2 from (298 to 623) K at 20 MPa. Is Triflate a Non ... - ACS Publications

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Limiting Conductivities and Ion Association in Aqueous NaCF3SO3 and Sr(CF3SO3)2 from (298 to 623) K at 20 MPa. Is Triflate a Non-Complexing Anion in High-Temperature Water? G. H. Zimmerman,†,§ H. Arcis,‡,§ and P. R. Tremaine*,‡ †

Department of Chemistry and Biochemistry, Bloomsburg University, Bloomsburg, Pennsylvania 17815, United States Department of Chemistry, University of Guelph, Guelph, Ontario, Canada N1G 2W1

‡

S Supporting Information *

ABSTRACT: Frequency-dependent electrical conductivities of solutions of aqueous sodium trifluoromethanesulfonate (“triflate”) and strontium triflate have been measured from T = 298 K to T = 623 K at p = 20 MPa, over a very wide range of ionic strength [(2·10−5 to 0.35) mol·kg−1], using a unique high-precision flowthrough AC electrical conductance instrument. Experimental values for the equivalent conductivity, Λ, of each electrolyte were used to calculate their equivalent conductivities at infinite dilution, Λ°, with the Turq−Blum−Bernard−Kunz (TBBK) ionic conductivity model. Values were derived for the limiting equivalent conductivity of the triflate ion, λ°(CF3SO3−), and the strontium ion, λ°(Sr2+). The TBBK fits to the concentration-dependent equivalent conductivity data for both NaCF3SO3 and Sr(CF3SO3)2 required statistically significant ionic association constants for the species NaCF3SO30 at temperatures T > 448 K, SrCF3SO3+ at T > 448 K, and for Sr(CF3SO3)20 at T > 548 K. The stepwise association constants, KA, for the charged species SrCF3SO3+, were found to be greater or equal to than the ones for the neutral species Sr(CF3SO3)20. The experimental value of KA for Sr(CF3SO3)20 was found to be similar to that for NaCF3SO30 at 548 K but increased more steeply with temperature. At temperatures above 548 K, association constants derived from the concentration-dependent equivalent conductivities were increasingly sensitive to the assumptions used to calculate solution densities. Procedures for minimizing these effects are reported. The temperature dependence of the experimental association constants and limiting equivalent conductivities from (298 to 623) K could be represented accurately as functions of solvent density and viscosity, respectively. compiled, and semiempirical “equations of state” for aqueous species have been formulated.7,8 The temperature range from (573 to 673) K remains relatively unexplored and presents a major opportunity for frontier research using quantitative measurement techniques. The challenges are formidable because the conditions are extremely aggressive; ion association is extensive but not complete, and solubilities can be very low.1,2 One of the key questions facing experimentalists is the need to identify thermally stable, noncomplexing anions and cations, so that the standard partial molar properties and transport properties of “free” unassociated ions can be measured. Although several anions show noncomplexing properties,9 the only candidates identified to date with sufficient thermal stability for hydrothermal applications are perchlorate,10 perhennate,11 and triflate.12 Triflate, CF3SO3−, is the anion of choice for most hydrothermal studies, because it has better thermal stability and is not a strong oxidizing agent.6

1. INTRODUCTION A major goal of modern physical chemistry is to extend the study of aqueous solutions to extremes of temperature and pressure. The properties of water change so dramatically from subambient temperatures to conditions approaching the critical point (Tc = 647.096 K and pc = 22.064 MPa) that measurements over wide variations of temperature and pressure can be used to provide new insights into the nature of ionic hydration and ion−ion interactions. Industrial and geochemical interest is centered on the need to model mass-transport, corrosion, and redox mechanisms under hydrothermal conditions in a variety of man-made and natural systems where few data exist.1−3 Recent examples include the Generation IV supercritical-watercooled nuclear reactor design concepts, oilfield brines, and deep-ocean hydrothermal vents.4,5 The past 30 years have seen major advances in the development of experimental techniques and understanding of the properties of hydrothermal systems up to ∼570 K.6 Accurate values of the standard partial molar properties and transport properties of many simple ions and nonelectrolytes have now been measured, databases have been © 2012 American Chemical Society

Received: July 13, 2012 Accepted: September 24, 2012 Published: October 30, 2012 3180

dx.doi.org/10.1021/je3007887 | J. Chem. Eng. Data 2012, 57, 3180−3197

Journal of Chemical & Engineering Data

Article

process of three samples, which agreed to within 0.18 % of each other. KCl purchased from Alfa Aesar (99.995 % metals basis, Lot No. E21U0) was dried at 300 °C until the mass difference between weighings was less than 0.01 %. This was used to make two stock solutions by mass with Nanopure water (resistivity 18.2 MΩ·cm). These solutions were found to be (0.02190 ± 0.00001) mol·kg−1 and (0.3206 ± 0.0001) mol·kg−1 after buoyancy corrections were made. These solutions were used to determine the cell constant. The solutions measured in the conductance instrument were prepared by mass dilution under argon from these stock solutions in sealed Pyrex bottles following the procedure given by Zimmerman et al.13 using Nanopure water and pumped from these same bottles directly into the conductivity cell via the injection system described below. 2.2. Experimental Apparatus. High-Temperature HighPressure Conductivity Cell. The high-temperature, high-pressure conductance flow cell used for this work was built at the University of Delaware by Hnedkovsky et al.,16 with improvements on the original designs of Zimmerman et al.13 and Sharygin et al.,15 to allow for measurement of more corrosive solutions. The cell has been used at temperatures as high as 673 K at 28 MPa, with ionic strengths as low as 10−5 mol·kg−1.16 A schematic diagram is presented in Figure 1a. Briefly, the cell consists of a 47 cm long temperature-controlled platinum inlet tube [1.0 mm inner diameter (i.d.); 1.6 mm outer diameter (o.d.)] that leads into a platinized cup (4.6 mm i.d.; 5.6 mm o.d.), which serves as the outer electrode for the cell. The inner electrode is a platinum rod (1.6 mm o.d.), electrodeposited with platinum black, and is a direct extension of the platinum tube, which carries the exiting solution away from the cell. A diamond shield protects the sapphire insulator from corrosion that would otherwise contaminate the solution. The entire electrode assembly is contained in a titanium cell body. A sapphire disk and a ceramic spacer provide electrical insulation between the two electrodes. The pressure seal inside the conductivity flow cell is maintained by compressing annealed thin gold disks, which sit between the sapphire insulator and a titanium end-cap, using a system of bolts and Inconel Belleville washers (Figure 1a). A four-wire measurement was used to acquire the AC impedance spectra. For the outer electrode, one of the leads was the Pt/Rh tube also used to flow the solution to the cell, and the other was a silver wire gold soldered to the tubing outside of the titanium body. Similarly, for the inner electrode, the Pt/Rh tubing served as one lead and another silver wire gold soldered to the tubing as the other lead. Although the resistance contribution in a four-leads measurement is zero, there remains a short portion of platinum/20 % rhodium tubing on both the inlet and outlet tubes and inner electrode that must be subtracted from the real portion of the impedance. This contribution becomes significant when measuring solutions with high concentrations, which have very low real impedance. Because some small modifications of this portion of the cell were done, the lead resistance contribution needed to be accurately redetermined. This was done as follows. The lead resistance calculated using the original dimensions of the instrument along with the resistivity of Pt/20 % Rh (124.8 ohms per circular mil foot, Platinum Labware, Johnson Matthey Catalog Company Inc., 2007) was found to be identical with that reported by De Leo and Wood (0.039 Ω).19 This confirmed that using resistivities could be used to accurately calculate the lead

Flow AC conductance methods provide an attractive tool for measuring the limiting ionic conductivities and ion-pair formation constants. Although conductivity techniques for measuring ion association at high temperatures and pressure have been available for many years, flow instruments sensitive enough to make measurements for very dilute solutions under extreme conditions have only recently been developed.13,14 This work reports conductivity measurements for a series of dilute solutions of sodium and strontium triflate from 298 K up to 623 K at a constant applied pressure of ∼20 MPa, using a state-of-theart, high-temperature, flow AC conductance cell built at the University of Delaware which is capable of operating at concentrations as low as 10−5 mol·L−1.13,15,16 The data were used to obtain temperature-dependent equilibrium constants for the ion association reactions, KA, and limiting ionic equivalent conductivities, λ°(Sr2+) and λ°(CF3SO3−), under conditions approaching the critical point of water. The values of λ°(CF3SO3−) and KA(NaCF3SO3) are important because they provide quantitative parameters for the use of triflate as a noncomplexing anion under these extreme conditions. Only one other conductivity study for aqueous NaCF3SO3 under these conditions has been reported.17 The strontium ion, Sr2+, is an important fission product in nuclear reactors and a component of naturally occurring radioactive material (“NORM”) scales in oilfield production systems, which form at these temperatures. Moreover, although Sr2+ is a useful model system for estimating the thermodynamic and transport properties of other M2+ cations, no values for λ°(Sr2+) or KA[Sr(CF3SO3)2] have been reported under hydrothermal conditions.

