Experimental determination of plagioclase dissolution rates as a function of its composition and pH at 22°C

Abstract The steady-state, far-from-equilibrium dissolution rates of nine distinct plagioclases ranging in composition from An2 to An89 were measured in mixed flow reactors at 22 ± 2 °C and pH from 2 to 11. The dissolution rates of all plagioclases based on silica release show a common U-shaped behaviour as a function of pH, where rates decrease with increasing pH at acid condition but rise with increasing pH at alkaline conditions. Consistent with literature findings, constant pH plagioclase dissolution rates increase with increasing anorthite content at acidic conditions; measured anorthite dissolution rates are ∼2.5 orders of magnitude faster than those of albite at pH ∼2. Perhaps more significantly, rates are independent of plagioclase composition at alkaline conditions. Interpretation and data fitting suggests that plagioclase dissolution rates are consistent with their control by the detachment of Si-rich activated complexes formed by the removal of Al from the mineral framework. Taking account of this mechanism and transition state theory yields equations describing plagioclase dissolution rates (r+) as a function of both the mineral and aqueous fluid compositions found in natural Earth surface systems. For pH ⩾ 6 rates are consistent with Log ( r + / ( mol / cm 2 / s ) ) = 0.35 Log ( a H + 3 / a Al 3 + ) - 11.53 and for pH  Log ( r + / ( mol / cm 2 / s ) ) = n acid Log ( a H + 3 / a Al 3 + ) + 0.033 An % - 14.77 where An% represents the percent anorthite in the plagioclase solid solution, ai corresponds to the activity of the ith aqueous species, and nacid is given by n acid = 0.004 An % + 0.05 .


THEORETICAL BACKGROUND
The standard state adopted in this study is that of unit activity of pure minerals, the plagioclases, and H 2 O at any temperature and pressure. For aqueous species other than H 2 O, the standard state is unit activity of the species in a hypothetical 1 molal solution referenced to infinite dilution at any temperature and pressure. The activity of plagioclase surface species was assumed equal to their mole fraction. All thermodynamic calculations reported in this study were performed using the PHREEQC computer code (Parkhurst and Appelo, 1999) together with its llnl.dat database to which thermodynamic data consistent with phase relations observed in altered basaltic rocks reported by Gysi and Stefánsson (2011) have been added for magnesite, siderite, thomsonite, scolecite, mesolite, laumontite, heulandite, analcime, Ca-stilbite, Ca-mordenite, Ca-clinoptilolite, Fe-celadonite, antigorite, amorphous SiO 2 , amorphous FeOOH, amorphous Al(OH) 3 , gibbsite, allophane, and imogolite. The solubilities and fluid saturation indexes of the various plagioclase feldspars were determined using equations and parameters reported by Arnorsson and Stefansson (1999) who generated effective equilibrium constants for plagioclase dissolution reactions consistent with the assumption of unit activity of the solid regardless of its compostion. Although some uncertainties are associated with this approach, the reactive fluids in this study were all highly undersaturated with respect to the dissolving plagioclase, such that uncertainties in the fluid saturation state with respect to plagioclase will negligibly effect the interpertations presented below.
Plagioclase dissolution at acid conditions can be represented by the reaction: where x denotes the mole fraction of Na in the plagioclase such that when x = 1, Eq. (1) corresponds to the dissolution of pure albite and when x = 0, Eq. (1) corresponds to the dissolution of pure anorthite. Taking account of the standard state adopted by Arnorsson and Stefansson (1999), the law of mass action for Eq. (1) can be written: Ca þ2 a Al þ3 a where K Plag stands for the equilibrium constant of Eq. (1) and a i represents the activity of the subscripted aqueous species. The chemical affinity for reaction (1), A Plag can be expressed as Ca þ2 a Al þ3 a SiO where R designates the gas constant, and T signifies absolute temperature.
