# A comprehensive and internally consistent mineral dissolution rate database: Part I: Primary silicate minerals and glasses

Matylda Heřmanská, Martin Voigt, Chiara Marieni, Julien Declercq, Eric Oelkers

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Matylda Heřmanská, Martin Voigt, Chiara Marieni, Julien Declercq, Eric Oelkers. A comprehensive and internally consistent mineral dissolution rate database: Part I: Primary silicate minerals and glasses. Chemical Geology, 2022, 597, pp.120807. 10.1016/j.chemgeo.2022.120807. hal-04917761

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Distributed under a Creative Commons Attribution 4.0 International License
1 Submitted to Chemical Geology

2 A comprehensive and internally consistent mineral dissolution rate database: Part I: Primary silicate minerals and glasses

4 Matylda Heřmanská¹, Martin J. Voigt², Chiara Marieni¹, Julien Declercq³, and Eric H. Oelkers¹

5

6 AFFILIATION :

7 ¹Géosciences Environnement Toulouse, CNRS, 14 Avenue Edouard Belin, 31400 Toulouse (France)

8 ²Institute of Earth Sciences, University of Iceland, Sturlugötu 7, 101 Reykjavík (Iceland)

9 ³SRK Consulting (UK) Limited, Churchill House, 17 Churchill Way, Cardiff, CF10 2HH, Wales, UK

10

11 Keywords: mineral dissolution rates, database, primary silicates, PHREEQC, TOUGHREACT

12 Abstract

13 Mineral dissolution rates control the temporal evolution of many natural processes on the surface and 14 upper crust of the Earth. This is the first of a series of papers describing the development and 15 implementation of a comprehensive and internally consistent database of the dissolution rates of the 16 major rock-forming minerals. In this paper, we describe the retrieval and regression of the dissolution 17 rates of the primary rock-forming silicates, including quartz and other SiO₂ polymorphs, feldspars, 18 pyroxenes, amphiboles, micas, volcanic glass, and olivines. Owing to the limited fluid chemistry data 19 available for many of the published experimental studies, BET surface area normalized mineral and 20 most glass dissolution rates (r) were regressed using

$$r = \sum_{i} \left( A_{i} a_{H^{+}}^{n_{i}} e^{\frac{E_{ai}}{RT}} \right) \left( 1 - \exp\left(-\frac{A}{\sigma RT}\right) \right)$$

21 where Aᵢ stands for pre-exponential factors, aH⁺ corresponds to the hydrogen ion activity, nᵢ refers to 22 reaction orders, T designates absolute temperature, R denotes the gas constant, Eₐᵢ represents activation 23 energies, σ stands for Temkin's average stoichiometric number, and A denotes the chemical affinity of 24 the dissolution reaction. Where relevant data were lacking, rates were extrapolated assuming that 25 mineral dissolution follows similar trends within the same mineral group. Regression was performed 26 using least-squares algorithms. The average difference between calculated and measured rates ranged 27 from 0.2 to 0.8 log units depending on the mineral. The obtained rate equations were implemented into 28 the carbfix.dat database for direct use in the PHREEQC software but can be extended to other 29 geochemical modeling software, such as TOUGHREACT. 30
## 1. Introduction

The dissolution of primary minerals plays a crucial role in many natural geological processes in the upper crust, including surface weathering, soil evolution, and mass transfer in surface waters and hydrothermal systems (e.g., Berner and Holdren, 1979; Colman, 1982; Berner et al., 1983; Eggleton, 1987; Drever, 1988; Banfield et al., 1991; Brady, 1991; Nesbitt and Wilson, 1992; Shoji et al., 1993; Brady and Carroll, 1994; Lasaga et al., 1994; Gislason et al., 1996; Kump et al., 2000; Chadwick and Chorover, 2001; Beig and Lüttge, 2006; Maher et al., 2009; Xiao et al., 2018). Mineral dissolution rates are also critical to geoengineered systems such as carbon capture and storage, nuclear waste management, and industrial waste neutralization (e.g., Malow et al., 1984; Crovisier et al., 1988; Van Herk et al., 1989; Jercinovic et al., 1990; Morgenstein and Shettel, 1993; Jonckbloedt, 1998; Xiao et al., 1999; Berg and Banwart, 2000; Oelkers and Schott, 2005; Bertier et al., 2006; McGrail et al., 2006; Stopar et al., 2006; Matter et al., 2007, 2016; Goldberg et al., 2008; Hausrath et al., 2008; Oelkers et al., 2008; Oelkers and Cole, 2008; Olsen and Rimstidt, 2008; Kampman et al., 2009; Matter and Kelemen, 2009; Prigiobbe et al., 2009; Schaef and McGrail, 2009; Schaef et al., 2009, 2010; Gislason et al., 2010; Hausrath and Brantley, 2010; King et al., 2010; Guyot et al., 2011; Köhler et al., 2013; Lu et al., 2013; Wang et al., 2013; Sissmann et al., 2013, 2014; Wang et al., 2013; Dehouck et al., 2014; Velbel, 2014; Olsen et al., 2015; Tutolo et al., 2015; Niles et al., 2017; Li et al., 2018). The quantification of mineral dissolution rates at conditions of major geochemical processes, including surface weathering and fluid-rock interaction, is, therefore, a major step towards constraining the temporal evolution of these processes.

Numerous experimental studies have reported the dissolution rates of primary and secondary minerals at various temperatures and initial fluid composition. Much of this work has been summarized in the literature (e.g., Blum and Stillings, 1995; Brantley, 2003; Marini, 2007; Brantley et al., 2008; Ganor et al., 2009; Grundwell, 2015). As noted by White and Brantley (1995) and Brantley et al. (2008), however, the interpretation and interlaboratory comparisons of mineral dissolution rates are challenging due to several factors, including changing aqueous solution and mineral surface compositions, secondary phase precipitation, and surface area variations as a function of elapsed time (c.f., Aagaard and Helgeson, 1982; Helgeson et al., 1984; Murphy and Helgeson, 1987; Oelkers, 2001a; Brantley, 2003). Moreover, experimental methods and sample preparation such as wet grinding or sieving can lead to preferential leaching and non-stoichiometric dissolution (Nagy, 1995). There has also been much debate about the consistency of laboratory-measured rates with those of natural processes (Walther and Wood, 1986; Schnoor, 1990; Swoboda-Colberg and Drever, 1993; Velbel, 1993) as summarized in White and Brantley (1995) and Brantley et al. (2008).

Several past studies have regressed some of the available mineral rate data (Sverdrup, 1990; Brantley and Chen, 1995; White and Brantley, 1995; Palandri and Kharaka, 2004; Marini, 2007;
Brantley et al., 2008; Schott et al., 2009). Zhang et al. (2019) incorporated some of these rate equations into a PHREEQC script to facilitate their use in geochemical modeling calculations, but made no effort to update or verify the internal consistency of these rates. This study builds on this past work by 1) updating the regression calculations to account for rates published over the past 20 years, 2) deriving an internally consistent database of the rate equations and parameters, and 3) formatting the database for direct use within PHREEQC (Parkhurst and Appelo, 1999) and TOUGHREACT (Xu et al., 2006, 2011). It is anticipated that this newly created database can serve as a benchmark enabling the direct comparison of the results of geochemical modeling calculations in dynamic and time-dependent fluid-mineral systems. The purpose of this manuscript is to introduce this new mineral dissolution rate database and to document the retrieval of rate parameters for the major rock-forming primary silicates. Subsequent series will provide similar documentation of the retrieval of rate parameters for other major rock-forming minerals.

## 2. Theoretical background

### Notation

<table><tr><td>a<sub>H+</sub></td><td>Activity of aqueous H<sup>+</sup></td><td>R<sup>2</sup></td><td>Coefficient of determination</td></tr><tr><td>A</td><td>Chemical affinity of the reaction dissolution reaction (kJ mol<sup>-1</sup>)</td><td>r</td><td>Dissolution rate (mol m<sup>-2</sup> s<sup>-1</sup>)</td></tr><tr><td>A<sub>0</sub>, A'<sub>0</sub></td><td>Temperature-independent pre-exponential factor (mol m<sup>-2</sup> s<sup>-1</sup>)</td><td>r<sub>+</sub></td><td>Forward (or far-from-equilibrium) dissolution rate (mol m<sup>-2</sup> s<sup>-1</sup>)</td></tr><tr><td>E<sub>a</sub></td><td>Activation energy (kJ mol<sup>-1</sup>)</td><td>S</td><td>Specific surface area (m<sup>2</sup> g<sup>-1</sup>)</td></tr><tr><td>E'<sub>a</sub></td><td>Apparent activation energy (kJ mol<sup>-1</sup>)</td><td>T</td><td>Temperature in K</td></tr><tr><td>k</td><td>Rate constant (mol m<sup>-2</sup> s<sup>-1</sup>)</td><td>ȳ</td><td>Average experimentally measured experimental rate</td></tr><tr><td>K</td><td>Equilibrium constant for the dissolution reaction</td><td>y<sub>i</sub></td><td>Measured experimental rate</td></tr><tr><td>n<sub>i</sub></td><td>Reaction order</td><td>σ</td><td>Temkin's average stoichiometric number</td></tr><tr><td>R</td><td>Gas constant (8.314 J K<sup>-1</sup> mol<sup>-1</sup>)</td><td></td><td></td></tr></table>

### 2.1 Fundamentals of mineral dissolution kinetics

This study focuses on quantifying the surface area normalized *steady-state* dissolution rates of minerals. Steady-state rates, rates that are proportional to the mineral surface area but do not vary with time, are thought to be most suitable for modeling natural processes. During the initial part of many mineral dissolution rate experiments, non-steady-state behaviors are observed, where the release rates of the elements vary significantly with time. Such behavior has been attributed to a number of processes including a preferential initial dissolution of fine particles adhering to larger grains in the
reactor (Holdren and Speyer, 1985; Talman and Nesbitt, 1988), the preferential removal of liable elements, such as alkali metals from feldspars (Chou and Wollast, 1985; Casey et al., 1993), and the rapid changes in reactive fluid composition including pH (Oelkers et al., 2001). Another factor that alters experimentally measured reactions rates over time are changes in mineral surface area. For example, Oxburgh et al. (1994) noted that the dissolution rates of plagioclase decreased continuously during their experiments. Such decreasing rates can potentially occur due to a decrease in the reactive surface area as the mineral dissolves (Köhler et al., 2005). Such factors make the definition of what is a steady-state rate in any experiment somewhat ambiguous. As it is not possible in most studies to determine a globally consistent definition of steady-state dissolution rates, the pragmatic approach adopted in this study is to accept the definition of steady-state as reported in each published study.

The steady-state surface area normalized dissolution rate of a mineral, r, can be considered to be the difference between the forward rate ($r_+$) and the reverse rate ($r_-$) such that

$$r = r_{+} - r_{-} = r_{+} \left(1 - \frac{r_{-}}{r_{+}}\right) \quad . \qquad (1)$$

Taking into account the law of detailed balancing, it can be shown that Eq. (1) is equivalent to

$$r = r_{+}(1 - \exp(-A/(\sigma RT))) \quad , \qquad (2)$$

where σ stands for Temkin's average stoichiometric number equal to the ratio of the rate of destruction of the activated or precursor complex relative to the overall dissolution rate, A denotes the chemical affinity or the Gibbs free energy of the dissolution reaction, T defines the absolute temperature, and R signifies the gas constant (Aagaard and Helgeson, 1977, 1982; Lasaga, 1981; Schott and Oelkers, 1995). The majority of mineral dissolution rates for the major silicate minerals reported in the literature have been performed at far-from-equilibrium conditions such that A >> σRT. At such conditions, $r_{-} \ll r_{+}$ and thus $r \approx r_{+}$. As a result, the parameter $r_{+}$ is often reported in the literature as the far-from-equilibrium dissolution rate.

As pointed out in Lichtner (2016), Temkin's average stoichiometric number (Temkin, 1963) is widely misunderstood by the geochemical community and has often been used as an empirical fit parameter. Rather than being empirical, this number normalizes the chemical formula used to represent a mineral to the rate-controlling process. For example, if the rate-controlling process of diopside dissolution is the release of a single silica tetrahedron from its mineral surface and the chemical formula used for diopside is Ca<sub>0.5</sub>Mg<sub>0.5</sub>SiO<sub>3</sub>, Temkin's number would be 1. If the chemical formula used for diopside is CaMgSi<sub>2</sub>O<sub>6</sub>, Temkin's number would be 2. Note that the chemical affinity for a mineral dissolution reaction scales to the mineral chemical formula such that the chemical affinity for the dissolution reaction of CaMgSi<sub>2</sub>O<sub>6</sub> is twice that of Ca<sub>0.5</sub>Mg<sub>0.5</sub>SiO<sub>3</sub>.
A number of studies have demonstrated the applicability of Eq. (2) to describe the dissolution rates as a function of chemical affinity (c.f., Schott et al., 2009). For example, Berger et al. (1994) showed that the constant temperature dissolution rates of quartz decreased systematically with decreasing chemical affinity in accord with Eq. (2) at 300 °C. Similarly, Pokrovsky and Schott (2004) showed the same trend for brucite at 25 °C, and Bénézeth et al. (2008) at constant pH for boehmite at 100 °C. In each case, Temkin's stoichiometric number was found to be one, consistent with the release of a single metal from the mineral structure being rate-limiting.

The forward, or far-from-equilibrium dissolution rate of a mineral ($r_+$) depends on its dissolution mechanism. Much of the early development of the field of mineral dissolution kinetics focused on the rates and dissolution mechanism of single oxide/hydroxide minerals, such as quartz and goethite. The dissolution mechanisms of these minerals require the breaking of a single type of metal-oxygen bond. Such bond breaking is promoted by the adsorption of either a proton, a hydroxide, or a water molecule onto the mineral surface (e.g., Pokrovsky et al., 2006). Several excellent examples of such behavior have been published, including the work of Furrer and Stumm (1986). They observed a close correlation between the dissolution rates of aluminum oxide and the degree of proton and/or hydroxide adsorption on the mineral surface. Other examples were presented or reviewed by Stumm et al. (1983), Wieland et al. (1988), and Stumm and Wieland (1990). Such observations lead to the conclusion that the dissolution of simple oxide/hydroxide minerals proceeds by a number of parallel mechanisms, each consisting of the adsorption of a proton, water, hydroxide, or ligand to the mineral surface. This surface species would then help destabilize the metal-oxygen bond at the surface leading to the dissolution of the mineral. Based on these mechanisms, the surface area normalized forward dissolution rates of single oxide/hydroxide minerals can be computed from

$$r_+ = \sum_i r_{+,i} \qquad (3)$$

where the $r_{+,i}$ refers to the forward dissolution rate of the ith parallel reaction. Each term in this rate equation is proportional to the concentration of the rate accelerating adsorbed species at the mineral surface. For example, in the simplest case, several parallel rates were assumed to be dependent on the adsorption of protons, or water and/or hydroxide on mineral surfaces and could be described using (e.g., Palandri and Kharaka, 2004; Marini, 2007; Grundwell, 2014)

$$r_{+,i} = k_i a_{H^+}^{n_i} \qquad (4)$$

where $k_i$ refers to the rate constant of the subscripted rate equation, $a_{H^+}$ designates the activity of aqueous $H^+$, and $n_i$ represents an empirical reaction order.

The early rationale for this approach stemmed from measurements of surface charge and the identification of the zero point of charge. The zero point of charge is the pH at which the net charge of the mineral surface is equal to zero. At lower pH, the surface tends to adsorb protons and
at high pH, the surface tends to desorb protons. For single oxide minerals, these can be related to the surface speciation of the mineral and related to its rate (c.f. Pokrovsky et al., 2006). What is reported in the literature as the zero point of charge for multi-oxide minerals, however, differs significantly from what is reported as the zero point of charge for the single oxide minerals. The measurement of zero point of charge commonly consists of measuring the net consumption of protons by the mineral surface as a function of pH. For the case of single oxide minerals, the consumption or liberation of protons is dominated by the adsorption or desorption of protons to the mineral surface. In contrast, in the case of multi-oxide minerals, the consumption or liberation of protons can be dominated by proton-exchange reactions with metals in the mineral structure (Oelkers et al., 2009). In such cases, proton-exchange reactions promote the dissolution of the minerals, affecting the reported zero points of charges for multi-oxide minerals (c.f., Oelkers et al., 1994; Schott et al., 2009).

Due to the potential for proton for metal exchange reactions, the dissolution mechanisms of multi-oxide minerals tend to be more complex due to the presence of more than one type of metal-oxygen bond. In multi-oxide minerals, each distinct metal-oxygen bond will break at vastly different rates. For example, Na-O bonds will break orders of magnitude faster than Si-O bonds via proton exchange reactions (Oelkers 2001a). Such reactions are similar to ion exchange reactions commonly observed in clay minerals and zeolites (summarized in, e.g., Sposito, 1981; Drummond et al., 1983; Townsend, 1991; Crooks et al., 1993; Colella, 1996; Whitworth, 1998; Coker and Rees, 2005; Dyer, 2007; Zaidi, 2012, and references therein). In these cases, rates are promoted by the removal of some of the metals from the mineral structure, distorting the adjacent slower breaking metal-oxygen bonds. This leads to forward dissolution rates that can depend on the concentration in aqueous solutions of those metals more readily removed from the mineral structure (Oelkers et al., 1994; Gautier et al., 1994; Oelkers 2001a).

Many experimental studies of mineral dissolution rates failed to measure and/or report the complete composition of the reactive aqueous fluids used in their multi-oxide mineral dissolution experiments. Instead, many reported just the dissolution rates based on Si release and the pH of the reactive aqueous fluid (e.g., Busenberg and Clemency, 1976; Rimstidt and Barnes, 1980; Velbel, 1985; Knauss and Wolery, 1986 and 1988; Holdren and Speyer, 1987; Mast and Drever, 1987; Brady and Walther, 1989; Casey et al., 1991; Wogelius and Walther, 1991; Knauss et al., 1993; Oxburgh et al., 1994; Knauss and Copenhaver, 1995; Kalinowski and Schweda, 1996; Carroll and Knauss, 2001; van Hees et al., 2002; Hodson, 2003; Balland et al., 2010). This greatly limits the ability to regress rate data consistently as a function of aqueous solution composition or to determine the chemical affinity of the reactive fluid. As a result, to generate a consistent database covering as extensively as possible all major rock-forming minerals, one is obliged to fit the existing rate data based on Si release to an
empirical function of pH. This approach is limited, as it does not allow explicit quantification of the effects of individual aqueous species, including dissolved CO₂ or organic ligands on rates.