2. EXPERIMENTAL SECTION 2.1. Chemicals and Solution Preparation. Sodium triflate was prepared from trifluoromethanesulfonic (“triflic”) acid from Alfa Aesar (98 %, Lot No. 10143564). After diluting the acid with Nanopure water (resistivity 18.2 MΩ·cm), three samples of this solution were then titrated using a syringe as a weight buret with a solution of carbonate-free NaOH (0.3325 ± 0.0002 mol·kg−1) that was prepared from 50 % (w/w) NaOH (Fisher ACS Certified, Lot No. 011474-24) according to the method of Sipos et al.18 and standardized with potassium hydrogen phthalate. The remaining triflic acid (0.5256 ± 0.0004 mol·kg−1) was then weighed and then neutralized with carbonate free NaOH until the pH was 6.60 as measured with a pH electrode. The final molality found using the masses after buoyancy corrections was (0.1162 ± 0.0002) mol·kg−1. This molality was checked gravimetrically by evaporation and was found to be in good agreement with the first method (0.1159 ± 0.0001 mol·kg−1). Strontium triflate was prepared in a similar fashion to the sodium triflate. Triflic acid from Alfa Aesar (98 %, Lot No. 10143564) was diluted with Nanopure water to a molality of about 0.5 m. Solid strontium hydroxide octahydrate from Alfa Aesar, (99 % pure, metal basis, Lot No. G16U029) was added to the triflic acid until the solution was basic. More triflic acid was added dropwise until the pH was about 6.4. The resulting solution contained a small amount of gray particulate matter, believed to be strontium carbonate, which was removed by filtration. The final stock molality was found to be (0.1716 ± 0.0001) mol·kg−1 by water evaporation of triplicate samples done in the same way as the sodium triflate. These agreed to within 0.04 % of each other. A subsequent stock solution was made and analyzed by the same method. This solution was found to be (0.04500 ± 0.00008) mol·kg−1 again by the evaporation 3181



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Figure 1. (a) Schematic of the AC conductivity cell: (1) platinum inlet tube; (2) platinum outlet tube; (3) diamond frit; (4) ceramic spacer; (5) Inconel belleville washers; (6) sapphire insulator; (7) titanium ram; (8) steel screws; (9) platinum outer electrode; (10) platinum inner electrode. (b) Schematic of the high pressure sample injection system: (A1) HPLC pump 1; (A2) HPLC pump 2; (B) deionized water reservoir; (C) Pyrex solution bottle; (D) peristaltic pump; (E1) six-port injection valve 1; (E2) six-port injection valve 2; (F) delay loop; (G) large air oven containing the conductivity cell within the temperature-controlled insulated air oven; (H) back pressure regulator; (I) valves; (J) pressure transducer; (K) pressure release valves; (L) waste solution reservoirs; (M) Fluke PM 6304 programmable automatic RCL meter; (N) data acquisition computer, (·-·-·) four-lead electrical connection in the high-temperature configuration.

Temperature Control and Measurement. The temperature of the conductivity cell was controlled using three independent systems that together were capable of controlling temperature to ±0.15 K over several hours. First, a large air oven containing the conductivity cell and inlet and exit tubes was used to maintain a constant temperature environment (∼5 ± 0.1) K below the temperature of the conductivity cell, using a the PID controller (Omega CNi3254), which was connected to a Pt 1000 Ω sensor and a heating element located ∼5 cm underneath the cell. Second, the temperature cell itself was maintained with two heating cartridges located in the titanium cell body, controlled by a Leeds & Northrup 6430 Series Electromax III PID controller that was connected to a Pt 1000 Ω sensor. The sensor formed one leg of a Wheatstone bridge circuit, which balanced a 4-decade variable resistor, which used to set the control point to increase the sensitivity to ± 0.01 K. The temperature of the cell was measured to an accuracy of ±

resistance. The total length of tubing contributing to the leads with an o.d. of 1.0 mm used for the in-flow tube in original instrument was 76.2 mm. In the present cell used, this was decreased to a total of 38.1 mm by gold soldering the silver lead wire closer to the Pt/Rh cup. Additionally, a 50.0 mm length of tubing (0.50 mm I.D. and 1.0 mm o.d.) was replaced with thicker tubing with a larger cross sectional area (1.0 mm I.D. and 1.6 mm o.d.). This further reduced this correction even further than the original instrument to a final value of 0.020 Ω with an estimated uncertainty of ± 0.004 Ω leads correction at room temperature as calculated with the resistivity of Pt/Rh 20 %. To further increase the accuracy of this correction, we also included the temperature coefficient of resistance (0.0014 Ω·K−1, Platinum Labware, Johnson Matthey Catalog Company Inc., 2007). This was calculated to be no more than 0.005 Ω at the highest temperature. 3182



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prepared by injecting a well-known mass of stock solution through the septum and mixing with a magnetic stirrer. A peristaltic pump, under computer-control was used to fill the sample loop with each solution from the sample bottle. After AC impedance data were collected for the full series of solutions at each temperature, the last most concentrated sample was followed by a long injection of deionized and degassed water from the main reservoir, typically 1000 mL, to rinse the equipment until the cell conductance had returned to its baseline value. A typical run for an electrolyte solution at given concentration, temperature, and pressure took about 1.5 h. 2.3. AC Impedance Measurements. The complex impedance Z(ω) of solutions in the conductance cell were measured at frequencies of (100, 200, 500, 1000, 2000, 5000, 10 000, 20 000, and 100 000) Hz using a programmable automatic RCL meter (Fluke model PM6304C) to obtain both the real ZRe(ω) and imaginary ZIm(ω) components of the impedance spectrum at each angular frequency, ω,

0.02 K with a platinum resistance thermometer consisting of a Hart Scientific model 5612 probe and a model 5707 6 1/2 Digit DMM. Third, to make sure the solution to be analyzed was brought as close as possible to the cell temperature, a preheater was used that consisted of a coaxial linear heating element placed in intimate contact with the inlet tube over a length of ∼47 cm. The dif ference in the temperature between the inlet end of the tube and the conductivity cell was monitored by two thermocouple junctions, one located on the inlet Pt tubing just before it entered the cell and the other on the titanium body cell. The output of this pair of thermocouples was connected to an Automation Direct Solo 4824 PID controller, which adjusted the heating power necessary to keep the temperature difference between the two thermocouples equal to zero. Flow Injection System. The injection system for the conductance equipment was very similar to that reported by Méndez De Leo and Wood19 and is shown in Figure 1b.20 Briefly, solutions were injected using two Lab Alliance Series 1500 dual piston high-performance liquid chromatography (HPLC) pumps. Pump A1, which was always turned on, was used to supply a continuous flow of degassed and deionized water from a large reservoir to the instrument at a pressure set by a back-pressure regulator (Circle Seal Controls No. BPR21U22542). Two 6-port valves, controlled through a computer with HewlettPackard VEE Version 6.1 software, determined whether water from the reservoir flowed directly through the conductance cell or whether it pushed solution from the injection loop through the cell. The sample to be injected was loaded into an HPLC injection loop (3.2 mm o.d., passivated stainless steel tubing from Restek, with a capacity of 50 mL) with a peristaltic pump, using procedures described below. Pump A2 was then used to pressurize the sample loop by pumping deionized water from the reservoir into the loop, so that the downstream water displaced by the sample in the loop bypassed the cell and flowed directly to the back-pressure regulator. Once the sample was pressurized, the computer switched the 6-port valves to push the sample into the conductance cell. Experiments were conducted at a flow rate of 0.5 mL·min−1. Pressure was measured with a digital pressure transducer (Paroscientific Inc. Model 760−6K) to an accuracy of ±0.01 MPa. The experimental design, described in the following section, requires sequential determination of the conductivities of aqueous solutions of NaCF3SO3 and Sr(CF3SO3)2 as a function of concentration at the same temperature, pressure, and flow rate. To minimize solvent corrections, solutions of each triflate salt at increasing concentrations were prepared in the same bottle, by injecting increments of stock solution from a weighed syringe through a septum into the solution. To observe the salts under conditions of complete dissociation, solutions were prepared at molalities as low as m ∼ 10−5 mol·kg−1. A very wide range of concentration [(10−5 to 0.2) mol·kg−1] was also used to ensure that association effects could be measured accurately. The procedure was repeated at each temperature. For this purpose, we used Pyrex glass bottles equipped with VAPLOCK Bottle Cap (1/4-28, GL45, 4-port). The first port was joined to a balloon full of argon to keep a positive pressure over the solution for the duration of the experimental runs, and the second one was connected to No-Ox tubing which kept the solution degassed as it traveled from the bottle to the injection loop. The third port had a septum, and the fourth port was capped. When preparing the solution, degassed and deionized water was introduced into an empty bottle purged with argon through the No-Ox tubing. Then the solutions to run were

Z(ω) = Z Re(ω) − j ·Z Im(ω)

(1)

Here, j = −1 and ω = 2πf, where f is the frequency. Eighty measurement cycles or more were taken with a computer over a time span 50 min or more at every temperature and pressure. Each cycle consisted of sequential measurements of ZRe(ω) and ZIm(ω) at each of the nine frequencies. The relative standard deviation of ZRe(ω) for the salt solutions was between (0.1 and 0.3) %, larger for the more concentrated solutions and at the higher temperatures. The relative standard deviation of ZIm(ω) for the salt solutions was between (0.1 and 0.5) %, except for a few cases at the highest concentrations and temperatures with relative standard deviations from (1 to 3) %. For the solvent measurements, the relative standard deviation for ZRe(ω) was usually between (1 and 3) % except at 623 K where the relative standard deviation for ZRe(ω) ranged between (3 and 16) % at the different frequencies. These were generally larger at the lower frequencies, but there was not a clear trend in this regard. The solvent resistance was found by linearly extrapolating the square of the three lowest frequencies (100, 200, and 500 Hz) to zero frequency. The impedance measurements on NaCF3SO3(aq) and Sr(CF3SO3)2(aq) reported here and experience in previous studies of other solutes to 623 K16,23 suggest that the calculated values of true solution resistance Rs obtained from high-temperature conductivity cells with concentric cylindrical electrodes can be dependent upon how the impedance measurements were extrapolated and that the associated statistical uncertainty in Rs may become larger as the concentration is increased. These extrapolation methods fall into two general categories. The first category uses equivalent circuit models to represent the angular frequency dependence of the complex impedance.22,24,25 The second category is based on extrapolations involving ZRe(ω) and frequency f. Following the detailed study by Zimmerman et al.,23 a generalized form of the expression for Warburg impedance, given by Hnedkovsky et al.,16 22

2

Z Re( f ) = R s + b1·f −n

(2)

yields best agreement with accurate low-temperature literature data for electrolyte solutions, over a wide range of concentrations in this type of cell. Here Rs is the solution resistance that we seek; b1 and the exponential term n are fitting parameters. This was the procedure adopted for the present study. 3183



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reported here.23 The calculation required knowledge of solution speciation, which we determined in an iterative process by fitting the TBBK model to our experimental conductivity data. Details of the speciation calculation are presented below, in Section 4. Briefly, solution densities, ρs, were calculated from the molar volume, Vs, using the relationships,