Within the context of Transition State Theory, surface reaction controlled dissolution rates can be considered to be the difference between the forward rate (r + ) and the reverse rate (r À ) such that: Taking account of the law of detailed balancing, it can be shown that Eq. (4) is equivalent to Helgeson, 1977, 1982;Lasaga, 1981;Helgeson et al., 1984): where r 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 rate. Experimental evidence suggests that the value of r in Eq. (5) is 1 for quartz (Berger et al., 1994) and 3 for the alkali-feldspars (Gautier et al., 1994;Oelkers and Schott, 1995). The form of Eq. (5) is such that overall rates (r) equal forward rates (r + ) when A ) rRT. The dissolution rates in the present study were measured at far-from-equilibrium conditions, that is where A ) rRT. At these conditions r À ( r + and thus r % r + . Dissolution rates in this study are thus symbolized r + . Such experimental results can be used to assess the effect of aqueous solution composition on forward dissolution rates independently from the effects of chemical affinity (Oelkers, 2001). Within the formalism of Transition State Theory, r + is proportional to the concentration of an activated complex (Eyring, 1935): where k + refers to a rate constant and [a] designates the concentration of the activated complex. The concentrations of activated complexes for mineral dissolution have been demonstrated to be proportional to the concentration of rate controlling surface complexes in accord with (c.f. Schott et al., 2009): where K a represents an equilibrium constant and [É ] denotes the concentration of the rate controlling surface complex. Combining Eqs. (6) and (7) leads to: A number of past studies have attempted to describe the dissolution rates of the plagioclase feldspars assuming that their dissolution is controlled by two or more distinct activated complexes formed by the adsorption or desorption of protons, water, or hydroxide ions on the mineral surface (e.g. Chou and Wollast, 1984;Murphy and Helgeson, 1987;Chen and Brantley, 1997;Bandstra and Brantley, 2008). Such an approach yields a rate equation that is the sum of two or more linear functions of pH (e.g. Sverdrup, 1990;Palandri and Kharaka, 2004;Marini, 2006). An alternative approach stems from the observation that multi-oxide silicate mineral dissolution occurs via a series of metal-proton exchange reactions (e.g. Gautier et al., 1994;Oelkers et al., 1994Oelkers et al., , 2009Carroll and Knauss, 2005;Dixit and Carroll, 2007). The rate at which each metal-oxygen bond breaks via these reactions depends on the relative strength of the corresponding metal-oxygen bond. This mechanism leads to the rate equation given by (c.f. Oelkers, 2001): the dissolution rates of the alkali rich plagioclases (<An 65 ) are proportional to the concentration of a Si-rich surface complex formed by the Al-proton exchange reactions leading to the following rate equation: The degree to which this equation can describe the dissolution rates as a function of pH and plagioclase composition will be explored below. Note that the combination of Eqs.
(5), (9), (10), and (11) yields a combined rate law that depends on (1) the chemical affinity of the fluid with respect to the dissolving mineral, (2) the fluid pH, and (3) the aqueous activity of the metal ions involved in the dissolution mechanism. The effect on rates of chemical affinity itself is limited to close to equilibrium conditions (r is within 5% of r + when A > 3rRT), so at 25°C and a r = 3 (Gautier et al., 1994), plagioclase dissolution rates are essentially independent of the reactive fluid chemical affinity when A exceeds $6 kJ/mol. Nevertheless, as chemical affinity can be a function of the aqueous activities of metals involved in the dissolution mechanism, rates can appear to depend on A at far greater affinities (see Oelkers et al., 1994;Oelkers and Schott, 1995). This factor has lead to significant confusion in the literature on the role of chemical affinity on reaction rates and the application of Transition State Theory to describe the kinetics of dissolving silicate minerals (e.g. Burch et al., 1993;Hellmann and Tisserand, 2006). Description of the dissolution behaviour of the intermediate plagioclases is confounded by their structure. Exsolution on the micro scale is common in plagioclase feldspars. It can consist of fine albite-rich and anorthite-rich intergrowths (Grove, 1977;Holdren and Speyer, 1987;Inskeep et al., 1991). Intergrowths are most common in three compositional ranges, An2-16, An43-58, and An67-90, named peristerite, Bøgghild, and Huttenlocher intergrowths, respectively (Smith and Brown, 1988). These heterogeneities are commonly not detectable by optical techniques or SEM, yet could influence the dissolution kinetics of the plagioclases. Oxburgh et al. (1994) suggested that heterogeneities including zoning and intergrowths, may lead to sig-nificant variations in the dissolution rates of plagioclases with similar bulk composition. Such ambiguities have led several researchers to assume that the dissolution rates of intermediate feldspars can be estimated by the sum of contributions of two distinct phases, e.g. albite and anorthite (White et al., 2005). The validity of such assumptions will be assessed below through the interpretation of dissolution rates obtained over the full range of feldspar compositions.

Plagioclase characterization and preparation
The plagioclase feldspars used in this study were collected from various locations; the sample localities are listed in Table 1. Most were purchased from Ward's Science. The most anorthite rich plagioclase (An89) was acquired from the Smithsonian Institution. One bytownite was collected from an anorthosite intrusion located on the Hrappsey Islands in Breidafjö rður, Western Iceland. The plagioclases were chosen to represent the entire plagioclase compositional series from albite to anorthite. All of the plagioclases were of metamorphic origin other than the anorthite and Hrappsey bytownite, which were of igneous origin.
