Electrochemical processes in high-temperature aqueous solutions

Aqueous Systems at Elevated Temperatures and Pressures: Physical Chemistry in Water, Steam and Hydrothermal Solutions D.A. Palmer, R. Ferna´ndez-Prini and A.H. Harvey (editors) q 2004 Elsevier Ltd. All rights reserved

Chapter 11

Electrochemical processes in high-temperature aqueous solutions Serguei N. Lvova,* and Donald A. Palmerb a Department of Energy and Geo-Environmental Engineering, The Energy Institute, The Pennsylvania State University, 207 Hosler Building, University Park, PA 16802, USA b Chemical Sciences Division, Oak Ridge National Laboratory, P.O. Box 2008, Building 4500S, Oak Ridge, TN 37831-6110, USA

11.1. Introduction Understanding the behavior of high-temperature aqueous solutions represents a new frontier in electrochemical studies that is both technically challenging and technologically important. Interest in this field has increased significantly over the last decade, mainly due to the many important electrochemical processes that take place in high-temperature aqueous environments. Water is the most ubiquitous of solvents and by virtue of its extraordinary physicochemical and transport properties it forms the medium in which diverse processes occur from biochemistry to geochemistry. However, due to the difficulty of performing electrochemical measurements at high temperatures and pressures, there is a scarcity of electrochemical studies at temperatures above 100 8C. This chapter provides a background of the techniques available at elevated temperatures, particularly as related to measurements of pH, and serves as a critical review of their application to electrochemical studies of high-temperature aqueous systems.

11.2. Fundamental Principles In general, electrochemical systems are heterogeneous and involve at least two fundamental processes — mass transport and an electron transfer reaction. Moreover, electrochemical reactions involve charged species so that the rate of the electron transfer reaction depends on the electric potential difference between * Corresponding author. E-mail: [email protected]

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the phases (e.g., between the electrode surface and the solution). The mass transport processes mainly include diffusion, migration and convection, and should be taken into account if the electron transfer reaction properties are to be extracted from the experimental measurements. The main property of the ith component in an electrochemical system is the electrochemical potential, m~ ai ; which is defined as:

m~ai ¼ mai þ zi FEa

ð11:1Þ

where mai and zi are the chemical potential and the charge of species, i; respectively; F is the Faraday constant (96 485 C·mol21); and Ea is the inner electric potential in a phase, a: Although Ea is not a measurable quantity, the difference, E, between the inner electric potentials of two electrically conducting phases can be either measured or established in electrochemical experiments. In addition, a part of the inner electric potential, which is called the zeta potential, can be obtained experimentally from electrokinetic studies of a solid/liquid interface. Zeta potential is one of the key parameters of the electrical double layer, EDL (see Chapter 14) and can be used in modeling the EDL structure. An example of such a modeling approach for the high-temperature solid oxidejaqueous solution interface has been published recently (Fedkin et al., 2003). A particular feature of the electrochemical technique is that the total rate of the electrochemical process can be defined by measuring the current density, j, flowing in the electrical circuit where the reaction rate, v (per unit of surface area), is related to the current density as follows: j ¼ nFv

ð11:2Þ

where n is the number of electrons involved in the electrochemical reaction. By considering a reduction/oxidation electrode reaction as a first-order interfacial process (Bard and Faulkner, 2001): kf

Oðxidized formÞ þ ne2 O Rðeduced formÞ kb

the reaction rate will be defined: (1) by the heterogeneous rate constants for the reduction, kf, and oxidation, kb, processes; and (2) by the activities of O, a†O ; and R, a†R ; at the electrode surface as follows: v ¼ kf a†O 2 kb a†R

ð11:3Þ

Within the framework of the activation complex theory, the rate constants can be related to the Gibbs energies of activation for the reduction, DG†R ; and oxidation, DG†O ; reactions as follows: kf ¼ Af expð2DG†R =RTÞ

ð11:4aÞ

kb ¼ Ab expð2DG†O =RTÞ

ð11:4bÞ

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where Af and Ab are the pre-exponential factors, R is the gas constant (8.3145 J·K21·mol21) and T is the temperature in K. The Gibbs energies of activation for the reduction and oxidation processes are different and depend on the potential difference, E, and the potential barrier symmetry, which is defined by the transfer coefficients, ared and aoxid, for the reduction and oxidation reactions, respectively. For a symmetrical barrier, ared ¼ aoxid ¼ 0:5; so for a simple reaction, ared þ aoxid ¼ 1. The relationships between the Gibbs energies of activation, the transfer coefficients and the potential difference between phases are well known, and can be presented for the reduction and oxidation processes as follows: DG†R ¼ DGoR† þ ared nFE

ð11:5aÞ

DG†O ¼ DGoO† 2 aoxid nFE

ð11:5bÞ

where DGoR† and DGoO† are the Gibbs energies of activation for the reduction and oxidation processes, respectively, if the potential difference between the phases is zero. The values of DGoR† and DGoO† can also be defined by corresponding rate constants, kfo and kbo ; as follows: kfo ¼ Af expð2DGoR† =RTÞ ¼ kf expðared nFE=RTÞ

ð11:6aÞ

kbo ¼ Ab expð2DGoO† =RTÞ ¼ kb expð2aoxid nFE=RTÞ

ð11:6bÞ

If standard state conditions prevail, i.e., E ¼ Eo ; then, kfo exp½2ared nFðE 2 Eo Þ=RT ¼ kbo exp½aoxid nFðE 2 Eo Þ=RT ¼ ko ; where ko is a key characteristic of the electron transfer reaction and is called the standard rate constant. The standard rate constant can be used to relate the rate constants, kf and kb, to the potential difference, E, and its equilibrium value, E o, as follows: kf ¼ ko exp½2ared nFðE 2 Eo Þ=RT

ð11:7aÞ

kb ¼ ko exp½2aoxid nFðE 2 Eo Þ=RT

ð11:7bÞ

Insertion of these relationships into Eqs. 11.2 and 11.3 yields the complete currentpotential characteristic (Bard and Faulkner, 2001): j ¼ nFko {a†O exp½2ared nFðE 2 Eo Þ=RT 2 a†R exp½aoxid nFðE 2 Eo Þ=RT}

ð11:8Þ

This is a general equation that can be used in the treatment of all heterogeneous electrochemical processes. The physical meaning of k o relates to the kinetic lability of a reducing/oxidizing electrochemical system. In other words, a system with a large k o will reach equilibrium quickly, whereas a system with a small k o is sluggish.

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At equilibrium, j ¼ 0; and the potential difference will approach the equilibrium value E eq, so that Eq. 11.8 can be written as: nFko a†O exp½2ared nFðEeq 2 Eo Þ=RT ¼ nFko a†R exp½aoxid nFðEeq 2 Eo Þ=RT ¼ jo

ð11:9aÞ

The value, jo, is the exchange current density, which is an important characteristic of the electrochemical system and its reversibility. Taking into account that at equilibrium the bulk activities of O, aO, and R, aR, are the same as at the surface, Eq. 11.9a can be converted to the well-known Nernst equation: Eeq ¼ Eo þ ðRT=nFÞlnðaO =aR Þ

ð11:9bÞ

This equation forms the basis for all potentiometric measurements so that electrode systems are often referred to as exhibiting Nernstian behavior or response during their calibration when the measured potential, E eq, is a linear function of ln(aO /aR) [or log10(aO /aR)] with a ‘theoretical’ slope of RT/nF [or RT/(nF ln(10)] as dictated by Eq. 11.9b.

11.3. Experimental Electrochemical Techniques The main emphasis of this discussion will be directed towards the measurement of pH as this is critical to almost all processes occurring in water and, as such, is cited in many chapters in this book. 11.3.1. ‘Low-temperature’, or General, pH Measurements Potentiometric measurements near ambient conditions have been made for decades with various commercially available glass electrodes. However, there is a saying, ‘pH is the easiest measurement to do and get wrong’. This provocative statement comes largely from the incorrect use of these electrodes, particularly with respect to calibration and the often-ignored contribution of liquid junction potentials to the reading of pH. A detailed discussion of glass electrodes is beyond the scope of this chapter, which is focused on high-temperature measurements, but a general discussion of calibration methods and estimations of liquid junction potentials is given in the sub-sections below. The IUPAC concept of pH (Buck et al., 2002) is based on the original definition in terms of the activity scale by Sørensen and Linderstrøm-Lang (1924): pH ¼ 2log10 aHþ ¼ 2log10 ðmHþ gHþ Þ

ð11:10Þ

where aHþ is the ‘single ion’ activity of the hydrogen ion, which is an immeasurable quantity by any thermodynamic method so that a convention is

