Dissolution kinetics as a function of the Gibbs free energy of reaction: An experimental study based on albite feldspar

Here we report on an experimental investigation of the relation between the dissolution rate of albite feldspar and the Gibbs free energy of reaction, ΔG_r. The experiments were carried out in a continuously stirred flow-through reactor at 150 °C and pH_(150 °C) 9.2. The dissolution rates R are based on steady-state Si and Al concentrations and sample mass loss. The overall relation between ΔG_r and R was determined over a free energy range of −150 < ΔG_r < −15.6 kJ mol⁻¹. The data define a continuous and highly non-linear, sigmoidal relation between R and ΔG_r that is characterized by three distinct free energy regions. The region furthest from equilibrium, delimited by −150 < ΔG_r < −70 kJ mol⁻¹, represents an extensive dissolution rate plateau with an average rate . In this free energy range the rates of dissolution are constant and independent of ΔG_r, as well as [Si] and [Al]. The free energy range delimited by −70 ? ΔG_r ? −25 kJ mol⁻¹, referred to as the ‘transition equilibrium’ region, is characterized by a sharp decrease in dissolution rates with increasing ΔG_r, indicating a very strong inverse dependence of the rates on free energy. Dissolution nearest equilibrium, defined by ΔG_r > −25 kJ mol⁻¹, represents the ‘near equilibrium’ region where the rates decrease as chemical equilibrium is approached, but with a much weaker dependence on ΔG_r. The lowest rate measured in this study, R = 6.2 × 10⁻¹¹ mol m⁻² s⁻¹ at ΔG_r = −16.3 kJ mol⁻¹, is more than two orders of magnitude slower than the plateau rate. The data have been fitted to a rate equation (adapted from Burch et al. [Burch, T. E., Nagy, K. L., Lasaga, A. C., 1993. Free energy dependence of albite dissolution kinetics at 80 °C and pH 8.8. Chem. Geol.105, 137-162]) that represents the sum of two parallel reactions

R=k₁[1-exp(-ng^m₁)]+k₂[1-exp(-g)]^m₂,     

Effect of solution saturation state and temperature on diopside dissolution

Steady-state dissolution rates of diopside are measured as a function of solution saturation state using a titanium flow-through reactor at pH 7.5 and temperature ranging from 125 to 175°C. Diopside dissolved stoichiometrically under all experimental conditions and rates were not dependent on sample history. At each temperature, rates continuously decreased by two orders of magnitude as equilibrium was approached and did not exhibit a dissolution plateau of constant rates at high degrees of undersaturation. The variation of diopside dissolution rates with solution saturation can be described equally well with a ion exchange model based on transition state theory or pit nucleation model based on crystal growth/dissolution theory from 125 to 175°C. At 175°C, both models over predict dissolution rates by two orders of magnitude indicating that a secondary phase precipitated in the experiments. The ion exchange model assumes the formation of a Si-rich, Mg-deficient precursor complex. Lack of dependence of rates on steady-state aqueous calcium concentration supports the formation of such a complex, which is formed by exchange of protons for magnesium ions at the surface. Fit to the experimental data yields where the Mg-H exchange coefficient, n = 1.39, the apparent activation energy, E _a = 332 kJ mol^-1, and the apparent rate constant, k = 10^41.2 mol diopside cm^-2 s^-1. Fits to the data with the pit nucleation model suggest that diopside dissolution proceeds through retreat of steps developed by nucleation of pits created homogeneously at the mineral surface or at defect sites, where homogeneous nucleation occurs at lower degrees of saturation than defect-assisted nucleation. Rate expressions for each mechanism (i) were fit to where the step edge energy (α) for homogeneously nucleated pits were higher (275 to 65 mJ m^-2) than the pits nucleated at defects (39 to 65 mJ m^-2) and the activation energy associated with the temperature dependence of site density and the kinetic coefficient for homogeneously nucleated pits (E_{b-homogeneous} = 2.59 × 10^-16 mJ K^-1) were lower than the pits nucleated at defects (E_{b-defect assisted} = 8.44 × 10^-16 mJ K^-1).     