3. EXPERIMENTAL CONDUCTIVITIES The experimental conductivity (specific conductance26) of the solution, κexp soln, was calculated from Rs, the resistance of the solution at infinite frequency using the expression: exp κsoln = kcell /R s

(3)

The cell constant kcell was determined before (kcell = 0.06529 ± 0.0002) and after (kcell = 0.06659 ± 0.0002) temperature cycling by measuring the conductivity for a series of five KCl standard solutions [(10−4 to 10−2) mol·kg−1] at 298.15 K and 20.00 MPa at the same frequency settings as the test solutions, using equations given by Barthel and co-workers for KCl(aq).27 Following the procedure used by previous workers,13−15,19,28−30 the dependence of the cell constant on temperature was calculated from the cell geometry and the thermal expansion coefficient of platinum. The experimental conductivities of the electrolyte solutions, κexp soln, were corrected for impurities within the solvent and the self-ionization of water by subtracting the experimental values for H2O, κwexp, for each run, using the method of Sharygin et al.:29 exp κ = κsoln − κ wexp

ρs =

Vs =

where the conductivities κ, and are in SI units of S·m−1. In this study, these were converted to units of S·cm−1. Theoretical conductivity equations make use of the equivalent conductivity of the solution, Λexp, which is defined as follows: κ Λexp = (5) N

κexp w

Here, N is the normality or equivalent concentration in moleq·L−1, giving the expression: N=

∑ cMcz Mc = ∑ c Xaz Xa

ccM, caX z+

zcM,

(6)

zaX

where and are the molarities and the charge of the cations M and the anions Xz−, respectively. Molarities, ci, and molalities, mi, are related by the expression, ci =

1000·mi ·ρs mi ·Mi + 1000

Vs

(8)

1000 + ρw

∑ mi ·Vi0 + 1000·A v i

I ln(1 + b· I ) b

(9)

Here, mi, Mi, and Vi° are the molality, molar mass, and standard partial molar volume of each species i; ρw is the density of water density; Av, in units of m3·mol−1, is the Debye−Hü ckel limiting slope for the apparent molar volume at the experimental temperature and pressure;16,37 and Pitzer parameter is b = 1.2 kg1/2·mol−1/2. Values for ρw and Av were calculated from the equation of state for the density and dielectric constant of water reported by Wagner and Pruss31 and Fernandez et al.,38 respectively. Standard partial molar volumes were calculated using the HKF parameters reported by Sverjensky et al.,36 except that our Born function used the water dielectric constant formulation reported by Fernandez et al.,38 as recommended by the National Institute of Standards and Technology (NIST). We note that the HKF Born function is based on an “effective” radius that includes the primary hydration sphere (dielectric saturation), calculated from the crystallographic radius, rx. Values of the HKF parameters39−42 for the triflate species, tabulated in the Supporting Information, were estimated using the assumptions V°(CF3SO3−) = V°(CCl3COO−); V°(NaCF3SO30) = V°(NaCH 3 COO0 ); V°(HCF 3 SO3 0 ) = V°(CH3 COOH 0 ); V°(SrCF3SO3+) = V°(SrCH3COO+); and V°[Sr(CF3SO3)20] = V°[Sr(CH3COO)20]. For the highest molality of NaCF3SO3 measured at 600 K, the solution density calculated using this procedure agreed with the experimental values of Xiao and Tremaine32 to within 1.3 %. The experimental quantities resulting from the measurements described in Section 2 are conductivities and solution molalities. The effects of small differences in temperature and pressure between measurements on the conductivities have been corrected to the average temperature and pressure by assuming that:

(4)

κexp soln,

∑i mi ·Mi

(7)

where Mi is the molar mass of the species i and ρs is the density of the solution. In the case of symmetrical 1−1 electrolytes like NaCl or NaCF3SO3, molarity and normality are identical, so that there is no difference between equivalent and molar conductivity. The calculation of equivalent conductivities, Λexp, requires us to convert molalities to normalities, according to eqs 5 to 7. This calculation requires accurate solution densities. Often this is done for dilute solutions by assuming that the density of the solution is equal to that of pure water, for which accurate pVT data formulations are known.31 However, at the high concentrations required for this study the densities deviate substantially from those of pure liquid water at temperatures above ∼570 K.6 Although the densities of aqueous NaCF3SO3 have been measured to 600 K,32 there are no values in the literature for Sr(CF3SO3)2(aq) under these conditions. As a result, we used a data treatment strategy based on the Helgeson−Kirkham−Flowers−Tanger (HKF) model to estimate the standard partial molar volumes V° of the aqueous ions and ion pairs in our solutions.33−36 The accuracy of the method was demonstrated in a similar conductivity study on NaCl, carried out as part of the same series of measurements

exp (T av , pav ) = κsoln

exp κsoln ( T , p ) · η( T , p) η(T av , pav )

(10)

The corrections were usually 0.2 % or less at temperatures equal to or below to 548 K and less than 0.3 % with the exception of two points at 598 K (0.57 %, 0.83 %) and two points at 623 K (0.65 %, 0.78 %, 0.47 %) for the system {NaCF3SO 3 + H 2O}. For the system {Sr(CF3SO3) 2 + H 2O}, they were less than 0.2 % at temperatures equal to or below to 548 K and less than 0.5 % with the exception of one points at 598 K (0.57 %) and two points at 623 K (0.65 %, 1.36 %). Experimental equivalent conductivities, Λexp, of aqueous av av NaCF3SO3 and Sr(CF3SO3)2 calculated from κexp soln(T , p ), are tabulated in Tables 1 and 2, along with the average temperature (IPTS-90) and pressure, and plotted against molarity, expressed 3184



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Table 1. Molality, Concentration, Conductivity, Experimental Equivalent Conductivities, and Equivalent Conductivities Calculated from the TBBK and the FHFP Equations from (447 to 623) K at p = 20 MPa for Aqueous Solutions of NaCF3SO3 m·103

c·103

6 κexp soln·10

Λexp

ΛTBBK

ΛFHFP

mol·kg−1

mol·L−1

S·cm−1

S·cm2·mol−1

S·cm2·mol−1

S·cm2·mol−1

κDH·qB·α0.5

487.6 482.6 473.6 460.7 450.2 436.5

0.02 0.04 0.09 0.12 0.18

634.5 623.6 617.1 609.2 583.3 563.0 529.6 507.0 472.5

0.03 0.05 0.07 0.13 0.19 0.30 0.37 0.49

753.0 742.0 735.5 724.6 712.3 690.7 642.2 591.8 551.9

0.03 0.04 0.07 0.10 0.15 0.29 0.45 0.57

879.5 871.3 865.3 847.0 828.2 782.0 743.8 662.1

0.02 0.03 0.07 0.11 0.22 0.32 0.55

995.0 980.8 972.3 945.7 915.8 840.0 766.5

0.03 0.05 0.10 0.15 0.30 0.45

−3

0 0.08755 0.7061 2.727 5.536 11.18 38.51

0 0.07922 0.6389 2.467 5.007 10.11 34.76

0 0.2011 0.5121 1.076 4.594 9.491 23.00 36.95 65.68 116.2

0 0.1698 0.4324 0.909 3.878 8.010 19.40 31.14 55.28 97.55

0 0.1201 0.3017 0.7930 1.657 4.059 15.14 63.40 38.08 116.2

0 0.09356 0.2350 0.6177 1.291 3.161 11.79 49.28 29.63 90.18

0 0.03370 0.09888 0.5017 1.254 4.938 10.70 33.38 62.91 116.2

0 0.02285 0.06703 0.3402 0.850 3.348 7.260 22.66 42.74 79.08

0 0.05013 0.1260 0.5614 1.412 5.729 14.06 48.44 33.38 116.2

0 0.02987 0.07507 0.3346 0.842 3.418 8.402 29.14 20.02 70.69

T = 447.92 K, p = 20.81 MPa, ρw = 904.84 kg·m −7 −7 κexp S·cm−1, κth S·cm−1 w = 30.68·10 w = 27.97·10 488.0 41.329 483.0 ± 3.0 481.5 305.59 473.5 ± 2.1 474.0 1139.2 460.6 ± 2.1 461.2 2255.7 449.9 ± 2.1 450.4 4419.8 436.8 ± 2.1 435.8 13826 397.6 ± 2.5 397.9 T = 502.33 K, p = 20.90 MPa, ρw = 844.36 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 42.63·10 w = 37.78·10 633.3 110.19 623.8 ± 3.1 622.5 271.17 617.3 ± 2.8 616.5 558.09 609.5 ± 2.7 609.0 2268.2 583.7 ± 2.7 583.9 4517.9 563.5 ± 2.7 563.8 10231 527.1 ± 2.9 529.9 15738 505.3 ± 3.1 507.0 26262 475.0 ± 3.7 474.7 43365 444.5 ± 4.8 438.1 T = 548.47 K, p = 20.59 MPa, ρw = 778.94 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 48.36·10 w = 36.15·10 751.8 74.232 741.7 ± 4.3 742.0 177.68 735.5 ± 3.4 735.3 452.94 725.4 ± 3.2 724.6 925.64 713.4 ± 3.2 712.6 2191.3 691.7 ± 3.1 691.3 7521.7 637.8 ± 3.2 641.3 17524 591.4 ± 4.3 590.0 27310 554.0 ± 3.7 555.9 46497 515.5 ± 5.7 510.7 T = 599.43 K, p = 20.50 MPa, ρw = 677.93 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 24.35·10 w = 23.20·10 874.0 22.517 878.9 ± 7.1 872.4 60.504 866.3 ± 4.3 862.8 289.20 843.1 ± 3.7 843.9 703.75 824.8 ± 3.7 826.1 2613.2 779.7 ± 3.6 781.4 5396.6 743.0 ± 3.6 743.1 15045 663.9 ± 4.0 667.9 26618 622.7 ± 4.8 617.6 44760 566.0 ± 6.2 565.0 T = 625.21 K, p = 20.65 MPa, ρw = 595.83 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 16.11·10 w = 12.95·10 990.5 31.078 986.5 ± 5.3 981.4 74.955 976.9 ± 4.5 971.0 317.02 942.7 ± 4.2 944.5 764.69 906.5 ± 4.0 915.4 2868.2 838.7 ± 3.9 840.1 6467.4 769.6 ± 3.8 768.4 13748 686.5 ± 4.4 686.2 18878 647.8 ± 4.1 648.6 39897 564.4 ± 6.2 560.8 3185