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381

needed for the evaluation of pH in this case. Moreover, there is obviously not a constant difference between pH as defined in Eq. 11.10 and 2log10 mHþ ; but this point will be discussed below with reference to the preferred use of the latter in most experimental studies, particularly at high temperatures when applied to the determination of equilibrium constants. Originally, Sørensen (1909) defined pH in terms of the concentration of hydrogen ions (mol·dm23), pHc ¼ 2log10 cHþ (referred to pHc here to avoid confusion and pHm is also used here to represent 2log10 mHþ ; when molality (mol·kg21) is used: where calibration standards or reference solutions contain acids or bases of known (stoichiometric) molarity or molality, respectively). The IUPAC recommendation for pH measurements on the single ion activity scale is that in order for them to be traceable to the SI (International System of Units) method employed, they must fulfill the definition of a ‘primary method of measurement’ which is set out by Buck et al. (2002). For cells without transference of ions (no liquid junction) as in the case of the so-called Harned cell, PtlH2(g)ltest solution (buffer), Cl2 ðaqÞlAgCllAg; in which the following reaction occurs, 12 H2 ðgÞ þ AgClðsÞ ! Hþ ðaqÞ þ AgðsÞ þ Cl2 ðaqÞ; the Nernst equation 11.9b can be rearranged to give (Mesmer and Holmes, 1992; Buck et al., 2002): pðaHþ gCl2 Þ ¼ 2log10 ðaHþ gCl2 Þ ¼ ðEeq 2 Eo Þ=½ðRT=FÞlnð10Þ þ log10 mCl2

ð11:11aÞ

where E o is the standard potential difference in the cell, and is therefore also that of the AgCljAg electrode, and gCl2 is the activity coefficient of the chloride ion. The IUPAC recommended procedure (Buck et al., 2002) for calculating pH is as follows: (1) the cell is first filled with a known dilute concentration of HCl, e.g., 0.01 mol·kg21 HCl solution and the potential is measured. By expressing the activity coefficient of Cl2(aq) in terms of the mean ionic stoichiometric activity coefficient of HCl, g^HCl, which can be determined from either the Debye– Hu¨ckel expression or from published experimental values, and by rearranging Eq. 11.11a: o 2 {2RT lnð10Þ=F}log10 ðmHCl g^HCl Þ Eeq ¼ EAgCljAg

ð11:11bÞ

o can be derived. the value of EAgCljAg (2) If the cell is then filled with solutions of a desired buffer of known ionic strength containing at least three known concentrations of Cl2(aq), the measured potential, E, can be extrapolated linearly to zero chloride, 2log10 ðaHþ gCl2 Þ ¼ 2log10 ðaHþ gCl2 Þo þ SmCl2 ; where S is an empirical temperature-dependent constant. o 2 Þ is calculated using the Bates– Guggenheim expression, log10 gCl2 ¼ (3) ðgClp pffiffiffi ffiffiffi 2A Im =ð1 þ 1:5 Im Þ; where A is the Debye– Hu¨ckel slope, leading to

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the value of ðaHþ Þo and hence from the fundamental definition in Eq. 11.10, pH. The Bates – Guggenheim approximation is deemed satisfactory up to concentrations of 0.1 mol·dm23, at least for monovalent ions, noting that the limit of the ionic strength of most standard buffer solutions is about 0.05 mol·dm23. The importance of performing concomitant estimations of the uncertainties in this ‘absolute’ measurement of pH is discussed in detail in Buck et al. (2002). The reader is referred to the concept raised by Knauss et al. (1990), and discussed briefly by Mesmer and Holmes (1992), of using two ion-selective electrodes in a ‘liquid-junction-free cell’, one being specific for Hþ(aq), the other to another dominant cation or anion of known concentration, and using the Pitzer ion interaction treatment (Pitzer, 1991) to compute a thermodynamic model of the solution. This cell can be calibrated with any number of solutions at the same ionic strength and whose compositions are calculated with the same computer code (i.e., the system is suitable for solutions of high ionic strength, such as those of geological interest) and pH, which is defined with the arbitrary convention, log10 gHþ ¼ 0; is calculated with the activity coefficients of the reference ion determined from the Pitzer model. Mesmer (1991) indicated a basic flaw in this convention, in that the choice of log10 gHþ ¼ 0 implies that gCl2 ¼ g2^ðHClÞ ; which is obviously invalid. Mesmer demonstrated that an arbitrary convention was unnecessary if the molality scale for pH is adopted (see discussion later in this section). In practice, most routine measurements of pH are made with cells with liquid junctions (glass combination electrodes, cells with salt bridges, concentration cells, etc., noting that a glass electrode used in combination with a separate AgCljAg reference electrode in a common test solution containing chloride ion is a cell without a liquid junction). Glass cells are generally non-Nernstian and therefore require calibration against known standard solutions. At temperatures from 0 to 50 8C, IUPAC (Buck et al., 2002) recommends six primary standards and eight secondary standards, whereby each solution is assigned a specific pH value at 5 K intervals over this range. The use of primary and secondary pH standards (buffers) can be tolerated if the ionic strength of the standard solution is similar to that of the test solution, so that in these relative measurements, differences in activity coefficients and liquid junction potentials are minimized. However, in a typical commercial combination glass electrode incorporating a reference electrode, Ag(s)jAgCl(s) in $3.5 mol·kg21 KCl(aq), where the concentrations of the standard(s) (Si) and test (X) solutions are low enough to ignore the liquid junction potential, the value of pH(X) should be determined from a linear regression of the Ei versus pH(Si), where the range of pH(Si) values incorporates the pH(X) value. Meinrath and Spitzer (2000) point out the need for tracing the uncertainties (both systematic and random) in reporting the pH of a solution for reliable pH measurements that mainly referred to the use of glass electrodes. They discuss

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383

multipoint calibrations to obtain meaningful statistics and use of methods other than simple linear regression for derivation of confidence limits. These methods include orthogonal regression, inverse regression and Monte Carlo simulations. This approach is particularly relevant in the measurement of pH of complex multicomponent systems, such as in the study of the hydrolysis of actinides. It should be mentioned that for the range from 100 to 400 8C, Seneviratne et al. (2003) employed a modified version of this standard calibration method by introducing a calibration coefficient, a, which takes into account the irreversible thermodynamic contributions presented later in Eq. 11.23. For example, for a flow-through YSZ(HgjHgO) pH-sensing indicator electrode (YSZ — yttriastabilized zirconia), the pH(X) was evaluated using the following expression: ! aH2 O ðSÞ EðXÞ 2 EðSÞ 1 pHðXÞ 2 pHðSÞ ¼ 2a 2 log10 aH2 O ðXÞ lnð10ÞRT=F 2 þ

Ed ðXÞ 2 Ed ðSÞ lnð10ÞRT=F

ð11:12Þ

where EðXÞ and EðSÞ are the open circuit potential for solutions X and S; respectively, and aH2 O ðXÞ and aH2 O ðSÞ are the corresponding activities of water, and Ed ðXÞ and Ed ðSÞ are the corresponding diffusion potentials of solutions X and S with respect to the reference electrode potential. The calibration coefficient, a, should be estimated over the range of pH of interest using reference buffer solutions (Covington et al., 1985; Lvov et al., 2000a). The coefficient, a, is a function of temperature and can deviate significantly from unity. The accuracy of these pH(X) measurements is between ^ (0.1 and 0.3) in pH. For cells with liquid junctions that behave in a Nernstian manner, the potential can be derived from the Nernst equation which is a further modification of Eq. (11.9b): Eeq ¼ Eo þ ðRT=nFÞlnð10Þ½log10 ðaHþ Þ þ Ej

ð11:13Þ

where Ej is the liquid junction potential and n(¼1) is the number of electrons involved in the electrochemical reactions. The salt bridge that forms the liquid junction must contain a salt solution at high concentration to minimize the contribution of Ej and usually KCl is employed because both ions have similar ionic mobilities. Ideally, if the ionic strength of the test solution is high (Im . 0.1 mol·kg21) the concentrations in the salt bridge, test and standard buffer solutions should be as similar as possible if Ej is to be minimized effectively. Bates (1964) provided a table (Table 11.1) of Ej values at 25 8C computed using the Henderson equation for various test solution compositions across a liquid junction (e.g., filling solution of a glass combination electrode containing either saturated KCl(aq) or 0.1 mol·dm23 KCl). The largest estimated Ej values occur for test solutions involving HX(aq) and MOH(aq) due to the much higher

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S.N. Lvov and D.A. Palmer

Table 11.1. Liquid-junction potentials (in mV) at 25 8C computed by the Henderson equation versus reference solutions of saturated KCl and 0.1 mol·dm23, respectively (given in Bates (1964), Table 3.1) Solution X