Numerous efforts have been made in the literature to include one or more parallel reactions to describe the influence of other aqueous species such as organic ligands and/or CO₂ on mineral dissolution rates. Such additional terms were not considered in this work, as it might lead to inconsistencies among the rates of different minerals (e.g., calculation of a specific effect on rates of an aqueous organic ligand on some minerals for which data was available but not for others for which data may be unavailable). Many of the available data of mineral dissolution rates as a function of some of the organic and inorganic acids have been included in the Appendix. These might serve as a starting point for a comprehensive description of the effect of these added species on rates. A promising alternative approach in this regard, which has not been verified for many minerals, is that the effect on rates of many aqueous species may stem indirectly from their effect on fluid pH or on the aqueous activities of metals such as Al, that directly affect the dissolution rates (e.g., Oelkers and Schott, 1998; Golubev et al., 2005).

The variation of mineral dissolution rates as a function of temperature has been almost exclusively described using some form of an Arrhenius equation. The application of the Arrhenius equation has, nevertheless, led to some confusion when applied to mineral dissolution rates. The Arrhenius equation suggests that the logarithm of the rate constant, k, which relates the rate to the concentration of the rate-controlling activated complex, should be approximately a linear function of reciprocal temperature in accord with (cf. Schott et al., 2009)

$$k = A_0 e^{-E_a/(RT)} \qquad (5)$$

where A₀ refers to a temperature-independent pre-exponential factor, and Eₐ stands for the activation energy. Confusion arises as many have applied a form of the Arrhenius equation to describe the temperature dependence of reaction rates rather than rate constants, for example, using

$$r = A'_{0} e^{-E'_{a}/(RT)} \qquad (6)$$

where A'₀ refers to a temperature-independent pre-exponential factor, but E'ₐ stands for an apparent activation energy (see Casey and Sposito, 1992). The difference between Eₐ and E'ₐ, therefore, stems from the temperature variation of the concentration of the activated or precursor species, for example, the temperature dependence of the concentrations of the >Si₂O-H⁺ and/or the >MgOH₂⁺ surface species in the Pokrovsky and Schott (2000) model for forsterite dissolution. This subtle difference is responsible in part for the inconsistencies in activation energies for mineral reactions reported in the literature (cf., Oelkers and Schott, 1999). In cases where the concentrations of the activated or rate-controlling species decrease rapidly with increasing temperature, negative apparent activation energies
can be observed, for example, for the case of carbonate mineral dissolution rates at acidic conditions (Pokrovsky et al., 2009; Schott et al. 2009).

It is commonly assumed that the overall reactivity of a mineral in water is proportional to its surface area. There is, however, considerable discussion over exactly which surface area should be considered in this regard. The simplest surface area that has been used to characterize mineral reactivity is the geometric surface area, which is the surface of a smooth geometric shape, such as a sphere or a cube of equal size to the mineral grains. A popular alternative is using the surface area measured by inert gas adsorption techniques together with the Brunauer, Emmett, and Teller (BET) approach (Brunauer et al., 1938). The advantage of this gas adsorption approach is that the size of the adsorbing gas (e.g., Kr, Ar, or N₂) is similar to that of H₂O, so is thought to be a good proxy for characterizing the interaction of a mineral surface with water. The ratio of the BET surface area to the geometric surface area is termed roughness factor, which is thus a measure of how different the BET surface area is compared to that of a smooth geometric shape of the same size.

Combining Eqs. (2) to (6) leads to the following equation that can be used to describe existing surface area normalized mineral or glass dissolution rate data:

$$r = \sum_i \left( A_i a_{H^+}^{n_i} e^{\frac{E a_i}{RT}} \right) \cdot \left( 1 - \exp(-A/(\sigma RT)) \right). \quad (7)$$

where the subscript i stands for either acidic, neutral, or basic conditions. These three conditions are denoted by a, b, and c, respectively in Table 2. It should be emphasized that this equation is largely empirical and should not be considered to yield mechanistic information. Note that the use of Eq. (7) to describe the dissolution rates of silicate minerals as a function of chemical affinity requires a value of σ, Temkin's average stoichiometric number. Consistent with the studies of single oxide minerals detailed above and the assumption that the rate-limiting step for the dissolution of silicate minerals is the release of a silicon atom from the mineral structure, the value of σ adopted in the study is equal to the number of Si in the chemical formula chosen to represent the mineral. Another major caveat to using Eq. (7) to fit available rate data is that a large percentage of the published mineral dissolution rates 1) were generated rates at far-from-equilibrium conditions, where the final term in Eq. (7) is indistinguishable from 1, and/or 2) did not provide sufficient reactive fluid chemistry data to calculate the chemical affinity term. Consequently, only rates performed at 'far-from-equilibrium conditions' ($r_+$) are considered in this study, which includes the vast majority of the published rates. For the purposes of geochemical modeling, for example, using the PHREEQC computer code, the chemical affinity of the dissolution reaction can be calculated using the carbfix.dat thermodynamic database (Voigt et al., 2018).

The form of Eq. (7) suggests that once it is parameterized to describe the dissolution rates for any mineral, it could also provide estimates of the precipitation rates of this mineral by taking into
account the change in sign in the term for the chemical affinity in the equation. The final term in Eq. (7) is positive in undersaturated solutions. At equilibrium, this term is zero, and in supersaturated solutions, this term is negative. As a result, as one crosses equilibrium from undersaturation to supersaturation, rates calculated using Eq. (7) will change sign and yield what appear to be precipitation rates. Although precipitation rates calculated this way may be applicable to some minerals, such an approach gives clearly inconsistent results compared to natural and laboratory observations for many rock-forming minerals (Schott et al., 2009). This inconsistency likely stems from differences in the mechanism of dissolution compared to that of precipitation. The dissolution of a mineral continuously creates new active sites on the mineral surface, which further removes material from these sites. Precipitation, however, in many cases destroys these active sites. In such cases, for precipitation to proceed, new active sites must be nucleated on the mineral surface (e.g., De Yoreo and Vekilov, 2003). As nucleation is a distinct process from the removal or attachment of material at an existing site, Eq. (7) is likely insufficient to describe the precipitation rates of many rock-forming minerals.

In contrast to the fitting of the dissolution rates of other solids in this study, sufficient data is available to account directly for the effect of aqueous Al basaltic glass dissolution rates. As such, the dissolution rates of basaltic glass, based on Si release can be quantified using (Oelkers and Gislason, 2001)

$$r_+ = \left( A * \exp\left(\frac{E_a}{RT}\right) \left(\frac{(a_{H^+})^3}{(a_{Al^{3+}})}\right)^{\frac{1}{n}} \right) \quad (8)$$

where $a_{Al^{3+}}$ is the activity of aqueous Al$^{3+}$. Aqueous aluminum activities considered in this study considered the formation of the AlOH$^{2+}$, Al(OH)$^{+2}$, Al(OH)$^{3-}$, and Al(OH)$^{-4}$ species.

## 2.2 Data selection

Experimental data were regressed using Eq. (7) or (8). The parameters A, $E_a$, and n in these equations were obtained via a two-step process, and the final chemical affinity term in Eq.(7) was set to 1 consistent with the far-from-equilibrium conditions considered in most published dissolution rate studies. To generate rate parameters, first, experimental datasets containing rates determined at far-from-equilibrium conditions were tabulated as a function of temperature and pH. All collected experimental datasets for each mineral group discussed here are listed in Table S1 in Appendix A. These experimental data were evaluated critically to assess the quality of the starting materials, their compositions, and their experimental conditions. Only rates obtained at a steady-state, performed at far-from-equilibrium conditions, and normalized to the initial surface area measured by the BET technique were retained for regression. This latter choice was pragmatic as relatively few studies reported BET surface areas after the completion of their experiments. For example, Gautier et al.
(2001) reported that the BET surface areas of quartz increased by a factor of 5.6 during its dissolution at a temperature of 200 and 250 °C over the course of 95 days. To ensure consistency, all rates used for the regression are based on silicon release rates unless stated otherwise. This too is a pragmatic choice as many studies failed to measure or report rates based on the release of other elements from the dissolving minerals. It should be noted, however, that in some cases, certain elements may be preferentially retained or released either initially or during the complete dissolution of the mineral. For example, Schott et al. (2012) observed the complete preferential removal of Ca from wollastonite at ambient temperatures and pH<2.2 during experiments lasting 3000 hours. Experimental data that were accelerated or slowed due to the presence of organic ligands, those where rates were affected by the formation of secondary minerals, or experimental data obtained from minerals containing major impurities, were not included in the regression calculations unless otherwise noted in the text below. Similar to Rimstidt et al. (2012), for some minerals, two parallel rate mechanisms were used to fit rate data as a function of pH and temperature; rates were fit by separating the experimental data into two groups divided by their point of zero charge. This choice is somewhat arbitrary but adequately works for some of the minerals. For other minerals, e.g., the feldspars or micas, three parallel rate mechanisms were considered, where the published rates were divided into three sets according to pH. For each subset, the activation energies, pre-exponential factors, and reaction orders were fit from selected dataset using Eqs. (7) and (8) and method of the least-squares minimization. These parameters are listed in Table 2. In cases where insufficient experimental data are available to regress these parameters for a given mineral, regression parameters are estimated based on the results of regression fits of similarly structured and composited minerals. When such an approach is used, it is noted explicitly below when describing the regression of a given dataset.

The quality of regression fits is evaluated in the present study by the differences between measured rates and those calculated from the regression equations. The difference between measured and calculated rates is referred to as residuals. The coefficient of determination ($R^2$) for each fit is calculated as

$$R^2 = 1 - \frac{\sum \text{residuals}^2}{\sum (y_i - \bar{y})^2} \qquad (9)$$

where $\bar{y}$ is the value obtained from the regression equation, and $y_i$ is its corresponding measured experimental value. $R^2$ values for each fit are reported in Table 2, along with the regressed rate constants.

To further characterize the quality of the regression fits, 95% confidence level bands ($y_{95}$) of regressed rates were determined using:
$$319 \quad y_{95} = \bar{y} \pm 1.96 \frac{SD}{\sqrt{N}} \qquad (10)$$

where *SD* symbolizes the standard deviation of the regression fit and *N* refers to the number of data points considered in the regression.

## 3. Regression of the experimental dissolution rate equations for primary silicate minerals

### 3.1 Amphiboles

Experimentally measured amphibole dissolution rates have been reviewed and summarized by Brantley and Chen (1995), Marini (2007), and Brantley et al. (2008). It is reasonable to assume similar dissolution mechanisms for all the minerals in the amphibole group. However, measured amphibole dissolution rates vary significantly due to Al content in the mineral structure. To account for the effect of Al in the mineral structure, we summarize amphibole dissolution in two subsections, one focused on Al-free amphiboles and the other on Al-bearing amphiboles. The former group was regressed assuming two parallel mechanisms (pH-dependent and pH-independent trends at acidic and basic conditions, respectively), while the latter three independent parallel mechanisms as a function of pH were considered.

#### 3.1.1. Al-free amphiboles

Sources of experimentally measured dissolution rates of Al-free amphiboles (e.g., tremolite, anthophyllite) are summarized in **Table 1**. To date, there have been relatively few studies of the dissolution rates of the amphiboles compared to many of the other major rock-forming minerals. Most available studies reported rates at 25 °C and pH from 1 to 9. At elevated temperatures, Diedrich et al. (2014) reported tremolite dissolution rates at temperatures from 25 °C to 150 °C, and Chen and Brantley (1998) reported anthophyllite dissolution rates from 25 °C to 90 °C. **Figure 1 A-D** shows experimentally measured Al-free amphibole dissolution rates as a function of pH and temperature. Substantial scatter is evident. For example, anthophyllite dissolution rates at pH 3 at 25 °C range over two orders of magnitude from $10^{-13.5}$ to $10^{-11.6}$ mol m$^{-2}$ s$^{-1}$. As is the case for most mineral-forming minerals, constant temperature dissolution rates decrease with increasing pH to at least neutral conditions. Tremolite dissolution rates decrease continuously with increasing pH from $10^{-11.4}$ mol m$^{-2}$ s$^{-1}$ at pH 1 to $10^{-12.4}$ mol m$^{-2}$ s$^{-1}$ at pH 9. Experimental data from Mast and Drever (1987) and Schott et al. (1981) were not included in the regression calculations as the solids used in these studies likely included impurities, and the experiments exhibited non-stoichiometric dissolution. Data from these two studies are indicated in **Figure 1** by circles and arrows.
<table><caption>**Table 1:** Sources of experimentally measured Al-free amphibole dissolution rates considered in this study</caption><thead><tr><th></th><th>T<br>°C</th><th>pH</th><th>Mineral<br>Composition</th></tr></thead><tbody><tr><td><strong>Anthophyllite</strong></td><td></td><td></td><td></td></tr><tr><td>Brantley and Chen (1995)</td><td>25</td><td>1.1-3.6</td><td>Mg<sub>5.7</sub>Fe<sub>1.0</sub>Al<sub>0.1</sub>Si<sub>7.8</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Chen and Brantley (1998)</td><td>25-90</td><td>1.2-3.4</td><td>Mg<sub>5.7</sub>Fe<sub>1.0</sub>Al<sub>0.1</sub>Si<sub>7.8</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Mast and Drever (1987)</td><td>25</td><td>2.0-9.2</td><td>Mg<sub>1.88</sub>Ca<sub>0.08</sub>Na<sub>0.04</sub>(Mg<sub>4.51</sub>Mn<sub>0.42</sub>Fe<sub>0.02</sub>Al<sub>0.02</sub>)Si<sub>8</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td><strong>Ferroactinolite</strong></td><td></td><td></td><td>no reported data</td></tr><tr><td><strong>Riebeckite</strong></td><td></td><td></td><td>no reported data</td></tr><tr><td><strong>Tremolite</strong></td><td></td><td></td><td></td></tr><tr><td>Diedrich et al. (2014)</td><td>25-150</td><td>1.9-7.5</td><td>Ca<sub>2.10</sub>Mg<sub>4.97</sub>Fe<sub>0.07</sub>Si<sub>8</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Mast and Drever (1987)</td><td>22</td><td>2.0-9.0</td><td>Ca<sub>0.07</sub>Mg<sub>6.4</sub>Si<sub>8</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Schott et al. (1981)</td><td>22</td><td>1.0-6.0</td><td>Ca<sub>1.91</sub>Mg<sub>5.09</sub>Fe<sub>0.03</sub>Si<sub>8</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr></tbody></table>

The rate parameters for anthophyllite were generated from regression of the experimental results of Chen and Brantley (1998) with an activation energy based on the variation of rates over the 25 to 90 °C temperature range. The rate parameters for tremolite were derived from a regression of the experimental rates reported by Diedrich et al. (2014) over the 37 to 90 °C temperature range. The activation energy at neutral and higher pH was set equal to that of anthophyllite due to a lack of relevant experimental data.

The resulting kinetic parameters are listed in **Table 2**, and rates calculated using these parameters can be compared with corresponding experimental rates in **Figures 1 and 2**. The rates displayed in this figure span the 25 °C to 150 °C temperature range and pH. The average difference between the measured and calculated far-from-equilibrium dissolution rates for anthophyllite is 0.14 log units, and 50% of the rates are within 0.09 log units of their corresponding calculated values. The average difference between the measured and calculated far-from-equilibrium dissolution rates of tremolite regression equation is 0.35 log units, and 50% of the rates are within 0.28 log units of their corresponding calculated values.

