethite in thepresence of 1µM desferrioxamine B (DFO-B). Symbols marked HQS refer to goethite dissolutionin the presence of 8-hydroxyquinoline-5-sulfonate with varying concentrations of Fe2+. Oxalate-promoted goethite dissolution was measured under non-reductive conditions. aHa refers to goethitedissolution in acetohydroxamic acid. Goethite dissolution rates in the presence of oxalate ± des-ferrioxamine B (DFO-B) at varying concentrations are indicated as filled squares. Symbols markedDFO-D1 represent goethite dissolution in the presence of 240µM desferrioxamine D1 and sym-bols marked EDTA represent goethite dissolution in 11.5µM EDTA. The solid line is described inthe caption for Fig. 5.9b. (b) Reductive dissolution rate data for Fe(III) (hydr)oxides. The dottedline is a linear fit (log (rate) = −10.98−0.43 ·pH) for the non-reductive, proton-promoted disso-lution rate of goethite and hematite (marked with × and +, respectively) as shown in Fig. 5.9a,and the solid line is the predicted dissolution rate of Fe(II)O. This rate was predicted based onthe proportionality observed for divalent metal oxides (see for example Fig. 5.10a) between thelog (dissolution rate) and the log (first-order rate constant, ksolv) for water exchange within theinner-coordination sphere of the hydrated metal ion (Casey et al., 1993a). These authors report dis-solution rates for BeO, NiO, CoO, MnO, ZnO, and CaO that can be modeled as log (rate at pH2)(mol m−2 s−1) = −17.20(±0.69)+1.68(±0.11) logksolv. Using log ksolv(s−1) = 6.5 for Fe2+, thedissolution rate of Fe(II)O at pH 2 was estimated to be 5.25×10−7 mol m−2 s−1. The slope of thelog rate – pH line for FeO was set equal to −0.4 based upon the slope for goethite (−0.43, dottedline). Symbols represent the dissolving phase: solid (goethite), open (hematite), upper-half filled(ferrihydrite), lower-half filled (magnetite), right-half symbols (lepidocrocite). Data are plottedfor 3,4 DHB (3,4-dihydroxybenzoic acid); ascorbate/citrate mixtures; ascorbate alone; catechol;cysteine; gallic acid; H2S; hydroquinone; oxalate/Fe2+ mixtures; pyrogallol; resorcinol; I−; cys-teine; HQS (8-hydroxyquinoline-5-sulfonic acid); HQS + humus mixtures and under photoreduc-tive conditions. Symbols represent initial rates of reductive dissolution of these minerals from datasources previously cited (Brantley et al., 2006). It is notable that all dissolution data is brackettedby the proton-promoted dissolution rates for Fe(III) and Fe(II) oxides.


unmeasurable at neutral pH in the presence of oxygen without complexing ligands(Kraemer, 2004). Indeed, enhancement of Fe oxide dissolution by micro-organisms(Banfield and Nealson, 1997) is often due to secretion of organic ligands. In par-ticular, to extract Fe from the environment, many organisms secrete the low mole-cular weight chelating ligands known as siderophores (Hersman, 2000; Kalinowskiet al., 2000b). Siderophores demonstrate high affinity for ferric iron. Experimentsutilizing purified siderophores or siderophore analogues show enhanced Fe releaseduring dissolution of goethite (Watteau and Berthelin, 1994; Holmen and Casey,1996; Kraemer et al., 1999; Cocozza et al., 2002; Yoshida et al., 2002; Cheah et al.,2003), hematite (Hersman et al., 1995) and hornblende (Kalinowski et al., 2000a, b;Liermann et al., 2000). Such dissolution may leave signatures on the mineral sur-face. For example, X-ray photoelectron spectroscopic analysis of Fe-silicate sur-faces after removal of adherent siderophore-secreting bacteria revealed that Fe waspreferentially depleted in the outermost surface after several days of bacterial growthin Fe-depleted culture medium (Kalinowski et al., 2000a).

5.2.2.6 Mechanism of Ligand-Promoted Dissolution

Many researchers attribute the effect of ligands on dissolution to the ligand-promoted dissolution model. According to this simple model, the strength of theligand-cation interaction at the mineral surface is thought to polarize and weakenthe bond between the cation and mineral lattice (Furrer and Stumm, 1983). Assum-ing that the ligand-promoted dissolution occurs in parallel with proton-promoteddissolution, then the overall rate of dissolution is expected to be additive:

r = kH [≡ SOH+2 ]q1 + kOH [≡ SO−]q2 +∑

ikLi [≡ SLi]q3 (5.13)

Here Li refers to a ligand, kLi refers to the rate constant for ligand-promoted dis-solution, and ≡ SLi represents a metal-ligand surface complex. It may be possibleto predict surface densities of some ligand-surface complexes based upon the ob-servation that the equilibrium constant for sorption of ligands to a metal surfaceincreases with the equilibrium constant for formation of the ligand-metal complexin solution (Sigg and Stumm, 1981). For example, both Fe oxides (Fig. 5.9a) andAl2O3 show variable rates of dissolution as a function of ligand identity in solu-tion. At pH between 3 and 5, dissolution of Al2O3 has been observed to decreasein the presence of organic ligands at constant concentration in the order salicylate> phthalate > benzoate (Furrer and Stumm, 1983, 1986). Such trends can be usedto predict dissolution behavior as a function of ligand chemistry and have beenused to explain dissolution behavior of basalts and granites (Neaman et al., 2005,2006).

Despite some predictive capability for this model, several lines of evidence sug-gest that the effect of ligands on mineral dissolution may be indirect rather thandirect. For example, whereas some researchers have suggested that organic ligandssuch as oxalate can increase the solubility and rate of dissolution of quartz at 25 C


(Bennett et al., 1988; Bennett, 1991), other researchers have pointed out that neitherevidence for oxalate complexation with aqueous Si nor adsorption of oxalate at thequartz surface have been observed or is theoretically predicted (Iler, 1979; Poulsonet al., 1997; Pokrovski and Schott, 1998; Kubicki et al., 1999). For example, inner-sphere adsorption for acetic, citric, benzoic, salicylic, and phthalic acids at pH 3 and6 on quartz and albite is not theoretically predicted, yet these ligands are observed toaffect dissolution of these phases. Kubicki et al. have suggested that complexationof charge-balancing alkali or alkaline earth cations by organic ligands followed byproton attack of the mineral surface may explain organic-promoted dissolution ofsome silicates.

Other indirect mechanisms have also been invoked to describe the effect oforganic ligands on aluminosilicate dissolution. Complexation of Al in solutioncould either decrease inhibition according to rate laws such as those discussed inSect. 5.2.2.3 or change the driving force for dissolution as discussed in Sect. 5.5(Drever and Stillings, 1997). As described in Sect. 5.2.2.3, the Oelkers and Schottmodel (Oelkers and Schott, 1998) attributes changes in feldspar dissolution ratein the presence of organic ligands to the effect of complexation reactions on freeAl3+ concentrations and the effect of aqueous Al3+ on dissolution (see Eq. (5.11)).These workers also invoke an affinity effect during dissolution (see Eq. (5.36)). Thechange in affinity caused by the presence of a ligand has also been inferred to affectthe dissolution rate of Fe phases (Kraemer and Hering, 1997).

Generally, enhanced mineral dissolution in the presence of siderophores hasbeen attributed to adsorption of the siderophores at the mineral surface (Holmenet al., 1997; Kalinowski et al., 2000a). However, complex dissolution behavioroccurs in the presence of multiple ligands, suggesting more complex mechanisms.For example, dissolution of goethite has been observed to double in the presenceof the siderophore desferrioxamine B upon the addition of oxalate, and disso-lution in the presence of oxalate is increased by an order of magnitude whenthe siderophore is added (Cheah et al., 2003). These workers inferred that thesiderophore removed Fe(III) from the oxalate complex in solution and allowedthe oxalate to react with the goethite repeatedly—enhancing the oxalate effect ondissolution.

The effects of naturally occurring high molecular weight organic acids may alsonot be well-predicted by equations such as Eq. (5.13): these organic molecules canboth inhibit and accelerate mineral dissolution (Lundstrom and Ohman, 1990; Ochset al., 1993). For example, adsorbed humic molecules inhibit dissolution at pH 4–4.5and accelerate dissolution at pH 3 (Ochs et al., 1993). These observations have beenattributed to the effects of protonation on complexation of the organic moleculeat the mineral surface (Ochs, 1996). Extracellular polysaccharides can also eitheraccelerate or inhibit dissolution of minerals (Welch and Ullman, 1999).