Albite dissolution kinetics as a function of distance from equilibrium: Implications for natural feldspar weathering

Determining the kinetics of many geologic and engineering processes involving solid/fluid interactions requires a fundamental understanding of the Gibbs free energy dependency of the system. Currently, significant discrepancies seem to exist between kinetic datasets measured to determine the relationship between dissolution rate and Gibbs free energy. To identify the causes of these discrepancies, we have combined vertical scanning interferometry, atomic force microscopy, and scanning electron microscopy techniques to identify dissolution mechanisms and quantify dissolution rates of albite single crystals over a range of Gibbs free energy (−61.1 < ΔG < −10.2 kJ/mol). During our experiments, both a previously dissolved albite surface exhibiting etch pits and a pristine surface lacking dissolution features were dissolved simultaneously within a hydrothermal, flow-through reactor. Experimental results document an up to 2 orders of magnitude difference in dissolution rate between the differently pretreated surfaces, which are dominated by different dissolution mechanisms. The rate difference, which persists over a range of solution saturation state, indicates that the dissolution mechanisms obey different Gibbs free energy dependencies. We propose that this difference in rates is the direct consequence of a kinetic change in dissolution mechanism with deviation from equilibrium conditions. The existence of this kinetic “switch” indicates that a single, continuous function describing the relationship between dissolution rate and Gibbs free energy may be insufficient. Finally, we discuss some of the potential consequences of our findings on albite’s weathering rates with a particular focus on the sample’s history.     

Temperature dependence of calcite dissolution kinetics between 1 and 62°C at pH 2.7 to 8.4 in aqueous solutions

The kinetics of calcite dissolution in aqueous KCl-solutions far from equilibrium, between 1 and 62°C in the pH-range 2.7 to 8.4 have been investigated using a rotating disc apparatus. At neutral and alkaline pH in the mixed kinetic regime the empirical apparent activation energy (EAAE) for the surface chemical reaction rate constant is 54 ± 4 kJ mole^?1 for Carrara marble and 46 ± 4 kJ mole^?1 for Iceland spar. Under similar conditions the EAAE of the transport rate constant increases with decreasing temperature, but has a mean value of 27 ± 2 kJ mole^?1. The corresponding diffusion coefficient has a mean EAAE of 37 ± 3 kJ mole^?1 and this high EAAE is consistent with transport dependence on product diffusion in this H⁺-independent regime.In contrast, in acid solutions, where the rate approaches end-member transport control, the EAAE of the diffusion coefficient is 16 kJ mole^?1, also decreasing with increasing temperature. This is compatible with H⁺-diffusion to the surface being rate-controlling.In inhibitor-free natural systems, calcite dissolution kinetics far from equilibrium can be described in terms of three regimes: an H⁺-dependent regime (pH < 4 at 25°C), a transition regime (4 < pH < 5.5 at 25°C) and an H⁺-independent regime (pH > 5.5 at 25°C). At lower temperatures these boundaries move to higher pH values. The presence of inhibitors in natural systems may enhance surface controlled kinetics.     

The kinetics of the dissolution of chlorite as a function of pH and at 25°C

Far from equilibrium, quasi-steady state dissolution rates of an iron rich chlorite (Mg_2.76Fe²⁺_1.90Fe³⁺_0.07Al_0.97)[Si_2.48Al_1.52O₁₀](OH)₈, have been measured as a function of H⁺ concentration for the pH range 3 to 10.5 and at 25°C. The rates were determined using a single pass flow through cell and with a time frame for observing the steady state condition of between 10 to 50 days. Rates are independent of the buffers used to control the pH, sample preparation, experimental methodology and chlorite composition. The results were collated with literature values allowing the rate to be expressed as a function of H⁺ as;

     

Morphological evolution of dissolving feldspar particles with anisotropic surface kinetics and implications for dissolution rate normalization and grain size dependence: A kinetic modeling study