Article

Table 2. Molality, Concentration, Conductivity, Experimental Equivalent Conductivities, and Equivalent Conductivities Calculated from the TBBK Equation from (295 to 623) K at p = 20 MPa for Aqueous Solutions of Sr(CF3SO3)2 m·103 mol·kg

−1

c·103 −1

mol·L

6 κexp soln·10

S·cm

−1

Λexp

ΛTBBK −1

S·cm ·mol 2

m·103 −1

S·cm ·mol 2

mol·kg

−1

0 0.2576 0.6216 1.681 2.740 4.179

0 0.2914 0.7697 1.217 2.983 9.940 22.71 43.49 79.71 171.7

0 0.1299 0.3566 0.6018 1.748 5.002 10.41 26.56 49.88 79.71 171.7

0.3718 67.883 91.0 ± 0.4 0.6912 124.21 89.7 ± 0.4 1.570 273.86 87.1 ± 0.4 2.415 414.66 85.8 ± 0.4 4.005 671.69 83.8 ± 0.4 T = 374.83 K, p = 21.06 MPa, ρw = 966.73 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 12.77·10 w = 9.32·10 0.2490 150.12 298.9 ± 1.3 0.6009 356.42 295.5 ± 1.3 1.625 931.57 286.3 ± 1.3 2.648 1483.7 279.9 ± 1.3 4.038 2205.1 272.9 ± 1.2 T = 445.93 K, p = 20.90 MPa, ρw = 906.85 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 34.82·10 w = 27.48·10 0.2642 274.39 512.7 ± 2.3 0.6980 703.34 501.4 ± 2.2 1.103 1090.5 492.7 ± 2.2 2.704 2543.1 469.5 ± 2.1 9.005 7637.9 423.9 ± 2.0 20.54 15435 375.6 ± 2.1 39.27 27620 351.7 ± 2.4 71.70 46538 324.5 ± 2.9 153.0 86862 283.9 ± 4.3 T = 501.97 K, p = 20.92 MPa, ρw = 844.83 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 49.30·10 w = 37.77·10 0.1098 0.3013 0.5084 1.476 4.224 8.79 22.39 41.98 66.92 143.1

154.85 411.21 679.22 1863.2 4889.3 9358.6 21103 36130 54898 106135

682.8 674.3 663.2 629.4 578.1 532.4 471.1 430.3 410.1 370.8

± ± ± ± ± ± ± ± ± ±

3.3 3.0 2.9 2.8 2.7 2.6 2.7 3.2 3.8 5.8

mol·L

−1

6 κexp soln·10

S·cm

−1

Λexp

ΛTBBK −1

S·cm ·mol 2

S·cm2·mol−1

T = 547.84 K, p = 20.51 MPa, ρw = 779.86 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 40.14·10 w = 36.21·10

T = 294.96 K, p = 17.88 MPa, ρw = 1005.76 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 1.88·10 w = 0.50·10 0 0.3697 0.6873 1.562 2.402 3.984

c·103

94.8 90.9 89.6 87.4 85.9 83.8

0 0.05991 0.2146 0.5872 1.260 2.779 4.259 10.69 21.79 45.00

313.6 299.8 295.0 285.7 279.6 273.4

0 0.01563 0.04625 0.1854 0.4333 2.079 3.951 9.977 21.79 45.00 171.65

545.2 513.9 501.7 492.5 467.8 421.2 382.6 350.4 319.8 280.3

0 0.02152 0.06067 0.1827 0.4654 1.212 2.677 3.952 4.692 9.978 45.00

725.4 681.6 675.0 664.5 629.2 577.0 533.0 473.3 433.8 405.4 359.3

as c1/2, in Figures 2 and 3. As noted above, the calculation of c and Λexp at temperatures above 570 K used densities estimated from the HKF model for standard partial molar volumes and speciation obtained from the TBBK conductivity models described in Section 4. Parameters derived from the treatments in Section 4 are also reported in Tables 1 and 2. The uncertainties in Tables 1 and 2 were estimated using the exact procedures reported in our previous study on NaCl(aq).23 For the lowest concentrations the largest contribution to the uncertainty was from the impedance measurements, maximally 0.3 %. For the highest concentrations, the two largest uncertainties were from the leads correction and the extrapolation of the impedance measurements. These were maximally 0.84 % and 1.26 %, respectively, for the highest concentration at 599.32 K for strontium triflate.

0.04672 77.459 786.0 ± 4.3 0.1674 268.36 789.7 ± 3.6 0.4579 700.92 761.0 ± 3.4 0.983 1430.0 725.5 ± 3.2 2.167 2946.9 679.1 ± 3.1 3.321 4328.1 651.0 ± 3.0 8.33 9677.9 580.3 ± 2.8 16.98 17770 523.2 ± 2.9 35.03 32542 464.4 ± 3.3 T = 599.32 K, p = 20.51 MPa, ρw = 678.27 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 25.45·10 w = 23.25·10 0.01060 20.605 851.9 ± 7.9 0.03137 60.268 920.0 ± 4.8 0.1258 231.29 909.4 ± 4.1 0.2939 515.74 873.0 ± 3.9 1.411 2117.0 749.5 ± 3.3 2.681 3714.4 692.2 ± 3.1 6.774 8036.3 593.0 ± 2.9 14.81 15458 521.8 ± 2.9 30.63 27598 450.5 ± 3.1 118.01 82784 350.8 ± 5.5 T = 625.39 K, p = 21.08 MPa, ρw = 597.74 kg·m−3 −7 −7 κexp S·cm−1, κth S·cm−1 w = 20.70·10 w = 13.29·10 0.01286 0.03627 0.1092 0.2783 0.7252 1.602 2.366 2.810 5.985 27.25

28.454 76.401 216.06 502.96 1133.8 2180.8 3015.1 3446.3 6273.1 20867

1025.4 1024.7 979.7 899.9 780.3 679.9 636.7 612.8 523.9 382.9

± ± ± ± ± ± ± ± ± ±

6.4 4.8 4.4 4.0 3.4 3.0 2.9 2.8 2.5 2.6

845.7 783.6 787.8 762.2 728.2 680.6 650.4 578.9 521.9 466.1

982.6 861.9 915.9 905.4 871.0 755.5 692.2 594.4 515.2 451.3 363.5

1106.8 1025.3 1025.7 977.1 899.0 788.6 684.5 632.9 610.4 518.0 387.4

4. DATA TREATMENT WITH THE TURQ−BLUM−BERNARD−KUNZ (TBBK) CONDUCTIVITY MODEL 4.1. The TBBK Model. The Turq−Blum−Bernard−Kunz (TBBK) conductivity model43 was used to treat all of the experimental equivalent conductivity measurements in this work, following the procedure used by Sharygin et al.29 and Méndez De Leo and Wood.19 The TBBK theory has been successful in modeling both symmetrical and unsymmetrical electrolytes at concentrations up to 1 mol·L−1 at room temperature.43 It is the model of choice for treating conductivity data at elevated temperatures and pressures because it is a practical model for unsymmetrical electrolytes, and it can be used to model solutions in which multiple ion association equilibria are present.16,19 In dilute aqueous solutions and at low temperature, sodium triflate and strontium triflate are known to be fully dissociated. 3186



Article

⎛ δν el ⎞⎛ δX ⎞⎟ λi = λi◦⎜⎜1 + i0 ⎟⎟⎜1 + ⎝ X⎠ νi ⎠ ⎝

(14)

where λi and λi° are the ionic equivalent conductivity of the ion i in solution and at infinite dilution. The electrophoretic and relaxation contributions, δνiel/νi0, and δX/X, were solved by Turq et al.,43 using the mean spherical approximation (MSA). To apply the TBBK treatment to the triflate systems, we used the equations from the original paper,43 corrected to address important misprints found by other authors.29,45 The activity coefficients of the ionic species in this model were calculated using the corresponding MSA expression:43,46 log γi = log γiel + log γi HS

(15)

γeli

γHS i

where is the Coulombic contribution and is the hard sphere contribution. The choice of the most appropriate radius for calculating these contributions for unsymmetrical electrolytes has been assessed by Bianchi et al.45 and Sharyagin et al.,29 who found that the TBBK results are relatively insensitive to the value that is used.45 Following Sharygin et al.,29 the Bjerrum distance was used for the Coulombic contribution in our study and crystallographic radii for the hard sphere contribution. For all neutral species, the activity coefficients were set equal to 1. To define the theoretical conductivity, κ, we used the mixing rule recommended by Wood and co-workers:15,16,19,29

Figure 2. Experimental equivalent conductivity of aqueous NaCF3SO3 from T = (445 to 623) K at p = 20 MPa: □, 448 K; ▲, 502 K; △, 548 K; ◊, 599 K; ○, 625 K; solid line, TBBK fit.