5.2.2.7 Mechanism for Redox-Sensitive Oxides

Dissolution of redox-sensitive minerals may be coupled with oxidation or reductionof cations, adding further complexity to the dissolution mechanism. For example,


oxidation of mineral sulfides generally enhances dissolution of these phases(Nordstrom, 1982, 2000). Such oxidative dissolution of sulfide minerals is of greatenvironmental significance in generation of acid mine or rock drainage but will notbe further discussed here.

Reduction of mineral surfaces can also enhance dissolution. For example, thereduction of surface Fe(III) to Fe(II) is thought to decrease the strength of thebond of Fe to the underlying lattice in oxide minerals (Suter et al., 1988, 1991),enhancing the dissolution rate. Such a model suggests that the upper limit for re-ductive dissolution of Fe(III) oxides should be the rate of dissolution of Fe(II) ox-ide. This idea is tested in Fig. 5.9b where reductive dissolution rates for Fe(III)oxide are plotted as a function of pH and ligand identity. The lines on the fig-ure, representing the proton-promoted dissolution rate for Fe(III) oxide (lower line)and the theoretically predicted proton-promoted dissolution rate for Fe(II) oxide(upper line), successfully bracket the measured rates of reductive dissolution forthe ferric oxides. The predicted rate for ferrous oxide dissolution was calculatedbased upon the observation that the rate constant for proton-promoted dissolu-tion of divalent metal-oxides of a given structure measured at a given pH varieswith the rate of exchange of water molecules around the metal cation in solution(Casey and Cheney, 1993). According to this idea (see Fig. 5.10a for the orthosil-icate structure), the rate of dissolution of Fe(II) oxide at pH 2 is predicted to be5.25×10−7 mol m−2 s−1 (Fig. 5.9b). The estimated line for dissolution of FeO wasplotted assuming this value and a slope of −0.4. The rate-limiting step of reductivedissolution is inferred to be the release of the Fe(II)-L complex from the mineralsurface.

The higher strength of Fe(III)-O bonds compared to Fe(II)-O bonds suggeststhat the rates of dissolution of Fe-containing oxide minerals should be slower un-der oxidative than reductive conditions (Casey and Cheney, 1993). Consistent withthis, several workers have observed that the dissolution rates of the pyroxenes, hy-persthene and bronzite decreased in the presence of oxygen (Schott and Berner,1983, 1985). However, oxidation of Fe (II) to Fe (III) in hornblende and augitehave been observed to increase dissolution rates (White and Yee, 1985; Zhang etal., 1990; Hoch et al., 1996). This increase in dissolution has been attributed tocoupled reactions at the mineral surface and the oxidative effect of ferric iron re-leased to solution during dissolution. During dissolution of ferrous silicates, re-lease of charge-balancing cations occurs simultaneously with hydrolysis and pro-tonation of the silicate structure or subsequent to oxidation (White and Yee, 1985;Kalinowski and Schweda, 1996; Perez et al., 2005). Fe3+ that is released to so-lution during dissolution can be reduced by ferrous ions in the mineral, regener-ating the oxidized Fe surface layer. The rate of oxidation of ferrous surface siteson various minerals has been modeled as first order in concentration of surfaceferrous sites and first order in dissolved oxygen concentration (see Eq. (5.19) inChap. 1) (Wehrli, 1990; Perez et al., 2005). More research is needed to investi-gate the relative effects of oxidative versus reductive dissolution of redox-activesilicates.


3 4 5 6 7 8 9

Co1.5Mg0.5Zn

Ni

Be

CaMg

CoMn

CaFe

Ca

Mn

Fe

Co

Mg

log (rate at pH 2)

log (rate constant)

log (Ksolv',S−1) A

Fig. 5.10 (a) Correlation between log dissolution rates of orthosilicates of different compositionmeasured at pH 2 (filled symbols) and the logarithm of the rate constants for exchange of wateraround the charge-balancing cations when the cation is hydrated in solution, ksolv (Westrich et al.,1993). Values of ksolv are derived from published sources (Hewkin and Prince, 1970). Westrichet al. identified this trend for the dissolution rates measured at pH 2; also plotted as open sym-bols are the values of the rate constants for the orthosilicate dissolution data fit to Eq. (5.9) (i.e.,the intercept of a log dissolution rate – pH plot) (Kump et al., 2000). These trends are consis-tent with a model wherein the relative tendency for dissolution of orthosilicates can be predictedfrom the rate of exchange of waters in the hydration shell of the central metal. (Figure afterKump et al., 2000) (b) Plot of the logarithm of rate constants for dissolution of individual min-erals plotted against the connectedness of the mineral (number of bridging oxygens per tetrahedralcation). Connectedness of 0 is an orthosilicate, 2 is a pyroxene, 2.5 is an amphibole, and 3 isa phyllosilicate. Dissolution rates decrease with increasing connectedness and as a function ofthe cations in the structure as shown. (Figure updated from original publication (Brantley, 2004))(c) Estimates of the activation energy for kH plotted versus connectedness for several minerals.Data sources are summarized in Table 5.5. The maximum and minimum estimates of the Ea areplotted for quartz and only the value estimated for anthophyllite using a temperature-dependentn is plotted (Table 5.5). Calculated estimates of activation energy are also included as indicated(Pelmenschikov et al., 2000; Pelmenschikov et al., 2001; Criscenti et al., 2006) (see text). Note thatcalculated and measured activation energies are only consistent for connectedness ≤2, suggestingthat the precursor molecules in the rate-limiting steps of dissolution of all silicates may generallyhave a connectedness ≤2. Such a conclusion is consistent with step retreat or removal of adatomsas the precursor for silicate dissolution (see text). (Figure updated from original publication(Brantley, 2004)).


0 1 2 3 4 5

Bridging oxygens per tetrahedron (connectedness)

MgCaMgCaMnCaFeCaFeMg

B

0 1 2 3 4 5

10

15

20

25

30

35

40

45

50 quartzPelmenschikovkaoliniteanthophylliteenstatiteK feldsparforsteritekyanitediopsideepidoteCriscenti

activ

atio

n en

ergy

(kc

al/m

ol)

connectedness C

Fig. 5.10 (Continued)


5.3 Rate Constants as a Function of Mineral Composition

The database of rate constants for dissolution of primary silicate minerals (Whiteand Brantley, 1995) has been updated in the Appendix of this book (Bandstra et al.,2007) and by other researchers (Palandri and Kharaka, 2004). In this chapter, wesummarize empirical rate equations for silica and carbonate phases (Sects. 5.3.1and 5.3.4) and for some silicates that were not discussed in the Appendix or Chap. 6(Table 5.2). Readers interested in the dissolution kinetics of secondary silicates, ox-ides, and sulfides that are not treated extensively in this book are directed to otherreferences and data compiled in Chap. 13 (Nordstrom, 1982; Sverjensky, 1992; Rim-stidt and Newcomb, 1993; Rimstidt et al., 1994; Nagy, 1995).

Compilations of rate data show that rates of dissolution of silicates are gen-erally found to be within ±0.25 log units within one laboratory but may differby up to ±2 log units among laboratories. Some of these discrepancies are re-lated to differences in laboratory technique, including duration of experiment (seeFig. 5.2), and others are related to differences in behavior of mineral specimensfrom different localities. In particular, short-duration dissolution experiments mayyield rates that are highly dependent upon the preparation of samples for dissolu-tion. Discrepancies among rate data make it difficult to fit compiled data (Chap. 6).In the future, general models to predict kinetic parameters (Sverjensky, 1992)should be used to discern which rate data are reliable and should lead to gener-alized rate equations. One such technique for comparing rate data is explained inSect. 5.3.3.

5.3.1 Silica

Quartz dissolution has been investigated more thoroughly than any other silicate.Bandstra et al. (Chap. 6) present a fit of quartz dissolution data to Eq. (5.9) at 25 Cwhich is plotted for comparison in Fig. 5.1. The rate of dissolution of quartz has alsobeen expressed by a rate equation similar to Eq. (5.10) (Dove, 1994, 1995):

r = kSiOH(T )θ≡SiOH + kSiO−(T )θ≡SiO−tot

(5.14)

where each rate constant describes the reaction at a given surface site as indicated,θ≡SiOH is the fraction of total neutral surface sites, and θ≡SiO− is the sum of thefractions of total sites existing as deprotonated surface hydroxyls and as sites withadsorbed Na+(≡ SiONa+). This equation successfully describes quartz dissolutionfrom 25 to 300 C for pH 2–12 in variable ionic strength and Na concentrations to0.5 m. The rate constants vary with temperature with an activation energy of 15.8and 19.8kcal mol−1 respectively (see Sect. 5.4.1). The rate of dissolution of quartzvaries such that the minimum dissolution rate occurs at a pH ≈ pHppzc.