No experimentally measured dissolution rates have been reported for the minerals riebeckite and ferroactinolite. Owing to a lack of experimental data, we recommend adopting a first approximation of the rates of tremolite dissolution to estimate the dissolution rates for ferroactinolite and riebeckite due to their similar structures and compositions until such rates might become available.
<figure><img src="image_2.png" /><figcaption>**Figure 1:** Far-from-equilibrium dissolution rates of the amphiboles. Experimental data shown as symbols can be compared with computed rates shown as curves as a function of pH in the left plots. Plots in the right column directly compare calculated versus measured rates. The symbol shape indicates the source of the data, whereas the shading of the symbol indicates the experimental temperature, where black symbols indicate 25 °C. The shaded regions in the left plots illustrate the 95% confidence limits of the regression fits performed at 25 °C.</figcaption></figure>
<table><caption>**Table 2:** Summary of parameters describing the far-from-equilibrium dissolution rates with Eq (7).</caption><thead><tr><th rowspan="2"></th><th colspan="4">Acid mechanism</th><th colspan="3">Neutral mechanism</th><th colspan="4">Basic mechanism</th><th rowspan="2">R<sup>2</sup></th></tr><tr><th>logk<sub>25</sub><br>mol m<sup>-2</sup> s<sup>-1</sup></th><th>A<sub>a</sub><br>mol m<sup>-2</sup> s<sup>-1</sup></th><th>E<sub>a<sub>a</sub></sub><br>kJ mol<sup>-1</sup></th><th>n<sub>a</sub></th><th>logk<sub>25</sub><br>mol m<sup>-2</sup> s<sup>-1</sup></th><th>A<sub>b</sub><br>mol m<sup>-2</sup> s<sup>-1</sup></th><th>E<sub>a<sub>b</sub></sub><br>kJ mol<sup>-1</sup></th><th>logk<sub>25</sub><br>mol m<sup>-2</sup> s<sup>-1</sup></th><th>A<sub>c</sub><br>mol m<sup>-2</sup> s<sup>-1</sup></th><th>E<sub>a<sub>c</sub></sub><br>kJ mol<sup>-1</sup></th><th>n<sub>c</sub></th></tr></thead><tbody><tr><td><strong>Amphiboles</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Anthophyllite</td><td>-12.4</td><td>5.7x10<sup>-4</sup></td><td>52.0</td><td>0.4</td><td>-13.7</td><td>5.0x10<sup>-6</sup></td><td>48.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.94</td></tr><tr><td>Ferroactinolite</td><td>-11.3</td><td>3.0x10<sup>-3</sup></td><td>50.0</td><td>0.2</td><td>-13.1</td><td>2.0x10<sup>-5</sup></td><td>48.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Riebeckite</td><td>-11.3</td><td>3.0x10<sup>-3</sup></td><td>50.0</td><td>0.2</td><td>-13.1</td><td>2.0x10<sup>-5</sup></td><td>48.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>-</td></tr><tr><td>Tremolite</td><td>-11.3</td><td>3.0x10<sup>-3</sup></td><td>50.0</td><td>0.2</td><td>-13.1</td><td>2.0x10<sup>-5</sup></td><td>48.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.77</td></tr><tr><td>Glaucophane</td><td>-6.10</td><td>2.2x10<sup>2</sup></td><td>50.0</td><td>0.7</td><td>-</td><td>-</td><td>-</td><td>-12.8</td><td>1.0x10<sup>-4</sup></td><td>48.0</td><td>-0.1</td><td>0.99</td></tr><tr><td>Hornblende</td><td>-10.7</td><td>5.0x10<sup>-3</sup></td><td>50.0</td><td>0.2</td><td>-</td><td>-</td><td>-</td><td>-13.4</td><td>2.1x10<sup>-5</sup></td><td>48.0</td><td>-0.1</td><td>0.16</td></tr><tr><td><strong>Feldspars</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Albite</td><td>-10.3</td><td>0.70</td><td>58.0</td><td>0.3</td><td>-11.19</td><td>0.21</td><td>60.0</td><td>-13.6</td><td>1.5x10<sup>-5</sup></td><td>50.0</td><td>-0.3</td><td>0.83</td></tr><tr><td>Andesine</td><td>-7.99</td><td>147</td><td>58.0</td><td>0.7</td><td>-11.23</td><td>0.19</td><td>60.0</td><td>-13.6</td><td>1.5x10<sup>-5</sup></td><td>50.0</td><td>-0.3</td><td>-</td></tr><tr><td>Anorthite</td><td>-5.17</td><td>9.8x10<sup>4</sup></td><td>58.0</td><td>1.2</td><td>-11.34</td><td>0.15</td><td>60.0</td><td>-13.6</td><td>1.5x10<sup>-5</sup></td><td>50.0</td><td>-0.3</td><td>0.81</td></tr><tr><td>Bytownite</td><td>-5.88</td><td>1.9x10<sup>4</sup></td><td>58.0</td><td>1.1</td><td>-11.28</td><td>0.17</td><td>60.0</td><td>-13.6</td><td>1.5x10<sup>-5</sup></td><td>50.0</td><td>-0.3</td><td>-</td></tr><tr><td>K-feldspar</td><td>-10.4</td><td>5.0x10<sup>-2</sup></td><td>51.7</td><td>0.5</td><td>-12.48</td><td>1.1x10<sup>-2</sup></td><td>60.0</td><td>-20.8</td><td>1.2x10<sup>-10</sup></td><td>62.0</td><td>-0.8</td><td>0.23</td></tr><tr><td>Microcline</td><td>-10.4</td><td>5.0x10<sup>-2</sup></td><td>51.7</td><td>0.5</td><td>-12.48</td><td>1.1x10<sup>-2</sup></td><td>60.0</td><td>-20.8</td><td>1.2x10<sup>-10</sup></td><td>62.0</td><td>-0.8</td><td>-</td></tr><tr><td>Labradorite</td><td>-6.39</td><td>5.9x10<sup>3</sup></td><td>58.0</td><td>1.0</td><td>-11.28</td><td>0.17</td><td>60.0</td><td>-13.6</td><td>1.5x10<sup>-5</sup></td><td>50.0</td><td>-0.3</td><td>-</td></tr><tr><td>Oligoclase</td><td>-9.33</td><td>6.8</td><td>58.0</td><td>0.4</td><td>-11.21</td><td>0.20</td><td>60.0</td><td>-13.6</td><td>1.5x10<sup>-5</sup></td><td>50.0</td><td>-0.3</td><td>-</td></tr><tr><td><strong>Glass</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Basalt</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Rhyolite</td><td>-9.10</td><td>1.6x10<sup>-3</sup></td><td>36.0</td><td>0.5</td><td>-</td><td>-</td><td>-</td><td>-16.3</td><td>7.0x10<sup>-8</sup></td><td>52.0</td><td>-0.6</td><td></td></tr><tr><td><strong>Mica</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Annite</td><td>-9.42</td><td>5.9x10<sup>-7</sup></td><td>18.2</td><td>0.5</td><td>-12.2</td><td>5.00x10<sup>-9</sup></td><td>22.0</td><td>-13.9</td><td>4.00x10<sup>-10</sup></td><td>25.5</td><td>-0.2</td><td></td></tr><tr><td>Biotite*</td><td>-9.42</td><td>5.9x10<sup>-7</sup></td><td>18.2</td><td>0.5</td><td>-12.2</td><td>5.00x10<sup>-9</sup></td><td>22.0</td><td>-13.9</td><td>4.00x10<sup>-10</sup></td><td>25.5</td><td>-0.2</td><td>0.38</td></tr><tr><td>Phlogopite</td><td>-9.42</td><td>5.9x10<sup>-7</sup></td><td>18.2</td><td>0.5</td><td>-12.2</td><td>5.00x10<sup>-9</sup></td><td>22.0</td><td>-13.9</td><td>4.00x10<sup>-10</sup></td><td>25.5</td><td>-0.2</td><td></td></tr><tr><td>Muscovite</td><td>-11.1</td><td>1.3x10<sup>-4</sup></td><td>41.3</td><td>0.4</td><td>-12.1</td><td>6.31x10<sup>-6</sup></td><td>39.0</td><td>-14.5</td><td>3.16x10<sup>-5</sup></td><td>57.0</td><td>-0.2</td><td>0.67</td></tr><tr><td><strong>Olivines</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Fayalite</td><td>-6.26</td><td>1.20x10<sup>6</sup></td><td>70.4</td><td>0.4</td><td>-</td><td>-</td><td>-</td><td>-7.39</td><td>1.91x10<sup>3</sup></td><td>60.9</td><td>0.2</td><td>0.29</td></tr><tr><td>Forsterite</td><td>-7.16</td><td>1.48x10<sup>5</sup></td><td>70.4</td><td>0.4</td><td>-</td><td>-</td><td>-</td><td>-8.33</td><td>2.20x10<sup>2</sup></td><td>60.9</td><td>0.2</td><td>0.92</td></tr><tr><td>Larnite</td><td>-3.61</td><td>5.25x10<sup>8</sup></td><td>70.4</td><td>0.4</td><td>-</td><td>-</td><td>-</td><td>-4.75</td><td>8.25x10<sup>5</sup></td><td>60.9</td><td>0.2</td><td>0.43</td></tr><tr><td><strong>Pyroxenes</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Augite</td><td>-8.20</td><td>1.52x10<sup>6</sup></td><td>81.8</td><td>0.7</td><td>-12.8</td><td>350</td><td>83.0</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.32</td></tr><tr><td>Bronzite</td><td>-9.80</td><td>9.5x10<sup>-4</sup></td><td>38.5</td><td>0.6</td><td>-11.7</td><td>7.6x10<sup>-1</sup></td><td>66.1</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.63</td></tr><tr><td>Diopside</td><td>-9.80</td><td>8.55x10<sup>-5</sup></td><td>32.7</td><td>0.3</td><td>-11.0</td><td>4.3x10<sup>-4</sup></td><td>43.9</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.75</td></tr><tr><td>Enstatite</td><td>-8.30</td><td>0.574</td><td>46.1</td><td>0.5</td><td>-11.9</td><td>6.3x10<sup>3</sup></td><td>89.5</td><td>-</td><td>-</td><td>-</td><td>-</td><td>0.84</td></tr><tr><td><strong>SiO<sub>2</sub> polymorphs</strong></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Cristobalite-alpha</td><td>-11.4</td><td>4.03x10<sup>-4</sup></td><td>45.6</td><td>0.3</td><td>-</td><td>-</td><td>-</td><td>-15.0</td><td>0.105</td><td>80.0</td><td>-0.4</td><td>0.89</td></tr><tr><td>Cristobalite-beta</td><td>-11.4</td><td>4.03x10<sup>-4</sup></td><td>45.6</td><td>0.3</td><td>-</td><td>-</td><td>-</td><td>-15.0</td><td>0.105</td><td>80.0</td><td>-0.4</td><td>0.89</td></tr><tr><td>Quartz</td><td>-11.4</td><td>4.03x10<sup>-4</sup></td><td>45.6</td><td>0.3</td><td>-</td><td>-</td><td>-</td><td>-15.0</td><td>0.105</td><td>80.0</td><td>-0.4</td><td>0.89</td></tr><tr><td>Amorphous SiO<sub>2</sub></td><td>-10.6</td><td>4.56x10<sup>-4</sup></td><td>41.6</td><td>0.3</td><td>-</td><td>-</td><td>-</td><td>-14.2</td><td>3.53x10<sup>-2</sup></td><td>73.0</td><td>-0.4</td><td>0.95</td></tr></tbody><tfoot><tr><td colspan="12">*Biotite here corresponds to generic mica (KFe<sub>1.5</sub>Mg<sub>1.5</sub>AlSi<sub>3</sub>O<sub>10</sub>(OH)<sub>2</sub>)</td></tr></tfoot></table>
### 3.1.2 Al-bearing amphiboles

Available experimentally measured dissolution rates of Al-bearing amphiboles (glaucophane and hornblende) are summarized in **Table 3**. Nickel (1973), Golubev et al. (2005), and Critelli et al. (2014) reported hornblende dissolution rates at pH up to 12 and up to 1 atm CO₂. The variation of constant temperature far-from-equilibrium dissolution rates of the Al-bearing amphiboles exhibits minimum values near pH ~6. Such behavior may be attributed to the rates being controlled by a precursor complex created by a proton for Al exchange reactions (Oelkers, 2001a). Hornblende dissolution rates vary from 10⁻⁸.⁴ at pH 1.6 to 10⁻¹².³ mol m⁻² s⁻¹ at pH 7.0. The glaucophane dissolution rates are similar to those of hornblende, decreasing from 10⁻⁸.⁶ to 10⁻¹¹.² mol m⁻² s⁻¹ with increasing pH from 3.23 to 6.83 (Sverdrup, 1990). Swoboda-Colberg and Drever (1993) compared glaucophane dissolution rates at laboratory and field conditions at pH 4.0 to 4.5. However, these data were not included in the regression calculations as they were normalized to geometric surface area. The effect of mineral chemical composition, the presence of organic ligands, and/or the presence of aqueous CO₂ on Al-amphibole dissolution rates have not yet been reported in the literature.

<table><caption>**Table 3:** Sources of experimentally measured Al-amphibole dissolution rates considered in this study</caption><thead><tr><th></th><th>T<br>°C</th><th>pH</th><th>Mineral<br>Composition</th></tr></thead><tbody><tr><td><strong>Glaucophane</strong></td><td></td><td></td><td></td></tr><tr><td>Sverdrup (1990)</td><td>25</td><td>3.1-6.8</td><td>Na<sub>0.14</sub>K<sub>0.09</sub>Ca<sub>2</sub>Fe<sub>1.78</sub>Mg<sub>2</sub>Al<sub>2</sub>Si<sub>7</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Swoboda-Colberg and Drever (1993)</td><td>25</td><td>4.0-4.5</td><td>Na<sub>0.14</sub>K<sub>0.09</sub>Ca<sub>2</sub>Fe<sub>1.78</sub>Mg<sub>2</sub>Al<sub>2</sub>Si<sub>7</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td><strong>Hornblende</strong></td><td></td><td></td><td></td></tr><tr><td>Critelli et al. (2014)</td><td>25</td><td>2.0-12.3</td><td>Na<sub>0.4</sub>Mg<sub>3.1</sub>Ca<sub>2.7</sub>Fe<sub>1.0</sub>Al<sub>0.9</sub>Si<sub>7.4</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Golubev et al. (2005)</td><td>25</td><td>2.1-11.1</td><td>-</td></tr><tr><td>Nickel (1973)</td><td>25</td><td>3.6-10.6</td><td>Na<sub>0.8</sub>Ca<sub>1.8</sub>Mg<sub>3.7</sub>Fe<sub>0.9</sub>Al<sub>0.1</sub>Si<sub>7.1</sub>Al<sub>0.9</sub>O<sub>22</sub>(OH)<sub>2</sub></td></tr><tr><td>Zhang et al. (1990)</td><td>25</td><td>3.6-4.0</td><td>K<sub>0.11</sub>Na<sub>0.66</sub>Ca<sub>1.66</sub>Mg<sub>3.11</sub>Fe<sub>1.34</sub>Al<sub>0.79</sub>Si<sub>6.36</sub>Al<sub>1.64</sub>O<sub>22</sub>(OH, F)<sub>2</sub></td></tr></tbody></table>

Regression of these data yielded the kinetic parameters listed in **Table 2**. Rates generated using the regression parameters produced in this study are compared with experimentally measured rates in **Figure 1**. The dissolution rate equation for glaucophane describes the experimentally measured rate data with an average difference of 0.07 log units. The mineral hornblende was regressed assuming its chemical formula is (Ca₂Mg₄Al₀.₇₅Fe₀.₂₅(Si₇AlO₂₂)(OH)₂). The average difference between measured and calculated dissolution rates of hornblende is 0.183 log unit, and 50% of the calculated rates are within 0.13 log unit of their corresponding measured rates.
<figure><img src="image_3.png" /><figcaption>**Figure 2:** Summary of the calculated far-from-equilibrium dissolution rates of amphiboles as a function of pH. Illustrated rates were calculated using Eq (7) and parameters listed in Tables 2 at (A) 25 °C, and (B) 150 °C.</figcaption></figure>

The quantification of amphibole dissolution rates is challenging due to the lack of experimental data, particularly at neutral to basic conditions and at temperatures above 25 °C. Although there is a general agreement among amphibole dissolution rates generated using the various regression equations available in the literature at acidic conditions and near to ambient temperature, these equations differ significantly at neutral to basic conditions suggesting either continuously decreasing rates as a function of pH (Brantley and Chen, 1995; Brantley et al., 2008; Diedrich et al., 2014) or pH-independent rates at neutral to basic conditions (Palandri and Kharaka, 2004). Such interpretative differences are largely due to the limited datasets available at these conditions and inconsistencies among these data. Moreover, suggested activation energies span the range of 18.9 up to 94.4 kJ mol⁻¹ (Brantley and Chen, 1995; Chen and Brantley, 1998; Palandri and Kharaka, 2004; Brantley et al., 2008; Diedrich et al., 2014). As a result, the various rate equations available in the literature generate rates for pH greater than pH 6 and elevated temperature that can differ by up to two orders of magnitude from one another. To address this issue, we recommend adopting the activation energies of tremolite dissolution to approximate the dissolution rates for glaucophane and hornblende to higher temperature due to their similar structures and compositions. A comparison of calculated dissolution rates generated in this study for both Al-free and Al-amphiboles for 25 and 150 °C can be seen in **Figure 2**. Due to the presence of Al in the framework, dissolution rates of Al-amphiboles appear to minimize as a function of pH at near to neutral pH, whereas this minimum is not evident in the Al-free amphiboles.

## 3.2 Feldspars

Experimentally measured feldspar dissolution rates have been reviewed and summarized by Blum and Stillings (1995), Marini (2007), Brantley et al. (2008), and Gudbrandsson et al. (2014). A list of the sources of experimentally measured feldspar dissolution rates is provided in **Table 4**. Due to the presence of Al in the feldspar structure, their rates minimize as a function of pH at near to neutral
426
427

conditions. To address this variation, feldspars dissolution rates were regressed assuming three parallel dissolution mechanisms dominating at acidic (pH<5), neutral (5<pH<7), and basic (pH >7) conditions.

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**3.2.1 Plagioclases**

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Experimentally measured albite dissolution rates have been reported for temperatures from 5 to 300 °C, and pH from 1.0 to 12.5. **Figures 3A** and **3B** illustrate far-from-equilibrium albite dissolution rates over a temperature range from 25 to 300 °C. Measured rates at 25 °C vary from as low as 10<sup>-11.8</sup> mol m<sup>-2</sup> s<sup>-1</sup> at pH 5.6 to as high as 10<sup>-9.40</sup> mol m<sup>-2</sup> s<sup>-1</sup> at pH 11.3. Constant pH rates increase by approximately two orders of magnitude as the temperature increases from 25 to 100 °C. Albite dissolution rates obtained by Gudbrandsson et al. (2014) are up to an order of magnitude faster than corresponding rates reported by Chou and Wollast (1985) and up to two orders of magnitude faster than dissolution rates reported by Knauss and Wolery (1986). As noted by Gudbrandsson et al. (2014), such a scatter can stem from several factors, including differences in experiment duration as dissolution rates tend to decrease with time in many experiments (Oxburgh et al. 1994), variability in mineral composition (0-12 An%), formation of non-stoichiometric layers on the surfaces of the dissolving feldspars (Chou and Wollast, 1985), a decrease in the reactive surface area as the mineral dissolves (Köhler et al., 2005), or a large range of grain size of the initial material used in the experiments (2µm up to 3 mm). See **Table 4 and Appendix** for further details on each experimental study.

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Experimentally measured dissolution rates of the intermediate plagioclases, including oligoclase, andesine, bytownite, and labradorite, are listed in **Table 4** and displayed in **Figure 3**. Most of these rates were obtained at 22-25 °C. Corresponding rates scatter significantly. Some of this scatter may be due to the presence of exsolution textures in the solids considered in the experiments (e.g., Gudbrandsson et al., 2014 and references therein). It appears that the measured dissolution rates may be independent of plagioclase composition at basic pH. The rates, however, increase with increasing anorthite content at acidic conditions. For example, bytownite dissolution rates were found to be more than an order of magnitude faster than those of oligoclase at pH 2. Similar to albite, experimental rates for the intermediate plagioclases from Oxburgh et al. (1994) are up to one order of magnitude slower than those presented in Gudbrandsson et al. (2014).

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Additionally, Busenberg and Clemency (1976), Welch and Ullman (1993), Stillings and Brantley (1995), Stillings et al. (1996), and Blake and Walther (1999) reported plagioclase dissolution rates in the presence of organic acids and CO<sub>2</sub>. The addition of CO<sub>2</sub> into the aqueous solution increased labradorite dissolution rates by approximately two orders of magnitude. The presence of organic acids both increased and decreased plagioclase dissolution rates, depending on acid composition and concentration as well as solution pH and mineral composition (see **Figure 3**). Oelkers and Schott
(1998) attributed the effects of aqueous organic ligands on rates to the formation of complexes with aqueous Al.