Nc

κ[Ic , Γc] = N

Na

∑ ∑ xMcx Xa ΛMX[Ic , Γc] M=1 X=1

(16)

and c xM =

However, as concentration and temperature increase up to hydrothermal conditions Na+, Sr2+, and CF3SO3− can associate to form a + charged or neutral ion-pair, Na(CF3SO3)0(aq), SrCF3SO3(aq) or a 0 triplet ion Sr(CF3SO3)2 (aq) according to the following equilibria:

(11)

Sr 2 +(aq) + CF3SO−3(aq) ⇌ SrCF3SO+3(aq) aSrCF3SO3+ K A1,SrCF3SO3+ = aSr 2+ ·aCF3SO3−

(12)

SrCF3SO+3(aq)

+

CF3SO−3(aq)

K A 2,Sr(CF SO3)02 = 3

⇌

x Xa =

c Xa|z Xa| N

(17)

where Ic is the molar ionic strength, Γc is the MSA shielding parameter, N is the equivalent concentration, xcM, xaM are the equivalent fractions of species in solution, and the sums are over all cations M and all anions X. The equivalent conductivity of the pure electrolyte, ΛMX[Ic,Γc], is calculated at the molar ionic strength of the mixture, Ic = (∑cMz2M + ∑cXz2X)/2. In our calculations, the properties of water (density, ρw; viscosity, ηw; and static dielectric constant, ε) were determined from the equations of state reported by Wagner and Pruss,31 Huber et al.,47 and Fernandez et al.,38 respectively. Values for the ionization constant of water, Kw (eq 18), were calculated from Bandura and Lvov:48 a +·a − H 2O ⇌ H+(aq) + OH−(aq) K w = H OH a H 2O (18)

Figure 3. Experimental equivalent conductivity of aqueous Sr(CF3SO3)2 from T = (298 to 623) K at p = 20 MPa: ⧫, 295 K; ●, 375 K; □, 446 K; ▲, 502 K; △, 548 K; ◊, 599 K; ○, 625 K; solid line, TBBK fit.

0 Na +(aq) + CF3SO−3(aq) ⇌ NaCF3SO3(aq) a NaCF3SO30 K A1,NaCF3SO3 = a Na+ ·aCF3SO3−

c c cM zM N

The TBBK model also requires the ionic radii and limiting conductivities of the species at T, p. The radii of single ions were set equal to the crystallographic radii compiled by Marcus.49 The radii of the ion pairs were calculated from the cube-root expressions used by Wood and his co-workers:15,16,19

0 Sr(CF3SO3)2(aq)

aSr(CF SO3)02

3 3 1/3 + + r rNaCF3SO30 = (r Na CF3SO3−)

(19)

3 1/3 −) rSrCF3SO3+ = (r Sr3 2+ + rCF 3SO3

(20)

3 1/3 −) rSr(CF3SO3)20 = (r Sr3 2+ + 2·rCF 3SO3

(21)

3

aSrCF3SO3+ ·aCF3SO3−

(13)

The TBBK equation is derived from the Fuoss−Onsager conductivity equation:44

To use the TBBK equation, an accurate estimate of the ionic equivalent conductivity for sodium was needed. Our treatment 3187



Article

Table 3. Experimental Equivalent Conductivity of Aqueous CF3SO3− and Auxiliary Parameters Used for Fitting the Data with the TBBK Equation T

a

λ°(CF3SO3−)a

ρw

p

−3

K

MPa

kg·m

447.92 502.33 548.47 599.43 625.21

20.81 20.90 20.59 20.50 20.65

904.84 844.36 778.94 677.93 595.83

S·cm ·mol 2

pKw 11.357 11.108 11.096 11.361 11.749

223.4 290.6 350.5 402.5 458.6

± ± ± ± ±

−1

1.5 2.3 2.2 3.5 6.3

λ°(Na+)b S·cm ·mol 2

264.5 342.7 401.3 471.5 531.8

−1

λ°(OH−)d

λ°(H+)c S·cm ·mol 2

791.5 856.0 884.4 906.4 912.7

−1

S·cm2·mol−1 607.0 707.3 771.0 819.0 840.2

From the TBBK fit. bFrom Zimmerman et al.23 cFrom Marshall.50 dFrom Ho et al.51

Figure 4. Flowchart for the TBBK fitting process.

is based on the experimental values of λ°(Na+) measured by Zimmerman et al.23 The fitted parameters for the reduced density relationship of Marshall,50 reported by Zimmerman et al.,23 were used to calculate λ°(Na+), at the desired temperature and pressure. The additivity of λ° then provided the path for all single ionic equivalent conductivities. Knowledge of λ°(Na+) permitted the calculation of λ°(CF3SO3−) from our sodium triflate conductivity measurements, and knowledge of λ°(CF3SO3−) permitted the calculation of λ°(Sr2+). The values for the limiting equivalent conductivity at infinite dilution were taken from Marshall50 for H+ and from Ho et al.51 for OH− (except at 295 K, the value used was taken from Marshall50). The limiting equivalent conductivity at infinite dilution for the + SrCF3SO3(aq) ion pair was estimated from the expression reported by Anderko and Lencka:1 ◦ λ ion pair =

adjusted using Marshall’s reduced density equation,50 at the temperature and pressure of interest. 4.2. Fitting Strategy. Our strategy for fitting the TBBK model to our data is summarized in Figure 4. All of our solutions were fitted with the equation for unassociated electrolytes before deciding whether to include an association constant or not. First, we set up some initial values for λ° and/ or KA,m and for the different species in solution. Molalities were converted into molarities by using the density of pure water for the first iteration. The chemical speciation was then determined following the mathematical treatment proposed in “Aquatic Chemistry” by Stumm and Morgan,53 which permits a relatively easy method to choose the required number of reactions occurring as well as the number of chemical species involved. The activity coefficients were calculated using the MSA theory in the molarity scale. The density for each solution was determined through a minimization process and was calculated as discussed previously. Finally we used the TBBK equation coupled with a simple mixing rule to calculate the conductivity of the solution. We considered all of the ions present in the solution, κ + κth w , including the contributions of all of the species from the ionization of water. The resulting difference in conductivity was negligible except at the most dilute concentrations. Finally, equivalent conductivities at infinite dilution and the association constants were obtained from the combination of the conductivities and the speciation data. The whole process was reiterated until the difference between the fitted values and the experimental data was minimized.

|z ion pair| ⎡ n ⎢∑i = 1 ⎣

3 ⎤1/3

( ) ⎥⎦ zi λi◦

(22)

where zion pair is the charge of the ion pair, zi the charge of the ion contributing to the ion pair formation, and n is the number of ions, n = 2. This method agreed well with the results of Bianchi et al.,52 for the MgCl+ ion pair. Temperature and pressure differences between our measurements on each NaCF3SO3 and Sr(CF3SO3)2 data point were sometimes substantial by up to 2 K and 0.5 MPa. To eliminate this, our ionic conductivities for CF3SO3− from Table 3 were 3188



Article

We started the fitting process by combining our experimental conductivity data for sodium triflate with the single-ion equivalent conductivities for sodium, λ°(Na+), from Zimmerman et al.,23 to obtain the single ion equivalent conductivities for the triflate ion, λ°(CF3SO3−), and KA,NaCF3SO3 if association had to be considered. Then from Λ°[Sr(CF3SO3)2] and λ°(CF3SO3−), we obtained λ°(Sr2+), KA,SrCF3SO3+, and KA,Sr(CF3SO3)2. Ionic equivalent conductivities and association constants were regressed by the Levenberg−Marquardt nonlinear, least-squares technique. The weights δi in the least-squares fit were estimated from statistical uncertainties of the experimental impedance measurements. The precision of our fitted model lies within the statistical uncertainties of our measurements, consistent with this observation. We believe the overall accuracy of the conductivity data to be ± 2 % or better and that the fitted equilibrium constants were accurate to ± 5 % or better. The residuals from the regressions calculated using the fit parameters Λ° and KA,m were usually random (Figure 5). Finally, as an independent check on the fitting process, the FHFP conductivity equation54,55 was used to fit the sodium triflate conductivity data. The FHFP equation is: Λ = Λ° − S · c1/2 + E ·c ln(c) + J1 ·c − J2 ·c 3/2

(23)

where S is the Onsager limiting slope and the terms E, J1, and J2 theoretical expressions related to the Bjerrum distance and solvent parameters, as given by Fernández-Prini.55 Details of the fit are given in the Supporting Information. Since the model is only valid for symmetrical electrolytes, it was not possible to apply it to the results for Λ[Sr(CF3SO3)2].

5. RESULTS 5.1. Limiting Equivalent Conductivities. Equivalent conductivities at infinite dilution and finite concentrations, Λ°, for sodium and strontium triflate, obtained by fitting the TBBK model to our experimental conductivity data for NaCF3SO3 and Sr(CF3SO3)2, are reported in Tables 1 and 2, respectively. The fitted values of equivalent conductivity at each experimental concentration are also tabulated. Table 1 also includes the values of Λ° and Λ obtained by fitting the FHFP model to the experimental conductivities for sodium triflate, using solution densities obtained from the TBBK fitting procedure. The results for Λ as well as the values for Λ° obtained from the two models agreed to within 1 % or less. The equivalent ionic conductivities at infinite dilution for triflate, λ°(CF3SO3−), and strontium, λ°(Sr2+), obtained from the TBBK fits are reported in Tables 3 and 4. Recently, Zimmerman et al.23,56,57 and Erickson et al.21 reported that equivalent conductivities at infinite dilution, Λ°, could be accurately represented by simple empirical functions of the solvent viscosity and density. The data reported here, along with the single data point reported by Okan and Champeney58 at room temperature, could be fitted accurately using the correlation reported in our earlier paper,23 which takes the form: ⎛ A ⎞ log Λ° = log A1 + ⎜⎜A 2 + 3 ⎟⎟ ·log ηw ρw ⎠ ⎝

Figure 5. (a) Relative deviations of the experimental equivalent conductivity data from the TBBK fit for aqueous NaCF3SO3 from T = (448 to 623) K at p = 20 MPa, plotted as the percent difference of the residuals versus the square root of the concentration: □, 448 K; ▲, 502 K; △, 548 K; ◊, 599 K; ○, 625 K. (b) Relative deviations of the experimental equivalent conductivity data from the TBBK fit for aqueous Sr(CF3SO3)2 from T = (295 to 623) K at p = 20 MPa, plotted as the percent difference of the residuals versus the square root of the concentration: ⧫, 295 K; ●, 375 K; □, 446 K; ▲, 502 K; △, 548 K; ◊, 599 K; ○, 625 K.