Net rates of dissolution for amorphous silica into solutions with and withoutNaCl have been described successfully using the following rate model (Icenhower


Table 5.1 Feldspar rate parameters at 25 C for r = kH(aH+)n + kH2O + kOH(aOH− )m

Log kH(Ea)(mol m−2s−1)(kcal/mol)

Log kH2O(Ea)(mol m−2s−1)(kcal/mol)

Log kOH(Ea)(mol m−2s−1)(kcal/mol) n m pHppzc

a

K-feldsparb −10.06(12.4) −12.41(9.08) −9.68(22.5) 0.500 0.823 6.1Albitec −9.62 — −9.64 0.403 0.376 5.2Albiteb −10.16(15.5) −12.56(16.7) −7.59(17.0) 0.457 0.572 5.2Oligoclaseb −9.67(15.5) −11.84(16.7) — 0.457 —Andesineb −8.88(12.8) −11.47(13.7) — 0.541 —Labradoriteb −7.87(10.1) −10.91(10.8) — 0.626 —Bytownitec −5.85(7.00) −9.82(7.53) — 1.018 —Anorthiteb −6.64 — — 0.985 — 5.6Anorthitec −3.50(3.97) −9.12(4.25) — 1.411 — 5.6

a Values of the pristine point of zero charge are calculated values (Sverjensky, 1994). Values ofpHppzc for feldspars may be significantly lower than these quoted values, depending upon the modelused for calculation (Parks, 1967) and upon the degree of proton-exchange of the surface.b Published values (Palandri and Kharaka, 2004).c Rate constants from Bandstra et al. (Chap. 6). See Appendix for data and fits.

and Dove, 2000):

r = k+

(aSiO2(aq)

)(aH2O)2 (1−Ω) (5.15)

Here, k+ is the dissolution rate constant and Ω = exp(∆G/RT) (see Sects. 5.5.1and 5.5.2). This phase dissolves at a rate approximately ten times faster than quartzunder comparable conditions.

5.3.2 Feldspar

As discussed earlier, feldspar dissolution has been described by empirical rate mod-els using Eq. (5.9) (see Table 5.1), and fits for albite and anorthite dissolution tothese equations are described in Bandstra et al. (Chap. 6). Where data is avail-able, the dissolution rate of feldspars shows an increase at low and high pH, ex-hibiting a V shape (Fig. 5.1). The lowest dissolution rate is observed to be near-neutral for all feldspar compositions. As mentioned earlier, one explanation forthese observations is that the low dissolution rate corresponds to the pH where thefeldspar surface has zero charge (pHppzc), consistent with the proton-promoted sur-face complexation model. However, the value of the pHppzc for feldspar is not gen-erally agreed upon (Parks, 1967; Sverjensky, 1994; Brantley and Stillings, 1996;Walther, 1996; Mukhopadhyay and Walther, 2001). Alternatively, the trough indissolution for feldspars may be explained by the effect of free Al ions in solu-tion and back-reactions at the mineral surface as described for the derivation ofEq. (5.11).


At pH 2–3 at ambient temperature, the log (rate) for dissolution of plagioclasefeldspar increases linearly with increasing Ca (anorthite) content from An0 to An80(Blum and Stillings, 1995). However, the rate of dissolution of An100 is signifi-cantly faster than the linear trend (Fleer, 1982; Chou and Wollast, 1985; Holdren andSpeyer, 1987; Mast and Drever, 1987; Amrhein and Suarez, 1988; Sjoberg, 1989;Sverdrup, 1990; Casey et al., 1991; Amrhein and Suarez, 1992; Oxburgh et al., 1994;Stillings and Brantley, 1995). It has been pointed out that the values for log kH andn in Eq. (5.9) vary systematically with the Al/(Al+Si) ratio in the feldspar (Caseyet al., 1991; Welch and Ullman, 1996). According to Blum and Stillings (using datafrom papers cited above), the value of n equals 0.5 from An0 to An70, but increasesto about 0.75 at An76 and 1.0 at An100. Apparently, a threshold Al content existssuch that dissolution behavior changes drastically (see Sects. 5.1.3 and 5.2.2.1).

5.3.3 Non-Framework Silicates

In Chap. 6, rate equations are summarized for the non-framework silicates biotite,diopside, forsteritic olivine, hornblende, and kaolinite. These equations were devel-oped from fits to the published rate data in the Appendix. For other non-frameworksilicates, parameters are summarized in Table 5.2. Generally, only rates under acidconditions for longer durations are summarized in the table, and, where multiple re-searchers have published rates, only those rates are summarized that were measuredunder controlled conditions (usually flow reactors). Only a very few minerals havebeen measured in multiple laboratories to allow high confidence in prediction of therate. It is often necessary therefore to predict rates for compositions that have neverbeen investigated: as mentioned earlier, such rate predictions can also be used tointerrogate rate data for errors.

For example, Fig. 5.10a documents that the dissolution rates of orthosilicates atpH 2 and 25 C (Casey and Westrich, 1992; Westrich et al., 1993) are correlated tothe rate constants of exchange of water (ksolv) for the corresponding hydrated, diva-lent cations (see also Fig. 4.4). This correlation reflects the observation that the easeof hydrolysis of metals in silicate structures is correlated with the exchange of waterin the hydration shell of the aqueous metal ions. Thus, the similarity of activatedsurface complexes for metal oxides and the corresponding aqueous complexes forthese metals (Ludwig et al., 1995) allows predictions of rates of dissolution. Dataand predictions from the literature (Blum and Lasaga, 1988; Wogelius and Walther,1991; Casey and Westrich, 1992; Wogelius and Walther, 1992; Casey et al., 1993b;Westrich et al., 1993; Chen and Brantley, 2000; Pokrovsky and Schott, 2000; Rossoand Rimstidt, 2000) have been used previously to test a similar correlation betweenthe rate constant of solvent exchange (ksolv) and the constant kH for rate Eq. (5.9)for orthosilicate dissolution (Fig. 5.10a, plotted as open symbols). The correlationbetween kH and ksolv was expressed (Brantley, 2004) as

log kH = 1.22log ksolv −13.6(±0.18) (5.16)


Table 5.2 Summary of rates for selected silicates at subneutral pH based on Eq. (5.9)

Phase log kH n pH range Data used Formula

fayalite −6.0 0.69 Wogelius and Walther, 1992 O4epidote −10.7 0.26 2–4 Kalinowski et al., 1998 O12 (OH)epidote −10.6 0.34 Palandri and Kharaka, 2004 O12 (OH)enstatite −8.6 0.11 2–7 Ferruzzi, 1993 O6enstatite −9.3 0.24 1–13 Oelkers and Gislason, 2001 O6enstatite −9.0 0.60 <7 Palandri and Kharaka, 2004 O6bronzite a −9.5 0.36 <5 Grandstaff, 1977; Schott and

Berner, 1983O6

augite a −6.7 0.85 <6 Siegel and Pfannkuch, 1984;Sverdrup, 1990

O6

wollastonitea −7.8 0.2 <7.2 Xie, 1994; Xie and Walther, 1994 O6wollastonitea −11 0.27 >7 Xie, 1994; Xie and Walther, 1994 O6wollastonitea −9 0 2–6 Weissbart and Rimstidt, 2000 O6Wollastonite −5.37 0.4 not given Palandri and Kharaka, 2004Rhodonite −9 0.27 2.1–7.1 Banfield et al., 1995 O6spodumenea −4.2 0.64 3–7 Sverdrup, 1990 O6jadeitea −7 0.18 3–6 Sverdrup, 1990 O6Anthophyllite −11.85 −0.05 2–5 Mast and Drever, 1987 O22(OH)anthophylliteb −12.5 0.24 1–4 Chen and Brantley, 1998 O22(OH)Anthophyllite −11.9 0.44 1–4 Chen and Brantley, 1998 (refit by

Palandri and Kharaka, 2004)O22(OH)

tremolitea −11.5 −0.11 1,6 Schott et al., 1981 O22(OH)glaucophanea −6.1 0.64 3–7 Sverdrup, 1990 O22(OH)Muscovite −11.8 0.14 1–4 Kalinowski and Schweda, 1996 O20(OH)4Phlogopite −10.5 0.40 1–4 Kalinowski and Schweda, 1996 O20(OH)4chrysotilea −10.0 0.24 Bales and Morgan, 1985 O5(OH)4talc −12.5 0 Lin and Clemency, 1981 O10(OH)2

All rates expressed as mol mineral m−2 s−1, where formula units are given and where rates derivefrom Si release. Only non-framework silicate minerals not summarized in Bandstra et al. (Chap. 6)of this volume are included here. For biotite, diopside, forsterite, olivine, hornblende, and kaolinite,see Chap. 6 for rate fits and see the Appendix for compiled data.a Indicates dissolution measured for less than 1000 h.b indicates normalized by final, rather than initial, surface area.