Experimentally measured anorthite dissolution rates are summarized in **Table 4** and **Figure 3**. This dataset consists of 11 studies with 149 reported rates of plagioclases having an anorthite component greater than 89 mol%. The majority of such studies were performed at ambient temperature conditions and at pH ranging up to 11.3 (Bailey, 1974; Fleer, 1982; Holdren and Speyer, 1987; Brady and Walther, 1989; Casey et al., 1991; Amrhein and Suarez, 1988, 1992; Oelkers and Schott, 1995; Hodson, 2003; Gudbrandsson et al., 2014). Berg and Banwart (2000) reported anorthite dissolution rates as a function of CO₂ concentration from 0.01 to 0.1 atm, and Oelkers and Schott (1995) reported rates at pH below 4 and temperatures ranging from 45 to 95 °C. Rates reported by Amrhein and Suarez (1992) and those from Gudbrandsson et al. (2014) scatter over two orders of magnitude at near to neutral pH conditions. This scatter may be the result of different experiment duration, the presence of aqueous CO₂, and secondary mineral precipitation. The anorthite dissolution rates reported by Hodson (2003) are likely slowed due to the presence of a Fe-rich coating, resulting in rates that are 3 log units lower than most of the other corresponding rates. At the same time, the rates obtained from Berg and Banwart (2000) are 3 log units higher on average than corresponding anorthite dissolution rates, potentially due to the presence of aqueous CO₂.

Plagioclase dissolution rates affected by CO₂ and organic acids in the aqueous solutions, secondary precipitation, mineral coating, and data influenced by the approach to chemical equilibrium are not considered in the regression calculations. These datasets are indicated in **Figure 3**.

<table><caption>**Table 4:** Sources of experimentally measured plagioclase dissolution rates considered in this study.</caption><thead><tr><th>References</th><th>T<br>°C</th><th>pH</th><th>Anorthite<br>content<br>(in mol%)</th><th>Comments</th></tr></thead><tbody><tr><td><strong>Albite</strong></td><td></td><td></td><td></td><td></td></tr><tr><td>Burch et al. (1993)</td><td>80</td><td>8.7-8.9</td><td>5</td><td>Function of Gibbs free energy of dissolution, experimental duration 1200 h, grain size 2-20µm</td></tr><tr><td>Busenberg and Clemency (1976)</td><td>25</td><td>5.0</td><td>1.1</td><td>+ 1atm CO₂, experimental duration 1160 hours, grain size &lt;37 µm</td></tr><tr><td>Casey et al. (1991)</td><td>25</td><td>2.0</td><td>2</td><td>Grain size 25-75 µm, experimental duration 556 hours</td></tr><tr><td>Chen and Brantley (1997)</td><td>5-90</td><td>1-4.5</td><td>3</td><td>Grain size 75-150 µm, experimental duration 4000-6000 hours</td></tr><tr><td>Chou and Wollast (1984)</td><td>25</td><td>2.5-3.5</td><td>3</td><td>Grain size 50-200 µm, experimental duration 280 hours on average</td></tr><tr><td>Chou and Wollast (1985)</td><td>25</td><td>1.0-12.5</td><td>3</td><td>Grain size 50-100 µm, experimental duration 280 hours on average</td></tr><tr><td>Gudbrandsson et al. (2014)</td><td>22</td><td>1.8-11.3</td><td>2</td><td>Grain size 45-125 µm, experimental duration 75-600 hours</td></tr><tr><td>Hellmann (1994)</td><td>100-300</td><td>1.3-10.0</td><td>1</td><td>Grain size &lt;1 mm, experimental duration 24-248 hours</td></tr><tr><td>Hellmann et al. (1989)</td><td>225</td><td>0.9-8.1</td><td>1</td><td>Grain size 150-180 µm, experimental duration 500-600 hours</td></tr><tr><td>Hellmann and Tisserand (2006)</td><td>150</td><td>9.2</td><td>1</td><td>Function of Gibbs free energy of dissolution; grain size 1-3 mm, experimental duration 2400 hours</td></tr></tbody></table>
<table><tbody><tr><td>Holdren and Speyer (1987)</td><td>25</td><td>3.0</td><td>N/R</td><td>Function of grain size (&lt;37 to &gt;600 µm), experimental duration 72 hours</td></tr><tr><td>Knauss and Copenhaver (1995)</td><td>70</td><td>4.0-9.5</td><td>1</td><td>Grain size 75-125 µm, experimental duration 1385 hours</td></tr><tr><td>Knauss and Wolery (1986)</td><td>25-70</td><td>1.4-11.8</td><td>1</td><td>Grain size 75-125 µm, experimental duration over 1200 hours</td></tr><tr><td>Lagache (1965)</td><td>200</td><td>7.3</td><td>N/R</td><td>Grain size 10-55 µm, experimental duration over 290 hours</td></tr><tr><td>Oelkers et al. (1994)</td><td>150</td><td>9.2</td><td>N/R</td><td>Effect of Al and chemical affinity</td></tr><tr><td>Rose (1991)</td><td>25</td><td>1.4</td><td>0.5</td><td>Grain size 50-100 µm, experimental duration 8-500 hours</td></tr><tr><td>Stillings and Brantley (1995)</td><td>25</td><td>3.0-3.6</td><td>2</td><td>Grain size 75-100 µm, experimental duration 3000 hours, added NaCl and organic acids</td></tr><tr><td>Welch and Ullman (1996)</td><td>25</td><td>3.0-6.0</td><td>2</td><td>Grain size 125 – 250 µm; added 1mM oxalate</td></tr><tr><td colspan="5"><strong>Oligoclase</strong></td></tr><tr><td>Casey et al. (1991)</td><td>25</td><td>3.0</td><td>20</td><td></td></tr><tr><td>Gudbrandsson et al. (2014)</td><td>22</td><td>2.01-11.1</td><td>19</td><td></td></tr><tr><td>Holdren and Speyer (1987)</td><td>25</td><td>3.0</td><td>24</td><td></td></tr><tr><td>Mast and Drever (1987)</td><td>22</td><td>4.0-9.3</td><td>13</td><td></td></tr><tr><td>Oxburgh et al. (1994)</td><td>25</td><td>3.0-5.1</td><td>12</td><td></td></tr><tr><td>Stillings and Brantley (1995)</td><td>25</td><td>3.0-5.0</td><td>22</td><td>+NaCl, + organic acids</td></tr><tr><td>Stillings et al. (1996)</td><td>25</td><td>2.9-5.7</td><td>22</td><td>+ 1 mM oxalate</td></tr><tr><td colspan="5"><strong>Andesine</strong></td></tr><tr><td>Busenberg and Clemency (1976)</td><td>25</td><td>5.0</td><td>43</td><td>+ 1atm CO<sub>2</sub></td></tr><tr><td>Casey et al. (1991)</td><td>25</td><td>2.0</td><td>47</td><td>Batch experiments</td></tr><tr><td>Holdren and Speyer (1987)</td><td>25</td><td>3.0</td><td>N/R</td><td></td></tr><tr><td>Mast and Drever (1987)</td><td>25</td><td>3.1-9.0</td><td>46</td><td></td></tr><tr><td>Oxburgh et al. (1994)</td><td>25</td><td>3.0-5.1</td><td>43</td><td></td></tr><tr><td>Stillings et al. (1996)</td><td>25</td><td>3.0-7.2</td><td>43</td><td>+organic acids</td></tr><tr><td>Stillings and Brantley (1995)</td><td>25</td><td>3.0-3.1</td><td>43</td><td>+organic acids, + NaCl</td></tr><tr><td>Sun (1994)</td><td>25</td><td>3.0-7.7</td><td>47</td><td>+ organic acids</td></tr><tr><td>Welch and Ullman (1993)</td><td>25</td><td>3.0-9.0</td><td>49</td><td>+ organic acids</td></tr><tr><td colspan="5"><strong>Labradorite</strong></td></tr><tr><td>Blake and Walter (1999)</td><td>80</td><td>6.0</td><td>70</td><td>+ organic acids, +NaCl</td></tr><tr><td>Busenberg and Clemency (1976)</td><td>25</td><td>5.0</td><td>53</td><td>+ 1atm CO<sub>2</sub></td></tr><tr><td>Carroll and Knauss (2001)</td><td>30-150</td><td>3.20-3.37</td><td>60</td><td>+ added CO<sub>2</sub> (aq)</td></tr><tr><td>Casey et al. (1991)</td><td>25</td><td>2.0</td><td>60</td><td></td></tr><tr><td>Gudbrandsson et al. (2014)</td><td>22</td><td>2.1-11.0</td><td>61-71</td><td></td></tr><tr><td colspan="5"><strong>Bytownite</strong></td></tr><tr><td>Brady and Walther (1989)</td><td>25</td><td>2.1-12.1</td><td>N/R</td><td></td></tr><tr><td>Casey et al. (1991)</td><td>25</td><td>3.0</td><td>76</td><td></td></tr><tr><td>Gudbrandsson et al. (2014)</td><td>22</td><td>2.0-11.2</td><td>76-78</td><td></td></tr><tr><td>Holdren and Speyer (1987)</td><td>25</td><td>3.0</td><td>N/R</td><td></td></tr><tr><td>Oxburgh et al. (1994)</td><td>25</td><td>3.1-7.2</td><td>86</td><td></td></tr><tr><td>Siegel and Pfannkuch (1984)</td><td>25</td><td>4.0</td><td>72</td><td></td></tr><tr><td>Stillings and Brantley (1995)</td><td>25</td><td>3.2-3.6</td><td>76</td><td>+NaCl, +organic acids</td></tr><tr><td>Welch and Ullman (1993)</td><td>25</td><td>3.2-10.0</td><td>77</td><td>+NaCl, +organic acids</td></tr><tr><td colspan="5"><strong>Anorthite</strong></td></tr><tr><td>Amrhein and Suarez (1988)</td><td>25</td><td>3.0-10.0</td><td>93</td><td>+CO<sub>2</sub>, secondary mineral precipitation</td></tr><tr><td>Amrhein and Suarez (1992)</td><td>25</td><td>3.6-7.4</td><td>96</td><td>+CO<sub>2</sub>, secondary mineral precipitation</td></tr><tr><td>Bailey (1974)</td><td>25</td><td>3.0-4.5</td><td>N/R</td><td></td></tr><tr><td>Berg and Banwart (2000)</td><td>25</td><td>5.7-8.4</td><td>93</td><td>+CO<sub>2</sub></td></tr><tr><td>Brady and Walther (1989)</td><td>25</td><td>1.9-12.0</td><td>95</td><td></td></tr><tr><td>Casey et al. (1991)</td><td>25</td><td>2.0</td><td>92</td><td></td></tr><tr><td>Fleer (1982)</td><td>25</td><td>2.0-5.6</td><td>N/R</td><td>Underestimated surface area</td></tr><tr><td>Gudbrandsson et al. (2014)</td><td>22</td><td>1.8-11.3</td><td>89</td><td></td></tr><tr><td>Hodson (2003)</td><td>25</td><td>2.6</td><td>93</td><td>Influence of Fe-rich coating</td></tr><tr><td>Holdren and Speyer (1987)</td><td>25</td><td>3.0</td><td>N/R</td><td>Secondary mineral precipitation</td></tr><tr><td>Oelkers and Schott (1995)</td><td>45-95</td><td>2.5-3.1</td><td>96</td><td></td></tr></tbody></table>

N/R = not reported

To assure internal consistency among the dissolution rates of the plagioclase mineral regression, the equation in this study is based on that of Gudbrandsson et al. (2014), who performed a systematic analysis of the dissolution rates of plagioclases of distinct compositions. Specifically, we used the
equations to describe dissolution rates as a function of pH for albite, oligoclase, andesine, labradorite, bytownite, and anorthite. Gudbrandsson et al. (2014) reported that far-from-equilibrium plagioclase dissolution rates depend strongly on the Ca content of the mineral at acidic conditions, whereas these rates were found to be independent of this composition at basic pH. As such, the dissolution rates for the plagioclases are here assumed to be mineral composition independent at basic pH but depend increasingly on pH as the aqueous fluids become more acidic at pH<6. In addition, the activation energies of all of the plagioclases were taken to be identical. Although this might seem arbitrary, regression of the plagioclase rate data for the individual compositions yielded scattered activation energies as a function of composition, and the activation energy for anorthite was significantly lower than that of albite. This latter difference would lead to albite dissolution rates that are substantially faster than those of anorthite at elevated temperatures, which is inconsistent with observations of natural systems. The choice of single activation energies for all plagioclases prevents such inconsistencies in the resulting database and is within the uncertainty in published rate data.

A comparison of far-from-equilibrium plagioclase dissolution rates calculated using Eq. (7) and parameters provided in Table 2 with corresponding experimentally measured values can be made with the aid of Figures 3 and 4. At pH<5, anorthite dissolves significantly faster than the more albitic plagioclases but dissolves at close to identical rates at basic conditions. The dissolution rate equation for albite describes the experimentally measured rate data with an average difference of 0.63 log units; 50% of the experimental data are within 0.54 log units of the corresponding calculated rates. The dissolution rate equation for anorthite describes the experimentally measured rate data with an average difference of 0.61 log units; 50% of the experimental data are within 0.41 log units of the corresponding calculated rates. The significant scatter in these experimental datasets may be due to effects of aqueous solution composition (Burch et al., 1993; Knauss and Copenhaver, 1995; Oelkers et al., 1994), due to the different methods used to measure rates, or be related to sample preparation. In addition, the dissolution rates of the plagioclases are affected by the aqueous activity of Al and, consequently, any aqueous ligand that might complex this metal in the aqueous phase. Oelkers et al. (1994), Blum and Stillings (1995), and Gudbrandsson et al. (2014) noted that the experimental dataset for anorthite dissolution is strongly affected by uncertainties in the measurement of the mineral surface area, for example, in the case of the data from Fleer (1982), and secondary mineral precipitation, for example in the case of the data from Amrhein and Suarez (1988, 1992) and Hodson (2003). Differences in experiment duration, as in the case of data from Oxburgh et al. (1994), may result to up to 1 log unit of difference between measured and calculated rates.

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<figure><img src="image_4.png" /><figcaption>**Figure 3:** Far-from-equilibrium dissolution rates of plagioclase minerals: A-B) comparison of measured experimental rates for albite, C) oligoclase, D) andesine, E) labradorite, F) bytownite, G-H) anorthite shown as symbols with corresponding values calculated using Eq. (7) together with the parameters provided in Table 2 shown as curves as a function of pH and temperature. The symbol shape and outlying color indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, with black symbols denoting 25 °C. The shaded regions in some of these plots illustrate the 95% confidence limits of the regression fits for the 25 °C data.</figcaption></figure>
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There are a number of differences between the results of the regression rate equation generated in this study and those presented by Palandri and Kharaka (2004) and Brantley et al. (2008). The anorthite dissolution rate models of Palandri and Kharaka (2004) and Brantley et al. (2008) are limited to acidic to neutral conditions, mostly due to the distribution of rate data available at the time of these studies. Perhaps the most significant difference between these past studies and the present involves the activation energies of these minerals. In the past studies, the activation energies for albite and anorthite were regressed independently, and the activation energies of anorthite were lower than that for albite. The activation energies for intermediate plagioclases were then derived graphically from activation energies of anorthite and albite. As a result, the activation energy for anorthite dissolution is substantially lower than for most primary silicates.

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Moreover, using parameters from Palandri and Kharaka (2004) and Brantley et al. (2008), albite-rich plagioclases are calculated to dissolve faster than anorthite-rich plagioclases at a temperature above 130 °C, which is inconsistent with field observations. This likely ambiguity was overcome in the present study by generating plagioclase dissolution rates assuming the activation energies for the plagioclase minerals are independent of the mineral composition. Such could be verified or improved with future studies.

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<figure><img src="image_5.png" /></figure>

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<caption>**Figure 4:** Far-from-equilibrium dissolution rates of the plagioclases as a function of pH calculated using Eq. (7) together with parameters listed in **Table 2**, compared with the rates calculated using kinetic parameters in Palandri and Kharaka (2004): A) 25 °C and B) 150 °C. In this figure Ab=albite, Ol=oligoclase, And=andesine, La=labradorite, By=bytownite, An=anorthite).</caption>

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### 3.2.2 K-feldspar

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Experimentally measured dissolution rates of K-feldspar, including those of orthoclase and microcline, are summarized in **Figure 5** and **Table 5**. Based on the similarity of K-feldspar and albite structures and compositions, these rates might be expected to be largely similar to one another. Nevertheless, the K-feldspar dissolution rates available in the literature are scattered in part due to the variations in composition of the feldspar samples used in the various experiments. Moreover, there are

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far less rate data available for K-feldspar than albite. The experimental dataset considered for the regression calculations includes rates obtained at ambient pCO₂ and in the absence of organic ligands. These data span in temperature from 13 to 150 °C (Siegel and Pfannkuch, 1984; Bevan and Savage, 1989; Gautier et al., 1994; Schweda, 1989; Swoboda-Colberg and Drever, 1993; Stillings and Brantley, 1995; Stillings et al., 1996; van Hees et al., 2002). Additional rates have been reported in the presence of 1 atm pCO₂ (Busenberg and Clemency, 1976) and in the presence of aqueous organic ligands (Tan, 1980; Manley and Evans, 1986; Welch and Ullman, 1993, 1996; Blake and Walter, 1999; Ullman and Welch, 2002). Experimentally measured rates in this dataset at 25 °C range from as high as 10⁻¹⁰.¹ at pH 2.0 to as low as 10⁻¹³.³ mol m⁻² s⁻¹ at pH 5.6. Rates obtained in the presence of 1 atm pCO₂ and/with added aqueous organic ligands are up to 1.5 log units faster than those measured at ambient pCO₂ and in the absence of organic ligands (Busenberg and Clemency, 1976; Tan, 1980; Bevan and Savage, 1989). Moreover, experimental data from Swoboda-Colberg and Drever (1993) obtained at field and laboratory conditions and normalized to the geometric surface area, and data from Gautier et al. (1994) obtained at various close-to-equilibrium chemical affinities were also not considered for the regression. Experimental datasets that are not included for the kinetic fit are marked in circles in **Figure 5** and indicated in **Table S1 in Appendix A**.