With previous two-dimensional (2D) simulations based on surface-specific feldspar dissolution succeeding in relating the macroscopic feldspar kinetics to the molecular-scale surface reactions of Si and Al atoms ( [Zhang and Lüttge, 2008] and [Zhang and Lüttge, 2009]), we extended our modeling effort to three-dimensional (3D) feldspar particle dissolution simulations. Bearing on the same theoretical basis, the 3D feldspar particle dissolution simulations have verified the anisotropic surface kinetics observed in the 2D surface-specific simulations. The combined effect of saturation state, pH, and temperature on the surface kinetics anisotropy has been subsequently evaluated, found offering diverse options for morphological evolution of dissolving feldspar nanoparticles with varying grain sizes and starting shapes. Among the three primary faces on the simulated feldspar surface, the (1 0 0) face has the biggest dissolution rate across an extensively wide saturation state range and thus acquires a higher percentage of the surface area upon dissolution. The slowest dissolution occurs to either (0 0 1) or (0 1 0) faces depending on the bond energies of Si-(O)-Si (Φ_Si-O-Si/kT) and Al-(O)-Si (Φ_Al-O-Si/kT). When the ratio of Φ_Si-O-Si/kT to Φ_Al-O-Si/kT changes from 6:3 to 7:5, the dissolution rates of three primary faces change from the trend of (1 0 0) > (0 1 0) > (0 0 1) to the trend of (1 0 0) > (0 0 1) > (0 1 0). The rate difference between faces becomes more distinct and accordingly edge rounding becomes more significant. Feldspar nanoparticles also experience an increasing degree of edge rounding from far-from-equilibrium to close-to-equilibrium. Furthermore, we assessed the connection between the continuous morphological modification and the variation in the bulk dissolution rate during the dissolution of a single feldspar particle. Different normalization treatments equivalent to the commonly used mass, cube assumption, sphere assumption, geometric surface area, and reactive surface area normalizations have been used to normalize the bulk dissolution rate. For each of the treatments, time consistence and grain size dependence of the normalized dissolution rate have been evaluated and the results revealed significant dependences on the magnitude of surface kinetic anisotropy under differing environmental conditions. In general, the normalized dissolution rates are strongly dependent on grain size. Time-consistent normalization treatment varies with the investigated condition. The modeling results suggest that the sphere-, cube-, and BET-normalized dissolution rates are appropriate under the far-from-equilibrium conditions at low pH where these normalizations are time-consistent and are slightly dependent on grain size.     

The effect of coherency stress on the mechanism of the reaction albite+K+⇌K-feldspar+Na+ and on the mechanical state of the resulting feldspar

Coherency stress and coherency strain energy generated by Na⁺?K⁺ ion exchange in alkali feldspars are calculated using an isotropic model, and deformation of single crystals of alkali feldspars exposed to molten alkali chlorides at \(P_{H_2 O} \) < 1 bar is described. Coherency stress in alkali feldspars can reach 10–20 kb. When it is large, partial relaxation by fracture and/or plastic deformation takes place under anhydrous conditions, but temporary build-up of stress is unavoidable even under hydrothermal conditions. Because of coherency strain energy, a thin layer of an end-member alkali feldspar produced by cation exchange on a grain of the other end-member alkali feldspar would be unstable with respect to dissolution. Therefore, under hydrothermal conditions one end-member alkali feldspar replaces the other by dissolution and precipitation. The mechanism of the reaction $$Na_x K_{1 - x} AlSi_3 O_{8_{(feld.)} } + yK^ + \rightleftharpoons Na_{x - y} K_{1 + y - x} AlSi_3 O_{8_{(feld.)} } + yNa^ + $$ is primarily controlled by \(P_{H_2 O} \) and by ΔK/(Na + K), the difference between the equilibrium value and the initial value of the atomic K/(Na + K) ratio of the feldspar. When ¦ΔK/(Na + K)¦ is small, the reaction proceeds by cation exchange. When ¦ΔK/(Na + K)¦ is large, cation exchange still occurs if \(P_{H_2 O} \) is very low, but under hydrothermal conditions replacement by dissolution and precipitation occurs.     

The influence of Fe-rich coatings on the dissolution of anorthite at pH 2.6

Surface coatings are very common on mineral grains in soils but most laboratory dissolution experiments are carried out on pristine, uncoated mineral grains. An experiment designed to unambiguously isolate the effect of surface coatings on mineral dissolution from any influence of solution saturation state is reported. Two aliquots of 53 to 63 μm anorthite feldspar powder were used. One was dissolved in pH 2.6 HCl, the other in pH 2.6 FeCl₃ solution, both for ∼6000 h in flow-through reactors. An amorphous Fe-rich, Al-, Ca- and Si-free orange precipitate coated the anorthite dissolved in the FeCl₃ solution. BET surface area of the anorthite increased from 0.16 to 1.65 m² g⁻¹ in the HCl experiment and to 3.89 m² g⁻¹ in the FeCl₃ experiment. The increase in surface area in the HCl experiment was due to the formation of etch pits on the anorthite grain surface whilst the additional increase in the FeCl₃ experiment was due to the micro- and meso-porous nature of the orange precipitate. This precipitate did not inhibit or slow the dissolution of the anorthite. Steady state dissolution rates for the anorthite dissolved in the HCl and FeCl₃ were ∼2.5 and 3.2 × 10⁻¹⁰ mol_feldspar m⁻² s⁻¹ respectively. These rates are not significantly different after the cumulative uncertainty of 17% in their value due to uncertainty in the inputs parameters used in their calculation is taken into account. Results from this experiment support previous theoretical and inference-based conclusions that porous coatings should not inhibit mineral dissolution.     