Ej

Solution X

Ej

1 M HCl 14.1 0.02 M KH2 citrate 2.9 0.1 M HCl 4.6 0.1 M KH2 citrate 2.7 0.01 M HCl 3.0 0.025 M Na2CO3 2.0 0.01 M HCl, 0.09 M NaCl 1.9 0.01 M Na2CO3 2.4 1.8 0.01 M HCl, 0.09 M KCl 2.1 0.01 M Na3PO4 0.1 M KCl 1.8 0.01 M NaOH 2.3 0.1 M KH3(C2O4)2 3.8 0.05 M NaOH 0.7 3.3 0.1 M NaOH 2 0.4 0.05 M KH3(C2O4)2 0.01 M KH3(C2O4)2 3.0 1 M NaOH 2 8.6 0.1 M KHC2O4 2.5 0.1 M KOH 2 0.1 0.05 M KH phthalate 2.6 1 M KOH 2 6.9 1.9 0.025 M NaHCO3, 0.025 M Na2CO3 1.8 0.025 M KH2PO4, 0.025 M Na2HPO4 0.05 M CH3COOH, 0.05 M CH3COONa 2.4 0.01 M CH3COOH, 0.01 M CH3COONa 3.1 0.1 M HCla 26.9 0.1 M NaOHa 2 19.2 9.1 0.1 M NaOHa 2 4.5 0.01 M HCla a

versus 0.1 mol·dm23 KCl.

mobility of Hþ(aq) and OH2(aq) compared to other ions. Therefore, the main goal of the discussion in this paragraph is to emphasize the importance of considering the concentrations of reference solutions used in typical pH calibrations/ measurements. Liquid junction effects at high temperatures are treated explicitly later in the text. Mesmer and Holmes (1992) state that from a consideration of a number of studies of electrolytes, in which an alkali metal ion was replaced systematically with hydrogen ions, the Henderson equation is accurate to about ^25% when based on the limiting ionic conductivities of the ions. In most experiments with the hydrogen-electrode concentration cell (described later) Ej values calculated with the Henderson equation are , l2lmV so that the uncertainty introduced by the presence of a liquid junction would be , ^0.008 in pHm at 25 8C and only , ^0.004 in pHm at 300 8C. As mentioned earlier in this section, pH can also be defined on a molality scale, since the mean activity coefficient of an electrolyte, MnM XnX ; defined as, gn^ ðMnM XnX Þ ¼ gnMM gnXX ; is a measurable quantity and is available for a large number of single and mixed electrolytes. As Mesmer and Holmes (1992) point out, the molality of hydrogen ions can be obtained conveniently from the relationship for a simple electrolyte, HX: 2log10 mHþ ¼ 2log10 ðaHþ aX2 Þ þ log10 g2^ðHXÞ þ log10 mX2

ð11:14Þ

The activity product, aHþ aX2 ; is calculated directly from the cell potential (cell without a liquid junction). This equation applies to pure acidic solutions and

Electrochemical processes in high-temperature aqueous solutions

385

electrolyte mixtures containing HX. Mesmer and Holmes cite examples of Harned cells and cells with zirconia membranes, YSZ(M/MX), versus AgCljAg electrodes where Eq. 11.14 is applicable directly. The use of the molality scale for pH is discussed below in reference to the application of concentration cells, which intrinsically are cells with a liquid junction, for experimental research aimed at determination of thermodynamic equilibrium constants (Mesmer et al., 1988a,b; references cited in Chapters 13 and 14). Guillaumont et al. (2003) in a review of the thermodynamics of selected actinides reinforce the utility of pH on a concentration basis when treating solution equilibria particularly for high ionic strengths, even at ambient temperatures. The use of Harned cells for determination of activity coefficients up to 60 8C was pioneered 70 years ago (e.g., Harned, 1935) and later to higher temperatures by Lietzke and coworkers (e.g., Lietzke, 1955; Lietzke and Vaughen, 1955; Lietzke and Stroughton, 1957, 1963). For more details on this aspect of potentiometry, see Chapter 8. 11.3.2. ‘High-temperature’ Potentiometric pH Measurements For reliable high-temperature potentiometric experiments the measured open circuit potential should be stable and reproducible within a few tenths to at the most several mV over the elapsed time of the experiment, which may be several hours to weeks. In addition, the electrodes should be resistant to chemical degradation (including poisoning of the electrodes by chemical components of the cell, oxidation/reduction of solutes by the electrodes or the prevailing atmosphere) and pressure (including mechanical stress at high temperature). The cell must either behave in a Nernstian manner (i.e., obey Eq. 11.9b) or be able to be calibrated with a linear response of Eeq to pH. As in the case of low-temperature electrochemical measurements, these cells incorporate both indicator and reference electrodes with and without liquid junctions, or as in the case of concentration cells employ the same electrode in each compartment and thereby provide a relative measure of acidity. If an electrode is reversible, the electrode electric potential, E eq, can be related to the Gibbs energy of the corresponding electrochemical half-reaction, Dr Gi ; as follows: Dr Gi ¼ 2nFEieq

ð11:15Þ

Conventionally, the standard values of both Dr Gi and Eieq are zero at all temperatures and pressures ðDr Goi ¼ 0; Eio ¼ 0Þ for the hydrogen electrode reaction, 2Hþ ðaqÞ þ 2e2 ! H2 ðgÞ; so that all other electrode potentials can be estimated with respect to the Standard Hydrogen Electrode (SHE) scale. Note that by convention the Gibbs energy of formation of the electron is assigned to be zero at all conditions so that the thermodynamic properties of the electron are never shown in connection with the electrochemical half-reactions. The standard electrode potentials, Eio ; of many half reactions have been measured experimentally

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at ambient conditions (25 8C and 1 bar) (e.g., Lide, 2000 –2001), however only a limited number of Eio values are known at high temperatures and pressures (e.g., Naumov et al., 1974). Therefore, the creation of a comprehensive list of Eio values estimated over a wide range of temperature remains a challenge in the electrochemistry of high-temperature aqueous solutions. The open-circuit potential, E eq, measured in a potentiometric system between two reversible electrodes is defined by the Nernst Eq. 11.9b. This equation relates the activities (and/or fugacities) of the species, ai ; involved in the electrochemical reactions within the cell and the standard open-circuit potential, E o, and generally can be presented as follows: X ð11:16Þ Eeq ¼ Eo 2 ðRT=nFÞ ni ln ai where ni is the stoichiometric number of the overall cell reaction, and is positive for products and negative for reactants. Note that the IUPAC convention assumes that E eq is the potential difference between the right-hand side and the left-hand side terminals of the cell. The standard value of the open circuit potential is related directly to the standard Gibbs energy, DrG o, of the chemical reaction taking place in the electrochemical system: Dr Go ¼ 2nFEo

ð11:17Þ

Since E eq is a measurable quantity and E o can be obtained using an appropriate extrapolation, in principle, DrG o can be derived from high-temperature potentiometric experiments where the electrochemical reactions are reversible and the electrode potential difference can be measured using a high-impedance electrometer. Conversely, if the value of DrG o can be calculated using available thermodynamic data, the activities (and/or fugacities) of the reacting species can be derived experimentally. Therefore, high-temperature potentiometric measurements can provide a powerful tool for studying a number of thermodynamic phenomena if the electrode electrochemical reactions are reversible, and the high-temperature potential measurements are reliable and reproducible to within a few mV, or preferably less. It should be mentioned that, if the hightemperature thermodynamic properties (the standard Gibbs energies and the activity/fugacity coefficients) are available for all species of an electrochemical reaction, both E o and E eq can be calculated theoretically and compared with observed potentiometric data. In this way the reliability of an experimental potentiometric system can be confirmed. 11.3.2.1. Reference Electrodes Ives and Janz (1961) devoted an entire book to the theory and practice of reference electrodes and other classic books of that era have dedicated chapters to this fundamental topic (e.g., Bates, 1964). In essence, a reference electrode must

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387

produce a stable and reproducible potential during the course of measurement and the potential should be unaffected if the test solution at the indictor electrode is varied. When the reference electrode solution is bridged into a test solution, then the liquid junction (diffusion) potential between the test and reference solutions should be taken into account. Among the list of pioneers in extremely precise electrochemical measurements are Young, Noyes, Harned and Bates who generally performed detailed potentiometric measurements from 5 to 60 8C at ambient pressure (0.1 MPa) to a precision of ca. , ^0.1 mV in a ‘Harned’ cell of the form: CujPtjH2 ðg; 0:1 MPaÞ; HClðmÞjAgCljAgjCu As mentioned previously, the Harned cell involves a SHE and a silver/silver chloride reference electrode both immersed in a solution of known and constant chloride concentration; in this case in a dilute HCl solution of molality, m, such that it is a cell without liquid junction. The molality was kept low to allow a simple extrapolation to the standard state of infinite dilution. Bates and Bower (1954) reported the standard potential for this reference electrode from 0 to 95 8C. The art of making such reproducible low-temperature AgjAgCl electrodes is described by Bates (1964). A great deal of effort has been expended in recent years to develop a reliable and stable reference electrode suitable for measurements in high-temperature aqueous solutions. Two approaches have been employed: (1) use of an internal reference electrode operating within the high-temperature environment, and (2) use of an external reference electrode working at room temperature, but connected to the high-temperature environment by a non-isothermal electrolyte bridge. The first approach requires solving the well-known problem of the diffusion potential whereas the latter approach also involves solving the problems of the thermal liquid junction and thermoelectric potentials. A number of electrochemical couples, such as AgjAgCl, AgjAgBr, HgjHg2Cl2, HgjHg2SO4, AgjAg2SO4, HgjHgO and PbjPbSO4 have been tested for application as an internal high-temperature reference electrode. However, only the AgjAgCl electrode (Lietzke and Stoughton, 1963) proved suitable at temperatures up to about 275 8C and only for a limited period of time. The potential of the reversible electrochemical reaction, AgClðsÞ þ e2 ! AgðsÞ þ Cl2 ðaqÞ; can be calculated from: eq o ¼ EAgjAgCl 2 ðRT=FÞlnðaCl2 Þ EAgjAgCl