Longinotti and Corti59 with the addition of the A3/ρw term. The extra term is required to fit the high temperature data and, in the fits reported here and below, the A3 parameter was found to be statistically significant. Following Zimmerman et al.,23 this correlation (eq 24) was also applied to single ions to obtain expressions for the ionic conductivities of CF3SO3− and Sr2+ at infinite dilution, λ°(CF3SO3−) and λ°(Sr2+). Results are plotted in Figures 6 and 7 and tabulated in Table 5. The set of equations developed by Marshall,50 based on a reduced density relationship, was also used to fit our data for λ°(CF3SO3−) and λ°(Sr2+) over the experimental range of temperature and density. Briefly, the correlation is based on a

(24)

Here, ηw is the solvent viscosity in Poise (1 Pa·s = 10 Poise), and A1, A2, and A3 are fitting parameters found by weighted leastsquares regression. Equation 24 was fitted to the temperatureand pressure-dependent experimental values of Λ° from Tables 1 and 2. We note that eq 24 is similar to that reported by 3189



Article

Table 4. Experimental Equivalent Conductivity of Aqueous Sr2+ and Auxiliary Parameters Used for Fitting the Data with the TBBK Equation T

p

ρw

λ°(CF3SO3−)b

λ°(Sr2+)a −3

K

MPa

kg·m

294.96 374.83 445.93 501.97 547.84 599.32 625.39

17.88 21.06 20.90 20.92 20.51 20.51 21.08

1005.76 966.73 906.85 844.83 779.86 678.27 597.74

pKw 14.039 12.153 11.370 11.108 11.096 11.360 11.734

−1

S·cm ·mol 2

55.1 179.8 324.6 435.2 496.0 580.3 649.6

± ± ± ± ± ± ±

−1

S·cm ·mol 2

0.2 0.8 5.5 4.3 4.0 11.0 15.1

λ°(OH−)d

λ°(H+)c −1

S·cm ·mol 2

39.7 133.9 220.5 290.2 349.8 402.3 457.2

333.6 637.8 788.5 855.7 884.1 906.4 912.7

−1

S·cm ·mol 2

185.2 440.1 603.3 706.6 770.3 818.9 840.1

λ°(SrCF3SO3+)e S·cm2·mol−1 / / 139.6 190.1 222.3 260.4 291.8

From the TBBK fit. bFrom fitting the Marshall reduced density model to data in Table 3. cFrom Marshall.50 dFrom Ho et al.51 eEstimated from eq 22.

a

Figure 6. Experimental equivalent conductivity of aqueous sodium and strontium triflate as a function of the viscosity of water from T = (298 to 623) K at p = 20 MPa: ○, Sr(CF3SO3)2 (this work); ◊, NaCF3SO3 (this work); ⧫, NaCF3SO3 (Okan and Champeney58). The solid lines represent the viscosity correlation (eq 24) and the dashed lines, the Marshall density correlation50 (eq 25).

Figure 7. Experimental single ion equivalent conductivity of aqueous strontium ion and triflate ion as a function of the viscosity of water from T = (298 to 623) K at p = 20 MPa: ○, Sr2+ (this work); ◊, CF3SO3− (this work); ⧫, CF3SO3− (Okan and Champeney58). The solid lines represent the viscosity correlation (eq 24) and the dashed lines, the Marshall density correlation50 (eq 25).

linear dependency of limiting ionic equivalent conductivity with density at constant temperature:

are likely due to the more restricted concentration range of validity of the FHFP model.45 The TBBK results were used in all subsequent calculations, here and elsewhere, for consistency with values for strontium triflate and other asymmetric electrolytes, for which the FHFP equation cannot be applied. The association constants obtained from the TBBK fit to our data for strontium triflate are also tabulated in Table 7 and plotted in Figure 9. Statistically significant formation constants for the charged ion pair, SrCF3SO3+, were observed at temperatures T ≥ 445 K. Association to form the neutral ion pair, Sr(CF3SO3)20, was found to be significant at temperatures T ≥ 547 K. We used the density model of Mesmer et al.60 (eq 26) to correlate these association constants over the temperature range investigated. The expression takes the form,

⎛ ρ ⎞ λ° = λ°°·⎜⎜1 − w ⎟⎟ ρh ⎠ ⎝

(25)

Here, λ°° and ρh are hypothetical (extrapolated) values of the limiting equivalent conductivity and solvent density ρw at a given temperature which correspond to values of ρ = 0 and λ° = 0, and ρw/ρh is the reduced density. The term ρh was used as an adjustable parameter to model the TBBK data in Tables 4 and 5 and was found to be dependent on the temperature from (445 to 625) K. Values of ρh for Sr2+ and CF3SO3− are tabulated in Table 6, for each experimental temperature. At temperatures below 445 K, values of λ° for each ion at 20 MPa were calculated by linear interpolation of the values of ρh given in Table 6. The results for λ°(Sr2+) and λ°(CF3SO3−) are plotted in Figures 6 and 7. 5.2. Association Constants. Statistically significant association constants were obtained for sodium triflate from both the TBBK and the FHFP models at temperatures T ≥ 445 K. The values of KA from the two models agreed to within the combined statistical uncertainties, with small differences that

log KA, m = a +

⎡ g ⎤ f b c d + 2 + 3 + ⎢e + + 2 ⎥ ·log ρw ⎣ T T T T T ⎦ (26)

where the constants a to g are adjustable fitting parameters; ρw is the density of water at the temperature and pressure of interest, taken from Wagner and Pruss.31 Regressions were done using many combinations of fitting parameters. Using 3190



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Table 5. Fitted Parameters for the Temperature Dependence of Limiting Equivalent Conductivities, Λ°(NaCF3SO3) and Λ°(Sr(CF3SO3)2), and Limiting Single-Ion Equivalent Conductivities, λ°(Na+), λ°(CF3SO3−), and λ°(Sr2+), According to the Viscosity−Density Model (eq 24) NTotala

species Λ°(NaCF3SO3) Λ°(Sr(CF3SO3)2) λ°(Na+)d λ°(CF3SO3−) λ°(Sr2+)

A1

A3

ΔX/Xb

N*c

± 0.027 ± 0.034

28.67 ± 12.06 35.02 ± 15.15

0.600 1.18

6 8

± 0.004 ± 0.059 ± 0.041

10.18 ± 2.09 50.19 ± 26.36 41.58 ± 18.19

3.66 1.30 1.41

82 6 8

A2

6 8

0.973 ± 0.073 0.974 ± 0.090

110 6 8

0.553 ± 0.005 0.426 ± 0.069 0.502 ± 0.056

Salts −0.998 −1.024 Single Ions −0.965 −1.035 −1.053

Number of experimental data points used to regress parameters A1 to A3. b100·∑ni (1/n)·(|Λ°i ,exp − Λ°i ,fit|/Λ°i ,exp) or 100·∑ni (1/n)·(|λ°i ,exp − λi°,fit|/λi°,exp). cNumber of points agreeing to the fit within the experimental error. dFrom Zimmerman et al.23 a

For the first association constant of strontium triflate, KA,m (SrCF3SO3+), both combinations of the adjustable parameters yielded relative absolute deviations of better than 3 %, with the b and f parameters as slightly more accurate. Statistically significant results for the second association of strontium triflate, KA,m [Sr(CF3SO3)20], were obtained only at the three highest experimental temperatures. Values of the a and e or b and f parameters are also listed in Table 8. The parameters a and b yielded the best statistical fit to log KA for the formation of Sr(CF3SO3)20. These were also included in Table 8.

Table 6. Fitted Parameters for the Limiting Ionic Equivalent Conductivities, λ°, According to the Marshall Reduced Density Model50 (eq 25)a T

p

ρw

ρh

K

MPa

kg·m−3

kg·m−3

298.15 447.92 502.33 548.47 599.43 625.21

0.1 20.81 20.90 20.59 20.50 20.65

997.047 904.84 844.36 778.94 677.93 595.83

1410 1377 1334 1318 1235 1213

294.96 374.83 445.93 501.97 547.84 599.32 625.39

17.88 21.06 20.90 20.92 20.51 20.51 21.08

CF3SO3−

6. DISCUSSION 6.1. Comparisons with Previous Studies. The only previous study of sodium triflate conductivities and association constants at elevated temperatures is by Ho and Palmer,17 who carried out their measurements in a static AC conductance cell. These results showed considerably more scatter than our data. A close examination of Ho and Palmer’s results17 revealed that most of the reported fits of the empirical Shedlovsky equation, to their data yielded systematic errors, with values of Λ°(NaCF3SO3) that were significantly smaller than the experimental values of Λ at the lowest concentrations. We attempted to refit their data with the FHFP equation to determine whether their use of the Shedlovsky equation61 was the source of this problem;15 however the same phenomena persisted unless KA was added as an adjustable parameter. Although the resulting values of Λ° were much more in accordance with our results, in no case was the KA statistically significant at the 95 % confidence limit. It may be that the disagreement is due to the lower precision and accuracy of these measurements, having been done with the older static conductivity cell at ORNL, or to their use of the density of pure water to convert molalities into molarities. Thus, it appears that the data by Ho and Palmer are not sufficiently accurate to permit statistically significant values of Λ° and KA to be determined. A comparison of our equivalent conductivity of aqueous NaCF3SO3, measured at T = 448 K (ρw = 904.84 kg·m−3) and at T = 502 K (844.36 kg·m−3), with Ho and Palmer’s data17 obtained at T = 473 K (850 kg·m−3), is shown in Figure 10 to illustrate these conclusions. 6.2. Limiting Conductivities. Ionic equivalent conductivities at infinite dilution for strontium ion, λ°(Sr2+), were also compared to those of calcium ion, λ°(Ca2+), magnesium ion, λ°(Mg2+) and, nickel ion, λ°(Ni2+), obtained respectively by Méndez de Leo and Wood19 and by Madekumfamba and Tremaine.62 These are plotted in Figure 11 versus the viscosity of water. Nonlinear least-squares fits of the viscosity model (eq 24) and Marshall reduced density model (eq 25) fits to the

Sr2+

a

1005.76 966.73 906.85 844.83 779.86 678.27 597.74

1672 1641 1824 1879 1852 1941 2140

The following expressions were fitted to the isothermal values of ρh. ρh (CF3SO3−) = 1807 − 0.9387·T

(445 K ≤ T ≤ 625 K)

7368 647.096 − T

(445 K ≤ T ≤ 625 K)