<table><caption>**Table 5:** Sources of experimentally measured K-feldspar dissolution rates considered in this study.</caption><thead><tr><th>References</th><th>T °C</th><th>pH</th><th>Composition*</th><th>Comments</th></tr></thead><tbody><tr><td>Bevan and Savage (1989)</td><td>70-95</td><td>1.0-9.0</td><td>Or<sub>93</sub>Ab<sub>7</sub></td><td>Added organic acids; orthoclase</td></tr><tr><td>Busenberg and Clemency (1976)</td><td>25</td><td>5.0</td><td>Or<sub>75.79</sub>Ab<sub>20-24</sub></td><td>1 atm CO<sub>2</sub>; orthoclase/microcline</td></tr><tr><td>Gautier et al. (1994)</td><td>150</td><td>9.0</td><td>Or<sub>81</sub>Ab<sub>15</sub></td><td>Function of chemical affinity; added Ba</td></tr><tr><td>Holdren and Speyer (1987)</td><td>25</td><td>2.0-3.0</td><td>Or<sub>78</sub>Ab<sub>21</sub>An<sub>1</sub></td><td>Function of grain fraction</td></tr><tr><td>Knauss and Copenhaver (1995)</td><td>70</td><td>4.0-9.5</td><td>Or<sub>94</sub>Ab<sub>6</sub></td><td>Added Na</td></tr><tr><td>Manley and Evans (1986)</td><td>13</td><td>3.8-5.7</td><td>Or<sub>67</sub>Ab<sub>31</sub>An<sub>2</sub></td><td>Added organics</td></tr><tr><td>Schweda (1990)</td><td>25</td><td>1.1-12.7</td><td>N/R</td><td>-</td></tr><tr><td>Siegel and Pfannkuch (1984)</td><td>25</td><td>4.0</td><td>Or<sub>66</sub>Ab<sub>32</sub>An<sub>2</sub></td><td>Microcline</td></tr><tr><td>Stillings and Brantley (1995)</td><td>25</td><td>3.0</td><td>Or<sub>78</sub>Ab<sub>22</sub></td><td>Microcline</td></tr><tr><td>Stillings et al. (1996)</td><td>25</td><td>3.12</td><td>Or<sub>78</sub>Ab<sub>22</sub></td><td>Microcline</td></tr><tr><td>Swoboda-Colberg and Drever (1993)</td><td>25</td><td>4.0-4.5</td><td>N/R</td><td>Laboratory and field experiments; geometric surface area</td></tr><tr><td>Tan (1980)</td><td>25</td><td>7.0</td><td>N/R</td><td>Added organic acids; microcline</td></tr><tr><td>van Hees et al. (2002)</td><td>25</td><td>3.5-5.0</td><td>Or<sub>70</sub>Ab<sub>25</sub>An<sub>5</sub></td><td>Microcline</td></tr></tbody></table>

N/R = not reported

*Or-orthoclase, Ab-albite

The K-feldspar experimental datasets spanning the range of temperature from 25 to 95 °C and pH from 2 to 12 were fit to Eq (7). A comparison of experimentally measured rates with those generated using the regression equation and the parameters in **Table 2** can be made with the aid of **Figure 5**. The activation energies retrieved in this study, 51.7, 38.0, and 62.2 kJ mol⁻¹, at acidic, neutral, and basic conditions, respectively, are similar to those previously reported by Helgeson et al. (1984), Bevan and Savage (1989), Schweda (1990), Sverdrup (1990), and Blum and Stillings (1995). The activation energies of Palandri and Kharaka (2004) at basic conditions are somewhat higher as they considered
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the rates of Gautier et al. (1994) in their regression. As seen in **Figure 5**, there is significant scatter
among the datasets leading to differences between calculated and measured rates in some cases.

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<figure><img src="image_6.png" /></figure>

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<caption>**Figure 5:** Far-from-equilibrium dissolution rates of K-feldspar: A) comparison of measured experimental rates shown as symbols with corresponding values calculated using Eq. (7) together with the parameters provided in B) Direct comparison of measured and calculated dissolution rates. The symbol shape and outline indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, where black symbols indicate 25 °C. The shaded region in the left plot illustrates the 95% confidence limits of the regression fit of the 25 °C rates.</caption>

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The dissolution rate equation for K-feldspar describes the experimentally measured rate data with an average difference of 0.53 log units; 7% of the experimental data are more than one log unit different from the corresponding calculated rate. Many of these larger differences may be due to the composition of the studied feldspar, which ranged from $Or_{66}$ to $Or_{94}$.

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**3.3. Volcanic Glass**

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Numerous studies have reported volcanic glass reactivity dissolution rates at ambient temperatures to elucidate weathering rates of the oceanic and continental crust (e.g., Colman, 1982; Eggleton, 1987; Banfield et al., 1991; Nesbitt and Wilson 1992). Other studies have reported volcanic glass dissolution rates at a higher temperature and at various $pCO_2$ to assess the potential of volcanic glass to store $CO_2$ and nuclear waste (e.g., Malow et al., 1984; Crovisier et al., 1988; Jercinovic et al., 1990; Morgenstein and Shettel, 1993; Oelkers and Schott, 2005; McGrail et al., 2006; Goldberg et al., 2008; Oelkers and Cole, 2008; Oelkers et al., 2008; Schaef and McGrail, 2009; Gislason et al., 2010; Schaef et al., 2010, 2009; Matter et al., 2016). Most studies have focused on basaltic glass, yet others have described the dissolution rates of borosilicate, rhyolitic and dacitic glass (Jantzen and Plodinec, 1984; Malow et al., 1984; Petit et al., 1990; Plodinec and Wicks, 1993; Wolff-Boenisch et al., 2004).
It is reasonable to assume similar dissolution mechanisms for basaltic and rhyolitic glass; however, measured dissolution rates vary significantly with glass composition (Wolff-Boenisch et al., 2004). Therefore, to account for variability in the glass composition, we summarize volcanic glass dissolution into two subsections, one focused on basaltic glass (<52 wt% SiO₂) and the other focused on rhyolitic glass (>68 wt% SiO₂).

### 3.3.1 Basaltic glass

Measured basaltic glass dissolution rates have been collected from 9 different studies containing 146 distinct data points. Aside from field data in Gordon and Brady (2002), all rates were measured in the laboratory. Laboratory rates have been measured as functions of aqueous solution composition and temperature. Gislason and Eugster (1987), Oelkers and Gislason (2001), Gislason and Oelkers (2003), Wolff-Boenisch et al. (2004), and Stockmann et al. (2012) used basaltic glass from Iceland as an analog for the oceanic crust, while Daux et al. (1997) focused their efforts on the synthetic glass; the compositions of the glass used in each study are provided in Table S1, Appendix A. Most of the experiments were performed at temperatures <100 °C (Gislason and Eugster, 1987; Daux et al., 1997; Oelkers and Gislason, 2001; Wolff-Boenisch et al., 2004; Stockmann et al., 2012), although Guy (1989) and Gislason and Oelkers (2003) reported rates at temperatures ranging up to 200 °C. Oelkers and Gislason (2001) and Stockmann et al. (2012) measured basaltic glass dissolution rates in the presence of organic acids and bacteria, and Crovisier et al. (1987) reported on basaltic glass dissolution in seawater. As the presence of seawater significantly accelerates the dissolution of basaltic glass (marked in circle on Figure 6), the experimental data from Crovisier et al. (1987) were not considered in the regression.

The dissolution rate equation adopted in this compilation is based on Stapafell (Iceland) basaltic glass (Oelkers and Gislason, 2001; Gislason and Oelkers, 2003). As this glass is similar in composition to that of mid-ocean ridge basalt, it is representative of much of the natural glass on our planet. In their work, it is assumed that the dissolution rates of basaltic glass are controlled by the breaking of the Al-Si-rich leached layer. In the case of basaltic glass, the majority of the published rate data report sufficient fluid chemistry data to permit the regression of the rate data using (Oelkers and Gislason, 2001; Gislason and Oelkers, 2003; Wolff-Boenisch et al. 2004; Stockmann et al., 2012) yielding:

$$r_+ = \left( 1.08 \cdot 10^{-4} \text{ mol m}^{-2}\text{s}^{-1} * \exp\left(\frac{-21500 \text{ J mol}^{-1}}{RT}\right) \left(\frac{(a_{H^+})^3}{(a_{Al^{3+}})}\right)^{\frac{1}{3}} \right) \quad (10)$$

where *R* stands for the gas constant, *T* signifies temperature in K, and *a*<sub>H⁺</sub> and *a*<sub>Al³⁺</sub> represents the activity of the subscripted aqueous species. The effect of the chemical affinity on calculated glass dissolution rates in Eq. (10) for use in modeling calculations was accounted for using the solubility of
635

636

a theoretical leached SiO$_{3}$-Al(OH)$_{3}$ glass framework. Its solubility was estimated as an ideal mixture of amorphous SiO$_{2}$ and Al(OH)$_{3}$ with the same stoichiometry as the basaltic glass (Bourcier, 1990).

637

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**Figure 6** illustrates the degree to which **Eq. (10)** describes the available experimental data. Rates generated using **Eq. (10)** are within two orders of magnitude of corresponding rates published in the literature. The average difference between calculated and measured rates is 0.49 log units, and 50% of the experimental data are within 0.44 log units of those generated with **Eq. (10)**. Relatively large differences were found between calculated rates and those measured by Daux et al. (1997) and Wolff-Boenisch et al. (2004). These studies considered a synthetic glass or a glass with a different Si and Al content than those from Stapafell (Iceland).

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### 3.3.2 Rhyolitic glass

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Fewer studies have focused on the dissolution rates of rhyolitic glass. The rhyolite glass dissolution dataset collected in this study comprises 93 data points. Wolff-Boenisch et al. (2004) compared dissolution rates of natural glasses as a function of their silica content from 25 to 74 °C, at pH~4 and 10.6. Karkhanis et al. (1980), White (1983), and Declercq et al. (2013) reported rhyolite glass dissolution rates over the temperature range of 40 to 200 °C as a function of pH and in the presence of organic ligands. Measured rhyolitic glass dissolution rates are one to four orders of magnitude slower than those of basaltic glass at corresponding temperature and pH conditions and range from $10^{-10.4}$ to $10^{-11.6}$ mol m$^{-2}$ s$^{-1}$ at neutral pH and ambient temperature conditions.

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A comparison of rhyolite glass dissolution rates calculated with **Eq. (7)** and parameters from **Table 2** with their corresponding experimentally measured rates is shown in **Figure 6C**. The dissolution rate equation for rhyolite glass describes the experimentally measured rate data with an average difference of 0.32 log units; 50% of the experimental data are within 0.22 log units of the corresponding calculated rates. Some of the differences between measured and calculated rates likely stem from the variable SiO$_{2}$ content of dissolved rhyolitic glass samples used in Wolff-Boenisch et al. (2004) and possibly uncertainties reported in surface area measurements in the experiments reported in Declercq et al. (2013).

661
<figure><img src="image_7.png" /><figcaption>**Figure 6:** *Experimentally measured far-from-equilibrium dissolution rates of silicate glass: A-B) Comparison of experimentally measured dissolution rates for basaltic glass with rates calculated using Eq. (10) at temperatures ranging from 25 to 300°C; C-D) Comparison of experimentally measured dissolution rates of rhyolite glass with rates calculated using Eq. (7) and parameters from Table 2 for rhyolitic glass and a temperature range from 25 to 200°C. The symbol shape and outline color indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, where black symbols indicate 25 °C. The shaded regions in Fig. 6(C) illustrate the 95% confidence limits of the regression fit of the 25 °C data.*</figcaption></figure>

## 3.4 Micas

Mica dissolution rates have been previously summarized and reviewed by Ross (1967) and Nagy (1995). The experimental datasets of biotite and muscovite dissolution considered in the present study are summarized in Table 6 and Figure 7. Constant temperature far-from-equilibrium mica dissolution rates tend to minimize as a function of pH at near to neutral conditions. The published dissolution rates of biotite appear to vary more strongly with pH than those of muscovite. Although the dissolution rates of both muscovite and biotite are comparable at 25 °C, muscovite dissolution rates appear to increase faster with increasing temperature. No significant effect has been observed of the magnesium to iron ratio of the biotite on its dissolution rate to date. Magnesium content is expressed as Mg number (Mg# = Mg/(Mg+Fe)) in Figure 7A.

### 3.4.1 Biotite

The experimental dataset collected in this study of biotite dissolution includes 19 studies with 129 data points. These studies focused on biotite having compositions ranging between its annite and
phlogopite endmembers; most of these reported rates were measured at temperatures near 25 °C and over the pH range of 1 to 8.5 (Sverdrup, 1990; Acker and Bricker, 1992; Kenoyer and Bowser, 1992; Kalinowski and Schweda, 1996; Malmström et al., 1996; Malmström and Banwart, 1997; Murphy et al., 1998; Taylor et al., 2000; Voinot et al., 2013). Samson et al. (2005) reported rates at pH up to 14.3. Biotite dissolution rates at temperatures up to 280 °C have been reported by Carroll et al. (2017). Other studies considered natural biotite weathering at pH from 4.0 to 6.0 at ambient temperature. These studies include those of Velbel (1985), Swoboda-Colberg and Drever (1993), Clow and Drever (1996), Murphy et al. (1998), and White et al. (2002). Acker and Bricker (1992) and Samson et al. (2005) reported that iron oxidation results in biotite dissolution rates that are substantially faster in oxidized fluids when compared to dissolution in oxygen-free conditions. Moreover, Clemency and Lin (1981) and Lin and Clemency (1981) carried out biotite dissolution experiments in open and closed systems in saturated $pCO_2$ aqueous solutions. According to these two studies, biotite dissolution is 67 times faster in an open system compared to a closed system.

Experimentally measured biotite far-from-equilibrium dissolution rates data are shown at temperatures up to 280 °C as a function of pH in **Figure 7**. As shown in **Figure 7A**, rates at constant pH scatter over up to three orders of magnitude at 25 °C. Bray et al. (2015) attributed these differences to a number of factors, including the distinct biotite sample locations of the considered solids, structural anisotropy, the composition of the studied biotites, the effect of aqueous fluid composition on rates, and experiment duration (see **Table 6** for further details of each experimental study). Further sources of scatter include the biotite iron content and the effect of oxidation. The addition of $CO_2$ to the aqueous solution results in slower biotite dissolution rates (Malmström et al., 1995), whereas some aqueous organic ligands can accelerate these rates (Balland et al., 2010; Bray et al., 2015). Rates measured in the presence of $CO_2$ and/or the presence of organic ligands were not considered in the regression calculations. Moreover, the rates from Velbel (1985) and White et al. (2002) were not considered in the regression either as the surface areas in these studies are likely to be overestimated. Experimental datasets not included in the regression are marked in circle or by arrow in **Figure 7** and **Appendix**.

<table><caption>**Table 6:** Sources of experimentally measured mica dissolution rates considered in this study.</caption><thead><tr><th></th><th>T °C</th><th>pH</th><th>Mg/Fe Ratio</th><th>Mineral sample</th><th>Experiments</th></tr></thead><tbody><tr><td><strong>Biotite</strong><br>Acker and Bricker (1992)</td><td>25</td><td>3.0-6.7</td><td>0.59</td><td>Bancroft, Ontario, (Canada)</td><td>Fluidized-bed reactors and flow-through columns; added H<sub>2</sub>SO<sub>4</sub>; non-stoichiometric dissolution; Fe-oxidation</td></tr><tr><td>Balland et al. (2010)</td><td>25</td><td>2.0-4.4</td><td>0.6</td><td>Raze, Limousin, (France) with Ca/Mn/Ti impurities;</td><td>Batch (closed system) experiments</td></tr></tbody></table>
<table>
  <tbody>
    <tr>
      <td>Bray et al. (2015)</td>
      <td>25</td>
      <td>2.0-6.0</td>
      <td>0.57</td>
      <td>Grasasen (Norway)</td>
      <td>with added organic acids<br/>Mixed-flow and batch (closed system)<br/>experiments with varying concentrations of organic acids and grain size</td>
    </tr>
    <tr>
      <td>Carroll et al. (2017)</td>
      <td>100-280</td>
      <td>3.0-7.5</td>
      <td>0.94</td>
      <td></td>
      <td>Mixed-flow reactors<br/>batch (open system) with added CO2</td>
    </tr>
    <tr>
      <td>Clemency and Lin (1981)</td>
      <td>25</td>
      <td>3.0</td>
      <td>0.93</td>
      <td>Madagascar</td>
      <td></td>
    </tr>
    <tr>
      <td>Clow and Drever (1996)</td>
      <td>25</td>
      <td>4.0</td>
      <td>0.5</td>
      <td>Field study</td>
      <td></td>
    </tr>
    <tr>
      <td>Kalinowski and Schweda (1996)</td>
      <td>25</td>
      <td>1.0-4.0</td>
      <td>0.91</td>
      <td>Bancroft, Ontario, Canada</td>
      <td>Dialysis-cell reactors</td>
    </tr>
    <tr>
      <td>Kalinowski and Schweda (1996)</td>
      <td>25</td>
      <td>1.0-4.0</td>
      <td>0.51</td>
      <td>Grasasen (Norway)</td>
      <td>Dialysis-cell reactors</td>
    </tr>
    <tr>
      <td>Kenoyer and Bowser (1992)</td>
      <td>25</td>
      <td>4</td>
      <td>0.5</td>
      <td>Field study</td>
      <td>Added CO2 batch (closed system) with added CO2</td>
    </tr>
    <tr>
      <td>Lin and Clemency (1981)</td>
      <td>25</td>
      <td>5.5</td>
      <td>0.93</td>
      <td>Madagascar</td>
      <td>Flow-through reactors; Fe-oxidation at pH&gt;7</td>
    </tr>
    <tr>
      <td>Malmström and Banwart (1997)</td>
      <td>25</td>
      <td>2.0-10.0</td>
      <td>0.38</td>
      <td>Moen (Norway);</td>
      <td></td>
    </tr>
    <tr>
      <td>Murphy et al. (1998)</td>
      <td>25</td>
      <td>4.5</td>
      <td>0.53</td>
      <td>Field study</td>
      <td></td>
    </tr>
    <tr>
      <td>Samson et al. (2005)</td>
      <td>22-25</td>
      <td>7.2-14.3</td>
      <td>0.59</td>
      <td>Bancroft, Ontario, Canada</td>
      <td>Stirred flow-through reactors; rates as a function of solution composition</td>
    </tr>
    <tr>
      <td>Sverdrup (1990)</td>
      <td>25</td>
      <td>4.0-5.0</td>
      <td>N/R</td>
      <td>N/R</td>
      <td>Mixed-flow experiments, K release rates</td>
    </tr>
    <tr>
      <td>Swoboda-Colberg and Drever (1993)</td>
      <td>25</td>
      <td>4.0-4.5</td>
      <td>0.5</td>
      <td>Field study; geometric surface area</td>
      <td>Fluidized bed reactors</td>
    </tr>
    <tr>
      <td>Taylor et al. (2000)</td>
      <td>25</td>
      <td>3.0-4.0</td>
      <td>0.8</td>
      <td>pegmatite deposits in the northwestern Adirondack Mountains.</td>
      <td>Flow-through reactor</td>
    </tr>
    <tr>
      <td>Velbel (1985)</td>
      <td>25</td>
      <td>6.0</td>
      <td>0.48</td>
      <td>Field study</td>
      <td></td>
    </tr>
    <tr>
      <td>Voinot et al. (2013)</td>
      <td>20</td>
      <td>3.0-4.5</td>
      <td>0.74</td>
      <td>Bancroft, Ontario, (Canada)</td>
      <td>Flow-through reactors</td>
    </tr>
    <tr>
      <td>White et al. (2002)</td>
      <td>25</td>
      <td>5.5-5.7</td>
      <td>0.5</td>
      <td>Field study</td>
      <td></td>
    </tr>
    <tr>
      <td><strong>Muscovite</strong></td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
      <td></td>
    </tr>
    <tr>
      <td>Cabrera and Talibudeen (1979)</td>
      <td>25</td>
      <td>3</td>
      <td>-</td>
      <td>&gt;1µm particles</td>
      <td></td>
    </tr>
    <tr>
      <td>Hurd et al. (1979)</td>
      <td>1</td>
      <td>8</td>
      <td>-</td>
      <td>&lt;100µm particles</td>
      <td></td>
    </tr>
    <tr>
      <td>Kalinowski and Schweda (1996)</td>
      <td>22</td>
      <td>1.1-4.1</td>
      <td>-</td>
      <td>10-20µm particle size</td>
      <td></td>
    </tr>
    <tr>
      <td>Knauss and Wolery (1989)</td>
      <td>70</td>
      <td>1.4-11.8</td>
      <td>-</td>
      <td>75-125µm particles</td>
      <td>Single-pass and batch reactors</td>
    </tr>
    <tr>
      <td>Lammers et al. (2017)</td>
      <td>100-280</td>
      <td>2.1-10.9</td>
      <td>-</td>
      <td>150-250 µm particle size</td>
      <td></td>
    </tr>
    <tr>
      <td>Nickel (1973)</td>
      <td>25</td>
      <td>0.2-10.6</td>
      <td>-</td>
      <td>20-35 µm particle size, +impurities</td>
      <td></td>
    </tr>
    <tr>
      <td>Oelkers et al. (2008)</td>
      <td>60-201</td>
      <td>1.0-10.3</td>
      <td>-</td>
      <td>50-100 µm particle size</td>
      <td>Function of Al and Si activity</td>
    </tr>
    <tr>
      <td>Swoboda-Colberg and Drever (1993)</td>
      <td>25</td>
      <td>4.0-4.5</td>
      <td>-</td>
      <td>Field study; 75-150 µm, geometric surface area</td>
      <td></td>
    </tr>
  </tbody>
</table>

N/R = not reported
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**Figure 7** compares measured rates with rates calculated using Eq. (7) and parameters listed in **Table 2**. The dissolution rate equation for biotite describes the experimentally measured rate data with an average difference of 0.43 log units; 50% of the measured dissolution rates are within 0.35 log units of those calculated.