ð11:18Þ

o is where aCl2 is the activity of the Cl2(aq) ions and should be known, and EAgjAgCl the standard AgjAgCl electrode potential, which can be calculated from the standard Gibbs energies of formation, Df Goi ; for all species involved in the electrochemical reaction: o ¼ 2Dr GoAgjAgCl =F ¼ 2ðDf GoAg þ Df GoCl2 2 Df GoAgCl Þ=F EAgjAgCl

ð11:19Þ

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o While all necessary thermodynamic properties for calculating EAgjAgCl are available at 25 8C, no reliable high-temperature internal reference electrode has been developed for a temperature range above 300 8C, apparently because of chemical degradation processes of the AgjAgCl couple and the enhanced solubility of AgCl(s) in this environment. The chemical stability problem of the reference electrode was resolved by the development of the external (pressure-balanced) reference electrode, in which the electrochemical couple (e.g., AgjAgCl) is maintained at ambient temperature and is connected to the high-temperature zone by a non-isothermal electrolyte bridge (Macdonald, 1978). While this approach overcomes the stability and chemical degradation problems, it introduces the Soret effect arising from a coupling of irreversible processes involving heat and mass transport along the non-isothermal electrolyte bridge. This generates an additional thermal diffusion potential, which is a function of temperature, composition and time, and can be of a significant magnitude. One of the latest designs applied a flow-through technique (Lvov et al., 1998), which minimizes interference from contaminants (e.g., corrosion products) and from the Soret effect, thereby providing a stable and accurate reference potential within about 2 mV or less. However, an additional streaming potential is generated as the electrolyte solution flows through a capillary channel and this must also be taken into account. The flow-through external reference electrode can be used at any desired temperature and pressure, and the stability of the electrode potential is independent of the prevailing conditions within the cell. This statement has been confirmed experimentally at temperatures from 25 to 400 8C and pressures up to 35 MPa. The specific feature of this design is that the reference solution flows through the electrode at a constant velocity. Therefore, the concentration of solution across the thermal junction remains constant and any uncertainty in the thermal diffusion potential can be minimized for calibration measurements at a given temperature and pressure. Moreover, the thermal liquid junction potential can be either calculated or estimated experimentally, such that the electrode potential value can be evaluated with respect to the SHE scale. Thus far, the flow-through external reference electrode has been used in a cell that has either a platinum (Lvov et al., 1999) or yttria-stabilized zirconia indicator electrode (Lvov et al., 2002, 2003) for pH measurements up to 400 8C. The potential of this reference electrode was found to be stable within 1–3 mV while the reference solution was pumped through the electrode using a high-pressure chromatography pump. The need for an additional high-pressure pump does add to the complexity of this technique.

11.3.2.2. Indicator Electrodes The indicator electrode must have a stable and reproducible potential during the course of the measurements and must respond in a Nernstian manner to varying conditions in the high-temperature aqueous environment. In other words,

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the activity of the dissolved species, ai ; and the value of E o should, in principle, be obtained by measuring the open circuit potential between the indicator and reference electrodes and applying Eq. 11.9b. While a number of electrodes have been tested for operation over a wide range of temperatures, only the platinumjhydrogen electrode and yttria-stabilized zirconia electrode containing a mercuryjmercuric oxide electrochemical couple, YSZ(HgjHgO), were found to operate in a Nernstian manner at temperatures up to 400 8C. The corresponding electrochemically-reversible reactions taking place at the Pt(H2) and YSZ(HgjHgO) electrodes are, 2Hþ ðaqÞ þ 2e2 ! H2 ðgÞ and 2Hþ ðaqÞ þ 2e2 þ HgOðsÞ ! HgðlÞ þ H2 OðlÞ; respectively. The corresponding equations for the electrode potentials of the Pt(H2) and YSZ(HgjHgO) electrodes can be written using Eq. 11.9b as follows: eq ¼ ðRT=2FÞlnða2Hþ =fH2 Þ; EPtðH 2Þ

ð11:20Þ

eq o EYSZðHgjHgOÞ ¼ EYSZðHgjHgOÞ þ ðRT=2FÞlnða2Hþ =aH2 O Þ;

ð11:21Þ

o where EYSZðHgjHgOÞ is the standard YSZ(HgjHgO) electrode potential, which is independent of the solution composition, but does depend on the standard Gibbs energies of formation, Df Goi ; of reaction species, Hþ(aq), HgO(s), Hg(l), and H2O(l): o EYSZðHgjHgOÞ ¼ 2Dr GoYSZðHgjHgOÞ =2F

¼ 2ðDf GoH2 O þ Df GoHg 2 Df GoHgO 2 2Df GoHþ Þ=2F

ð11:22Þ

Note that Df GoHþ and Df GoH2 are zero at any temperature. Furthermore, it should be o is independent of the YSZ membrane properties so that mentioned that EYSZðHgjHgOÞ for this electrode to operate effectively it only requires sufficient O22 conductivity through the membrane at the temperature of interest. At high temperatures this electrode requires a high-impedance (. 1014 V) voltmeter, but the membrane impedance is too high to be used effectively at temperatures below 100 8C. The Pt(H2) indicator electrode has been widely used for measuring pHm in concentration cells housed in stirred Teflon-lined autoclaves (Palmer et al., 2001) and in a flow-through design at temperatures below 300 8C (Sweeton et al., 1973). Flow-through electrochemical systems have been used at temperatures up to 400 8C (Lvov et al., 1999). The YSZ(HgjHgO) indicator electrode has also been used in both static (Eklund et al., 1997) and flow-through systems (Lvov et al., 2002, 2003) up to about 450 8C. These systems were found to be Nernstian and capable of measuring the electrode potential to a precision of ^5 mV or less. The main disadvantage of the Pt(H2) electrode is that the reversibility of the electrode can be significantly biased by certain ‘poisons’ that interfere with the normal operation of the hydrogen electrode (e.g., sulphides). Also, the fugacity of H2 should be well established for estimating the activity of Hþ(aq) using Eq. 11.20.

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The main disadvantages of the YSZ(HgjHgO) electrode are the relative complexity of the design, its brittleness and the variability in both performance from batch to batch and reproducibility. Also, the activity of H2O must be known to calculate the activity of Hþ(aq) using Eq. 11.21. In addition, the chemical stability of commercially available membranes is still insufficient if the electrode is to be used in an aggressive, high-temperature, aqueous environment (Lvov et al., 2003). Note that other electrochemical couples (e.g., CujCuO) have been tested for incorporation into the YSZ electrode, but have not demonstrated the necessary chemical stability as found for the Hg/HgO couple. The usefulness of a number of metaljmetal oxide (e.g., IrjIrO2, ZrjZrO2, WjWO2, etc.) electrodes has been tested over a wide range of temperatures. However, compliance with the Nernstian equation has not as yet been well demonstrated. For example, Kriksunov et al. (1994) constructed a flow-through cell with tungsten/tungsten oxide and YSZ(HgjHgO) pH-sensing electrodes versus an external pressure-balanced AgjAgCl electrode from 200 to 300 8C. The tungsten electrode, which is a simple, rugged probe, showed good Nernstian response at 200 8C with a slope of (95 ^ 5) mV·pH21 (cf. calculated value: 93.9 mV·pH21), but the deviation increased with temperature to (104 ^ 3) mV·pH21 at 300 8C, (cf. calculated value: 113.7 mV·pH21). Significant improvement in the response of this electrode would be needed for use in potentiometric studies. Kriksunov and Macdonald (1994) showed that a simple thick-walled Pyrex glass tube with an AgjAg2SO4 in H2SO4(aq) inner electrode could be used as an indicator electrode from 20 to 250 8C in acidic to mildly basic solutions. No details of the method used to estimate pH were provided, but an example was given of the mV/pH slope at 235 8C being 114 compared to the calculated Nernst slope of 100.8. Innovative glass electrodes have been used in conjunction with an AgCljAg reference electrode (preferably kept at ambient temperature with a salt bridge providing electrical and thermal contact) in potentiometric measurements from 70 to ca. 200 8C with a reported precision of ^2 mV (Diakonov et al., 1996). This particular glass electrode utilizes a Li– Al– B-silicate glass bulb whose inner surface is coated with a thin layer of a Li– Sn alloy, which has direct electrical contact with an internal Ni– Cu wire and hence requires no internal electrolyte solution. Although glass indicator electrodes are restricted in temperature range to ,250 8C, and silica is soluble in alkaline solutions, and it is not stable over long periods of time, it provides a cheap and readily obtainable tool for many pH measurements. Furthermore, it is suitable for use with reducible solutes, such as Cuþ(aq), Cu2þ(aq), Fe3þ(aq) and UO2þ 2 (aq), whereas Pt(H2) electrodes reduce them spontaneously. 11.3.2.3. Liquid Junction Potential Calculations Liquid junction potential (ED) as well as thermal diffusion (ETD), thermoelectric (ETE) and streaming (ESTR) potentials, must be accounted for in