Similar correlations have been investigated for inosilicates (Banfield et al., 1995).In general, values of kH (inosilicate) are slower than kH (orthosilicate), becausethe dissolution rate decreases with an increase in the connectedness (the averagenumber of bridging oxygens around each Si atom, Fig. 5.10b). This trend in dis-solution rate constant as a function of connectedness can be predicted from theratio of non-tetrahedrally to tetrahedrally coordinated cations, X/Si, which varieswith connectedness. X/Si equals 2 for orthosilicates, 1 for pyroxenes and pyrox-enoids, 0.875 for amphiboles, 1.5 for chrysotile, and 0.75 for talc. The log rateconstant (expressed in units of mol Si released m−2 s−1) of dissolution decreaseswith X/Si:

kH = 1013.51 log(0.5 X/Si)+1.22logksolv−13.6/vSi (5.17)


Table 5.3 Values of ksolv and predicted dissolution rate constants for selected ortho-, ino-, andphyllosilicates using Eq. (17)

logkHb (mol silicate m−2s−1)

Ortho-c single-chaind double-chaine Phyllo-silicates

log ksolva pred- meas- pred- meas- pred- meas- pred- meas-

M (s−1) icted ured icted ured icted ured icted ured

Ca 8.5 −3.3 −3.5 −7.7 −7.8 −6.0Mn 7.6 −4.4 −4.2 −8.7 −9.0 −10.1Zn 7.5 −4.5 −8.9 −10.2Fe 6.5 −5.7 −6.0 −10.1 −11.4Co 6.4 −5.8 −6.4 −10.2 −11.5Mg 5.2 −7.2 −7.3 −11.6 −8.6 −13.0 −11.8 −9.2 −9.9 f

5.2 −9.3 −13.0 −12.2 −13.6 −12.5g

Ni 4.4 −8.2 −12.6 −14.0Be 3.5 −9.3 −13.6 −15.1CaMg 6.8 −5.3 −4.8 −9.6 −9.4 −11.0

−10.5

Values listed are log rates of ortho- and inosilicate hypothetical end-members. Some end-membersmay not exist in nature. Rate constants for mixed composition silicates can be calculated asweighted averages of log rate constants of the end members. Rate equation is expressed: kH =1013.51log(0.5X/Si)+1.22logksolv−13.6/νSia Data from literature compilation (Hewkin and Prince, 1970).b Log rate constant at 25 C fit to Eq. 9 for “measured” or “predicted” from rate Eq. (17). SeeTable 5.2 for data sources for measured values of ino- and phyllosilicates.c Orthosilicates of composition M2SiO4. Data from published rates (Casey and Westrich, 1992;Westrich et al., 1993) or from Chap. 6.d Single-chain inosilicates of composition M2Si2O6. Data summarized in Table 5.2 for measuredrates (Ferruzzi, 1993; Knauss et al., 1993; Xie, 1994; Banfield et al., 1995; Chen and Brantley,1998; Weissbart and Rimstidt, 2000; Oelkers and Schott, 2001). Multiple measured rates are sum-marized for some phases (see Table 5.2).e Double-chain inosilicates of composition M7Si8O22(OH)2. Data for measured rates (Mast andDrever, 1987; Chen and Brantley, 1998). More than one measured rate is summarized for antho-phyllite (see Table 5.2).f Chrysotile of composition Mg3Si2O5(OH)4 (Bales and Morgan, 1985).g Talc of composition Mg3Si4O10(OH)2. Rate was assumed to be constant with pH (Lin andClemency, 1981; Nagy, 1995).

where kH is the rate constant at 25 C for the rate model expressed in Eq. (5.9) (inmol silicate m−2 s−1), and νSi is the number of Si in the mineral formula, e.g.,νSi = 2 for pyroxene and 8 for amphibole (Brantley, 2004).

This predictive equation estimates silicate dissolution accurately (Table 5.3) formany minerals but not all. Where discrepancies exist (e.g., Eq. (5.17) predicts thatkH (enstatite) < kH (diopside) but the data compiled in Table 5.3 shows the op-posite), more experimental measurements are needed. Correlations such as thoseshown in Fig. 5.10a and 5.10b and others summarized in the literature (Sverjensky,1992) should become increasingly useful to cull data for artifacts, to understandanomalous mineral dissolution behavior, or to predict dissolution behavior for min-erals for which no data has been measured.


As discussed in Sect. 5.2.2.2, no well established theory is available to predictthe pH dependence of dissolution rate as a function of structure or composition. Theliterature data for ortho-, soro-, ino- and phyllosilicate dissolution at 25 C bracketthe value of n in Eq. (5.9) between 0 and 0.6 at 25 C (Table 5.4). Data in this tableare derived from experiments of duration longer than a month except for forsteriteand wollastonite. Some of the variability in n might be better explained if the depen-dence upon cation concentrations using Eq. (5.11) were taken into account (Oelkers,2001b).

5.3.4 Carbonates

One composite rate equation can be used to describe the rates of calcite dissolu-tion based upon the three reactions summarized in Sect. 5.2.1.1. Reactions given byEqs. (5.3)–(5.5) are assumed to occur in parallel with the back-reaction, summingto rnet , the net rate of dissolution minus precipitation (Plummer et al., 1978):

rnet = k1aH+ + k2aH2CO∗3+ k3aH2O − k4aCa2+aHCO−

3(5.18)

Here k1, k2, k3 are rate constants for reactions given by Eqs. (5.3)–(5.5), and k4

represents the rate constant for the precipitation of calcite. The values for these rateconstants (mmol cm−2 s−1) can be described as a function of temperature, T (K):

logk1 = 0.198−444/T (5.19)

logk2 = 2.84−2177/T (5.20)

logk3 = −1.10−1737/T (5.21)

The rate constant for the precipitation reaction is described by

k4 =K2

Kc

⎛⎝k1

′ +1

aH+(s)

⎞⎠(k2aH2CO∗

3(s)+ k3aH2O

)(5.22)

Here, K2 is the equilibrium constant for dissociation of bicarbonate, Kc is the solu-bility product constant for calcite, k1’ is a modified rate constant for reaction givenby Eq. (5.3), and the subscript (s) refers to concentrations in the surface adsorptionlayer. Importantly, as noted earlier, even under ambient conditions, calcite disso-lution is fast and can become transport-controlled (Sect. 5.2.1). The low activationenergy for reaction (5.3) is consistent with transport control for low pH dissolution.Eqs. (5.19) and (5.20) successfully describe dissolution over the temperature range5–48 C, while Eq. (5.21) only describes dissolution from 25 to 48 C. At highertemperatures, different mechanisms may become important or the rate-limiting stepmay change. Such equations have been used by other workers to describe dolomiteas well as calcite dissolution (Busenberg and Plummer, 1982; Chou et al., 1989).


Tabl

e5.

4pH

depe

nden

cefo

rse

lect

edno

n-fr

amew

ork

silic

ates

asa

func

tion

ofte

mpe

ratu

re(p

H<

7)

Pha

sen

Run

dura

tion

Solu

tion

Ref

eren

ce

Ort

hosi

lica

tes

0.5a

fors

teri

te0.

48(2

5C

)0.

47(3

5C

)0.

53(4

5C

)

5000

–250

00m

inH

NO

3+

H2O

Ros

soan

dR

imst

idt,

2000

fors

teri

te0.

49(2

5C

)0.

70(6

5C

)B

lum

and

Las

aga,

1988

;W

ogel

ius

and

Wal

ther

,199

1;C

hen

and

Bra

ntle

y,20

00

Soro

sili

cate

s0.

2a

epid

ote

0.20

(90

C)

Ros

e,19

91ep

idot

e0.

15to

0.62

(25

C)

1000

–470

0h

H2O±

H2SO

4±

HC

lK

alin

owsk

ieta

l.,19

98

Sing

lech

ain

0.2a

sili

cate

sen

stat

ite0.

2515

00–2

000

h0.

1M

buff

erso

lutio

nsFe

rruz

zi,1

993

enst

atite

0.24

(25

C)

0.24

(50

C)

0.23

(150

C)

0.00

01m

Mg,

0.01

mio

nic

stre

ngth

Oel

kers

and

Gis

laso

n,20

01

diop

side

b0.