The chemical composition of the plagioclase samples was determined from standard wavelength dispersive techniques using a JEOL Superprobe JSL 8200 electron microprobe located at the GET/CNRS in Toulouse, France. These analyses were performed using an acceleration voltage of 15 kV, a beam current of 15 nA, and a beam diameter of 2 lm. Natural and synthetic minerals and glasses were used as standards to check for potential drift. The anorthite percentage of each plagioclase and its corresponding chemical formula are given in Table 1. The resulting chemical composition of each plagioclase as oxide percent is given in Table 2.
All plagioclase samples were dried at room temperature for several days before being crushed with a hammer and then an agate mortar. The ground material was dry sieved to obtain the 45-125 lm size fraction. This size fraction was Table 1 Origin, chemical composition, and specific surface area of the plagioclases used in this study.

Origin
Chemical analysis Surface Area (cm 2 /g) General formula first gravitationally settled to remove fine particles and subsequently cleaned ultrasonically 5 times in de-ionized water and then in acetone. The resulting powder was oven-dried at 50°C for several days. SEM images of some of the result-ing powders are shown in Fig. 1. The surfaces are essentially free of fine particles. The surface area for each initial cleaned powder was determined via 11 point krypton adsorption using a Quantachrome Gas Sorption system Table 2 Chemical composition of the plagioclases used in this study as determined by microprobe analysis.  and the BET method (Brunauer et al., 1938). The surface area for each plagioclase is given in Table 1. The uncertainty of these measurements is estimated to be ±10%.

Experimental methods
Plagioclase dissolution experiments were performed at pH from 2 to 11 in two distinct reactor systems. The first is a Parre mixed flow reactor system, shown in Fig. 2. This system consists of a 300 mL titanium reactor with external temperature and stirring controls. Reactive fluids were injected into this reactor via a High Pressure Liquid Chromatography (HPLC) pump allowing a constant flow rate from 2 to 3 g/min. The fluid passed through a 0.2 lm titanium filter while leaving this reactor system. A detailed description of this reactor system has been provided by Gudbrandsson et al. (2011). The second reactor system consisted of 250 mL polyethylene reactors containing a Nalgenee floating stirring bar and placed in a temperature controlled water bath. Reactive fluids were injected into this reactor using a peristaltic pump. The reactive fluid passed through a 2 lm filter while exiting this reactor system. This reactor system has been described in detail by Stockmann et al. (2011). All inlet fluids were comprised of deionized water and Merck analytical grade NH 4 Cl, HCl, and NH 4 OH. The ionic strength of all inlet fluids was 0.01 mol/kg; the compositions of these fluids are listed in Table 3. The alkaline inlet fluids were initially bubbled with N 2 and then continuously kept under a N 2 atmosphere to prevent CO 2 dissolution into the fluid. The lack of significant CO 2 dissolution into the fluid was verified by regular analysis of reactive fluid pH. Each reactor was cleaned thoroughly, assembled, and run for at least 24 h with deionized water and then for another 24 h with the inlet fluid to rinse the tubing and clean the reactor prior to each experiment. At the end of this cleaning cycle an outlet fluid sample was taken for chemical analysis and used as a blank.
Experiments were initiated by placing between 3 and 4 g of dry plagioclase powder into the reactor. The reactor was then filled with the initial inlet fluid and sealed. Reactive fluid flow, temperature, and stirring rates were adjusted to desired settings. The fluid/plagioclase powder mixture was  continuously stirred at 350-400 rpm in both reactor systems. Gislason and Oelkers (2003) observed that rotation speeds in excess of 325 rpm were sufficient to maintain surface reaction control of basaltic glass dissolution at pH 3.3. Experiments performed in the polyethylene reactors were run in series. An experimental series consisted of several distinct steady-state rate measurements performed on a single plagioclase powder at several different pH. In each series, a single inlet fluid was pumped through the reactor for 75 h. After 75 h, the inlet fluid was replaced by the next inlet fluid in the series. In each experimental series, the initial inlet fluid had a circum-neutral pH and subsequent inlet fluids were progressively more acidic or more alkaline. Note that experiments in this study were not performed at 5.5 < pH < 8 in an attempt to limit secondary phase precipitation, and to avoid the use of pH buffers that might affect rates. Each experimental series is distinguished by the prefix on the experiment number. For example, series 'Ab-acid' consists sequentially of experiments Ab-acid-5, Ab-acid-4, Ab-acid-3, etc., where the last number denotes the approximate inlet fluid pH. Each experimental series was stopped before 5% of the initial mineral was dissolved. Further details of the experiments performed in each series are listed in Table 4. Experiments performed in the titanium reactors were run individually. In these individual experiments, a mineral powder was placed in the reactor and a reactive fluid of a single composition was passed through the reactor for at least 250 h. Once each individual experiment was completed, the fluid and remaining mineral was removed and the reactor cleaned in advance of initiating  Table 5. Outlet fluids were regularly sampled and filtered using 0.2 lm cellulose acetate filters. Part of the fluid was used to measure pH at 22°C using a Eutech InstrumentsÓ Cyberscan pH 310 pH meter coupled to a Eutech Instru-mentsÓ electrode with a 3 M KCl outer filling solution. The electrode was calibrated with NBS standards at pH 4.01, 7, and 10 with an average error less than 0.05 pH units. The other part of the sampled reactive fluid was acidified with concentrated supra-pure HNO 3 prior to analysis for Si, Mg, Na, Al, Fe, and Ca by Spectro Cirios Vision Inductively Coupled Plasma Optical Emission Spectrometry (ICP-OES), with detection limits for Si of 25 ppb, for Al of 3 ppb, for Ca of 1, and for Na of 2 ppb. The uncertainties on these measurements, based on reproduced analyses are estimated to be ±10%.