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flow-through systems and due to uncertainties in assessing their magnitudes, it is desirable to minimize them whenever possible. The generalized Nernst equation becomes: X ð11:23Þ Eeq ¼ Eo 2 ðRT=nFÞ ni ln ai þ ðED þ ETD þ ETE þ ESTR Þ: Note that the four potentials mentioned above are irreversible in nature and can only be understood properly on the basis of linear irreversible thermodynamics. The diffusion potential arises when two solutions are in contact and is also common to all liquid junctions. This phenomenon is a result of the different ionic mobilities and its magnitude can be estimated if the individual ionic conductivities and activities of the species are known (see discussion above of the Henderson equation). As discussed above, at temperatures below 350 8C, if ED is not minimized, it could be as substantial as 30 mV or larger. Mesmer and Holmes (1992) showed that for a given cell composition, the values of ED generally decrease with increasing temperature while the Nernst slope increases. Although there is concern that the Henderson equation could be difficult to apply at near critical conditions as the electrolytes become more associated, it is reasonable to assume that the contribution of the diffusion potential will also be smaller (Zhou et al., 2000). The thermal diffusion potential arises when there is a temperature gradient within an electrochemical system. This phenomenon is due to heat transport by ionic species and can be accounted for if the entropy of transport, conductivity and activity coefficients of the individual ions are known. Therefore, the magnitude of ETD depends on the temperature, pressure and composition of the electrolyte liquid junction, and is also a function of the temperature gradient. The value of ETD can be as high as tens to hundreds of mV. The thermoelectric potential is due to heat transport by the electrons and arises if an electron conductor (usually a wire) is in a non-isothermal condition. Consequently, ETE is a function of the temperature gradient and, for the most common wire materials, is usually only a few mV. However, the magnitude of ETE can be calculated over a wide range of temperatures for most common wires, such as those made from Pt, Ag, Cu, Fe, Ni, etc. The electric potential, which is created at zero electric current in a capillary channel (or porous material) due to a mass flow of solution, is called the streaming potential, ESTR. The magnitude of ESTR depends on (1) the capillary channel material, (2) the composition of flowing solution, (3) the solution flow rate and (4) the temperature. Presently, there are no data to evaluate ESTR theoretically at high temperatures. However, if the flow rate is sufficiently low there is a linear dependency between the streaming potential and flow rate that can be used to eliminate ESTR by extrapolating the measured potentials to zero flow rate. An example for estimating the values of ED, ETD, ETE and ESTR is shown in Lvov et al. (1999).

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11.3.2.4. Reference and Buffer Solutions For assessing the viability and accuracy of high-temperature potentiometric measurements, reference systems should be used with a known activity of Hþ(aq), aHþ : One approach, which is applicable at temperatures below 300 8C, is to use dilute aqueous solutions of strong acids and basis, such as HCl(aq) [or F3CSO3H(aq)], which is a strong organic acid used commonly in experimental studies as the large anion interacts only weakly, if at all, with most cations (see Chapters 13 and 14) or NaOH(aq), to establish either aHþ ; or the molality of hydrogen or hydroxide ions, mHþ and mOH2 ; for comparison of the measured and calculated potentials. If these standard solutions are used at temperatures above 300 8C, then the ion association constants of the electrolytes must be considered, i.e., the speciation of the solutions’ components must be known. Consequently, at these temperatures the activity or concentration of Hþ(aq) becomes more uncertain. According to Lvov et al. (2000a), even in the low-density, supercritical regime, several three-component aqueous reference solutions can be found to test the accuracy of the Pt(H2) or YSZ(HgjHgO) electrodes within # ^ 3 mV (remembering that at 400 8C, the Nernst slope in Eq. 11.9b is 133.6 mV·pH21, so even 3 mV corresponds to only 0:022log10 mHþ units). Such three-component aqueous solutions may consist of NaCl and either HCl or NaOH such that the concentration of NaCl is significantly greater than the concentration of the other solute (HCl or NaOH). This ‘relative’ approach was confirmed theoretically and experimentally at temperatures up to 400 8C and densities down to 0.17 g·cm23 and does not require any knowledge of the association constants (Lvov et al., 2000a). The three-component reference solutions for verifying Nernstian behavior of this particular electrode system have also been used as standard solutions in the hydrogen-electrode concentration cells (HECC) system at temperatures below 300 8C, where various supporting strong electrolytes have been employed. Nevertheless, for a standard solution, whose pH is known accurately at high temperatures over a range of pressures, to be used at high temperatures, a rigorous or ‘speciation’ treatment of the hydrogen ion concentration or activity must be available (i.e., a treatment that accounts for the actual nature of all the species in solution distinguishing between, for example, free hydrogen ions from those associated with other solutes and therefore not contributing to pH). Fortunately, data from the latest flow-through conductivity cells operated to super-critical temperatures and recent advances in treating the conductance of mixed electrolytes make the creation of a fully speciated high-temperature standard solution a distinct reality (see Chapter 10). Solubility limitations of electrolytes under super-critical conditions, particularly at low pressures, must be carefully considered in making these solutions. Buffer solutions play a significant role in the standardization of pH meters and in testing whether electrochemical cells exhibit Nernstian behavior in lowtemperature potentiometric measurements. It is highly desirable to have available

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sets of the buffer solutions that can be used at temperatures above 100 8C. IUPAC has recommended only a 0.05 mol·kg21 potassium hydrogen phthalate solution as an ‘traceable’ buffer system to be used at temperatures up to about 225 8C (Covington et al., 1985). However, many buffer systems have been investigated at Oak Ridge National Laboratory (ORNL), some up to 300 8C over wide ranges of ionic strength (see Chapter 13), so these are available as secondary pH standards and are defined on an consistent experimental basis. 11.3.2.5. Potentiometric Measurements below 300 8C During the last 30 years, ORNL and others have used HECC for potentiometric measurements of homogeneous (Chapter 13) and heterogeneous (Chapter 14) protolytic aqueous systems to 300 8C over wide ranges of ionic strength. Many acid–base, metal ion hydrolysis, metal complexation, metal oxide solubility and surface adsorption reactions have been studied using this technique (e.g., Mesmer et al., 1970, 1988a; Be´ne´zeth and Palmer, 2000; Wesolowski et al., 2000; Palmer et al., 2001). The most recent design of the stirred HECC (Fig. 11.1) is described in detail by Palmer et al. (2001). Briefly, the pressure vessel is usually machined from Hastelloy B, which was chosen for its resistance to corrosion, especially stress-cracking in the presence of chloride, and to hydrogen embrittlement. Two concentric internal cups are machined from Teflon with the smaller, inner compartment containing a reference solution whose acidity or basicity is fixed by a known ‘stoichiometric’ amount of a strong acid or strong base, or buffer. The H2(g) pressure is the same throughout the cell so that the pHm measurements do not require knowledge of the partial pressure of hydrogen, which is fixed by conducting at least five pressurizations and release cycles at room temperature to purge the cell of free oxygen. The final pressure of H2(g) is typically 1 – 3 MPa. The cell is then heated in an oil bath or furnace to the desired temperature while the solutions in both compartments are stirred magnetically. A liquid junction is maintained between the two solutions via a small porous plug of Teflon compressed into a hole in the bottom of the reference cup. Titrations are conducted by injection of a titrant through PEEK (at low temperature) and platinum lines (at high temperature) from a calibrated Zircalloy positive displacement pump. The electrochemical configuration of the HECC is as follows: PtðH2 ÞlReference Hþ ðaqÞ=H2 ðaqÞ Sol: 1kIndicator Hþ ðaqÞ=H2 ðaqÞ Sol: 2lPtðH2 Þ; where a single vertical bar is used to represent a phase boundary, and the double vertical bars represent the liquid junction between miscible liquids. Using the generalized Nernst Eq. 11.9b, the open-circuit potential, EHECC, can be presented as follows: EHECC ¼ ðRT lnð10Þ=FÞlog10 ½ðmHþ Þ2 =ðmHþ Þ1  þ ED

ð11:24Þ

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Fig. 11.1. The stirred (static) hydrogen concentration cell for potentiometric measurements to 300 8C (Palmer et al., 2001).

where mHþ is the hydrogen ion molality and ED is the diffusion liquid junction potential, which is computed from the Henderson equation (Bates, 1964). The subscripts 1 and 2 symbolize the molalities in the reference and test solutions, respectively. Fundamental to operation of the HECC is that both solutions be maintained at the same ionic strength by addition of a strong ‘supporting or inert’ electrolyte, such as NaCl or NaF3CSO3, such that Im q ðmHþ Þ1;2 : This is crucial to the assumption that the activity coefficients of the hydrogen ions are the same in both compartments of the cell and the value of ED is minimized by the predominance of the same ions on both sides of the junction. The precision of these pHm measurements is generally ^0.01 for well behaved electrolyte solutions. The original flow-through HECC (Sweeton et al., 1973) provided accurate hydrolysis data for a number of solutes, including the hydrolysis of water itself