2(2

5,70

,90

C)

40–6

0da

ysbu

ffer

solu

tions

pH2–

10K

naus

set

al.,

1993

diop

side

c0.

19(2

5C

)0.

76(9

0C

)34

00h

HC

l-H

2O

Che

nan

dB

rant

ley,

1998

wol

last

onite

0.24

80–2

20h

HC

l±H

2O±

KC

lX

ie,1

994;

Xie

and

Wal

ther

,199

4

rhod

onite

/pyr

ox-m

anga

nite

and

synt

hetic

rhod

onite

0.27

2000

–350

0h

buff

erso

lutio

nsB

anfie

ldet

al.,

1995


Tabl

e5.

4(C

onti

nued

)

Pha

sen

Run

dura

tion

Solu

tion

Ref

eren

ce

Dou

ble

chai

n0.

2(w

/oFe

)a

sili

cate

s0.

4(w

/Fe)

a

anth

ophy

llite

b0

1000

–200

0h

HC

l+H

2O

Mas

tand

Dre

ver,

1987

anth

ophy

llite

c0.

24(2

5C

)34

00h

HC

l+H

2O

Che

nan

dB

rant

ley,

1998

0.63

(90

C)

horn

blen

de0.

47(2

5C

)Fr

ogne

ran

dSc

hwed

a,19

98ho

rnbl

ende

0.4

(25

C)

1ye

arH

Cl-

H2O

Giv

ens

and

Bra

ntle

y,un

pub.

Phy

llos

ilic

ates

0.14

a

mus

covi

te0.

14(2

5C

)30

00h

H2SO

4+

HC

l+H

2O

Kal

inow

skia

ndSc

hwed

a,19

96m

usco

vite

0.37

(70

C)

buff

erso

lutio

nsK

naus

san

dW

oler

y,19

89

aSu

gges

ted

valu

efo

rgr

oups

ofsi

licat

esat

25 C

.b

Indi

cate

sno

rmal

ized

byin

itial

surf

ace

area

.c

Indi

cate

sno

rmal

ized

byfin

alsu

rfac

ear

ea.


5.4 Temperature Dependence

5.4.1 Activation Energy

Extrapolation of the rate constant for dissolution to other temperatures, kH (T), canbe accomplished with the Arrhenius equation as described in Chap. 1:

kH(T ) = kH(To)e−(Ea/RT ) (5.23)

where kH (To) (mol mineral m−2 s−1) is the temperature-independent pre-exponential factor, Ea is the apparent activation energy, R is the gas constant, andT is absolute temperature.

Interestingly, the measured activation energies for silicate dissolution do notshow a discernible pattern as a function of the connectedness of the mineral ex-cept perhaps for minerals of connectedness ≤2.5 (Fig. 5.10c). Given that dissolu-tion of a silicate requires depolymerization of the Si from the lattice as depicted inFig. 5.7, we might have expected more highly polymerized minerals to have higheractivation energies than less polymerized minerals. For example, ab initio calcula-tions suggest that the activation energy of hydrolysis of a Si-Obr bond (where thesubscript refers to a bridging bond) decreases with decreasing connectedness of theSi atom. Such values are plotted in Fig. 5.10c (asterisks) for clusters that were as-sumed to experience no relaxation of the molecular geometry at the mineral surfaceas a function of lowered connectedness (see Chap. 2). These values decrease from49kcal mol−1 (connectedness of 4) to 33 (3) to 22 (2) to 17 (1) (Pelmenschikovet al., 2000., 2001). If the cluster is allowed to relax structurally, as it might if theSi atom were found at the mineral surface (see also Chap. 2), the calculated Ea de-creases by several kcal/mol, as shown for a Q3 Si on Fig. 5.10c, but the calculatedvalue is still much larger than the experimental values (Criscenti et al., 2006). Onlythe experimental values of Ea for minerals with connectedness ≤2 on Fig. 5.10c areroughly consistent with the calculated values for clusters of appropriate connected-ness.

We infer from these observations that the connectedness of the Si atom in theprecursor molecule for silicate dissolution is most likely ≤2 for all silicates regard-less of connectedness (Fig. 5.10c). If Q3, Q2, and Q1 sites (where Qi refers to tetra-hedrally coordinated atoms surrounded by i bridging oxygens) are conceptualizedas perfect surface, step, and adatom sites respectively (see also Fig. 3.7), then thisconclusion suggests that the rate-limiting step of silicate dissolution is consistentwith step retreat or removal of adatoms (hydrolysis of Q2 or Q1 sites respectively)rather than pit nucleation on perfect surface (see Sects. 5.2.1.2 and 5.5.2). For ex-ample, for biotite and other sheet silicates, edge sites rather than basal sites oftencontrol the overall dissolution rate under acid conditions (Kalinowski and Schweda,1996). These conclusions are also consistent with the published prediction from the1980s of an average activation energy for mineral oxide dissolution of 13kcal mol−1

(Wood and Walther, 1983).


5.4.2 Solution Chemistry and Temperature Dependence

The activation energy describes how the rate constant changes with temperaturefor a given dissolution mechanism. If the rate-limiting step of dissolution changeswith temperature, then the form of the rate equation, including the reaction order,might change as well as the rate constant. For example, as mentioned earlier, Eqs.(5.19)–(5.21) have been used to predict calcite dissolution successfully, suggestingthat the rate-limiting mechanism is unchanged within the interval 25 < T < 48 C.Outside of this interval, however, it is impossible to know whether the rate equationsare still valid. Commonly, as temperature is increased, a reaction may change frominterface-limited at low temperature to transport-limited at high temperature becausethe activation energy of interface reactions is generally larger than the activationenergy of transport (Fig. 5.11).

One complicating factor in predicting mineral dissolution rates versus tempera-ture lies in the fact that, in addition to a temperature-dependent rate constant, the

0.0020 0.0025 0.0030 0.0035 0.0040

ln k

1/T

High activation energy

Low activation energy

Fig. 5.11 Schematic Arrhenius plot demonstrating how the rate-limiting step generally changeswith temperature. For a reaction mechanism with consecutive steps operating at low temperature(T), the step with the high activation energy (steeper slope on this plot) is typically rate-limiting(e.g., solid line), while at high T, the rate-limiting step often changes to the step with the loweractivation energy (e.g., dashed line). For example, the activation energy of the mineral interfacereaction (∼15kcal/mol) is often higher than the activation energy of diffusion (∼5kcal/mol):therefore, at low temperature, mineral dissolution is often interface-limited, but at high tempera-ture, reactions are often transport-limited. Where the two rate constants are similar, the reactionexhibits mixed control.


orders of dissolution with respect to H+(n) and OH− (m) are often temperature-dependent (Table 5.4). Given that the ∆H of sorption of protons onto surfaces isnegative, an increase in temperature will result in an increase in n in Eq. (5.9) forpH < pHppzc (Brady and Walther, 1992; Casey and Sposito, 1992). However, bothincreased values of n (Carroll and Walther, 1990; Chen and Brantley, 1998) and in-significant changes in n have been observed as a function of temperature for varioussilicates (Casey and Cheney, 1993; Hellmann, 1994; Chen and Brantley, 1997, 2000;Rosso and Rimstidt, 2000). The variation of n in describing silicate dissolution hasgenerally been neglected entirely or modeled as linearly dependent on temperature(Kump et al., 2000).

Where n varies with temperature, a pH-dependent (apparent) activation energy,Ea’, has been reported by investigators who plot ln (rate) (instead of log (rate con-stant) versus 1/T and calculate the activation energy. This Ea’ is valid only at the pHof measurement. A pH-independent value for Ea can be determined from a plot of ln(kH) versus 1/T (Chen and Brantley, 1998). Where n is independent of temperature,Ea’ = Ea. Arrhenius activation energies for mineral dissolution are theoretically pre-dicted to be lowest at pH values near the pHppzc (Casey and Sposito, 1992; Caseyand Cheney, 1993).

The temperature dependence of cation back-reactions must also be understood topredict dissolution rates (Fig. 5.8, top). For example, the inhibitory effect of aqueousAl on dissolution of albite could increase with increasing temperature due to the en-hanced adsorption of cations onto surfaces with increasing temperature (Machesky,1989; Chen and Brantley, 1997). In general, the effect of dissolved Al on the disso-lution rate of aluminosilicates is not well understood as a function of temperature(Oelkers, 2001a).