RESULTS
In total, 71 distinct plagioclase dissolution experiments were performed. Steady state reactive fluid Si, Al, Ca, and Na concentrations of all experiments performed in this study are reported in Tables 4 and 5. Measured outlet fluid Si and Al concentrations were used to calculate dissolution rates using where c i represents the concentration of the ith element in the outlet fluid, F stands for the fluid flow rate, A refers to the specific surface area of the plagioclase prior to the experiment, and m denotes the mass of plagioclase in the reactor at the beginning of the experiment. Note that as the inlet fluids in all experiments were Si and Al free, c i in Eq. (12) corresponds to the change in the fluid concentration of these elements between the inlet and outlet fluid. Mass balance calculations indicate that the mass of plagioclase in the reactor changed by no more than 4% during the experiments, so the mass in Eq. (12) was not adjusted for loss by dissolution. Rates were not calculated based on measured steady state Na and Ca concentrations, because many of these concentrations were below the analytical detection limit, and as these metals reside outside the Al-Si framework of the plagioclase their release rate might not reflect the overall mineral dissolution rate. The temporal variation of measured rates based on Si release during all experiments can be seen in Annex A, corresponding rates based on Al are presented in Annex B. It can be seen that measured rates based on Al and Si tend towards steady-state over the course of most experiments. Steady-state is assumed if the rate calculated for three consecutive fluid samples taken at least 3 residence times apart from one another are equal within experimental uncertainty. The residence time is defined as the volume of the reactor divided by the reactive fluid flow rate. Rates obtained from experiments that adhere to this steady-state criterion are noted in bold font in Tables 4 and 5.
Outlet fluid compositions were used to calculate the saturation state of primary and potential secondary mineral phases in all experiments. The results of these calculations for the primary and selected potential secondary minerals are shown in Annex C. The fluid compositions of all experiments were strongly undersaturated with respect to those minerals in the adopted revised llnl database but not included in Annex C. The outlet fluids were calculated to be undersaturated with respect to all primary and potential secondary minerals apart from the fluids at pH 5-9, which were calculated to be supersaturated with respect to the Al-oxyhydroxides gibbsite, boehmite, and diaspore. No secondary minerals, however, were detected by SEM-EDS analysis on the recovered solids following the experiments. Nevertheless, as described below, the precipitation of secondary Al-rich phases is consistent with the observed Al/ Si release rates of experiments performed at basic pH.
Steady-state rates based on Si release obtained from the experiments performed in series and individually are shown as a function of pH in Fig. 3. In general, rates based on Si release decrease with increasing pH at acid pH and rise with increasing pH at basic pH. At acid conditions, rates increase substantially with the An content of the plagioclase, whilst there is little to no dependence of rates on An content at basic conditions. Plagioclase dissolution rates based on Al release are illustrated as a function of pH in Fig. 4. These rates exhibit similar pH dependence as rates based on Si release with the exception of the high pH rates obtained from the individual experiments which appear not to increase with increasing pH. A possible explanation for this observation is the precipitation of Al-rich secondary phases during the high pH experiments. The possibility that such phases precipitate during some experiments is supported by the computed saturation states listed in Annex  C. Diaspore and boehmite are computed to be close to equilibrium or supersaturated in many of the high pH experiments. Oxburgh et al. (1994) suggested that plagioclase dissolution rates decrease with time, and distinct apparent steadystate conditions are attained at distinct time intervals. Here we repeated several dissolution experiments over longer time periods to assess this possibility. Rates obtained from the experimental series, tend to agree within uncertainty with those obtained from the individual experiments performed over at least 250 h. Nevertheless, rates obtained from the individually run experiments tend to exhibit more scatter and tend to be less systematic than those obtained from the experiments run in series (see Figs. 3 and 4).