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Previous equations describing far-from-equilibrium biotite dissolution rates have been presented by Acker and Bricker (1992), Kalinowski and Schweda (1996), Malmström and Banwart (1997), Palandri and Kharaka (2004), and Bray et al. (2015). Most of these equations were limited to acidic to neutral conditions other than that of Malmström and Banwart (1997), which described biotite dissolution rates to pH 10. However, this latter study included rates affected by Fe oxidation and therefore yields higher rates than that of other regression efforts. The regression equation generated in the present study yields rates similar to that of Bray et al. (2015) and Carroll et al. (2017) but 1) clarifies the variation of rates as a function of biotite composition, and 2) takes into consideration an increase in dissolution rates with increasing pH at pH>10, and 3) considered the rate data to temperatures up to 280 °C.

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### 3.4.2 Muscovite

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The experimental dataset for muscovite collected in this study includes 136 data points from 8 experimental studies. Nickel (1973) described muscovite dissolution rates measured in stirred tank reactors at 25 °C and pH 0.2, 3.6, 5.6, and 10.6. These rates were normalized to BET surface areas by Nagy (1995). Cabrera and Talibudeen (1979) and Kalinowski and Schweda (1996) investigated muscovite dissolution rates at 25 °C over a 1 to 4.1 pH range. Lin and Clemency (1981) measured muscovite dissolution rates at pH 4.6 and 5.1 and CO₂-saturated solutions in closed system reactors. Moreover, Swoboda-Colberg and Drever (1993) compared muscovite dissolution rates at <25 °C observed in the field and measured in the laboratory conditions. Hurd et al. (1979) reported muscovite dissolution rates at 1 °C and pH 8 in seawater. Knauss and Wolery (1986), Oelkers et al. (2008), and Lammers et al. (2017) derived equations describing muscovite dissolution rates based on flow-through experiments over wide ranges of pH at temperatures up to 280 °C.

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Published far-from-equilibrium dissolution rates are shown in **Figure 7** as a function of pH at 25, 100, 150, 200, and 250 °C. Experimental datasets from Nickel (1973), Cabrera and Talibudeen (1979), and Kalinowski and Schweda (1996) have comparable values at temperatures 22 to 25 °C, and pH ranging from 0.3 to 4.1. Rates increase with increasing temperature; the fastest rate $10^{-8.5}$ mol m⁻² s⁻¹ was measured at 250 °C as reported by Lammers et al. (2017). Rates reported by Swoboda-Colberg and Drever (1993) differ by up to one log unit from corresponding rates of other studies as they were normalized to the geometric surface area. Therefore, the rates reported in these studies were not considered in the regression calculations.

738

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<figure><img src="image_8.png" /><figcaption>**Figure 7:** Far-from-equilibrium dissolution rates of mica minerals: comparison of A) measured biotite dissolution rates at 25 °C; B) comparison of experimentally measured biotite dissolution rates shown as symbols with rates generated using the regression equations generated in this study at temperatures from 25 to 280 °C, and C) residuals of the biotite regression analysis as a function of pH. D-E) Measured muscovite dissolution rates at 25 °C. The symbols represent experimentally measured rates, whereas the blue dashed curve represents rates calculated using the regression equation generated in this study. The symbol shape and outline indicate the source of the data. The shading of the symbol indicates the composition of biotites in Figure 7A, but the temperature of the measurement in Figure 7B-7F. The shaded regions in the plots illustrate the 95% confidence limits of the corresponding regression fits at 25 °C.</figcaption></figure>

**Figures 7D and 7E** compare experimentally measured muscovite dissolution rates with those generated from the equations and parameters generated in this study. The dissolution rate equation for muscovite describes the experimentally measured rate data with an average difference of 0.55 log units; 50% of the experimental data are within 0.45 log units of the corresponding calculated rates. Less than 13% of the measured rates differ by more than one log unit from the corresponding calculated rates. Most of the rates exceeding this difference were reported by Knauss and Wolery
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(1989) at intermediate pH; these rates may have been affected by the precipitation of secondary
minerals.

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769

The regression fit generated in the present study yields similar rates as the equations proposed by Kalinowski and Schweda (1996), Palandri and Kharaka (2004), and Lammers et al. (2017), with a difference of less than 0.5 log unit in corresponding rates. Moreover, the retrieved activation energies obtained in this study compare well with those of Lammers et al. (2017). At the same time, the activation energies of Palandri and Kharaka (2004) are substantially lower than those reported here. This difference is likely due to the former study having limited their regressed dataset to temperatures of 70 °C or less.

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## 3.5 Olivines

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Experimentally measured olivine dissolution rates have been reported over wide ranges of temperature, mineral, and aqueous solution composition. Most experimental results have been concentrated on the reactivity of Mg-rich olivines due to their dominance in natural systems and ease of acquisition. Rimstidt et al. (2012) and Oelkers et al. (2018) summarized and reviewed olivine dissolution rate data and compared previous rate equations describing these rates. Some datasets are available for fayalite, with less than 10 mol% MgO in this site. Regressions of the experimentally measured rates of the olivine minerals were performed assuming two parallel rate mechanisms, one dominating at acidic conditions and the second dominating at basic conditions.

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### 3.5.1 Forsterite

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795

Experimentally measured far-from-equilibrium forsterite dissolution rates have been collected from 16 studies reporting 583 rates. The majority of these studies quantified the reactivity of forsterite having from 91 to 93 mol% of MgO in its divalent metal site and at temperatures ranging from 25 to 150 °C (Luce et al., 1972; Bailey, 1974; Siegel and Pfannkuch, 1984; Grandstaff, 1986; Van Herk et al., 1989; Casey et al., 1993; Westrich et al., 1993; Chen and Brantley, 2000; Pokrovsky and Schott, 2000; Rosso and Rimstidt, 2000; Oelkers, 2001b; Golubev et al., 2005; Hänchen et al., 2006; Olsen, 2007; Prigiobbe et al., 2009; Shirokova et al., 2012; Olsen et al., 2015). Additionally, Bailey (1974), Wogelius and Walther (1991, 1992), Pokrovsky and Schott (2000), Golubev et al. (2005), and Prigiobbe et al. (2009) reported experimentally measured forsterite dissolution rates in the presence of organic acids and as a function of CO₂ up to 178 atm, and in the presence of bacteria. Forsterite dissolution rates decrease as the pH increases, from $10^{-7.2}$ mol m⁻² s⁻¹ at pH 1.8 to $10^{-10.4}$ mol m⁻² s⁻¹ at pH 11.9 at 25 °C. As observed for many silicates, the dissolution rates increase as temperature increases, with rates increasing by two orders of magnitude from 25 to 90 °C, and increasing by four orders of magnitude from 25 to 150 °C (Siegel and Pfannkuch, 1984; Van Herk et al., 1989; Wogelius and Walther, 1991, 1992; Casey et al., 1993; Jonckbloedt, 1998; Chen and Brantley, 2000; Oelkers, 2001b; Hänchen et al., 2006; Prigiobbe et al., 2009). Wogelius and Walther (1991) and Pokrovsky and
Schott (2000) suggested that the addition of CO₂ to the reactive aqueous fluid slows forsterite dissolution as the pH increases beyond pH 6. The experimental results of Wogelius and Walther (1991), however, exhibited non-stoichiometric release of metals to the aqueous phase. Therefore, the rates they reported may have been influenced by the formation of secondary minerals in their reactors. Dissolution rates reported by Pokrovsky and Schott (2000) were calculated based on Mg release rates and possibly could have been influenced by the formation of a brucite-leached layer or magnesite precipitation at the mineral surface (Olsen, 2007). More recently, Golubev et al. (2005) and Prigiobbe et al. (2009) observed no significant changes in forsterite dissolution rates with increasing pCO₂. These authors attribute the previous observations of the effect of aqueous CO₂ on rates to the change in pH of the aqueous fluid due to the CO₂ addition. According to the results of Shirokova et al. (2012), the presence of both live and dead bacteria increases somewhat olivine dissolution rates. There is also some experimental evidence that the presence of organic acids might affect olivine dissolution rates (Bailey, 1974; Wogelius and Walther, 1991), insufficient systematic data are available to quantify such effects. Hence, the results of the latter two studies were not considered in the data regression. The study of Siegel and Pfannkuch (1984) was not considered due to the contamination of the mineral structure, and experimental data from Grandstaff (1986) were not considered due to ambiguities in quantifying the surface area of their forsterite grains. Note that experimental datasets that were not considered in the regression, including data from Gradstaff (1977), Siegel and Pfannkuch (1984), and those affected by added organic acids and presence of CO₂, are marked in **Figure 8** and **Table S1 in Appendix**.

The regression of the existing results performed in this study differs insignificantly from the fit proposed by Rimstidt et al. (2012); therefore, we chose to adopt the Rimstidt et al. (2012) rate equation in this study. This equation suggests activation energy of 70.4 kJ mol⁻¹ at acid conditions and 60.9 kJ mol⁻¹ at basic conditions. These are within an upper limit of a previously published range for forsterite, comparable with corresponding values proposed by Olsen (2007). Rimstidt et al. (2012) noted that higher values of activation energy might be due to a heterogeneous distribution of rates over the pH and temperature range. The reaction order in this rate equation with respect to proton activity changes from 0.44 at acidic conditions to 0.22 at pH ~8.8 (Oelkers et al., 2018). This pH value corresponds approximately to the pH at which forsterite switches from preferential initial Si to preferential initial Mg release (Pokrovsky and Schott, 2000).

**Figure 8** shows a comparison between forsterite far-from-equilibrium dissolution rates generated from Eq. (7) and the parameters listed in **Table 2** with corresponding rates generated from experiments at temperatures from 25 to 150 °C. The scatter is evenly distributed across the range of temperature and pH. The average difference between measured and calculated rates is 0.28 log units. In total, 50% of the measured rates differ by 0.18 log units or less from their corresponding calculated values.
<figure><img src="image_9.png" /></figure>

**Figure 8:** Far-from-equilibrium dissolution rates of olivine minerals: A-B) Comparison of experimentally measured forsterite dissolution rates with values calculated from Eq. (7) and the parameters listed in Table 2 at temperatures from 25 to 150 °C as a function of pH; C) comparison of far-from-equilibrium forsterite dissolution rates calculated using equations and parameters available in the literature; D) comparison of measured far-from-equilibrium dissolution rates for selected olivine minerals with values calculated from Eq. (7) and the parameters listed in Table 2 at 25 °C as a function of pH. The symbol shape and outline color indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, with black symbols being 25 °C. The shaded regions in the plots illustrate the 95% confidence limits of the corresponding regression fits at 25 °C.

**Figure 8C** shows a comparison of forsterite far-from-equilibrium dissolution rates generated from Eq. (7) compared with previously suggested fit equations. The rate equations published in Wogelius and Walther (1991), Pokrovsky and Schott (2000), Palandri and Kharaka (2004), Olsen (2007), Brantley et al. (2008), Grundwell (2014) at acidic pH are similar to one another and to rates generated using Eq. (7). At basic pH, the models of Wogelius and Walther (1991), Palandri and Kharaka (2004), and Brantley et al. (2008) differ by up to one order of magnitude from that adopted in this study, as some of these fits took into account experimental data from Pokrovsky and Schott

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(2000). The rate equation of Wogelius and Walther (1991) took into account some experimental data obtained at non-steady-state conditions and hence overestimated forsterite dissolution rates by up to two orders of magnitude.

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### 3.5.2 Non-forsteritic olivines

854

In comparison to forsterite, relatively few studies have reported the dissolution rates of olivines with non-forsteritic composition. Siever and Woodford (1979), Casey and Westrich (1992), and Wogelius and Walther (1992) reported the dissolution rates of fayalite from pH 2 to 4.5 at ambient temperature ranged from $10^{-6.52}$ to $10^{-9.60}$ mol m$^{-2}$ s$^{-1}$. Larnite dissolution rates reported in Westrich et al. (1993) for the same temperature and pH ranging from 2 to 4.9 are one to four orders of magnitude faster. Due to a scarcity of experimental data, activation energies and reaction orders for fayalite and larnite were taken to be identical to those of forsterite. Moreover, it is not possible to independently regress the fayalite and larnite dissolution rates at pH<5; therefore, activation energies and reaction orders for these minerals are taken from those of forsterite.

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**Figure 8D** compares the calculated versus measured far-from-equilibrium dissolution rates for larnite and fayalite at a temperature of 25 °C with corresponding calculated rates. The large average difference between the calculated and measured rates for fayalite of 0.88 log units is caused by slower reported dissolution rates from Siever and Woodford (1979), possibly affected by iron oxidation and silica precipitation (Wogelius and Walther, 1992). The average difference between the calculated and measured rates for larnite is 0.23 log units, and 50% of the experimentally measured rates are within 0.22 log units of the corresponding calculated rates. Calculated dissolution rates for larnite compare well with the fit suggested in Westrich et al. (1993).

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### 3.6 Pyroxenes

872

The pyroxene mineral structures are made up of linear chains of silica tetrahedra consisting of Si-O-Si bonds. These chains are held together in the pyroxene structure by divalent metal-oxygen bonds. Oelkers and Schott (2001) presented evidence that the dissolution mechanism of the pyroxene minerals consists first of the rapid exchange of the divalent metals near the mineral surface with protons in the aqueous phase, followed by the slow rate-limiting breaking of the Si-O bonds adjacent to the removed cations. This mechanism was further confirmed by Oelkers et al. (2009), who showed that the rapid exchange of divalent metals with the divalent cations at pyroxene surfaces occurs at fixed proportions over wide ranges of pH. Such studies suggest that the far-from-equilibrium rates of pyroxene dissolution in the absence of other accelerating aqueous species would be proportional to the aqueous activity ratio $a_{H^+}^2/a_{M^{2+}}$. The value of this ratio depends on the concentration of the $M^{2+}$ cation in the aqueous solution. Aqueous $M^{2+}$ cations form negligible hydroxide complexes. This implies that the aqueous activity ratio and thus the far-from-equilibrium dissolution rates of the pyroxenes will decrease monotonically with pH at constant $M^{2+}$ concentration.

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The generation of an accurate expression describing the dissolution rates of the pyroxenes is challenging due to the relative scarcity of experimental data and the large range of composition of natural pyroxene samples. Brantley and Chen (1995) summarized the experimentally measured dissolution rates available at the time of this publication. Most of the data have been reported for acidic pH conditions. As previously mentioned for the case of amphiboles, the lack of experimentally measured data at basic pH leads to significant uncertainties in the fit of the data at these conditions. Similar to the amphiboles, Palandri and Kharaka (2004) proposed a two-term fit of the available data where rates are pH-independent at basic conditions, while the fits of Knauss et al. (1993) and Brantley et al. (2008) suggested that these rates continuously decrease with increasing pH. The current study adopted the former approach as it provides a better description of the available experimental data.

### 3.6.1 Clinopyroxenes

The sources of experimentally measured far-from-equilibrium dissolution rates of diopside and augite dissolution are summarized in Table 7. The dataset consists of 11 studies, of which the majority focused on clinopyroxene dissolution at ambient temperature and over the pH range of 1 to 7. Some of these studies reported pyroxene dissolution rates at pH up to 12 and, or temperatures up to 90 °C (Schott and Berner, 1985; Knauss et al., 1993; Chen and Brantley, 1998; Golubev et al., 2005; Stockmann et al., 2008; Daval et al., 2010). Several studies reported the effect of CO₂ and aqueous organic acids on clinopyroxene dissolution rates. Knauss et al. (1993) reported diopside dissolution rates in the presence of 10⁻³.⁵ to 1 atm pCO₂ for pH 1-12 and temperature range 1 to 70 °C. This study suggested that diopside dissolution rates are not appreciably changed by the concentration of CO₂ in the aqueous solution at these conditions.