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(Chapter 13), particularly those that are volatile [e.g., NH3(aq), Hitch and Mesmer (1976); CO2(aq) Paterson et al. (1982, 1984); cyclohexylamine and morpholine, Mesmer and Hitch (1977); and acetic acid, Mesmer et al. (1988b)]. Although it was later shown that the static HECC could also be used to study the hydrolysis of the latter three less-volatile solutes, the flow-cell, which does not contain a vapor phase, also allowed the pressure to be varied over a small range to give an approximate DrV value. However, as the inner wetted components of the cell were machined from Teflon, the measurements were restricted to , 300 8C and operation was somewhat erratic due to compression of the Teflon which often led to blockage of the flow. On the other hand, the presence of Teflon ensured that corrosive solutions could be studied without contamination. It should be mentioned that fluoride ion was never detected (, 1025 mol·kg21 with a fluoride sensitive electrode) in test solutions exposed to Teflon in the HECC even after experiments at 300 8C. Sweeton et al. (1973) reported that for this flow-through HECC, experimental measurements of dilute HCl(aq) in KCl(aq) were within 0.02 pHm units of the stoichiometric concentration from 0 to 100 8C, increasing to 0.05 units by 300 8C. 11.3.2.6. Potentiometric Measurements above 300 8C The HECC described immediately above cannot be used at temperatures above 300 8C because Teflon loses its thermal stability and there is a common vapor phase that allows transfer of volatile solutes, particularly HCl, between the compartments at very high temperatures. However, flow-through potentiometric systems (Lvov et al., 1999, 2003; Sue et al., 2001, 2002; Seneviratne et al., 2003) can eliminate these problems. A schematic of one of these electrochemical cells is shown in Fig. 11.2 (Seneviratne et al., 2003). This type of cell is usually machined from a corrosion-resistant alloy and has four ports into which different devices can be sealed for use at high pressures and temperatures. The device described in Lvov et al. (2003) and Seneviratne et al. (2003) includes a flow-through external AgjAgCl reference electrode, a flow-through Pt(H2) indicator electrode, a flowthrough YSZ(HgjHgO) indicator electrode and a thermocouple. The design has a four-way, once-through circulation system that can pump fluid through the electrodes at rates faster than thermal diffusion so that no concentration gradients result from the Soret effect. Only the sensing portion of the system is maintained at a controlled temperature and pressure. The purity and concentration of the solutions are assured by maintaining a relatively rapid flow rate. In other words, as in most flow systems, contamination is minimized and corrosion of the system is significantly reduced. Because the low-temperature input flow comes only in contact with glass, Teflon, and PEEK tubes, and at high temperature the solutions only contact zirconia and platinum, the solution composition at the sensing portion of the system is well controlled. The precision of the potentiometric measurements using this design is # ^ 5 mV. The association constants of HCl(aq) at

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Fig. 11.2. A flow-through electrochemical cell for potentiometric measurements at temperatures above 100 8C (Seneviratne et al., 2003; Lvov et al., 2003).

temperatures from 300 to 400 8C were measured recently using this system with an uncertainty of ^0.4 pK units (Lvov et al., 2000b, 2002, 2003). It was shown that reliable potentiometric results can be obtained using the flow-through electrochemical cell to temperatures of 400 8C and densities down to 0.17 g·cm23. Moreover, using similar cells fitted with Pt(H2) and YSZ(HgjHgO) electrodes, the Henry’s constant of H2(aq) was obtained at temperatures between 300 and 450 8C (Eklund et al., 1997; Ding and Seyfried, 1995). An electrochemical diagram of the non-isothermal electrochemical system (thermocell), consisting of the flow-through external AgjAgCl reference electrode and a flow-through YSZ(HgjHgO) electrode, can be presented as follows:

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397

where T1 is the ambient temperature and T2 is any temperature higher than T1 : Note that Cu in this diagram represents the wires connecting the terminals of the system to a high-impedance electrometer. The open-circuit potential of this thermocell, ETC, can be expressed as: o o ETC ¼ ½EYSZðHg=HgOÞ T2 2 ½EAg=AgCl T1 þ ðRT2 =FÞln½ðaHþ ÞT2 ða20:5 H2 O ÞT2 

þ ðRT1 =FÞln½ðaCl2 ÞT1  þ ED þ ETD þ ETE þ ESTR

ð11:25Þ

One of the disadvantages of any flow-through electrochemical system is the existence of a streaming potential, which must be taken into account. To eliminate, ESTR, it is necessary to extrapolate the measured open-circuit potentials to zero flow rate so that at least four experimental points should be measured to provide a reliable linear extrapolation. Other disadvantages include: (1) the reduced accuracy inherent in the flow system due to the thermal diffusion potentials mentioned above; (2) the time required to change solution compositions compared to the use of static cells where only minutes are required to add a titrant and for the cell to re-equilibrate; (3) the need for pumps and the higher risk of leaks and concomitant safety concerns. However, additional advantages are the ability to: (1) study the protolytic behavior of volatile solutes; (2) investigate the pressure dependence of protolytic reactions; (3) study thermally unstable solutes due to the small retention time at elevated temperature; and (4) apply this technology to industrial environments. Sue et al. (2001) recently introduced a version of the flow-through thermocell, which was based on the approach developed by Lvov et al. (1999) while incorporating some aspects of a HECC, and was tested to 400 8C and 35 MPa. The Hastelloy-B2 body was coated internally with Al2O3 to minimize acid corrosion, but is therefore subject to corrosion in basic solutions. The reference Pt(H2) electrode was maintained at ambient temperature with the flow of both reference and test solutions coming from opposite ends of the cell past each electrode, then through baffles to minimize cross contamination, and finally exiting the center of the cell. Similar to the results presented by Lvov et al. (1999), the streaming potential was shown to be substantial so generally 5 – 9 different flow rates (1.0–5.5 g·min21) were investigated to allow a linear extrapolation to zero flow rate. The streaming potential was largest at low pressures and high temperatures [e.g., at 400 8C, 25.0 MPa, EHECC ¼ 20:4 mV at 5.5 g·min21 to (131.0 ^ 4.0) mV at 0.0 g·min21]. The value of ED was estimated from the Henderson equation confirming the hypothesis of Mesmer and Holmes (1992) that these values could be small at 400 8C. As noted previously (Lvov et al., 1999), Sue et al. (2001) compared two HCl solutions in 0.1 mol·kg21 NaCl with agreement between measured versus the calculated stoichiometric pH of , ^0.03. The authors used Pitzer parameters (Pitzer, 1991) to estimate activity coefficients with an extrapolation from their 25– 300 8C reported range to 400 8C. Ion association

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constants for HCl(aq), NaOH(aq) and NaCl(aq) were calculated from the analytical equations of Lvov et al. (2000a), which were based on recent conductance measurements at ORNL (see Chapter 10). This technique offers great promise for future pH measurements to supercritical temperatures and it will be hopefully soon applied to re-measurement of the dissociation constant of water. Sue et al. (2002) have subsequently reported the acid dissociation constant for phenol to 400 8C and 34.9 MPa. An intriguing aspect of this thermocell technique is that the reference solution is at ambient temperature where the solution thermodynamics are well known (i.e., ion association is minimal and activity coefficients are known accurately); whereas, these data are needed for a concentration cell where the test solution and reference solution are above 300 8C to determine the extent of ion pairing of hydrogen/hydroxide ions with the supporting electrolyte, the ionic strength, activity coefficients and liquid junction values (i.e., a ‘speciated’ treatment is applicable). Analyses of the pH values determined with the thermocells described above, and possibly a future isothermal HECC, would provide a quantitative measure of the reliability of these pH values. 11.3.2.7. Other Techniques for Measuring pH at High Temperatures Spectrophotometry provides a means to ‘observe’ pH changes remotely from the changes in the absorbance of pH indicators. This method has application to certain industrial settings when injection of an indicator solution into a side stream through an optical cell is practical. In the laboratory, this technique has been used to supercritical conditions (note that at present flow is stopped while spectra are recorded). Johnston and coworkers (Xiang and Johnston, 1994; Xiang et al., 1996; Ryan et al., 1997; Wofford et al., 1998) have pioneered the use of pH indicators that are thermally stable to supercritical temperatures, e.g., 2- or b-naphthol, 2-naphtholic acid, s-collidine and acridine. Corrosion of the sapphire windows is a technical problem with this technique requiring frequent measurements of the baseline absorption and use of disposable sapphires. Xiang and Johnston (1994) give a detailed description of this technique in their measurement of the ionization constant of b-naphthol from 25 to 400 8C, which then can be used to measure the pH of hydrothermal solutions in the range of the detectable ionization of the indicator (pKa ¼ 9:63 at 25 8C). Typical concentrations of indicator were 4 £ 1024 to 1 £ 1023 mol·dm23 and distinct absorption bands were assigned to the acid and base forms. It was necessary to measure the spectrum of both forms at each temperature, because although the lmax of the ‘acid’ peak did not change significantly with temperature, the lmax of the ‘base’ peak and their peak areas varied with temperature. Unfortunately, an experimental uncertainty (precision) is only quoted for the area of the ‘acid’ peak of , 5% and ‘usually less than 1 – 2%’ so that it is difficult to gauge the accuracy of the actual pH readings at high temperatures. The procedure for determining the ratio of protonated to unprotonated forms of b-naphthol