The stoichiometry of Al versus Si release at the end of all experiments can be assessed in Fig. 5 and Tables 4 and 5, which shows the ratio of steady-state plagioclase dissolution rates generated from Al release to those generated from Si release. In general, the experiments exhibit a systematic trend; the release rate of Al versus Si is within 0.3 log units of stoichiometric at acidic pH. In contrast, Al release rates generally become slower than those of Si at basic conditions. This observation is consistent with the possibility that one or more Al-rich secondary phases precipitated during some of the experiments performed at alkaline conditions.
The variation of plagioclase dissolution rates measured in the serial experiments as a function of their composition are illustrated in Fig. 6. Rates appear to be independent of plagioclase composition at pH P 5. At pH $4, anorthite dissolution rates are approximately one order of magnitude faster than those of albite. This rate difference increases with decreasing pH; at pH $2 anorthite dissolution rates are approximately two and one half orders of magnitude faster than those of albite. Moreover, the bulk of the increased rates with anorthite content occur in the anorthite-rich plagioclases. This observation is consistent with the conclusions of Blum and Lasaga (1988) who suggested that the mechanism of plagioclase dissolution changes at an An content of $70% due to the increase in the percentage of Al in its tetrahedral framework. At this concentration, it becomes possible to break this tetrahedral structure without breaking Si-O bonds (c.f. Blum and Lasaga, 1988;Oelkers and Schott, 1995).

Comparison with past work
This study builds upon past work on the experimental characterization of plagioclase dissolution rates at ambient temperatures. Most past studies on the dissolution rates of plagioclases have been performed on the albite end-member (e.g. Wollast, 1984, 1985;Knauss and Wolery, 1986;Holdren and Speyer, 1987;Blum and Stillings, 1995;Stillings and Brantley, 1995;Stillings et al., 1996). Of these studies, Chou and Wollast (1985) and Knauss and Wolery (1986) published measured albite dissolution rates as a function of pH from acidic to alkaline conditions. Other studies have focused on the effect of the presence of alkali metals (Stillings and Brantley, 1995) and organic ligands (Franklin et al., 1994;Blake and Walter, 1996;Welch and Ullman, 1996;Ullman and Welch, 2002) on albite dissolution rates. A detailed summary of these rates is provided by Blum and Stillings (1995), Brantley (2003Brantley ( , 2008, and Ganor et al. (2009). Some of these rates are illustrated in Fig. 7. In the absence of complexing ligands, the pH variation of albite dissolution rates at constant temperature exhibits a U-shaped dissolution behaviour, where rates decrease with increasing pH at acid conditions and rise with increasing pH at alkaline conditions. Note that there are significant inconsistencies among rates measured at identical conditions in different laboratories. For example, rates reported by Chou and Wollast (1985) are from 0.5 to 1.5 orders of magnitude higher than corresponding rates reported by Knauss and Wolery (1986).
Studies on intermediate feldspars have, as for other plagioclases, mainly focused on characterising rates at acid conditions (e.g. Mast and Drever, 1987;Casey et al., 1988Casey et al., , 1989aStillings, 1994, 1996;Fig. 5. Ratio of plagioclase steady-state dissolution rates based on Al versus those based on Si release. The solid line corresponds to stoichiometric dissolution. Open symbols represent rates obtained from experiments run in series for approximately 75 h, whereas filled symbols correspond to rates determined from individual experiments that ran for minimum of 250 h. The analytical uncertainties on the ratios are estimated to be 0.02 log units and are within the symbols in the figures.  Oxburgh et al., 1994;Stillings and Brantley, 1995;Stillings et al., 1996;Yang et al., 2014a,b). Some of these studies have been aimed at exploring the effects on rates of organic ligands (Mast and Drever, 1987;Welch and Ullman, 1993;Stillings et al., 1996;Oelkers and Schott, 1998) and alkali metals (Muir and Nesbitt, 1991;Stillings and Brantley, 1995). Plagioclase dissolution rates at alkaline conditions are rare in the literature; one exception is Casey et al. (1988) who reported some plagioclase dissolution rates at pH 12. Among the most comprehensive studies is that of Oxburgh et al. (1994) who reported the dissolution rates of several plagioclases as a function of pH at acid and neutral conditions. Some of these rates are illustrated in Fig. 7b and c. Similar to rates obtained in this study, plagioclase rates increase with increasing An content at acidic solutions.