5.5 Chemical Affinity

5.5.1 Linear Rate Laws

The driving force for reaction, ∆G, controls whether a mineral dissolves or precipi-tates under a given set of conditions. For example, as described in Chap. 1 for albitedissolution,

NaAlSi3O8(s) +4H2O(aq) +4H+(aq) → Na+

(aq) +Al3+(aq) +3H4SiO4(aq) (5.24)

∆G is defined as

∆G = RT ln(Ω) (5.25)

where Ω is the ratio of the reaction activity quotient, Q(= aNa+aAl3+a3H4SiO4

/a4H+)

and the equilibrium constant, Keq, for the reaction at the specified temperature andpressure (Ω = Q/Keq). The chemical affinity of the reaction, defined as equal to-∆G, equals 0 at equilibrium. Note that the sign of ∆G depends on which directionthe chemical reaction is written (e.g. Eqn. 5.24). In this chapter we have strictly


Table 5.5 pH-independent Ea for dissolution of selected minerals far from equilibrium

Phase Ea (kcal/mol) Temperatures ( C) Reference

Carbonatescalcite 2 5–48 Eq. (11), Plummer et al., 1978

calcite 10 5–48 Eq. (12), Plummer et al., 1978

calcite 8 25–48 Eq. (13), Plummer et al., 1978

Orthosilicatestephroite 22 25–45 Casey et al., 1993

monticellite 17 25–45 Westrich et al., 1993

forsterite 16 25–65 Palandri and Kharaka, 2004

kyanite 13 108–194 Palandri and Kharaka, 2004

SorosilicatesEpidote 17 25–90 Palandri and Kharaka, 2004

Pyroxenesenstatite 12 28–168 Oelkers and Gislason, 2001,

Ea measured at pH 2

enstatite 19 not given Schott and Berner, 1985 (refitby Palandri and Kharaka, 2004)

diopside 23 25–90 Chen and Brantley, 1998 (fit witha temperature-dependent n)

diopside 23 not given Palandri and Kharaka, 2004

Amphibolesanthophyllite 19 25–90 Chen and Brantley, 1998 (fit with

a temperature-dependent n)anthophyllite 12 25–90 Chen and Brantley, 1998 (refit with

a temperature-independent n byPalandri and Kharaka (2004))

Phyllosilicateskaolinite 16 Palandri and Kharaka, 2004montmorillonit 11 Palandri and Kharaka, 2004

Tectosilicates (see also Table 5.1)am. silica 18 25–250 Rimstidt and Barnes, 1980;

Mazer and Walther, 1994;Icenhower and Dove, 2000

quartza 16–18 25–300 Rimstidt and Barnes, 1980quartza 21 25–625 Tester et al., 1994quartza 19 100–300 Polster, 1994quartza 17 175–290 Dove, 1999

a Data only compiled for dissolution in distilled deionized water.


discussed rates measured far-from-equilibrium, except for the cases of amorphoussilica (Eq. (5.15)) and calcite (Eq. (5.18)). Dissolution rates for both carbonates andsilicates are described below as a function of chemical affinity.

Transition state theory (TST) is generally considered to be appropriate only forelementary reactions. However, if a complex mechanism is rate-limited by a singleelementary reaction, then TST may be usefully applied to the overall reaction. Inthat regard, TST suggests that the forward rate minus the reverse rate, rnet (Lasaga,1981; Aagaard and Helgeson, 1982; Lasaga, 1984), is linear with respect to ∆G nearequilibrium according to the following equation with n1 = 1:

rnet = −k+Πam jj

(1− exp

(n1∆GRT

))(5.26)

Here k+ is the rate constant for the forward rate, a j is the activity of species j inthe rate-determining reaction, m j and n1 are constants, R is the gas constant, andT is the absolute temperature. The sign of rnet varies depending upon which direc-tion the reaction is written. Explicitly, this rate expression with n1 = 1 is derivedfor a reaction such as that given in Eq. (5.24) by i) writing the forward and reversereactions, ii) assuming these are elementary reactions, iii) writing the rates of theforward and reverse reactions, and iv) calculating the net rate = forward – reverserate. For a positive rnet , a reaction such as that given by Eq. (5.24) proceeds for-ward as written, and for a negative value, the reaction proceeds in reverse. In sometreatments, the ∆G term is also divided by Temkin’s average stoichiometric num-ber, a constant that refers to the relative rate of destruction of the activated complexdivided by the overall dissolution rate (Oelkers et al., 1994; Oelkers, 2001b). Thereader is referred to several discussions in the literature of this equation with respectto transition state theory and irreversible kinetics (Alekseyev et al., 1997; Lasaga,1995; Lichtner, 1998; Oelkers, 2001a; Hellmann and Tisserand, 2006).

Rate Eq. (5.26) with n1 = 1 has been used successfully to predict net dissolutionand precipitation of silica phases including quartz over a wide range in tempera-ture and pressure (Rimstidt and Barnes, 1980; Dove, 1995). For example, Eq. (5.15)(Sect. 5.3.1) has been used for amorphous silica (note that Ω = exp(∆G/RT)). Rateexpressions of this form with n1 = 0.5 or 1 have also been used to describe calciteprecipitation (Nancollas and Reddy, 1971; Reddy and Nancollas, 1971; Sjoberg,1976; Kazmierczak et al., 1982; Rickard and Sjoberg, 1983; Sjoberg and Rickard,1983; Shiraki and Brantley, 1995). A rate equation for dissolution that is linearlyproportional to ∆G near equilibrium as described by Eq. (5.26) with n1 = 1 is con-sistent with a mechanism rate-limited by sorption at the mineral surface (Nielsen,1983; Shiraki and Brantley, 1995). Other mechanisms could also be consistent withsuch a rate law.

5.5.2 Non-Linear Rate Laws

Many minerals show dissolution and growth behavior that cannot be fit by equationssuch as Eq. (5.26) that are linear in ∆G near equilibrium (Fig. 5.12). For example,


00

2

4

n=0.5, m=1n=1, m=1n=5, m=1

Dis

solu

tion

Rat

e

A

Dissolution plateau

Fig. 5.12 (A) (B) Schematic diagrams depicting the dissolution rate of a phase as a function of ∆G(arbitrary units) based upon Eqs. (5.29) or (5.30). The legend indicates how the function changeswith n1 and m1 (written on the figures as n or m for simplicity). Note that when m1 = 1 as predictedby transition state theory (A), the predicted curves are not sigmoidal, but when m1 does not equal1 dissolution becomes a sigmoidal function of ∆G (B). Dissolution rates of many phases (e.g.,albite shown in (C)) exhibit sigmoidal behavior. In (C), rate of albite dissolution was determinedby averaging the release rate of Si, Al, and Na after correction for stoichiometry (Hellmann andTisserand (2006)). A curve based on transition state theory (e.g., Eq. (5.26)) is shown by the dashedline while a sigmoidal curve that fits the data better is shown as the solid line. According to theauthors, the sigmoidal curve is based upon a rate law such as Eq. (5.31), but a reasonable fit wasalso produced from an equation such as Eq. (5.29). As shown in (a) and (b), the sigmoidal behaviorof the rate law increases as the exponent m1 in rate law 29 increases. (Figure (c) reprinted fromHellmann and Tisserand 2006. With permission from Elsevier).

the following rate model that is nonlinear in ∆G describes calcite dissolution undersome conditions (Morse, 1978):

rnet = k(1−Ω)m1 (5.27)

Rewriting this equation using Ω = exp(∆G/RT) yields:

rnet = ±k

(∣∣∣∣1− exp

(∆GRT

)∣∣∣∣)m1

(5.28)

For small ∆G, such a rate equation predicts that the net rate varies as ∆Gm1 . Non-linear rate laws such as Eqs. (5.27) and (5.28) (m1 = 1), often considered usefulto describe reactions controlled by crystal defects (Lasaga and Kirkpatrick, 1981),have been used to model dissolution and growth of kaolinite (Nagy et al., 1990,


00

1

2

3

4

n=1, m=0.5n=1, m=1n=1, m=5n=1, m=10n=1, m=20

Dis

solu

tion

Rat

e

B

Transition region

Near-equilibriumregion

0.0−80 −70 −60 −50 −40 −30 −20 −10 0

TST rate curve

b

C

Fig. 5.12 (Continued)

1991), gibbsite (Nagy and Lasaga, 1992), quartz (Berger et al., 1994), and analcime(Murphy et al., 1992).

Many researchers have attempted to explain values of m1 in terms of mechanismsof dissolution or precipitation. For example, spiral growth at screw dislocations isoften well-described by rate Eq. (5.28) with m1 = 2 (Burton et al., 1951; Blum andLasaga, 1987; Teng et al., 2000). However, attribution of a mechanism on the basisof the value of this exponent is generally not defensible without further observations.


Rate equations that include two exponents n1 and m1 have been used to describeprecipitation of calcite (Inskeep and Bloom, 1985):

rnet = k

(exp

(n1∆GRT

)−1

)m1

(5.29)

Equation (5.29) is equivalent to

rnet = k (Ωn1 −1)m1 (5.30)

As written, rnet > 0 refers to precipitation and rnet < 0 refers to dissolution. (Com-pare Figure 5.12 where rnet for dissolution is plotted as a positive value).

One of the first examples of the use of a form of Eq. (5.29) for silicate dissolutionwas the treatment of albite dissolved at 80 C near pH 8.8 (Burch et al., 1993):

r = k5[1− exp

(−(

n1 |∆G |RT

)m1)

+ k6[1− exp

(−( |∆G |

RT

)m2)

(5.31)

where k5 and k6 are rate constants, and n1, m1 and m2 are fitting parameters. Thisequation contained two rate terms to describe two parallel reactions and was usedbecause the rate of albite dissolution varies sigmoidally as a function of ∆G. Farfrom equilibrium, Burch et al. pointed out that the rate reaches a constant or “dis-solution plateau”. As the dissolution rate decreases to zero as the driving force de-creases, an inflection point occurs in the rate-∆G function. Similarly, it has beenshown that albite dissolution at 150 C and pH 9.2 is well fit by an equation likeEq. (5.31) (Fig. 5.12c). Consistent with arguments described in Sect. 5.2.1.2, Burchet al. argued that the rate decreased sharply below the dissolution plateau when etchpits stopped nucleating at dislocation outcrops at the mineral surface: this occurs atthe critical saturation index of etch pit nucleation at dislocations, Ωcrit, as describedin Eq. (5.8). Closer to equilibrium, etch pits do not open even at dislocation outcrops(Brantley et al., 1986a, b; Blum and Lasaga, 1987; Lasaga and Luttge, 2001). Forthese smaller values of undersaturation (Ωcrit < Ω < 1), dissolution occurs by stepretreat without nucleation of pits.

A sigmoidal function of dissolution versus ∆G was also observed for labradoritedissolved in column reactors with inlet pH ∼ 3 under ambient conditions (Tayloret al., 2000a). Similar to the work of Burch et al., far-from-equilibrium dissolu-tion (∆G < −42kJ/mol) was attributed to defect-driven etch pit formation duringlabradorite dissolution. Using equations such as Eqs. (5.7) and (5.8), Taylor et al.calculated the critical value of ∆G for etch pit nucleation on labradorite, ∆Gcrit, tolie between −26 and −11kJ/mol, roughly in agreement with the transition they ob-served between the dissolution plateau and the affinity-dependent region. Taylor etal. calculated the following expression for rnet as a function of ∆G in the columnreactors using inverse modelling:

r = −kmin

0.76

[1− exp

(−1.3x10−17

(∆GRT

)14)]

−0.24

[1− exp

(−0.35 |∆G|RT

)](5.32)


where kmin is the far-from-equilibrium rate constant. The two terms in Eqs. (5.31)and (5.32) have been interpreted as describing the parallel reactions of etch pit-driven dissolution and non-pit related surface retreat of the mineral surface (seeChap. 3 and Sect. 5.2.1.2).

Although Burch et al. and Taylor et al. both used functions describing parallelreaction steps, rate Eq. (5.29) can also be used to describe sigmoidal rate behav-ior as shown in Fig. 5.12c (Hellmann and Tisserand, 2006). In contrast, the moresimple linear equation given by Eq. (5.26) cannot predict the sigmoidal rate-∆Gbehavior (Fig. 5.12a): for values of m1 = 1, a plot of dissolution rate (plotted asa positive value) versus ∆G is everywhere concave down and shows no inflec-tion point. As m1 increases but n1 remains constant in Eq. (5.29), however, therate becomes a sigmoidal function of ∆G with both concave and convex regions(Fig. 5.12b). Both nonsigmoidal (Gautier et al., 1994; Oelkers et al., 1994; De-vidal et al., 1997; Oelkers and Schott, 1999; Dove et al., 2005) and sigmoidal(Burch et al., 1993; Berger et al., 1994; Alekseyev et al., 1997; Taylor et al., 2000a)functions for rate versus ∆G have been observed for mineral reactions. As ex-emplified in Fig. 5.12c, some researchers have referred to these two types of be-havior as either consistent with TST (nonsigmoidal) or not consistent with TST(sigmoidal).

Researchers point to various lines of evidence in explaining why sigmoidal andnonsigmoidal functionalities are observed. For example, samples of albite dissolvedhydrothermally reveal that log (rate) versus ∆G is sigmoidal when measured oncleaved, untreated samples (Beig and Luttge, 2006). These workers observed veryslow dissolution near equilibrium which they attributed to the lack of formationof dislocation etch pits. When crystals were pre-dissolved under conditions whereetch pits formed and then were dissolved close to equilibrium, however, the ob-served rate of near-equilibrium dissolution was faster than observed for the un-treated samples due to transient dissolution of the pre-existing etch pits. They fur-ther suggested that nonsigmoidal rate dependences described by other researcherscould be attributed to the pre-etching of samples as experiments were started upfar-from-equilibrium. As also described in Chap. 3, these researchers emphasizethe importance of so-called dissolution stepwaves generated by etch pits and haveproposed a generalized model to describe sigmoidal functions of rate versus ∆G(Lasaga and Luttge, 2001).

It is important to remember that all such rate laws, including Eqs. (5.26) and(5.28) represent complex reaction mechanisms for composite reactions. Since ex-trapolation of a rate from one system to another is only strictly guaranteed for anelementary reaction, the extrapolation of these rate models to new conditions isproblematic (see Chap. 1). For example, both Eqs. (5.26) and (5.28) were unsuc-cessful in extrapolating calcite growth to conditions of undersaturation, and differentversions of Eqs. (5.26) and (5.30) were needed for different conditions of solutionchemistry (Shiraki and Brantley, 1995; Teng et al., 2000). The presence of low con-centrations of aqueous ions was also observed to affect the mechanism of calcitegrowth and the value of exponents in these equations (Davis et al., 2000). Indeed, itis impossible to predict reaction rates of calcite over the full range of ∆G with onerate equation; rather, a family of such curves is needed to describe dissolution andprecipitation as a function of the relevant variables such as pH, PCO2 , total inorganic


carbon, and impurity concentration (Shiraki and Brantley, 1995). Use of equationslike Eq. (5.18) that incorporate individual reaction steps may be more successful inextrapolating rates across conditions than equations such as Eq. (5.26) or Eq. (5.30)(Shiraki and Brantley, 1995).

Recently, models have been developed (Dove et al., 2005) that predict the rate ofdissolution over a range of undersaturation by incorporating homogeneous, impuritypit, and dislocation pit nucleation (see Sect. 5.2.1.2). This work emphasizes that thesurface normal retreat rate of a crystal, rn, is affected by the step spacing, Γ , the stepheight, h, and the horizontal retreat rate of a moving step, v:

rn =hvΓ

(5.33)

The step density is controlled by the presence of pre-existing pits, or by the nu-cleation of dislocation etch pits, impurity etch pits, and vacancy islands. The stepretreat rate can be calculated as a function of ω (the molecular volume), β (kineticcoefficient for the step), and the equilibrium constant Keq to document that stepretreat is a simple linear function of ∆G:

v = ωβKeq (Ω−1) (5.34)

Thus near-equilibrium dissolution without pit nucleation can be discussed in thecontext of Eqs. (5.33)–(5.34). When 2D nucleation occurs (pitting), then the re-treat rate of the crystal is a function of the step retreat rate and the pit nucleationrate J:

rn = hv1/3J2/3 (5.35)

Equations such as (5.7) and (5.8) were used by Dove et al. with Eqs. (5.33)–(5.35)and expressions for the pit nucleation rates to derive rate dependencies for the differ-ent dissolution regimes. With this derivation, the nucleation rate is expected to showa complex dependence upon Ω, and when all the terms are summed, a rate versus∆G function is derived that fits rate data for dissolution of quartz, kaolinite, andpotassium feldspar (other researchers have also applied the model to diopside (Dixitand Carroll, 2007). Dove et al. also provided direct microscopic evidence to supportthe hypothesis that dissolution within the dissolution plateau is characterized by for-mation of all sorts of etch pits while the slower dissolution rates observed closer toequilibrium are characterized by a lack of dislocation etch pitting. The model allowsprediction of the transition from homogeneous nucleation to defect-driven etchingbased on parameters such as the mineral-water interfacial energy and step energyand also provides some understanding for how salt affects dissolution of silicates.Such a model may be more successful in rate extrapolations than the generic rateEq. (5.29) that is currently used in many reactive transport models. However, themodel may also need more fit parameters to be useful.