ρh (Sr 2 +) = 1796 +

more than two parameters did not lead to statistically significant improvement. The results are tabulated in Table 8 and plotted in Figures 8 and 9. For sodium triflate, poor fits to KA,m were obtained using every combination of parameters (average relative difference > 12 %). The best results were acquired when using parameters a and e or b and f. The former is slightly more accurate, while the latter is consistent with the form of the “density” model reported by Anderson et al.,61 which leads to the following simple expressions for the standard partial molar properties, ΔHm°, ΔCp,m°, and ΔVm° useful for extrapolating data from 298.15 K. ΔHm° = −R[ln 10·b + f ·(T ·αw + ln ρw )]

(27)

ΔCp , m° = −f ·RT (∂αw /∂T )p

(28)

and ΔVm° = −f ·R ·βw

(29)

Here, αw and βw are the thermal expansivity and isothermal compressibility of water at the temperature and pressure of KA,m. 3191



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Table 7. Experimental Association Constant Determined when Fitting the Data with the TBBK and FHFP Equations species NaCF3SO30 NaCF3SO30 NaCF3SO30 NaCF3SO30 NaCF3SO30 SrCF3SO3+ SrCF3SO3+ SrCF3SO3+ SrCF3SO3+ SrCF3SO3+ Sr(CF3SO3)20 Sr(CF3SO3)20 Sr(CF3SO3)20

T

p

ρw

K

MPa

kg·m−3

pKw

KA,m (TBBK)

447.92 502.33 548.47 599.43 625.21 445.93 501.97 547.84 599.32 625.39 547.84 599.32 625.39

20.81 20.90 20.59 20.50 20.65 20.90 20.92 20.51 20.51 21.08 20.51 20.51 21.08

904.84 844.36 778.94 677.93 595.83 906.85 844.83 779.86 678.27 597.74 779.86 678.27 597.74

11.36 11.11 11.10 11.36 11.75 11.37 11.11 11.10 11.36 11.73 11.10 11.36 11.73

2.11 ± 0.44 2.98 ± 0.38 3.58 ± 0.38 5.70 ± 0.69 17.2 ± 1.7 11.4 ± 3.2 23.7 ± 2.8 46.7 ± 5.4 106 ± 21 378 ± 54 6.0 ± 3.4 38 ± 14 77 ± 19

KA,m (FHFP) 1.3 3.2 4.0 8.4 23.0

± ± ± ± ±

0.4 0.4 0.4 1.7 5.0

Table 8. Fitted Parameters for the Temperature and Density Dependence of Association Constants, KA, According to the Density Model, eq 26 solute

a

b·10−3

f·10−3

ΔK/Ka

−3.39 ± 1.34 −6.09 ± 0.68 −6.15 ± 15.97

9.68 ± 4.14

10.12 ± 3.84 18.5 ± 2.0 18.3 ± 44.9 −4.87 ± 2.51

0.136 0.027 0.087 0.013

NaCF3SO30 SrCF3SO3+ Sr(CF3SO3)20 Sr(CF3SO3)20 a

fit exp ∑ni (1/n)·(|Kexp A,i − KA,i|/KA,i ).

Figure 9. Experimental values for the association constants KA,m of NaCF3SO3 and Sr(CF3SO3)2 from T = (445 to 623) K at p = 20 MPa, as derived from the TBBK equation: △, NaCF3SO3; ○, Sr(CF3SO3)2 (first association); ●, Sr(CF3SO3)2 (second association). The solid lines represent the density model fit (eq 26) with parameters b and f for the association of NaCF3SO3 and the first association of Sr(CF3SO3)2 and parameters a and b for the second association of Sr(CF3SO3)2.

Figure 8. Experimental values for the association constants of NaCF3SO3 in H2O from T = (445 to 623) K at p = 20 MPa derived from the TBBK equation (○) and the FHFP equation (◊). The solid line corresponds to the density model fit (eq 26) with parameters b and f.

values for λ°(Sr2+) are also included in Figure 11. The agreement between the values for λ°(Sr2+) and λ°(Ca2+) at temperatures above 373 K is within ± 2 %, at all temperatures except 473 K, where Méndez de Leo and Wood reported a large experimental uncertainty in λ°(Ca2+), ± 97 S cm2·mol−1. The values for λ°(Mg2+) and λ°(Ni2+) are lower than those for λ°(Sr2+) at 473 K by about 15 %, rising to values about 15 % higher than λ°(Sr2+) at 625 K. These small systematic differences may be due to differences in the ionic radii and

hydration numbers of the aquo-ions, which have been determined over a wide range of temperatures by neutron diffraction and EXAFS. Data from the recent review by Seward and Driesner63 show that the primary hydration numbers of Ca(H2O)n2+ and Sr(H2O)n2+ are similar, and that both decrease from n = 8 to n = ∼6 as temperature is raised from (298 to 373) K. The primary hydration number of Ni(H2O)n2+ is 3192



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predictive model of the Arrhenius form but did not include strontium or triflate ions in their work. Likewise, the two models used in interpreting our experimental values of λ°, the viscosity relationship (eq 24) and Marshall’s reduced density relationship (eq 25), do not include parameters for strontium or triflate ions with which to compare our results. Both models have the potential to be used as predictive tools by developing correlations to estimate parameters for “missing” species. We have not yet attempted to reformulate these models using modern data, to assess their accuracy for this purpose, or to develop appropriate correlations. We note that Marshall’s reduced density relationship50 is based on the observation that the limiting behavior of λ° for all ions approaches a common value in the high-temperature, low-density limit. The second approximation incorporated into this model was that ρh, the fitting parameter associated with the limiting value of the density extrapolated to λ° = 0, is a temperatureindependent constant for each ion. More accurate modern data, such as those in Table 6, show that this is not strictly true but that values of ρh above about 380 K are well-behaved. Figures 6, 7, and 11 offer a comparison of the viscosity model (eq 24) and the Marshall model (eq 25) for the salts and the CF3SO3− and Sr2+ ions. For the temperatures between room temperature and some temperature between (353 to 363) K (corresponding to −3.45 ≥ log η ≥ −3.50), the Marshall model (dashed line) yields more positive results than the viscosity model (solid line) for all ions. This same trend was also seen for the Na+ and Cl− ions (in Figure 7 of Zimmerman et al.23). Because it was found that the viscosity model yielded better fits than that of Marshall in this temperature range for Na+ and Cl− ions and because the trends in the curves are the same for the CF3SO3− and Sr2+ ions, we believe that the viscosity model is the most accurate model for reproducing experimental data in this low-temperature range. Above this temperature the two models become equally good, as indicated by the merging of the solid and dashed lines. 6.3. Association Constants. Since first proposed by Fabes and Swaddle,12 triflate has been used as a thermally stable, noncomplexing anion in hydrothermal studies by experimentalists, who were seeking to measure equilibrium constants, transport properties, and spectra of cations without the complications of cation−anion association. Many of these studies are summarized in the recent IAPWS critical review of the physical chemistry of hydrothermal systems.6 To the best of our knowledge, with the exception of the conductivity study for aqueous NaCF3SO3 by Ho and Palmer,17 the present study is the first reported attempt to quantify the degree of association in cationtriflate solutions at these low concentrations under hydrothermal conditions. The TBBK fits to the concentration-dependent equivalent conductivity data for NaCF3SO3 and Sr(CF3SO3)2 yielded statistically significant ionic association constants, KA,m, for the species NaCF3SO30 at temperatures T ≥ 448 K; SrCF3SO3+ at T ≥ 448 K, and for Sr(CF3SO3)20 at T ≥ 548 K. As would be expected from simple electrostatic arguments, the values of KA,m, for SrCF3SO3+ are greater than those for the sodium ion pair, NaCF3SO30, and for the neutral strontium species Sr(CF3SO3)20. The association constant for Sr(CF3SO3)20 is similar to that of NaCF3SO30 at 548 K but increases more steeply with temperature. The results in Table 7 show that significant association to form the triflate complex (KA > 10) for the monovalent Na+ cation should be of concern to experimentalists at temperatures above ∼600 K. Association with the

Figure 10. Comparison between the experimental equivalent conductivities of aqueous NaCF3SO3 from this work: ○, 448 K (ρw = 904.84 kg·m−3); ◊, 502 K (ρw = 844.36 kg·m−3), and those of Ho and Palmer:17 ▲, 473 K (ρw = 850 kg·m−3). The solid lines represent the TBBK fit to our data.

Figure 11. Experimental single ion equivalent conductivities of aqueous ○, Sr2+; ◊, Ca2+;19 △, Mg2+;62 and □, Ni2+;62 plotted as a function of the viscosity of water from T = (298 to 623) K. The solid line represents the viscosity correlation (eq 24), and the dashed line is the Marshall density correlation50 (eq 25), both fitted to the λ°(Sr2+) data alone.

defined by ligand field effects and decreases from n = 6 to n = ∼5 over the same temperature range. The atomic radii (M−O distance), which are independent of temperature, also differ: r(Ca2+) = 2.45 Å; r(Sr2+) = 2.60 Å; r(Ni2+) = 2.06 Å. Unfortunately, no hydrothermal data for Mg2+ are cited in the review. The behavior of λ° for these M2+ ions at higher temperatures also undoubtedly includes the contribution of long-range polarization, which is the dominant hydration effect under hydrothermal conditions.60 It is of interest to compare the measured values for λ°(Sr2+) and λ°(CF3SO3−) reported here with estimates from predictive correlations. Oelkers and Helgeson64,65 reported a predictive model for calculating λ°. Their correlation is based upon an Arrhenius type of equation. The estimated values of λ°(Sr2+) reported by Oelkers and Helgeson along the saturation curve are greater than those calculated with the viscosity model by about 10 % between (298 and 623) K. This includes a disagreement of 12 % at 298.15 K with the value reported in Robinson and Stokes.66 Anderko and Lencka1 also reported a 3193



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Figure 12. Distribution of species in aqueous solutions of (a) NaCl,23 (b) NaCF3SO3 (this work), and (c) Sr(CF3SO3)2 (this work), at temperatures T = 548 K and T = 623 K, p = 20 MPa: ○, free cation; ⧫, charged ion pair; ●, neutral ion pair.