Far fewer studies have been published on the dissolution rates of anorthite-rich plagioclase than on the albite end member. Anorthite dissolution rate measurements have only been reported at acid to neutral pH (pH < 7.8). Selected published anorthite dissolution rates are shown as a function of pH in Fig. 7d. Steady-state anorthite dissolution rates decrease with increasing pH at acid to neutral conditions. Rates reported by Holdren and Speyer (1987) are in close agreement with those from Amrhein and Suarez (1992) and Oelkers and Schott (1995). Note that Oelkers and Schott (1995) extrapolated the 25°C rates from their reported rates at 45°C. The rates reported by Amrhein and Suarez (1992) at neutral conditions scatter over approximately two orders of magnitude.
The rates obtained in this study are compared with some of the rates available in the literature in Fig 7. Albite dissolution rates obtained in this study are 0.5-1 orders of magnitude faster than corresponding rates reported by Chou and Wollast (1985), and 1-2 orders of magnitude faster than corresponding rates reported by Knauss and Wolery (1986). Similarly, rates obtained for the intermediate plagioclases in this study are 0.5-1 order of magnitude faster than those of Oxburgh et al. (1994). The major difference between rates obtained in this study for anorthite and those obtained by Amrhein and Suarez (1992) is at intermediate to basic pH. Rates in this study increase with pH at basic conditions, whereas those of Amrhein and Suarez (1992) suggest these rates decrease continuously with increasing pH.
The distribution of data points in Fig. 7 demonstrates significant inconsistencies among the various plagioclase dissolution rate data sets. There are numerous potential explanations for these inconsistencies. First, various experimental studies have been performed over different durations. Experiments in this study were performed from 75 to 600 h, those of Chou and Wollast (1985) were performed over 280 h on average, those of Knauss and Wolery (1986) were performed over $1200 h, those of Oxburgh et al. (1994) were performed over 500-2000 h, and those of Fig. 7. Comparison of measured plagioclase dissolution rates determined in this study with selected values of plagioclases with comparable chemical compositions reported in the literature. Open symbols represent rates obtained from experiments run in series for approximately 75 h, whereas filled symbols correspond to rates determined from individual experiments that ran for more than 250 h. The error bars correspond to 2r of rates based on measured Si concentration. Amrhein and Suarez (1992) were performed over 19, 000-29,400 h. Oxburgh et al. (1994) suggested that plagioclase dissolution rates decrease with time during laboratory experiments. Some of this effect might be due to the formation of non-stoichiometric layers on the surfaces of the dissolving feldspars (c.f. Chou and Wollast, 1985) or by a decrease in the reactive surface area as the mineral dissolves (c.f. Kö hler et al., 2005). Second, differences in measured rates can stem from slight differences in the composition of the plagioclase samples. The albite used by Chou and Wollast (1985) and Knauss and Wolery (1986) was collected from Amelia, Virginia, USA, and had an An content of 1.5 to 3% whereas that used in the individual experiments reported in this study was collected from Ontario, Canada and had 9% An content. Third, rates can be affected significantly by the degree of order of the Si-Al-O framework in the plagioclase structure (e.g. Yang et al., 2014b); Lü ttge (2007, 2009a) report that highly disordered albite should have dissolution rates 8 times faster than that of fully ordered albite. Fourth, grain size can play a role; Fischer et al. (2012) and Zhang and Lü ttge (2009b) argued that plagioclase grain size can strongly influence measured surface area normalized rates. Fourth, differences in sample preparation can alter dramatically plagioclase dissolution rates; Beig and Lü ttge (2006) observed that sample preparation can alter albite dissolution rates by up to 2 orders of magnitude. Fifth, inconsistencies can be attributed to differences in mineral composition, mineral micro structure, and the presence of exsolution boundaries, (e.g. Speyer, 1985, 1987;Inskeep et al., 1991). The significant scatter and large number of factors influencing plagioclase dissolution kinetics suggests that laboratory measured rates in these and other laboratory studies might only provide a first approximation to the reactivity of plagioclase in natural water-rock systems.