Effect of pH and organic ligands on the kinetics of smectite dissolution at 25 °C

Forward dissolution rates of Na-Montmorillonite (Wyoming) SWy-2 smectite (Ca_0.06Na_0.56)[Al_3.08Fe(III)_0.38Mg_0.54] [Si_7.93 Al_0.07]O₂₀(OH)₄ were measured at 25 °C in a mixed-flow reactor equipped with interior dialysis compartment (6-8 kDa membrane) as a function of pH (1-12), dissolved carbonate (0.5-10 mM), phosphate (10⁻⁵ to 0.03 M), and nine organic ligands (acetate, oxalate, citrate, EDTA, alginate, glucuronic acid, 3,4-dihydroxybenzoic acid, gluconate, and glucosamine) in the concentration range from 10⁻⁵ to 0.03 M. In organic-free solutions, the Si-based rates decrease with increasing pH at 1 ? pH ? 8 with a slope close to −0.2. At 9 ? pH ? 12, the Si-based rates increase with a slope of ∼0.3. In contrast, non-stoichiometric Mg release weakly depends on pH at 1 ? pH ? 12 and decreases with increasing pH. The empirical expression describing Si-release rates [R, mol/cm²/s] obtained in the present study at 25 °C, I = 0.01 M is given by

     

Experimental study of the effect of pH and temperature on the kinetics of montmorillonite dissolution

The effect of pH on the kinetics of smectite (K-montmorillonite) dissolution was investigated at 50 and 70 °C in stirred flow-through reactors over the pH range of 1-13.5. Experiments done at very acidic and very basic pH were far from equilibrium. Near neutral pH experiments were closer to equilibrium. The Al/Si release ratio, while initially being incongruent, ultimately approached the stoichiometric value in most of the experiments. Temperature, extreme pH, and time favor congruency. Rates can be described by:

     

A Study on the Dissolution Kinetics of Basalt—Water Interaction under Different pH Conditions I：Release of Elements and pH Neutralization Effect

Experimental research on the chemical weathering of alkaline-olivine basalt from Huangyi Mountain,Kuandain County,Liaoning.Province and olivine basalt from Dayangke,Mingxi County,Fujian Province has shown that the acidity of the solution tends to become neutral regardless of what the acidity of the starting solution would be during basalt0-water interaction.We call this phenome-non“pH neutralized Effect”.The dissolved species in the solution were determined and unreacted and reacted sample-surface chemical components involved or uninvolved in reaction were analyzed using X-ray photoelectron spectroscopy(XPS).The results revealed two different mechanisms of dissolution of basalt in acidic and basic solutions.     

The kinetics and mechanisms of simulated British Magnox waste glass dissolution as a function of pH,silicic acid activity and time in low temperature aqueous systems

Dissolution of a simulated British Magnox waste glass is governed by two pH-dependent processes. At low pH, dissolution is governed by reactions occurring predominantly at non-Si sites and residual Si-rich gels develop at the glass surface as B, Al and modifier cations are selectively leached. Here, extensive proton promoted hydrolysis of BO and AlO bonds is coupled with hydration and ion exchange processes. Hydrolysis of siloxane bonds governs the rate of dissolution at high pH and the glass dissolves congruently as the silicate network breaks down extensively. Differences in the surface chemistries and morphologies of glass samples reacted in strongly acidic and highly alkaline media reflect the net effects of these processes. The rate of the congruent dissolution process is influenced by the activity of silicic acid. The results are compared with published data for other glass formulations and are discussed in the context of proposed kinetic dissolution models.     