divalent Sr2+ cation to form SrCF3SO3+ becomes important at temperatures above 445 K. Quantitative calculations of these ion pairing effects can be made with the “density” model of Anderson et al.60 using the parameters in Table 8. The ion-pair formation constants determined in the current study (Table 7) and those for NaCl from Zimmerman et al.23 were used to calculate the distribution of species in aqueous solutions of NaCF3SO3, Sr(CF3SO3)2, and NaCl. To illustrate the effect of temperature, the results for T = (548 and 623) K at p = 20 MPa are plotted in Figure 12 for molalities m ≤ 0.05 mol·kg−1. At both temperatures, NaCl is more strongly associated than NaCF3SO3. At molality m = 0.01 mol·kg−1, the relative concentrations of the neutral ion pairs NaCl0 and NaCF3SO30 are ∼ 4 % and ∼ 2 %, respectively, at T = 548 K; and ∼ 13 % and ∼ 8 % at T = 623 K. As expected from the higher charge density of Sr2+, Sr(CF3SO3)2 is more heavily associated than either of the 1:1 electrolytes, at all concentrations. At T = 548 K and m = 0.01 mol·kg−1, over 18 % of aqueous Sr2+ is associated, with SrCF3SO3+ as the dominant ion-pair. At T = 623 K and the same molality, the associated species comprise over 50 % of the solution, and the concentration of the neutral species Sr(CF3SO3)20 is significant. At molalities m ≥ 0.04 mol·kg−1, Sr(CF3SO3)20 is the dominant species at this temperature. Such behavior is predicted by simple ion association models, such as the Bjerrum and Fuoss equations,67 because the decrease in the static dielectric constant of water with increasing temperature destabilizes more highly charged ionic species relative to the associated ion-pairs. As mentioned above, many experimentalists have used triflate as a noncomplexing anion for studies under hydrothermal

conditions. Clearly this assumption becomes less valid at temperatures above 548 K. The ion association constant parameters in Tables 7 and 8 provide a way to quantify these effects.

7. CONCLUSIONS This paper reports frequency-dependent electrical conductivity measurements for aqueous sodium trifluoromethanesulfonate (“triflate”) and strontium triflate from ambient temperatures to T = 623 K at p = 20 MPa, over a very wide range of ionic strengths. We note that, at temperatures above 548 K, association constants derived from the concentration-dependent equivalent conductivities were increasingly sensitive to the assumptions used to calculate solution densities, and that experimental data or accurate estimates are required under these extreme conditions. The significance in the work lies in the experimental values for the limiting equivalent conductivity of the triflate ion, λ°(CF3SO3−) and the strontium ion, λ°(Sr2+); the successful application of this TBBK modeling procedure; and the association constants, KA,m, for the species NaCF3SO30, SrCF3SO3+, and Sr(CF3SO3)20. The temperature dependence of the limiting equivalent conductivities and association constants from (298 to 623) K could be represented accurately as functions of viscosity and solvent density, respectively. The successful application of the viscosity correlation reported by Zimmerman et al.23 to these new data suggests that it may provide an alternative to Marshall’s reduced density model,50 as a tool for predicting limiting conductivities at elevated temperatures and pressures. Finally, these results provide the foundation for similar experimental studies of the complexation of Sr2+, with other anions under extreme hydrothermal 3194



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Water, Steam and Aqueous Solutions; Elsevier Academic Press: Amsterdam, 2004. (7) Shock, E. L.; Oelkers, E. H.; Johnson, J. W.; Sverjensky, D. A.; Helgeson, H. C. Calculation of the Thermodynamic Properties of Aqueous Species at High Pressures and Temperatures. J. Chem. Soc., Faraday Trans. 1992, 88, 803−826. (8) Sedlbauer, J.; O’Connell, J. P.; Wood, R. H. A new equation of state for correlation and prediction of standard molal thermodynamic properties of aqueous species at high temperatures and pressures. Chem. Geol. 2000, 163, 43−63. (9) Krossing, I.; Raabe, I. Noncoordinating AnionsFact or Fiction? A Survey of Likely Candidates. Angew. Chem., Int. Ed. 2004, 43, 2066− 2090. (10) Henderson, M. P.; Miaserk, V. I.; Swaddle, T. W. Kinetics of Thermal Decomposition of Aqueous Perchloric Acid. Can. J. Chem. 1971, 49, 317−324. (11) Djamali, E.; Chen, K.; Cobble, J. W. Standard State Thermodynamic Properties of Aqueous Sodium Perrhenate using High Dilution Calorimetry up to 598.15 K. J. Chem. Thermodyn. 2008, 41, 1035−1041. (12) Fabes, L.; Swaddle, T. W. Reagents for High Temperature Aqueous Chemistry: Trifluoromethanesulfonic Acid and its Salts. Can. J. Chem. 1975, 53, 3053−3059. (13) Zimmerman, G. H.; Gruskiewicz, M. S.; Wood, R. H. New Apparatus for Conductance Measurements at High Temperatures: Conductance of Aqueous Solutions of LiCl, NaCl, NaBr, and CsBr at 28 MPa and Water Densities from 700 to 260 kg m−3. J. Phys. Chem. 1995, 99, 11612−11625. (14) Ho, P. C.; Bianchi, H.; Palmer, D. A.; Wood, R. H. Conductivity of Dilute Aqueous Electrolyte Solutions at High Temperatures and Pressures Using a Flow Cell. J. Solution Chem. 2000, 29, 217−235. (15) Sharygin, A. V.; Wood, R. H.; Zimmerman, G. H.; Balashov, V. N. Multiple Ion Association versus Redissociation in Aqueous NaCl and KCl at High Temperatures. J. Phys. Chem. B 2002, 106, 7121− 7134. (16) Hnedkovsky, L.; Wood, R. H.; Balashov, V. N. Electrical Conductances of Aqueous Na2SO4, H2SO4, and Their Mixtures: Limiting Equivalent Ion Conductances, Dissociation Constants, and Speciation to 673 K and 28 MPa. J. Phys. Chem. B 2005, 109, 9034− 9046. (17) Ho, P. C.; Palmer, D. A. Electrical Conductances of Aqueous Sodium Trifluoromethanesulfonate from 0 to 450 °C and Pressures to 250 MPa. J. Solution Chem. 1995, 24, 753−769. (18) Sipos, P.; May, P. M.; Hefter, G. T. Carbonate Removal from Concentrated Hydroxide Solutions. Analyst 2000, 125, 955−958. (19) Méndez De Leo, L. P.; Wood, R. H. Conductance Study of Association in Aqueous CaCl 2 , Ca(CH 3 COO) 2 , and Ca(CH3COO)2·nCH3COOH from 348 to 523 K at 10 MPa. J. Phys. Chem. B 2005, 109, 14243−14250. (20) The schematic diagram in Erickson et al.21 contains connection errors; Figure 1b is correct. (21) Erickson, K. M.; Arcis, H.; Raffa, D.; Zimmerman, G. H.; Tremaine, P. R. Deuterium Isotope Effects on the Ionization Constant of Acetic Acid in H2O and D2O by AC Conductance from 368 to 548 K at 20 MPa. J. Phys. Chem. B 2011, 115, 3038−3051. (22) Bard, A. J.; Faulkner, L. R. Electrochemical methods: Fundamentals and applications; John Wiley & Sons: New York, 2001. (23) Zimmerman, G. H.; Arcis, H.; Tremaine, P. R. Limiting Conductivities and Ion Association Constants of Aqueous NaCl under Hydrothermal Conditions: Experimental Data and Correlations. J. Chem. Eng. Data 2012, 57, 2415−2429. (24) Balashov, V. N.; Fedkin, M. V.; Lvov, S. N. Experimental System for Electrochemical Studies of Aqueous Corrosion at Temperatures above 300 °C. J. Electrochem. Soc. 2009, 156, C209−C213. (25) Impedance Spectroscopy, Theory, Experiment and Applications; Barsoukov, E., MacDonald, J. R., Eds.; Wiley-Interscience: New York, 2005. (26) Cohen, E. R.; Cvitaš, T.; Frey, J. G.; Holmström, B.; Kuchitsu, K.; Marquardt, R.; Mills, I.; Pavese, F.; Quack, M.; Stohner, J.; Strauss,

conditions relevant to supercritical water nuclear reactors and geothermal applications.

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ASSOCIATED CONTENT

* Supporting Information S

Details on the data treatment strategy based on the Helgeson− Kirkham−Flowers−Tanger (HKF) model and values of the HKF parameters39−42 for the triflate species are tabulated in Section S1. Details of the fit done with the FHFP equation55 regarding the analysis of the NaCF3SO3 conductivity data are given in Section S2. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*Phone: 519-824-4120, ext. 56076. Fax: 519-766-1499. E-mail: [email protected]. Funding

This research was supported by the National Science and Engineering Research Council of Canada (NSERC), Ontario Power Generation Ltd. (OPG), the University Network of Excellence in Nuclear Engineering (UNENE), and Bloomsburg University for sabbatical leave (G.H.Z.). G.H.Z. would like to express appreciation for the financial support provided by Fulbright Canada and gratitude for the support of the governments of Canada and the United States in making this program possible. Notes

The authors declare no competing financial interest. § E-mail: [email protected]; [email protected].

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ACKNOWLEDGMENTS The authors express deep gratitude to Prof. Robert H. Wood, University of Delaware, for donating the AC conductance cell to the Hydrothermal Chemistry Laboratory at the University of Guelph, for providing us with the benefit of his extensive operating experience, and for many fruitful discussions. We are also grateful to Mr. Ian Renaud and Mr. Case Gielen of the electronics shop and machine shop in the College of Physical and Engineering Science at the University of Guelph, for their very considerable expertise in maintaining and modifying the instrument and its data acquisition system. Technical advice and encouragement were provided by Dr. Dave Guzonas, Atomic Energy of Canada Ltd.; Dr. Dave Evans, OPG; and Dr. Mike Upton, Bruce Power Ltd.

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REFERENCES

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