Stoichiometry of metal release during plagioclase dissolution
Silicon appears to be released faster than Al from all plagioclases at pH > 9 as seen in Fig. 5. A preferential release of Si suggests the formation of an Al-rich surface layer or secondary phase during these experiments. The reactive fluids are close to equilibrium or supersaturated with respect to gibbsite and diaspore in these experiments. No secondary phases are evident in SEM images of the grains recovered after each experiment. Nevertheless, as the Si to Al release ratios suggest that Al was retained in the solid phase, and as Al-hydroxide phases readily precipitate from supersaturated aqueous solutions (e.g. Hellmann, 1995;Hellmann and Tisserand, 2006), their precipitation during the experiments at basic conditions cannot be excluded. The formation of Al-rich phases may be promoted in cases where the bulk fluid is somewhat undersaturated with respect to such phases along exsolution boundaries where slow transport rates may increase fluid saturation states locally (i.e. Hellmann, 1995;. An alternative explanation for the retention of Al in the solid phase during plagioclase dissolution at basic conditions is preferential Si release during the dissolution experiment. This explanation, however, is inconsistent with the results of albite surface titration experiments that indicate that Al is preferentially removed from albite during its initial dissolution (c.f. Oelkers et al., 2009), and the observation that the relative Si to Al release rate tends to be independent of time in most of the experiments performed at basic conditions in this study.
Smaller non-stoichiometric element release rates are evident at other pH conditions. These observations could stem from the dissolution or precipitation of minor Al-bearing phases either originally present in the solids or formed during some of the experiments. For example, the experiments performed in series were initiated in reactive fluids at near to neutral conditions and subsequent reactive fluids were either more acidic or more basic. In many cases, the original near neutral reactive fluids were at equilibrium or slightly supersaturated with respect to Al-hydroxide phases, which could have precipitated in these fluids then redissolved when the fluid became more acidic or basic. As such it is likely that measured Si release rates are more representative of the plagioclase dissolution process than the measured Al release rates.

Quantitative description of plagioclase dissolution rates as a function of anorthite content and aqueous fluid composition
The creation of a consistent set of dissolution rates spanning a wide range of plagioclase compositions and pH enables retrieval of equations that can be used to estimate these rates in reactive transport algorithms. A critical question is determining the degree to which plagioclase dissolution occurs via the dissolution of a single phase or two distinct end members, one albite and another anorthite rich. The latter assumption has been adopted in a number of geochemical modelling studies (e.g. Johnson et al., 1998;Gaus et al., 2005;Xu et al., 2005), and assumes that the dissolution rates of intermediate plagioclase can be assumed to be a linear combination of its end-members. A similar approach was used to describe the dissolution behaviour of crystalline basalts (Gudbrandsson et al., 2011). Plagioclase dissolution rates at acidic conditions, as shown in Fig. 6, however, exhibit a strongly non-linear dependence on plagioclase composition, where rates increase dramatically with composition close to the anorthite end-member. In contrast, the rates obtained for the An18 sample are similar to that measured for the An2 sample. This strong nonlinearity would only be consistent with the possibility that plagioclase dissolved as two distinct end-member phases if the relative surface area of the two distinct end-members varied hugely with plagioclase composition. As such, rates in the present study were quantified assuming plagioclase dissolves as a single homogeneous phase. It should nevertheless be emphasized that the observed non-linear variation of measured plagioclase dissolution rates as a function of composition does not preclude the presence of exsolution textures of intermediate plagioclase composition in some of the solids considered in this study.
Logarithms of measured plagioclase dissolution rates based on Si release are depicted as a function of the logarithm of the aqueous species activity ratio ða 3 H þ =a Al 3þ Þ in Fig. 8. Several observations are apparent in this figure. First, the dissolution rates of the anorthite-rich feldspars plot as a single linear function of ða 3 H þ =a Al 3þ Þ , consistent with Eq. (11) at all pH. It can be seen that the rates of all the plagioclases at basic conditions are consistent with those of the plagioclase An89, for which a linear regression through the data points has been added to Fig. 8b. The slope of the line passing through the anorthite-rich rates yields a value of n of approximately À1/3, which itself is equal to that reported for albite at 150°C and pH 9 by Oelkers et al. (1994). Rates at acidic conditions depend strongly on plagioclase composition, where the absolute values of the reaction order term n decreases systematically with decreasing anorthite component. A similar decrease of the reaction order n at acidic conditions with increasing Si content of a solid was reported for the case of natural glasses by Wolff-Boenisch et al. (2004). To a first approximation, the slopes describing plagioclase steady-state dissolution rates at acid conditions in Fig. 8a converge at a single point of log(r + /(mol/cm 2 /s)) % À15.3 and logða 3 H þ =a Al 3þ Þ % À9:8. An equation describing plagioclase dissolution rates at 22°C can be obtained by combining the observations summarized in Fig. 8 with Eq. (11) to yield for pH P 6 Logðr þ =ðmol=cm 2 =sÞÞ ¼ 0:35Logða 3 H þ =a Al 3þ Þ À 11:53 ð13Þ and for pH < 6 Logðr þ =ðmol=cm 2 =sÞÞ ¼ n acid Logða 3 H þ =a Al 3þ Þ þ 0:033An% À 14:77 where n acid refers to the value of the n generated from a least squares fit of the slopes of the linear correlations shown in Fig. 8a given by An% represents the percent anorthite in the plagioclase solid solution. Note that Eqs. (13) and (14) account for the effects of the presence of various aqueous species on Fig. 8. Variation of the logarithm of plagioclase steady-state dissolution rates, based on Si release, obtained from experiments run in series for approximately 75 h, as a function of the logarithm of the aqueous fluid activity ratio ða 3 H þ =a Al 3þ Þ. Rates obtained at acidic and alkaline conditions are shown in (a) and (b), respectively. Fig. 9. Comparison of measured steady-state plagioclase dissolution rates determined in this study with corresponding rates calculated using Eqs. (13) and (14). Open symbols represent rates obtained from experiments run in series for approximately 75 h whereas filled symbols correspond to rates determined from individual experiments that ran for more than 250 h. rates through their effect on the activity of the aqueous Al 3+ species.