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involves fitting two Gaussian curves with four adjustable parameters to the observed spectrum at each temperature. This calculation was based on knowledge of the parameters for the ‘acid’ spectrum at that temperature. An additional complication can be caused by interference of other light absorbing species at the wavelengths of interest. Xiang et al. (1996) determined the first dissociation constant of sulfuric acid from 200 to 400 8C using the indicator, acridine, at a concentration of ca. 1024 mol·kg21 for which the measurable pH range shifted from 2 to 4 at rw ¼ 0:60 g·cm23 to 4.5– 7 at rw ¼ 0:24 g·cm23 (i.e., at 400 8C). Experimentalists at the University of Texas (Wofford et al., 1998) also measured the ionization constant of boric acid from 300 to 380 8C using ca. 5 £ 1024 mol·kg21 2-naphthol. The pH of these solutions at a pressure of 24.1 MPa appeared to vary from 8.3 at 300 8C to 9.8 at 380 8C with an uncertainty of ^0.1 pH units, whereas the experimental uncertainty in the ionization constant of the indicator was given as ^0.2 log10 units. These studies all based on the treatment of pH on a ‘speciated’ model taking into account the association of the electrolytes (KOH in the last example) and estimating activity coefficients for these generally dilute solutions from the Pitzer extended Debye– Hu¨ckel equation (Pitzer, 1991). Although generally spectrophotometric measurements do not provide the same accuracy as electrochemical measurements of pH, this relatively simple technique may also prove applicable to systems that are unstable in the presence of certain electrodes and may also have industrial applications. Certainly it would be advantageous to measure the ionization constants of these indicators by electrochemical methods to affirm their use as independent standards. Interestingly, here is a technique that measures the concentration of hydrogen ion, which is then converted via convention to the activity scale, which is a step that may be unnecessary for practical measurements of thermodynamic equilibria. 11.4. High-Temperature Potential — pH (Pourbaix) Diagrams Electrochemical reactions occurring in high-temperature aqueous solutions can be described thermodynamically by Eq. 11.15. In water Hþ(aq) ions can be reduced electrochemically as follows: 2Hþ ðaqÞ þ 2e2 ! H2 ðgÞ

ð11:26Þ

and molecular oxygen O2(g) can be reduced electrochemically as follows: 1 2

O2 ðgÞ þ 2Hþ ðaqÞ þ 2e2 ! H2 OðlÞ

ð11:27Þ

Application of Eqs. 11.10 and 11.15 to the electrochemical reactions 11.26 and 11.27 yields the two primary expressions for constructing potential– pH diagrams: EHeqþ jH2 ¼ EHo þ jH2 2 ½lnð10ÞRT=FpH

ð11:28Þ

400

EOeq2 jH2 O ¼ EOo 2 jH2 O 2 ½lnð10ÞRT=FpH

S.N. Lvov and D.A. Palmer

ð11:29Þ

where EHo þ jH2 ¼ 0 and EOo 2 jH2 O ¼ 2Df GoH2 O =F; because Df GoHþ ¼ Df GoO2 ¼ Df GoH2 ¼ 0 at any temperature. Note that Eqs. 11.28 and 11.29 are written assuming that the fugacities of hydrogen and oxygen are equal to 0.1 MPa. If this were not the case, these equations should be changed according to the Nernst Eq. 11.9b. The equilibrium electrochemical reactions 11.26 and 11.27 can be represented graphically in Eeq i –pH plots by straight lines with an intersect corresponding to the standard electrode potential, Eio ; and a negative slope, ln(10)RT/F. Clearly, if the total pressures and/or temperatures are changed, then the values of Eio and slope will be changed accordingly. Two other kinds of lines are represented on Pourbaix diagrams, viz., vertical and horizontal lines. A vertical line corresponds to a pure chemical reaction (no electrons are involved) whereas a horizontal line corresponds to an electrochemical reaction in which no Hþ(aq) ions are involved. Given this information an equilibrium potential– pH diagram can be constructed at any desired temperature if all the thermodynamic data are available for all the possible chemical and electrochemical reactions. In other words, the list of the possible chemical reactions is defined by the availability of the standard Gibbs energies of formation for all chemical compounds of interest. For example, a Pourbaix diagram for copper was constructed by Beverskog and Puigdomenech (1997) for a temperature of 300 8C. The standard Gibbs energies of formation of the aqueous species used in constructing this potential– pH diagram were calculated using the semi-empirical Helgeson– Kirkham– Flowers approach (Johnson et al., 1992). It should be noted that Anderko et al. (1997) have taken the activity coefficients of the aqueous species into account in constructing the potential–pH diagrams to treat the nonideality at high concentrations. Moreover, other independent variables, such as the total concentration of species were varied in this paper over the temperature range, 25– 300 8C. The Pourbaix diagram is a very useful tool for understanding the corrosion/ speciation of a chemical element as functions of pH, temperature and pressure. For example, the lowest area in these diagrams usually represents the region of immunity for a metal, i.e., where there is no corrosion/oxidation. The region where the metal oxide/s is/are thermodynamically stable is the area of passivation, where the metal tends to become coated with this oxide. Generally, the oxide forms on the metal as either a non-porous film, practically preventing all direct contact between the metal and the aqueous solution, or as a porous deposit, which only partially protects the metal from further corrosion. Therefore, the presence of a porous deposit does not imply a resistance to corrosion. An independent electrochemical kinetic study is needed to provide a reliable evaluation of the stability of a metal in the areas of apparent passivation. A large number of Pourbaix diagrams have been constructed for ambient conditions (25 8C and 0.1 MPa)

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(Pourbaix, 1974). However, only a limited number of the diagrams have been created at higher temperatures and pressures, particularly above 300 8C. Therefore, obtaining a comprehensive collection of the Pourbaix diagrams applicable to extremes of temperature and pressure encountered in industrial processing and power generation is still a major challenge for electrochemists. The reader is referred to a recent article by Dooley et al. (2003) for a practical discussion of the interpretation of oxidation/reduction potential (ORP — defined as the potential of a cell with Pt versus a reference electrode — usually AgjAgCl — see Chapter 17) in terms of various corrosion mechanisms with particular relevance to conventional power generation. 11.5. High-Temperature Electrochemical Kinetics A systematic understanding of the kinetics and mechanisms of electrochemical reactions, including corrosion processes, requires measurements of the appropriate kinetic parameters in Eqs. 11.8 and 11.9a. In particular, there is a significant scarcity of the following key electrochemical kinetic parameters: the exchange current densities ( jo), and the anodic (aoxid) and cathodic (ared) transfer coefficients for charge transfer reactions. Even the most important hydrogen electrode reaction (HER) and oxygen electrode reaction (OER) have rarely been studied systematically at temperatures above 100 8C. The reason for this state of affairs is not difficult to determine — the electrochemical kinetic measurements are difficult to perform at elevated temperatures and few of the available electrochemical sensors, and/or systems, are currently available for performing high-quality electrochemical kinetic experiments. Most of these reactions are heterogeneous processes and the experimental data obtained reflect both mass transfer and charge transfer phenomena. However, the parameters ( jo, aoxid and ared) involve strictly charge transfer so it is necessary to delineate these phenomena in any electrochemical kinetic experiment. In order to solve the problem one needs to carry out these electrochemical kinetic studies under welldefined hydrodynamic conditions. The traditional rotating-disk electrochemical system, which has been used widely at ambient temperatures, has not yet been implemented properly in high-temperature electrochemical studies. Thus far, only a few controlled hydrodynamic systems for the measurement of electrochemical kinetic parameters at elevated temperatures have been tested. A study of the HER on mercury in HCl(aq) solutions has been carried out at temperatures up to 300 8C (Tsionskii et al., 1991). A high-temperature, wall-tube electrode cell for electrochemical kinetic studies at temperatures to 200 8C has also been developed by Trevani et al. (1997). Other high-temperature, tubular, flow-through electrochemical cells have been designed to operate at temperatures to about 250 8C (Macdonald et al., 1988; Nagy et al., 1991). Finally, welldefined, steady-state cyclic voltammetry has been applied to study a number of

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electrochemical reactions in near- and supercritical fluids to 385 8C (Liu et al., 1997). It is well known that electrochemical systems can exhibit apparent random fluctuations (electrochemical noise) in the current and potential readings around their open circuit values and these noise signals can contain valuable kinetic information (Zhou et al., 2001). The value of this technique, which is called electrochemical noise analysis, lies in its simplicity and can be considered for industrial applications. The approach requires no reference electrode, but instead employs two identical electrodes of the metal or alloy under study. Electrochemical noise sensors have been recently developed for measuring electrochemical kinetics and corrosion rates in sub- and supercritical hydrothermal systems (Zhou et al., 2001). This system, which is shown in Fig. 11.3, has been

Fig. 11.3. Schematic diagram of an electrochemical noise sensor and data acquisition system (Zhou et al., 2001).