Oxidation state may affect the dissolution rates of the iron-bearing pyroxenes. Siever and Woodford (1979), Schott and Berner (1985), and White and Yee (1985) described the effect of iron oxidation at 20 to 50 °C and pH range 1 to 9 for augite and other Fe-bearing pyroxenes at oxic and anoxic conditions. They concluded that in comparison to anoxic conditions, pyroxene dissolution rates at pH<6 decreased when exposed to air, which they explained by precipitation of less reactive iron hydroxides on primary grains (Casey and Cheney, 1993). At pH>6, however, no effect of oxidation state on rates was observed.

<table><caption>Table 7: Sources of experimentally measured clinopyroxene dissolution rates considered in this study.</caption><thead><tr><th></th><th>T<br>°C</th><th>pH</th><th>Exp<br>Duration<br>(d)</th><th>Mineral<br>composition*<br>(%)</th><th>Comments</th></tr></thead><tbody><tr><td><strong>Augite</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Schott and Berner (1985)</td><td>20-72</td><td>6</td><td>16</td><td>N/R</td><td>-</td></tr><tr><td>Siegel and Pfannkuch,<br>(1984)</td><td>22</td><td>4.1</td><td>29</td><td>En<sub>22</sub>Fs<sub>44</sub>Wo<sub>34</sub></td><td>+Al, Na in mineral structure</td></tr><tr><td>Sverdrup (1990)</td><td>25</td><td>2.5-6.8</td><td>2-25</td><td>En<sub>45</sub>Fs<sub>27.5</sub>Wo<sub>27.5</sub></td><td>-</td></tr><tr><td>Sverdrup (1990)</td><td>25</td><td>3.1-6.5</td><td>2-25</td><td>En<sub>51</sub>Fs<sub>55</sub>Wo<sub>44</sub></td><td>-</td></tr><tr><td><strong>Diopside</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Chen and Brantley (1998)</td><td>25-90</td><td>1.2-3.8</td><td>77</td><td>Wo<sub>44.45</sub>En<sub>44.51</sub>Fs<sub>111</sub></td><td>+Al in mineral structure</td></tr><tr><td>Daval et al. (2010)</td><td>90</td><td>4.9-5.2</td><td>23-122</td><td>Wo<sub>51.1</sub>En<sub>48.7</sub>Fs<sub>80.2</sub></td><td>+Al in mineral structure</td></tr></tbody></table>
<table><tr><td>Eggleston et al. (1989)</td><td>25</td><td>1.0</td><td>1</td><td>WO51En48Fs1</td><td>Effect of age</td></tr><tr><td>Golubev et al. (2005)</td><td>25</td><td>1.0-11.8</td><td>1-6</td><td>WO49.7En49.2Fs1</td><td>+Al, Mn, Na, Ti, Cr in mineral structure; +CO2</td></tr><tr><td>Hoch et al. (1996)</td><td>25</td><td>5.8</td><td>25-183</td><td>WO49En47Fs4</td><td>At atmospheric conditions, +Fe, Na, Al in the mineral structure</td></tr><tr><td>Knauss et al. (1993)</td><td>25-70</td><td>2.0-12.0</td><td>60</td><td>WO50En46Fs4</td><td>+Al in mineral structure; +CO2</td></tr><tr><td>Schott et al. (1981)</td><td>20-25</td><td>1.0-6.0</td><td>2-40</td><td>WO51En48Fs1</td><td>Non-stoichiometric dissolution, +Al in the mineral structure</td></tr><tr><td>Stockmann et al. (2008)</td><td>25-70</td><td>4.3-8.5</td><td>Up to 164</td><td>WO50En49Fs1</td><td>+Al, Cr, Mn, Na, Ti in mineral structure</td></tr></table>

N/R = not reported

* Wo-wollastonite, En – enstatite, Fs- ferrosilite

Experimental data that were not included for the regression are marked in **Figure 9** and include datasets from Schott et al. (1981), Hoch et al. (1996), and Daval et al. (2010). The data of Hoch et al. (1996) were obtained from experiments on diopside containing substantial mineral impurities. The data of Schott et al. (1981) were obtained from experiments that did not attain a steady state. Finally, the data of Daval et al. (2010) were obtained at close to equilibrium conditions such that the chemical affinity term in Eq. (7) could influence the measured rates.

<figure><img src="image_10.png" /><figcaption>**Figure 9:** Far-from-equilibrium dissolution rates of diopside and augite: A-B) Comparison of measured experimental rates with rates calculated from Eq. (7) together with parameters listed in Table 2 as a function of pH at temperatures from 25 to 90 °C. C) Comparison of the diopside dissolution rates generated from the equations and parameters generated in this study compared with the results of previously published rate equations. D) Comparison of measured augite experimental rates with rates calculated from Eq. (7) together with parameters listed in Table 2 as a function of pH at temperatures from 25 to 70 °C. The symbol shape and</figcaption></figure>
outline color indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, where black symbols being 25 °C. The shaded regions in the plots illustrate the 95% confidence limits of the corresponding regression fits at 25 °C.

**Figure 9A-C** compares the calculated versus measured far-from-equilibrium dissolution rates for diopside at 25 to 90 °C. The average difference between the calculated and measured rates is 0.23 log units, and 50% of the experimentally measured rates are within 0.19 log units of the corresponding calculated rates. Rates generated using equations and parameters in this study are compared with the results of previously proposed diopside rate equations in **Figure 9C**. Despite the availability of more recent experimentally measured rates, the rate equations provide largely similar results. The present regression equation provides similar rates as the equations of Palandri and Kharaka (2004), while they differ by as much as 0.4 log units from those calculated using the equation proposed by Knauss et al. (1993). Measured far-from-equilibrium dissolution rates of augite are shown in **Figure 9D**. Rate parameters for augite were obtained from fitting the experimental data of Siegel and Pfannkuch (1984), Schott and Berner (1985), and Sverdrup (1990). The average difference between experimentally measured rates and corresponding values obtained using the regression equation is 0.68 log units. This relatively large difference likely stems at least in part from the varying composition of augite used in the experiments.

### 3.6.2 Orthopyroxenes

The sources of experimentally measured far-from-equilibrium dissolution rates of enstatite and bronzite dissolution are summarized in **Table 8**. The dataset consists of 10 studies, of which the majority focused on orthopyroxene dissolution at ambient temperature and over the pH range of 1 to 7. Some of these studies reported pyroxene dissolution rates at pH up to 12 and, or temperatures of up to 168 °C (Brady and Walther, 1989; Oelkers and Schott, 2001; Halder and Walther, 2011). Several studies reported the effect of CO₂ and aqueous organic acids on clinopyroxene dissolution rates. Bailey (1974) and Grandstaff (1977) reported bronzite and enstatite dissolution rates in the presence of aqueous organic acids for the pH range 1 to 4.1 and the temperature range 1 to 42 °C; however, they found no evidence that added organic acids affect dissolution rates of the pyroxenes. Schott and Berner (1983) reported on bronzite dissolution in the presence of atmospheric oxygen. They concluded that, as in the case of clinopyroxenes, the reactivity of orthopyroxenes at acidic pH up to pH 6 decreased when exposed to air.

**Figure 10A-C** compares the calculated versus measured rates for enstatite dissolution. The average difference between the calculated and measured rates is 0.32 log units, and 50% of the measured data are within 0.39 log units of their corresponding calculated values. Fewer than 5% of the measured rates are more than 1 log unit different from their corresponding calculated values. The fit
based on the pH polynomial in this study is close to the same quality as that based on a mechanistic model reported by Oelkers and Schott (2001).

<table><caption>**Table 8:** Sources of experimentally measured orthopyroxene dissolution rates considered in this study.</caption><thead><tr><th></th><th>T<br>°C</th><th>pH</th><th>Exp<br>Duration<br>(d)</th><th>Mineral<br>Composition</th><th>Comments</th></tr></thead><tbody><tr><td><strong>Bronzite</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Grandstaff (1977)</td><td>1-42</td><td>1.2-4.1</td><td>2-22</td><td>En<sub>77</sub>FS<sub>21</sub>WO<sub>2</sub></td><td>K<sub>2</sub>SO<sub>4</sub>, H<sub>2</sub>SO<sub>4</sub>, HNO<sub>3</sub>, KNO<sub>3</sub>, +Al, Na in the mineral structure, + organic acids</td></tr><tr><td>Schott and Berner (1983)</td><td>25</td><td>1.0-6.0</td><td>60</td><td>En<sub>89</sub>FS<sub>11</sub></td><td>+at atmospheric conditions</td></tr><tr><td><strong>Enstatite</strong></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Bailey (1974)</td><td>25</td><td>4.0</td><td>N/R</td><td>N/R</td><td>Added organic acids</td></tr><tr><td>Brady and Walther (1989)</td><td>25</td><td>8.0-12.5</td><td>N/R</td><td>N/R</td><td></td></tr><tr><td>Ferruzzi (1993)</td><td>25</td><td>2.0-7.0</td><td>62-84</td><td>En<sub>100</sub></td><td>0.1M buffer solutions</td></tr><tr><td>Halder and Walther (2011)</td><td>24</td><td>8.0-13.0</td><td>80-137</td><td>En<sub>100</sub></td><td></td></tr><tr><td>Luce et al. (1972)</td><td>25</td><td>1.6</td><td>1-4</td><td>En<sub>92.5</sub>FS<sub>7.5</sub></td><td></td></tr><tr><td>Oelkers and Schott (2001)</td><td>28-168</td><td>2.0-10.8</td><td>3-10.5</td><td>En<sub>85</sub>FS<sub>13.6</sub>WO<sub>0.4</sub></td><td></td></tr><tr><td>Schott et al. (1981)</td><td>22-72</td><td>1.0-6.0</td><td>2-40</td><td>En<sub>99.6</sub>FS<sub>0.4</sub></td><td>+Na, Al in mineral structure</td></tr><tr><td>Siegel and Pfannkuch<br>(1984)</td><td>22</td><td>4.0</td><td>29</td><td>En<sub>70</sub>FS<sub>28</sub>WO<sub>1.27</sub></td><td>+Na, Al in mineral structure</td></tr></tbody></table>

N/R = not reported

The far-from-equilibrium dissolution rates of bronzite are shown in **Figure 10D**. The rate parameters for bronzite were obtained by fitting experimentally measured dissolution rates of Grandstaff (1977) and Schott and Berner (1983). The average difference between measured rates and those obtained from the regression equation is 0.17 log units, and 50% of the rates are within 0.08 log units of their corresponding calculated values. Rates calculated using the equations and parameters generated in the present study are slower than corresponding values generated using equations and parameters reported by Palandri and Kharaka (2004) at acidic conditions, as their regression considered only the experimental data of Sverdrup (1990).

**Figure 11** shows a comparison of the calculated far-from-equilibrium dissolution rates for clinopyroxene and orthopyroxene minerals generated from Eq. (7) together with the parameters listed in **Table 2** at 25 and 150 °C. The rates among the different pyroxenes range over roughly an order of magnitude at any single pH and temperature, with enstatite being the most reactive and bronzite the least reactive at acidic conditions, and augite being the least reactive and diopside the most reactive at basic conditions. The dissolution rates of augite appear to be most affected by pH variations. Such differences, however, may be due to minor inconsistencies among the dissolution rate data sets reported in the literature rather than distinct rate behaviors of the different pyroxenes, as these differences are largely within the uncertainties and scatter of the various experimentally measured dissolution rates.
<figure><img src="image_11.png" /><figcaption>**Figure 10:** Far-from-equilibrium dissolution rates of enstatite and bronzite: **A** and **B**) Comparison of measured experimental rates with rates calculated from Eq. (7) together with parameters listed in **Table 2** as a function of pH at the indicated temperatures; **C**) comparison of the enstatite dissolution rates generated from the equations and parameters generated in this study compared with the results of previously published rate equations. **D**) Comparison of bronzite measured experimental rates with rates calculated from Eq. (7) together with parameters listed in **Table 2** as a function of pH at the indicated temperatures. The symbol shape and outline color indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, where black symbols being 25 °C. The shaded regions in the plots illustrate the 95% confidence limits of the corresponding regression fits at 25 °C.</figcaption></figure>

<figure><img src="image_12.png" /><figcaption>**Figure 11:** Comparison of the far-from-equilibrium dissolution rates of pyroxene minerals calculated using Eq. (7) together with the parameters listed in **Table 2** at (A) 25 °C, and (B) 150 °C.</figcaption></figure>
1000

## 3.7 Quartz and other SiO₂ polymorphs

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1003

A large number of studies have reported the dissolution rates of quartz and other SiO₂ polymorphs. A summary of these studies is presented in **Table 9** and **Figure 12**. All silica polymorphs were regressed assuming pH-dependent dissolution rates at acidic and basic conditions.

1004

### 3.7.1 Quartz

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Experimentally measured dissolution rates of quartz have been previously compiled and reviewed in Dove (1994), Bickmore et al. (2006), and Rimstidt (2015). The experimental rate dataset in the present study includes 410 distinct rates presented in 24 publications. This dataset covers a temperature range of 25 to 430 °C and a pH range from 0 to 12.3. Schwartzentruber et al. (1987), Knauss and Wolery (1988), Brady and Walther (1990), and House and Orr (1992) investigated the effect of pH on quartz dissolution rates at 25 °C. Kamiya et al. (1974), Rimstidt and Barnes (1980), Bird et al. (1986), Brady and Walther (1989), Dove and Crerar (1990), Casey et al. (1990), Dove (1994, 1999), Hellmann (1994), Tester et al. (1994), Murphy et al. (1998), and Bickmore et al. (2006) reported quartz dissolution rates at temperatures up to 430 °C, and pH ranging from 0 to 12.3. Rates of quartz dissolution at 25 °C vary from $10^{-13.5}$ mol m⁻² s⁻¹ at pH 6 to up to $10^{-10}$ mol m⁻² s⁻¹ at pH of 12.3, and these rates increase by ~5 orders of magnitude by increasing temperature from 25 to 200 °C at constant pH. Dove and Crerar (1990), Dove (1994), and Dove and Nix (1997) reported on the effect of the presence of aqueous alkali metals on quartz dissolution rates. Kamiya and Shimokata (1974), Wollast and Chou (1988), Dove and Crerar (1990), Bennett (1991), Dove (1994), and Dove and Nix (1997) noted that the presence of aqueous sodium, potassium, magnesium, and/or calcium can enhance quartz dissolution rates by up to two orders of magnitude at temperatures ~25 °C. In contrast, the presence of aqueous divalent or trivalent metals, such as iron or aluminum, tends to decrease quartz dissolution rates as such metals tend to precipitate on the quartz surface in the form of hydroxides or aluminosilicate. The presence of such aqueous cations can slow quartz dissolution rates by up to eight orders of magnitude (Lier et al., 1960; Hurd, 1973; Kamiya and Shimokata, 1974; Bennett, 1991). Additionally, Bennett et al. (1988) and Bennett (1991) reported that the presence of aqueous organic ligands could enhance quartz dissolution rates by up to four orders of magnitude. Due to the considerable effect of added (Na, K, Li)Cl, (Pb, Ca, Ba)Cl₂, NaNO₃, and organic ligands on quartz dissolution rates, these datasets were not considered in the regression calculations. Experimental data affected by the addition of these species are marked in **Figure 12** and **Table S1 in Appendix**. As the regression of data in the present study is limited to temperatures up to 350 °C, the quartz rates reported by Murphy and Helgeson (1989) were also excluded from the regression calculations. Moreover, the study of Kamiya et al. (1974) does not provide the BET surface areas of their quartz; therefore, this dataset is not included in the regression calculation.

1034

1035

**Figure 12A-C** shows a comparison of quartz dissolution rates generated using equations and parameters of this study with corresponding experimentally measured rates. Fifty percent of calculated
rates are within 0.56 log units of their corresponding measured values. Average difference between the logarithm of measured and calculated rates is 0.60. Much of this difference may stem from variations in dislocation density and sample preparation (Blum et al. 1990) or the identity of added acids (Dove, 1994, 1999). Moreover, some of the data presented in Rimstidt and Barnes (1980) and Tester et al. (1994) show scatter greater than one order of magnitude, potentially due to uncertainties in reactive fluid pH. The fit of quartz dissolution rates in this study differs somewhat from previous efforts. In the present study, far-from-equilibrium quartz dissolution rates were assumed to be composed of two distinct trends for acidic and basic conditions. In contrast, Knauss and Wolery (1988) and Tester et al. (1994) assumed the rates at acidic conditions were pH-independent, while Grigsby (1989) and Brantley et al. (2008) suggested pH-dependent dissolution at acidic conditions. This latter conclusion is consistent with the results of Pokrovsky et al. (2006) who successfully described measured quartz dissolution rates assuming these were controlled by a >SiOH₂⁺ surface species. The rates generated by the regression calculation in this study agree well with the corresponding regressions of Grigsby (1989) and Brantley et al. (2008).