The degree to which Eqs. (13) and (14) describe the measured plagioclase steady-state dissolution rates can be assessed with the aid of Fig. 9. The average difference between calculated rates and the 40 rates measured during the experiments run in series is 0.22 log units. The corresponding difference between calculated and the 31 rates measured in the individual experiments is 0.5 log units. It is evident that rates obtained from the experiments run in series for approximately 75 h are better described by these equations than those obtained in the longer individual experiments, due to the better internal consistency of the former dataset.

Effects in natural waters and regional metamorphism
The dissolution behaviour of primary minerals in basaltic rocks controls the availability of cations for secondary mineral formation (Gislason and Eugster, 1987;Neuhoff et al., 2000;Fridriksson et al., 2001;Neuhoff and Ruhl, 2006;Rogers et al., 2006;Arnorsson and Neuhoff, 2007). At acid conditions, plagioclase dissolution rates increase with increasing An% promoting Ca-rich secondary phase formation. At basic conditions the far-from-equilibrium dissolution rates of all plagioclases are identical. It follows that, during the weathering of basaltic terrains which results in high pH fluids, the cation availability reflects the plagioclase composition of the system (Gudbrandsson et al., 2011). This is evident in the low temperature alteration of Icelandic terrain were the availability of Na, Ca, and Al results in the formation of the zeolites phillipsite, thomsonite, and chabazite, and smectite clay layers (Walker, 1960;Kristmannsdottir and Tomasson, 1978;Neuhoff et al., 2000;Fridriksson et al., 2001).

Consequences for subsurface carbon storage
Basaltic rocks are desirable targets for mineral carbon storage due to their high divalent metal cation concentration Assayag et al., 2009;Matter and Kelemen, 2009;Matter et al., 2011;Alfredsson et al., 2013). The dissolution of basalt by acidic CO 2 -rich fluids both neutralizes the fluid and releases divalent metal cations. The released divalent metals can promote mineral carbon storage through carbonate mineral precipitation. Much of the divalent cations released by this process stems from anorthite-rich plagioclase dissolution. The results presented in this study suggest that although the dissolution rates of the anorthite-rich plagioclases decrease dramatically with increasing pH at acid conditions, these rates minimize and rise with increasing pH at basic conditions. As such, divalent cation release and CO 2 mineralization may be enhanced at elevated pH where Ca-release due to plagioclase dissolution could promote the precipitation of calcite and/or other carbonate minerals. This conclusion is consistent with observations reported by Gudbrandsson et al. (2011) showing that the Ca percent of the divalent metal cations released during the dissolution of crystalline basalt increases continuously with increasing pH; at pH 11, >80% of the divalent metal flux stemming from crystalline basalt dissolution was due to Ca release from plagioclase. CO 2 mineralization via calcite precipitation at high pH conditions may be particularly favourable due to the low solubility of carbonate minerals at these conditions.

CONCLUSIONS
The results described above illuminate the dissolution behaviour of the plagioclase feldspars as a function of their composition and fluid pH. Rates depend strongly on plagioclase composition at acid conditions, where the dissolution rates increase with the increasing anorthite content of the plagioclase. In contrast, at alkaline conditions plagioclase dissolution rates are independent of its composition. Regression of the experimental results generated in this study enable the generation of a simple equation describing plagioclase dissolution rates. The success of this equation to describe rates over wide ranges of fluid and plagioclase compositions suggests this equation can provide useful dissolution rate estimates in a variety of ambient temperature natural and industrial systems.