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tested for flowing aqueous solutions at temperatures from 150 to 390 8C at a pressure of 25 MPa. In principle, the rate of the electrochemical reaction can be estimated under hydrothermal conditions by measuring simultaneously the coupled electrochemical noise potential and current. Electrochemical noise analysis is not yet an exact quantitative science, because a relationship between the noise measured experimentally and the rate of the electrochemical reaction has not been firmly established. Nevertheless, the results obtained by Zhou et al. (2001) demonstrate that this method is an effective tool for studying electrochemical kinetic phenomena in high-temperature and high-pressure aqueous environments. Finally, it should be mentioned that as this is an underdeveloped field of research and a significant effort will be needed to make this a reliable and well-understood technique.

11.6. High-Temperature Electrokinetic Studies As mentioned in Section 11.1, the inner electric potential of a phase a, Ea ; is not a measurable quantity, but a part of Ea ; which is called the zeta potential, can be obtained from electrokinetic measurements. Four well-known electrokinetic phenomena that can be studied experimentally are: (1) electroosmosis — created when there is movement of a liquid over a solid surface in an electric field, (2) electrophoresis — stems from movement of a solid suspended in a liquid in an electric field, (3) streaming potential — corresponds to the potential difference between the upstream and downstream ends of a liquid flowing through either capillary tubes or porous plugs and (4) sedimentation potential — is formed during settling of suspended solid particulates from an aqueous electrolyte solution. Only the electrophoresis and streaming potential measurements have been applied so far in high-temperature and high-pressure electrochemical studies. Using the electrokinetic approaches mentioned above, the zeta potential can be derived and is usually defined as the potential of the electric double layer at the slipping plane between the bulk solvent and the relatively stagnant layer close to the solid surface. Zeta potential generally depends on temperature and pH, and is usually positive in highly acidic solutions and negative in highly basic solutions (see Chapter 14 for a brief discussion of surface charging and adsorption phenomena). The pH value at which the zeta potential is zero is defined as the isoelectric point (IEP) and as such is an important property of a metal oxide/water interface chemistry. In Fig. 11.4 a schematic of a high-temperature microelectrophoresis zetameter is presented (Zhou et al., 2003). The first measurements with this apparatus have been carried out for ZrO2jwater (Zhou et al., 2003) and TiO2jwater (Fedkin et al., 2003) interfaces at temperatures up to 200 8C. No reliable electrokinetic studies have been carried out at temperatures above 200 8C.

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Fig. 11.4. Schematic diagram of a high-temperature microelectrophoresis cell (Zhou et al., 2003).

11.7. Conclusions In the solubility studies of metal oxides discussed in Chapter 14 and the liquid– vapor partitioning of electrolytes discussed in Chapter 12, pH is usually the single most important variable. Advances in potentiometric techniques with the development of new cell configurations and pH-sensing and reference electrodes have been outlined, as well as independent spectrophotometric methods. Comparisons of these methods for specific systems would provide a benchmark for their utilization as tools for thermodynamic measurements, but such a comparison must be accompanied by a rigorous treatment of the experimental uncertainties associated with each technique. An early re-evaluation of the dissociation constant of water, which is the corner stone to most hydrothermal measurements, is urgently required to supercritical temperatures. Perhaps independent conductance measurements will provide complementary information in the near future. Agreement is also needed on a pH scale that is most appropriate for hightemperature measurements and sets of standard reference solutions are required that can be used universally.

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Much of the discussion of pH has centered on measurements made in the laboratory at a particular temperature and pressure. For readers not familiar with pH as defined in the electric power industry, for example, it should be noted that in the United States for conventional steam generators using fossil fuels, pH always refers to the value at 25 8C, and is converted from or to the pH of operation using the dissociation constant of water, whereas the nuclear industry records pH as the value at 300 8C. In Europe, the conventional and nuclear power industries both refer to pH as the value at 25 8C. Whereas the standard potentials of many half-cell reactions have been measured at ambient conditions and can be found in a number of reference books, only a limited number of high-temperature/pressure values are properly reported. Therefore, the creation of a comprehensive list of standard potentials measured over a wide range of temperature remains a challenge to electrochemists. As is the case for established low-temperature potentiometric and pH measurements, it is highly desirable to have reliable, stable reference electrodes for high-temperature electrochemical measurements. Although a suitable external AgjAgCl reference electrode has been tested successfully to 400 8C, a reliable internal reference electrode suitable for operation above 300 8C has yet to be found. The development of a reliable and convenient pH sensor electrode that can operate reproducibly from 100 to 450 8C also remains a goal for electrochemists. This pH sensor must provide a stable, reproducible potential during the course of the measurement, which may involve long periods of time and harsh environments (oxidizing, reducing, thermal shocks, etc.). The design of YSZ(HgjHgO) electrodes has improved significantly (e.g., Lvov et al., 2002, 2003), but substantial effort is still needed to provide accurate laboratory scale pH measurements to these extreme temperatures and to develop a rugged version of this electrode for industrial applications. The potential– pH (Pourbaix) diagram provides a powerful tool for understanding the corrosion behavior of a metal or alloy in severe hydrothermal environments, particularly as required for use by a number of industries. However, again there is a dearth of such information pertaining to these conditions. Similarly a real problem exists in electrochemistry associated with the lack of kinetic (including corrosion) studies, which are the key to understanding the behavior of conducting material exposed to severe hydrothermal environments. If we want to obtain a comprehensive understanding of the interaction between a metal (or metal alloy) and a hydrothermal solution, then electrochemical kinetic (or corrosion) studies must be carried out. In particular, there are almost no data on the exchange current densities or the anodic and cathodic transfer coefficients for most metals at hydrothermal conditions. Even the primary hydrogen electrode and oxygen electrode reactions have been poorly studied above 100 8C. In order to understand the surface chemistry at the solid oxidejwater interface, high-temperature electrokinetic studies must be carried out. Recently,

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microelectrophoretic studies of the ZrO2 – and TiO2 –water suspensions to 200 8C showed that such measurements are possible for other systems, but substantial effort will be needed to extend these measurements to higher temperatures. Moreover, in order to gain insights into electrochemical characteristics of the electrical double layer such as the zeta potential and isoelectric point, additional electrokinetic studies should be performed with careful analyses of the results obtained before a final recommendation as to the validity of these properties can be given. In regard to electrochemical measurements in general, a need was specified in this chapter for the standard potentials of redox couples to super-critical conditions. A basic understanding of the phenomenon of electrochemical noise is also required before such information can be applied to practical systems. Although electrochemical corrosion has not been discussed in this chapter, it is an obvious crucial application to industrial and natural processes. A new frontier is the development of deterministic models for predictions of corrosion damage due to corrosion fatigue in such environments as low-pressure steam turbines. Acknowledgements DAP wishes to acknowledge financial support by the Division of Chemical Sciences, Geosciences and Biosciences, Office of Basic Energy Sciences, U.S. Department of Energy, under contract DE-AC05-00OR22725 with Oak Ridge National Laboratory, managed and operated by UT-Battelle, LLC. SNL acknowledges financial support of the Department of Energy and Geo-Environmental Engineering and the Energy Institute of the College of Earth and Mineral Sciences at the Pennsylvania State University. SNL also wishes to acknowledge partial support of this work by the National Science Foundation (NSF grants EAR-9725191 and EAR-0073722), the U.S. Army Research Office (ARO grant DAAD-19-00-1-0446), and the U.S. Department of Energy (DOE Contract DE-AC-00OR22725). References Anderko, A., Sanders, S.J. and Young, R.D., Corrosion, 53, 43 – 53 (1997). Bard, A.J. and Faulkner, L.R., Electrochemical Methods: Fundamentals and Applications. 2nd edn., Wiley, New York, 2001. Bates, R.G., Determination of pH, Theory and Practice. Wiley, New York, 1964. Bates, R.G. and Bower, V.E., J. Res. Natl Bur. Stand., 53, 283 – 290 (1954). Be´ne´zeth, P. and Palmer, D.A., Chem. Geol., 167, 11– 24 (2000). Beverskog, B. and Puigdomenech, I., J. Electrochem. Soc., 144, 3476– 3483 (1997). Buck, R.P., Rondinini, S., Covington, A.K., Baucke, F.G.K., Brett, C.M.A., Camo˜es, M.F., Milton, M.J.T., Mussini, T., Naumann, R., Pratt, K.W., Spitzer, P. and Wilson, G.S., Pure Appl. Chem., 74, 2169– 2200 (2002).

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