<table><caption>**Table 9: Sources of experimentally measured silica polymorph dissolution rates considered in this study.**</caption><thead><tr><th>Reference</th><th>T<br>°C</th><th>pH</th><th>Comments</th></tr></thead><tbody><tr><td colspan="4"><strong>Quartz</strong></td></tr><tr><td>Bennett (1991)</td><td>25</td><td>1.1-7.0</td><td>+NaCl</td></tr><tr><td>Bennett et al. (1988)</td><td>25-70</td><td>1.1-7.0</td><td>+NaCl</td></tr><tr><td>Berger et al. (1994)</td><td>25-300</td><td>1.6-6.5</td><td>+NaCl, PbCl<sub>2</sub>, Pb(NO<sub>3</sub>)<sub>2</sub>, NaNO<sub>3</sub></td></tr><tr><td>Bickmore et al. (2006)</td><td>89-200</td><td>8.2-11.3</td><td>+NaNO<sub>3</sub></td></tr><tr><td>Blake and Walter (1999)</td><td>70</td><td>6.0</td><td>+Organic acids, NaCl</td></tr><tr><td>Blum et al. (1990)</td><td>80</td><td>5.7</td><td>Effect of heterogeneities in mineral structure</td></tr><tr><td>Bolt (1957)</td><td>25</td><td>4.0-12.3</td><td></td></tr><tr><td>Casey et al. (1990)</td><td>25-70</td><td>3.0</td><td>Added 0.001 M NaCl</td></tr><tr><td>Dove (1994)</td><td>200-300</td><td>1.5-9.1</td><td>+NaCl</td></tr><tr><td>Dove (1999)</td><td>175-290</td><td>5.7</td><td>+Mg, Ca, Na, Ba</td></tr><tr><td>Dove and Crerar (1990)</td><td>200-300</td><td>5.7</td><td>+NaCl, KCl, MgCl<sub>2</sub></td></tr><tr><td>Dove and Nix (1997)</td><td>200</td><td>5.7</td><td>+MgCl<sub>2</sub>, CaCl<sub>2</sub>, BaCl<sub>2</sub>, LiCl, KCl, and NaCl</td></tr><tr><td>Grigsby (1989)</td><td>25</td><td>0.0-4.5</td><td>-</td></tr><tr><td>House and Orr (1992)</td><td>25</td><td>4.4-10.5</td><td>+NaCl, KCl</td></tr><tr><td>Knauss and Copenhaver (1995)</td><td>70</td><td>4.0-9.5</td><td>Effect of malonate</td></tr><tr><td>Knauss and Wolery (1986)</td><td>70</td><td>7.6-11.7</td><td></td></tr><tr><td>Knauss and Wolery (1988)</td><td>70</td><td>1.4-11.8</td><td></td></tr><tr><td>Murphy and Helgeson (1989)</td><td>385-430</td><td>4.8-5.3</td><td></td></tr><tr><td>Pokrovsky et al. (2006)</td><td>25</td><td>0.0-2.9</td><td>+NaNO<sub>3</sub>/HNO<sub>3</sub></td></tr><tr><td>Rimstidt and Barnes (1980)</td><td>105-305</td><td>5.7</td><td>pH not monitored/reported</td></tr><tr><td>Schwartzentruber et al. (1987)</td><td>90</td><td>9.5-11.4</td><td>+NaCl</td></tr><tr><td>Tester et al. (1994)</td><td>25-200</td><td>6</td><td>pH not monitored/reported</td></tr><tr><td>Wollast and Chou (1988)</td><td>25</td><td>1.3-12.3</td><td>+NaCl</td></tr><tr><td colspan="4"><strong>SiO<sub>2</sub>(am)</strong></td></tr><tr><td>Elmer and Nordberg (1958)</td><td>95</td><td>7.0</td><td></td></tr><tr><td>Icenhower and Dove (2000)</td><td>60-250</td><td>5.7</td><td>0-0.15 M NaCl</td></tr><tr><td>Loucaide et al. (2008)</td><td>25</td><td>6.3-8.1</td><td>0-50 % seawater fraction, + NaCl, KCl, MgCl<sub>2</sub>, CaCl<sub>2</sub>; diatom frustules, phytoliths, two diatomaceous lake sediments, a siliceous ooze, diatomite deposit, and a synthetic amorphous silica</td></tr><tr><td>Mazer and Walther (1994)</td><td>40-85</td><td>7.0</td><td></td></tr><tr><td>Niibori et al. (2000)</td><td>33</td><td>13.0</td><td>+NaOH, synthetic SiO<sub>2</sub></td></tr><tr><td>Pokrovsky et al. (2006)</td><td>25</td><td>0-1.92</td><td>Constant IS 1M</td></tr><tr><td>Rimstidt and Barnes (1980)</td><td>25</td><td>7.0</td><td></td></tr><tr><td>Seidel et al. (1997)</td><td>25</td><td>7.0</td><td>Monospheres; +NaCl</td></tr><tr><td>Van Cappellen and Qiu (1997)</td><td>5-35</td><td>6.0-9.0</td><td>Biogenic SiO<sub>2</sub></td></tr></tbody></table>
1050 **3.7.2 Other SiO₂ polymorphs**

1051 Experimentally measured dissolution rates of amorphous SiO₂ have been reported over the
1052 temperature and pH range of 18 to 290 °C and 4 to 9, respectively (Rimstidt and Barnes, 1980; Mazer
1053 and Walther, 1994; Van Cappellen and Qiu, 1997; Pokrovsky et al., 2006). Amorphous silica
1054 dissolution rates in the absence of rate accelerating cations were found to vary from 10⁻¹¹.⁸ mol m⁻² s⁻¹
1055 at pH 6.0 to 10⁻¹⁰.⁴ mol m⁻² s⁻¹ at pH 8.0. Icenhower and Dove (2000) and Loucaide et al. (2008)
1056 reported the dissolution rates of synthetic and biogenic amorphous SiO₂ in aqueous NaCl solutions at
1057 temperatures from 25 to 290 °C. These studies show that amorphous SiO₂ dissolution rates increase
1058 with increasing salinity. Notably, the addition of 0.05 M NaCl to the reactive aqueous solution was
1059 found to increase rates by up to a factor of 21 compared to rates in deionized water (Icenhower and
1060 Dove, 2000), while the apparent activation energy remains unaltered by the presence of these rate
1061 accelerating cations (Icenhower and Dove, 2000). Such observations are coherent with results from
1062 experimental studies describing quartz dissolution in the presence of NaCl (Dove and Crerar, 1990;
1063 Dove, 1994; Dove and Nix, 1997). In all cases, amorphous SiO₂ dissolution rates are independent of
1064 the origin of the silica and method of rate measurement (Icenhower and Dove, 2000).

1065 **Figure 12** compares measured SiO₂ polymorph dissolution rates at 25 °C with corresponding
1066 rates obtained from Eq. (7) and parameters listed in **Table 2**. While there are sufficient measured rates
1067 to quantify relatively precisely quartz dissolution rates over wide ranges of pH and temperature, fewer
1068 dissolution rates have been published on amorphous SiO₂ or cristobalite. It is reasonable to assume,
1069 however, that amorphous silica and cristobalite dissolution rates follow similar trends as quartz,
1070 although the dissolution rates of quartz are ~10 times slower due to differences in surface energy and
1071 mineral structure (Icenhower and Dove, 2000). Therefore, the activation energies and reaction order of
1072 amorphous SiO₂ were assumed to be the same as those for quartz, while the pre-exponential factor for
1073 amorphous SiO₂ at acidic conditions was set to be 10 times faster than that of quartz as suggested in
1074 Icenhower and Dove (2000). Owing to the lack of available experimental data the rates of both forms
1075 of cristobalite, whose crystalline structure consists of Si-O bonds were assumed to be the same as
1076 those of quartz.
1077

1077
<figure><img src="image_13.png" /><figcaption>**Figure 12:** Far-from-equilibrium dissolution rates of SiO₂ polymorphs: **A)** Comparison of 25 °C quartz dissolution rates calculated with parameters regressed in this study as shown with the solid curve with previous regression equations shown in non-solid curves and measured rate data shown as symbols. **B-C)** Comparison of measured experimental quartz dissolution rates shown as symbols with rates calculated using Eq. (7) with parameters from **Table 2** as a function of pH at a temperature range from 25 to 300 °C. **D-E)** Comparison of measured amorphous silica dissolution rates with those calculated from Eq. (7) and parameters from **Table 2** as a function of pH at a temperature range from 25 to 200 °C. The symbol shape and outline color indicate the source of the data, whereas the shading of the symbol indicates the experimental temperature, where black symbols are 25 °C. The shaded regions in the plots illustrate the 95% confidence limits of the corresponding regression fits at 25 °C.</figcaption></figure>

**Figures 12 D and E** show calculated amorphous SiO₂ dissolution rates displayed as a function of temperature and pH compared with experimental data from Rimstidt and Barnes (1980), Mazer and Walther (1994), Van Cappellen and Qiu (1997), Icenhower and Dove (2000), and Pokrovsky et al.
1092 (2006). Fifty percent of the calculated rates are within 0.27 log units of their corresponding measured
1093 rate, with an average difference of 0.30 log units.

1094 **4. Discussion**

1095 This article provides a compilation of experimentally measured dissolution rates and regression
1096 equations describing the dissolution rates of 27 primary silicate minerals. Rates in this study were
1097 normalized to the initial mineral-fluid interfacial surface area measured by the BET technique. As
1098 such, any application of these rates to natural systems must take into account the differences between
1099 BET surface area and that of the natural system and any changes in this surface area over time. This
1100 may depend significantly on the hydrology of the system and the effect of biotic or abiotic mineral
1101 surface coatings. The rate equations generated in this study were added into the thermodynamic
1102 database *carbfix.dat* (Voigt et al. 2018) in the form of RATE blocks. This database can thus be directly
1103 used in the PHREEQC geochemical software (Table 2 and Appendix B) and can be readily adapted
1104 for other software such as TOUGHREACT. However, aqueous solubilities for some of the minerals,
1105 and notably solid solutions including andesine, bytownite, labradorite, oligoclase, ferroactinolite,
1106 riebeckite, glaucophane, augite, and bronzite are missing in the *carbfix.dat* database. This has been
1107 resolved in the version of the kinetic database for PHREEQC by calculating the saturation index of
1108 these phases by assuming the ideal mixing of appropriate endmembers.

1109 **Table 10** provides a summary of the temperature and pH range of the experimental data
1110 considered in the regression calculations of this study. Within the temperature and pH range listed in
1111 this table, the equations and parameters presented in this study provide rates that can be considered
1112 interpolations. It seems reasonable to use the regression equations to estimate the dissolution rates of
1113 the primary silicate minerals beyond these limits, over temperatures ranging from 0 to 300 °C and pH
1114 from 1 to 12. Nevertheless, it should be kept in mind that the likely uncertainties in the rates will
1115 increase as one extrapolates rates beyond the limits of the experimental data.

1116 What is clear when reviewing this effort to create a consistent mineral dissolution rate database is
1117 that, despite decades of experimental studies, large uncertainties remain. A typical difference between
1118 computed and measured rates is on the order of 0.5 log units. The average differences between
1119 measured and calculated rates tend to increase with the number of studies. In addition, effects on rates
1120 other than temperature and pH could be of one order of magnitude or greater. These observations
1121 suggest that there are large uncertainties when attempting to quantify the temporal evolution of any
1122 natural water-rock system. It should also not be overlooked that all rates in this study are normalized
1123 to a water-mineral interfacial surface area. This surface area may be challenging to determine
1124 unambiguously due to preferential fluid flow paths and the opening and closing of fractures in
1125 subsurface rocks. As a result, calculations made using the regression calculations reported in this study
1126 should be considered provisional estimates until a more accurate mineral-fluid database can be
1127 developed.

1128

<table><caption>Table 10: Summary of pH and T conditions for regressed mineral dissolution rates where data were available</caption><thead><tr><th rowspan="2"></th><th rowspan="2"></th><th colspan="2">T (°C)</th><th colspan="2">pH range</th><th rowspan="2">Quality of the fit*</th><th rowspan="2">Comments</th></tr><tr><th>Min</th><th>max</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td rowspan="2">Amphiboles</td><td>Anthophyllite</td><td>25</td><td>100</td><td>1</td><td>12</td><td>0.090</td><td></td></tr><tr><td>Ferroactinolite</td><td>20</td><td>250</td><td>1</td><td>12</td><td>-</td><td>-due to the lack of experimental data ferroactinolite dissolution rates and kinetic parameters (A, E, n) are assumed to equal those of tremolite due to their similar structures and compositions</td></tr><tr><td></td><td>Glaucophane</td><td>25</td><td>25</td><td>2</td><td>12</td><td>0.07</td><td>-the thermodynamics of this mineral was not included in the <i>carbfix.dat</i> database, its stability in the RATE block of the database is based on the ideal mixing of its Na-Mg endmembers</td></tr><tr><td></td><td>Hornblende</td><td>25</td><td>25</td><td>2</td><td>12</td><td>0.13</td><td>-assumed mineral composition of Mg-endmember (Ca<sub>2</sub>(Mg<sub>4</sub>Al)(Si<sub>7</sub>Al)<i>O</i><sub>22</sub>(OH)<sub>2</sub>)</td></tr><tr><td></td><td>Riebeckite</td><td>20</td><td>250</td><td>1</td><td>12</td><td>-</td><td>-the thermodynamics of this mineral is not included in the <i>carbfix.dat</i> database, its stability in the RATE block of the database is based on the ideal mixing of its Ca-Mg endmembers</td></tr><tr><td rowspan="6">Feldspars</td><td>Tremolite</td><td>20</td><td>250</td><td>1</td><td>12</td><td>0.28</td><td>-due to the lack of experimental data, the dissolution rates and kinetic parameters (A, n, E) of this mineral were adopted from tremolite due to their similar structures and compositions</td></tr><tr><td>Andesine</td><td>5</td><td>300</td><td>1</td><td>12</td><td>0.42</td><td>-the thermodynamics for this mineral is not included in the <i>carbfix.dat</i> database, its stability is computed in the RATE block of the database assuming ideal mixing between albite and anorthite</td></tr><tr><td>Anorthite</td><td>5</td><td>300</td><td>1</td><td>12</td><td>0.41</td><td></td></tr><tr><td>Albite</td><td>5</td><td>300</td><td>1</td><td>12</td><td>0.54</td><td></td></tr><tr><td>Bytownite</td><td>5</td><td>300</td><td>1</td><td>12</td><td>0.56</td><td></td></tr><tr><td>K-feldspar</td><td>25</td><td>100</td><td>1</td><td>12</td><td>0.40</td><td>-the thermodynamics for this mineral is not included in the <i>carbfix.dat</i> database, its stability is computed in the RATE block of the database assuming ideal mixing between albite and anorthite</td></tr><tr><td></td><td>Labradorite</td><td>5</td><td>300</td><td>1</td><td>12</td><td>0.55</td><td></td></tr><tr><td></td><td>Oligoclase</td><td>5</td><td>300</td><td>1</td><td>12</td><td>0.50</td><td>-the thermodynamics for this mineral is not included in the <i>carbfix.dat</i> database, its stability is computed in the RATE block of the database assuming ideal mixing between albite and anorthite</td></tr><tr><td></td><td>Sanidine</td><td>25</td><td>100</td><td>1</td><td>12</td><td>-</td><td>-due to the lack of experimental data the rates and kinetic parameters (A, E, n) are adopted from K-feldspar</td></tr><tr><td rowspan="2">Glass</td><td>Basalt</td><td>7</td><td>300</td><td>0</td><td>12</td><td>0.44</td><td></td></tr><tr><td>Rhyolite</td><td>25</td><td>200</td><td>1</td><td>12</td><td>0.22</td><td></td></tr><tr><td rowspan="3">Mica</td><td>Annite</td><td>25</td><td>280</td><td>1</td><td>14</td><td></td><td>-no visible trend between Mg-rich and Fe-rich biotite dissolution</td></tr><tr><td>Biotite</td><td>25</td><td>280</td><td>1</td><td>14</td><td>0.35</td><td>-due to lack of data the kinetic parameters (A, n, E) for annite and phlogopite were set equal to those of</td></tr><tr><td>Phlogopite</td><td>25</td><td>280</td><td>1</td><td>14</td><td></td><td></td></tr></tbody></table>
<table><tbody><tr><td rowspan="4">Olivines</td><td>Muscovite</td><td>25</td><td>250</td><td>1</td><td>12</td><td>0.45</td><td>biotite.</td></tr><tr><td>Fayalite</td><td>25</td><td>25</td><td>0</td><td>12</td><td>0.60</td><td>-due to a lack of experimental data at pH&gt;4.5 and temperature &gt; 25 °C the kinetic parameters (A, E, n) for this mineral was set equal to those of forsterite</td></tr><tr><td>Forsterite</td><td>7</td><td>300</td><td>0</td><td>12</td><td>0.18</td><td></td></tr><tr><td>Larnite</td><td>25</td><td>25</td><td>0</td><td>12</td><td>0.22</td><td>-due to a lack of experimental data at pH&gt;4.5 and temperature &gt; 25 °C the kinetic parameters (A, E, n) for this mineral was set equal to those of forsterite</td></tr><tr><td rowspan="2">Pyroxenes</td><td>Augite</td><td>20</td><td>25</td><td>2</td><td>12</td><td>0.32</td><td>-the thermodynamics for this mineral is not included in the carbfix.dat database; its stability is computed in the RATE block of the database assuming ideal mixing between pyroxene Ca-Fe-Mg endmembers</td></tr><tr><td>Bronzite</td><td>1</td><td>100</td><td>2</td><td>12</td><td>0.08</td><td>-the thermodynamics of this mineral is not included in the carbfix.dat database; its stability is computed in the RATE block of the database assuming ideal mixing between pyroxene Ca-Fe-Mg endmembers</td></tr><tr><td rowspan="5">SiO<sub>2</sub><br>polymorphs</td><td>Diopside</td><td>25</td><td>50</td><td>2</td><td>12</td><td>0.19</td><td></td></tr><tr><td>Enstatite</td><td>25</td><td>100</td><td>2</td><td>12</td><td>0.39</td><td></td></tr><tr><td>Cristobalite<br>(alpha)</td><td>1</td><td>25</td><td>1</td><td>12</td><td>-</td><td>-due to lack of experimental data, reaction orders are assumed to be the same as those of amorphous silica</td></tr><tr><td>Cristobalite<br>(beta)</td><td>1</td><td>25</td><td>1</td><td>12</td><td>-</td><td></td></tr><tr><td>Quartz</td><td>25</td><td>300</td><td>0</td><td>12</td><td>0.56</td><td></td></tr><tr><td></td><td>SiO<sub>2</sub>(am)</td><td>25</td><td>200</td><td>1</td><td>12</td><td>0.27</td><td>-due to lack of data, reaction orders and pre-exponential factors are derived based on the assumption that rates for amorphous silica are ~ ten times faster than those of quartz, as suggested in Icenhower and Dove (2000)</td></tr></tbody></table>

* Median of residuals in log units

1129

## 5. Conclusions

This study is the first of at least three contributions generating a comprehensive and internally consistent database of the dissolution rates of the rock-forming minerals. It is anticipated that the resulting database, made available in the readily applied form will provide a benchmark for comparing directly the results of temporal geochemical modeling calculations performed using various reactive transport algorithms in a variety of natural and geoengineered systems. Despite these efforts, considerable uncertainties remain. At present, the ability to quantify in a consistent manner the effects of fluid ionic strength, the presence of organic and inorganic aqueous species, the biotic activity, mineral coatings, and mineral surface area in natural systems is hindered by lack of consistent observations and/or theories. Nevertheless, it is anticipated that the compilation of rates presented in these studies, together with the comparison of computational results with both laboratory experiments and field observations, will lead to the continuous improvement of our ability to describe accurately geochemical processes as a function of distance and time.

## 1143 Acknowledgments
1144 This research has been carried out within the CarbFix2 and GECO projects that have received funding from the European Union's Horizon 2020 research and innovation program under grant agreements No 764760 and number 818169, respectively. EHO would like to dedicate this work to the memory of William M. Murphy, who was both a trusted friend and one of the pioneers in interpreting and quantifying reaction rates through his pioneering work at Prediction Central, Berkeley, California, in the 1980s.

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