An EFTEM/HRTEM high-resolution study of the near surface of labradorite feldspar altered at acid pH: evidence for interfacial dissolution-reprecipitation

Using an approach combining high-resolution and energy-filtered transmission electron microscopy (HRTEM and EFTEM), we have studied with Å to nm-spatial resolution the interfacial region that delimits the near-surface altered zone and non-altered labradorite feldspar after dissolution under acid pH conditions. The interface is characterized by extremely sharp and spatially coincident changes in structure and chemistry. The 500-nm-thick altered zone is depleted in interstitial cations (Ca, Na, K) and Al, a framework element, whereas it is enriched in H, O, and Si. Modeling H⁺-alkali interdiffusion within a 500-nm-thick altered zone shows that volume interdiffusion cannot reproduce the sharp chemical interfaces measured by EFTEM. Based on these new data, we propose that the near-surface altered zone is a result of interfacial dissolution-reprecipitation, and not of preferential leaching of cations and interdiffusion with H⁺. This implies an intrinsic dissolution process that is stoichiometric, where the breaking of bonds and release of interstitial cations and framework elements (Al, Si, and O) to solution occur contemporaneously at equal relative rates from the original fluid–mineral interface.     

Experimental study of the effect of pH on the kinetics of montmorillonite dissolution at 25 °C

The effect of pH on the kinetics of smectite (K-montmorillonite) dissolution was investigated at 25 °C in batch and stirred flow-through reactors over the pH range of 1-13.5, in KNO₃ solutions. Dissolution rates were obtained based on the release of Si and Al at steady-state under far from equilibrium conditions. Dissolution was non-stoichiometric between pH 5 and 10, due to adsorption/precipitation of Al. Dissolution rates computed from batch and flow-through experiments were consistent, irrespective of the Si and Al concentrations. Sample pre-treatment and the interlayer cation do not affect the steady-state dissolution rate or stoichiometry of cation release. The rate dependence on pH can be described by:

     

Factors affecting the dissolution kinetics of volcanic ash soils: dependencies on pH,CO2, and oxalate

Laboratory experiments were conducted with volcanic ash soils from Mammoth Mountain, California to examine the dependence of soil dissolution rates on pH and CO₂ (in batch experiments) and on oxalate (in flow-through experiments). In all experiments, an initial period of rapid dissolution was observed followed by steady-state dissolution. A decrease in the specific surface area of the soil samples, ranging from 50% to 80%, was observed; this decrease occurred during the period of rapid, initial dissolution. Steady-state dissolution rates, normalized to specific surface areas determined at the conclusion of the batch experiments, ranged from 0.03 μmol Si m⁻² h⁻¹ at pH 2.78 in the batch experiments to 0.009 μmol Si m⁻² h⁻¹ at pH 4 in the flow-through experiments. Over the pH range of 2.78–4.0, the dissolution rates exhibited a fractional order dependence on pH of 0.47 for rates determined from H⁺ consumption data and 0.27 for rates determined from Si release data. Experiments at ambient and 1 atm CO₂ demonstrated that dissolution rates were independent of CO₂ within experimental error at both pH 2.78 and 4.0. Dissolution at pH 4.0 was enhanced by addition of 1 mM oxalate. These observations provide insight into how the rates of soil weathering may be changing in areas on the flanks of Mammoth Mountain where concentrations of soil CO₂ have been elevated over the last decade. This release of magmatic CO₂ has depressed the soil pH and killed all vegetation (thus possibly changing the organic acid composition). These indirect effects of CO₂ may be enhancing the weathering of these volcanic ash soils but a strong direct effect of CO₂ can be excluded.     

The effect of fluid pressure on oxygen isotope exchange between feldspar and water

The rate of oxygen isotope exchange between adularia and 2 M KCl solution has been measured at 650°C at pressures from 125 to 4000 bar. Isotropie diffusion coefficients calculated from these data show a positive dependence on the fluid pressure. This dependence is opposite to the predicted effect of hydrostatic pressure and is attributed to the activity of ‘water’ (H₂O, H⁺ or OH^?) in the feldspar.     