5.5.2.1 Aluminum Inhibition and Affinity

As we have previously discussed, the presence of aqueous Al3+ has been ob-served to decelerate dissolution of aluminosilicates (Chou and Wollast, 1984, 1985;Gautier et al., 1994; Oelkers et al., 1994; Chen and Brantley, 1997). This effecthas been ascribed to Al-inhibition (see Sect. 5.2.2.3), decreased chemical affinity, orboth. For example, the decrease in dissolution rate of albite in the presence of dis-solved aluminum was attributed to increasing adsorption of the trivalent cation withincreasing temperature (Chen and Brantley, 1997). One way to distinguish affinityeffects from inhibition effects are isotach plots: these plots of constant rate con-toured on activity-activity diagrams have been used to determine the relative impor-tance of ∆G and aAl(aq) during albite and K-feldspar dissolution respectively (Burchet al., 1993; Gautier et al., 1994).

Both the effect of aluminium inhibition and chemical affinity have been usedin the cation exchange model for aluminosilicate dissolution described earlierwith Eq. (5.11). Model Eq. (5.11) attributes the inhibitory effect of Al3+ on dis-solution of some aluminosilicates to back-reactions occurring at specific precur-sor surface sites. However, the dissolution rates of certain aluminosilicates dis-solving at low pH may be best modeled by modifying Eq. (5.11) to incorpo-rate both aqueous aluminum activity and chemical affinity (Oelkers et al., 1994;Schott and Oelkers, 1995):

rnet = k+

⎛⎜⎜⎝

(a3s

H+as

Al3+

)∏i

aυiAi

1+KAl

(a3s

H+as

Al3+

)∏i

aυiAi

⎞⎟⎟⎠(

1− exp

(∆G

νSiRT

))(5.36)

Here, νSi signifies the stoichiometric number of moles of Si in one mole of dissolv-ing aluminosilicate and other variables are defined earlier for Eq. (5.11). Such amodel may be generalized for minerals that dissolve both nonstoichiometrically orstoichiometrically by extending the concept of chemical affinity to describe miner-als whose surface chemistry differs from the bulk (Oelkers, 2001a).

5.6 Conclusion

Our understanding of mineral dissolution kinetics has advanced significantly overthe last several decades. The relative rates of mineral weathering in the laboratoryare established for many minerals and some minerals such as quartz and calcitehave been thoroughly investigated. Many minerals have been fit to simple modelsof dissolution for behavior as a function of pH. More complex rate models have alsobeen parameterized for some minerals to incorporate pH, dissolved species, surfacechemistry, surface topography, and chemical affinity. At present however, differ-ent classes of rate models are available and no generalized rate equation can beused to model mineral dissolution over the full range of geochemical conditions.


As theoretical molecular geochemistry elucidates mechanisms of dissolution ofminerals, experimental dissolution rates can be tested against results of new spec-troscopies to synthesize rate data into more useful rate models.

Datasets for activation energies of mineral dissolution are not as well-constrainedas rate data under ambient conditions largely because less data exists for high-temperature dissolution of minerals. However, activation energies of dissolution forsilicates generally vary between 10 and 25kcalmol−1. Lack of reproducibility inactivation energies measured for a given mineral are presumed to be related to dif-ferences in mineral preparation or chemistry, solution chemistry, or experimentalprotocol. Effort is needed in both the prediction and measurement of such activationenergies.

Quantitative extrapolation of laboratory rates to field systems remains difficultdue to multiple contributing factors related to concepts discussed in this chapter.Intrinsic factors related to differences in mineral samples prepared in the laboratoryor weathered in the field contribute to the laboratory-field discrepancy. Perhaps themost important intrinsic factor is the reactive surface area of dissolving mineral. Asof yet, no general theory or measurement protocol for reactive surface area has beenadvanced. In addition, laboratory rates are generally measured far from equilibriumwhile natural weathering often occurs closer to equilibrium especially at naturalmineral-water interfaces where fluid flow rates may be very low (White, Chap. 7).Dissolution of laboratory samples may therefore be rate-limited by the interfacereaction while dissolution in field systems may be at least partially rate-limitedby transport. Modeling that accurately incorporates both reaction and transport isnecessary to elucidate the complexities of mineral reaction kinetics across thesescales.

Acknowledgements

SLB acknowledges A. White for discussions, A. Zimmerman for Fig. 5.4, J. Band-stra for Fig. 5.1, J. Moore for help on Fig. 5.12, and all the students of Penn StateGeosciences 560. This chapter is based upon work supported by the Center for En-vironmental Kinetics Analysis funded by the National Science Foundation underGrant No. CHE-0431328 and the U.S. Department of Energy, Biological and Envi-ronmental Research (BER).

5.7 Glossary of Symbols

a depth of a pit on dissolving crystal surfaceai activity of species i in solutionb Burgers vector


Ea activation energyE ′

a apparent activation energy measured at a given pH valueh step height on a crystal surfaceH2CO∗

3 CO2(aq) +H2CO3(aq)[i] concentration of species iJ pit nucleation rate on a crystal surfacek rate constantkH rate constant for proton-promoted dissolutionkH2O rate constant for dissolution in neutral pHkmin rate constant measured far from equilibrium for Eq. (5.32)kOH rate constant for hydroxyl-promoted dissolutionkLi rate constant for ligand-promoted dissolutionkSiOH rate constant for reaction at ≡ SiOHkSiO− rate constant for reaction at ≡ SiO− and ≡ SiONaksolv rate constant for water exchange around a cation in

solutionk1,k2,k3,k4 rate constants in the mechanism of

dissolution/precipitation of calcitek5,k6 rate constants in the albite dissolution rate Eq. (5.31)k′1 modified rate constant for reaction given by Eq. (5.3)k+ forward rate constantKads

H equilibrium constant for proton adsorption (Eq. (5.12))Kads

Miequilibrium constant for cation adsorption (Eq. (5.12))

K2 dissociation constant for bicarbonateKc solubility product constant for calciteKi equilibrium constant for cation-proton exchange

(Eq. (5.21))Keq equilibrium constantLi ligand im order with respect to a reactant in Eq. (5.9)m1,m2 constants used in rate Eqs. (5.26)–(5.32)m j order with respect to species in Eq. (5.26)Mi cationObr bridging oxygenn order with respect to a reactant in Eq. (5.9)n1 constant in rate Eqs. (5.26), (5.29), (5.30)pHppzc pH of pristine point of zero chargeq1,q2,q3 order with respect to surface species in Eqs. (5.10), (5.13)qA,qB charge on a speciesQi a tetrahedrally coordinated atom surrounded by i bridging

oxygensr surface-area normalized rate of reactionr′ dissolution rate in units of mol L−1 t−1

rn surface normal retreat rate of a crystalrnet net rate of reaction (forward rate – backward rate)R gas constants stoichiometric coefficient for precursor species (Eq.

(5.11))≡ S metal cation at a surface site on a mineral≡ SLi surface metal-ligand complex≡ SO− deprotonated surface hydroxyl≡ SOH surface hydroxyl species≡ SOH+

2 protonated surface hydroxyl≡ SiOAl ≡ bridging oxygen linkage between Si and Al cations


≡ SiOSi ≡ bridging oxygen linkage between two Si cations≡ SiONa surface silanol with adsorbed Na iont timeT TemperatureTo reference temperaturev horizontal retreat rate of a moving step on a crystal surfaceV molar volumeX number of cations in non-tetrahedral sites in a mineral

structureX/Si ratio of cations in nontetrahedral sites to cations in

tetrahedral sitesβ kinetic coefficient for the step on a crystal surface∆G Gibbs free energy of reaction∆Gdislocation Gibbs free energy of dissolution at a dislocation outcrop∆Gcrit critical Gibbs free energy for formation of dislocation etch

pitsε radius of cylindrical etch pitεo dislocation core radiusγ crystal-water interfacial energyΓ step spacing on a crystal surfaceθ≡SiOH fraction of the silica surface covered by silanol groupsθ≡SiO−

totsum of the fractions of total sites existing as deprotonated

surface hydroxyls and as sites with adsorbed Na+ on asilica surface

τ energy factor for a dislocationνi stoichiometric coefficient for species iνSi number of Si in mineral formula in Eq. (5.17)ω molecular volumeΩ ratio of activity quotient to equilibrium constant for a

reaction

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