The dissolution kinetics of a granite and its minerals—Implications for comparison between laboratory and field dissolution rates

The present study compares the dissolution rates of plagioclase, microcline and biotite/chlorite from a bulk granite to the dissolution rates of the same minerals in mineral-rich fractions that were separated from the granite sample. The dissolution rate of plagioclase is enhanced with time as a result of exposure of its surface sites due to the removal of an iron oxide coating. Removal of the iron coating was slower in the experiment with the bulk granite than in the mineral-rich fractions due to a higher Fe concentration from biotite dissolution. As a result, the increase in plagioclase dissolution rate was initially slower in the experiment with the bulk granite. The measured steady state dissolution rates of both plagioclase (6.2 ± 1.2 × 10⁻¹¹ mol g⁻¹ s⁻¹) and microcline (1.6 ± 0.3 × 10⁻¹¹ mol g⁻¹ s⁻¹) were the same in experiments conducted with the plagioclase-rich fraction, the alkali feldspar-rich fraction and the bulk granite.Based on the observed release rates of the major elements, we suggest that the biotite/chlorite-rich fraction dissolved non-congruently under near-equilibrium conditions. In contrast, the biotite and chlorite within the bulk granite sample dissolved congruently under far from equilibrium conditions. These differences result from variations in the degree of saturation of the solutions with respect to both the dissolving biotite/chlorite and to nontronite, which probably was precipitating during dissolution of the biotite and chlorite-rich fraction. Following drying of the bulk granite, the dissolution rate of biotite was significantly enhanced, whereas the dissolution rate of plagioclase decreased.The presence of coatings, wetting and drying cycles and near equilibrium conditions all significantly affect mineral dissolution rates in the field in comparison to the dissolution rate of fully wetted clean minerals under far from equilibrium laboratory conditions. To bridge the gap between the field and the laboratory mineral dissolution rates, these effects on dissolution rate should be further studied.     

Orthoclase dissolution kinetics probed by in situ X-ray reflectivity: effects of temperature, pH, and crystal orientation

Initial dissolution kinetics at orthoclase (001) and (010) cleavage surfaces were measured for ∼2 to 7 monolayers as a function of temperature using in situ X-ray reflectivity. The sensitivity of X-ray reflectivity to probe mineral dissolution is discussed, including the applicability of this approach for different dissolution processes and the range of dissolution rates (∼10⁻¹² to 10⁻⁶ mol/m²/sec) that can be measured. Measurements were performed at pH 12.9 for the (001) surface and at pH 1.1 for the (001) and (010) surfaces at temperatures between 46 and 83°C. Dissolution at pH 12.9 showed a temperature-invariant process with an apparent activation energy of 65 ± 7 kJ/mol for the (001) cleavage surface consistent with previous powder dissolution results. Dissolution at pH 1.1 of the (001) and (010) surfaces revealed a similar process for both surfaces, with apparent activation energies of 87 ± 7 and 41 ± 7 kJ/mol, respectively, but with systematic differences in the dissolution process as a function of temperature. Longer-term measurements (five monolayers) show that the initial rates reported here at acidic pH are greater than steady-state rates by a factor of 2. Apparent activation energies at acidic pH differ substantially from powder dissolution results for K-feldspar; the present results bracket the value derived from powder dissolution measurements. The difference in apparent activation energies for the (001) and (010) faces at pH 1.1 reveals an anisotropy in dissolution kinetics that depends strongly on temperature. Our results imply a projected ∼25-fold change in the ratio of dissolution rates for the (001) and (010) surfaces between 25 and 90°C. The dissolution rate of the (001) surface is higher than that of the (010) surface above 51°C and is projected to be lower below this temperature. These results indicate clearly that the kinetics and energetics of orthoclase dissolution at acidic pH depend on crystal orientation. This dependence may reflect the different manifestation of the Al-Si ordering between the T1 and T2 tetrahedral sites at these two crystal faces and can be rationalized in terms of recent theoretical models of mineral dissolution.     

The effect of fluoride on the dissolution rates of natural glasses at pH 4 and 25°C

Far-from-equilibrium, steady-state dissolution rates at pH 4 of a suite of natural glasses, ranging from basaltic to rhyolitic in composition, have been determined as a function of aqueous fluoride concentrations up to 1.8 × 10⁻⁴ mol/kg in mixed-flow reactors. Dissolution rates of each of these glasses increase monotonically with increasing aqueous fluoride concentration. Measured dissolution rates are found to be consistent with both the Furrer and Stumm (1986) surface coordination model and the Oelkers (2001) multi-oxide dissolution model. Application of the latter model yields the following equation that can describe all measured rates as a function of both glass and aqueous solution composition: