Chemical thermodynamic data. 1. The concept of links to the chemical elements and the historical development of key thermodynamic data

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Chemical thermodynamic data. 1. The concept of links to the chemical elements and the historical development of key thermodynamic data Thomas J. Wolery a,⇑, Carlos F. Jove´ Colo´n b a

Nuclear Fuel Cycle Program, Lawrence Livermore National Laboratory, L-223, P.O. Box 808, Livermore, CA 94550, United States b Sandia National Laboratories, Nuclear Waste Disposal Research and Analysis, P.O. Box 5800, MS 0779, Albuquerque, NM 87185, United States Received 4 December 2015; accepted in revised form 19 September 2016; available online 26 September 2016

Abstract Chemical thermodynamic data remain a keystone for geochemical modeling and reactive transport simulation as applied to an increasing number of applications in the earth sciences, as well as applications in other areas including metallurgy, material science, and industrial process design. The last century has seen the development of a large body of thermodynamic data and a number of major compilations. The past several decades have seen the development of thermodynamic databases in digital form designed to support computer calculations. However, problems with thermodynamic data appear to be persistent. One problem pertains to the use of inconsistent primary key reference data. Such data pertain to elemental reference forms and key, stoichiometrically simple chemical species including metal oxides, CO2, water, and aqueous species such as Na+ and Cl
. A consistent set of primary key data (standard Gibbs energies, standard enthalpies, and standard entropies for key chemical species) for 298.15 K and 1 bar pressure is essential. Thermochemical convention is to define the standard Gibbs energy and the standard enthalpy of an individual chemical species in terms of formation from reference forms of the constituent chemical elements. We propose a formal concept of ‘‘links” to the elemental reference forms. This concept involves a documented understanding of all reactions and calculations leading to values for a formation property (standard Gibbs energy or enthalpy). A valid link consists of two parts: (a) the path of reactions and corrections and (b) the associated data, which are key data. Such a link differs from a bare ‘‘key” or ‘‘reference” datum in that it requires additional information. Some or all of its associated data may also be key data. In evaluating a reported thermodynamic datum, one should identify the links to the chemical elements, a process which can be time-consuming and which may lead to a dead end (an incomplete link). The use of two or more inconsistent links to the same elemental reference form in a thermodynamic database will result in an inconsistency in the database. Thus, in constructing a database, it is important to establish a set of reliable links (generally resulting in a set of primary reference data) and then correct all data adopted subsequently for consistency with that set. Recommended values of key data have not been constant through history. We review some of this history through the lens of major compilations and other influential reports, and note a number of problem areas. Finally, we illustrate the concepts developed in this paper by applying them to some key species of geochemical interest, including liquid water; quartz and aqueous silica; and gibbsite, corundum, and the aqueous aluminum ion. Ó 2016 Elsevier Ltd. All rights reserved.

⇑ Corresponding author.

E-mail address: [email protected] (T.J. Wolery). http://dx.doi.org/10.1016/j.gca.2016.09.028 0016-7037/Ó 2016 Elsevier Ltd. All rights reserved.

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Keywords: Chemical thermodynamic data; Key reference data; Thermodynamic database; Internal consistency; Standard Gibbs energy; Standard enthalpy; Standard entropy

1. INTRODUCTION Chemical thermodynamic data have long been applied in the analysis and modeling of geochemical and petrologic systems (see for example Garrels and Christ, 1965; Krauskopf, 1967; Krauskopf and Bird, 1994; Stumm and Morgan, 1970, 1996; Robie et al., 1978; Powell, 1978; Holland and Powell, 1985, 1990, 1998, 2011; Nordstrom and Munoz, 1985; Berman, 1988; Chatterjee, 1991; Walther, 2009; Nordstrom and Campbell, 2014; and references cited therein). Such data play an important role in many areas outside the earth sciences including metallurgy, materials science, and industrial process design (see for example Devereaux, 1989; Alcock, 2001; Gaskell, 2008; and Roy and Bose, 2014; and sources cited therein). Other areas of application of thermodynamic data concern combustion, explosives, and rocket fuel (see for example Burcat and Ruscic, 2005; Sutton and Biblarz, 2010; Turns, 2011; and references therein). These are areas which drove some of the earliest efforts to develop numerical methods for calculating chemical equilibria (see for example Zeleznik and Gordon, 1968; van Zeggeren and Storey, 1970; Smith and Missen, 1982; and references cited therein). Such methods have continued to be developed for use in geochemistry (see for example de Capitani and Brown, 1987; Karpov et al., 1997, 2001; and references cited therein). The widespread availability of mainframe computers beginning in the 1960s led to the development of computer programs for geochemical modeling focused on aqueous solutions and minerals. Such programs included PATHI (Helgeson et al., 1969, 1970), REDEQL (Morel and Morgan, 1972), WATEQ (Truesdell and Jones, 1974), MINEQL (Westall et al., 1976), EQ3/6 (Wolery, 1979), PHREEQE (Parkhurst et al., 1980) and SOLVEQ (Reed, 1982). Nordstrom et al. (1979) reviewed a number of early codes and compared results from them for specified problems, finding that many differences were likely due to differences in the thermodynamic data employed. Most of these codes and their associated databases were developed for ‘‘low temperature” applications, though some (including PATHI, EQ3/6, and SOLVEQ) were developed for use to about 300 °C. Recently, thermodynamic data have been used in reactive transport modeling of groundwater systems (see Steefel et al., 2005; Seaman et al., 2012; and references cited therein), often using databases developed for use with other codes. Databases for such codes have been extended and improved in recent years (see for example Wolery and Jove´ Colo´n, 2007; and Nordstrom and Campbell, 2014). More chemical species have been included, and temperature and pressure limits have increased. Recent versions of such codes including EQ3/6 v. 8.0a (https://www-gs. llnl.gov/about/energy-security/technologies/geochemistry) and PHREEQC v. 3 (http://wwwbrr.cr.usgs.gov/projects/

GWC_coupled/phreeqc/) are distributed with multiple databases, with the recommendation that the user should choose the one best suited to a given problem and make appropriate additions or corrections. The above codes use databases in which the data are represented in terms of equilibrium constants (typically expressed as logKr, where r denotes a reaction). A number of these databases have been developed using the code SUPCRT92 (Johnson et al., 1992), which has its own thermodynamic database in the form of standard Gibbs energies, enthalpies, and entropies at 298.15 K and 1 bar along with other data needed to compute values of these and other thermodynamic functions (including equilibrium constants) over a wide range of temperatures and pressures. Most of the mineral data in SUPCRT92 databases is based on the work of Helgeson et al. (1978). The code includes a model for the properties of water over a wide range of temperature and pressure (Helgeson and Kirkham, 1974a,b). The treatment is partly based on an equation of state (EOS) model. In early versions of SUPCRT, the water EOS was that of Keenan et al. (1969). This was replaced in SUPCRT92 by the Haar et al. (1984) EOS and the Levelt Sengers et al. (1983) EOS, the latter used near the critical point of water (see Johnson et al., 1992). The SUPCRT92 database supports ‘‘HKF equation of state” models (first developed by Walther and Helgeson, 1977; Helgeson and Kirkham, 1976; and Helgeson et al., 1981) to calculate Gibbs energies and associated functions for aqueous solute species at elevated temperatures and pressures. The HKF treatment is not a true EOS model, as it supports only the calculation of standard state thermodynamic data. The original HKF treatment was subsequently modified into the form presently used (Shock and Helgeson, 1988; Shock et al., 1989) with accompanying change of parameter values (see also Shock et al., 1997). Interest in the HKF model remains high (see for example Sverjensky et al. 1991; Heinrich et al., 1996; Dolejsˇ and Baker, 2004; Dolejsˇ and Wagner, 2008; Sverjensky et al., 2014; and Miron et al., 2016). Alternative models based on correlations with water density (Anderson et al., 1991; Dolejsˇ, 2013) are also of current interest, though they are not presently in SUPCRT92. Many codes for computing chemical equilibria use databases containing standard Gibbs energies and associated data (analogous to SUPCRT92 databases) in place of equilibrium constants. Usage of such data in making chemical equilibrium calculations is often associated with using a ‘‘Gibbs energy minimization” approach as opposed to an ‘‘equilibrium constant” approach (see for example Zeleznik and Gordon, 1968). The true distinction between the two approaches is in the class of numerical algorithm (is mass balance relaxed or not?), not the type of thermodynamic data used, but such alignment is more common than not. Recent examples of ‘‘Gibbs energy minimization” codes for geochemical applications include the GEM-

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Selektor package (Wagner et al., 2012; Kulik et al., 2013; see also references cited therein) and the Cantera code suite (Moffat and Jove´ Colo´n (2009). However, the present paper is about thermodynamic data, not algorithms for computing equilibria. Work to improve thermodynamic databases is ongoing, with efforts being made to include additional chemical species, extend the range of temperatures and pressures, better deal with non-ideality in various forms, and test and increase accuracy and consistency. Some recent works in this direction include Sverjensky et al. (1991), Heinrich et al. (1996), Dolejsˇ and Wagner (2008), Holland and Powell (2011), Dolejsˇ (2013), Sverjensky et al. (2014), Tutolo et al. (2014), and Miron et al. (2016). One notably important work is the continuing NEA TDB (Nuclear Energy Agency/Thermodynamic Data Base) series of volumes on thermodynamic data. Recent works in this series, which focuses on data needed to deal with radioactive waste disposal, include Rand et al. (2007), Gamsja¨ger et al. (2012), and Lemire et al. (2013). The full series will be discussed later in this paper. The purpose of the present paper is to address the role of key reference data in building thermodynamic databases. The ‘‘G-H-S” data at 298.15 K and 1 bar for chemical species of simple stoichiometry are the most important, as these data are used to derive data for more complex species and have a definitive impact on the results. These simple species, which may be termed ‘‘key species,” usually represent a chemical element in some oxidation state, often combined with one or two other chemical elements. Examples include chemical elements in their thermochemical reference forms such as molecular oxygen, simple oxides and hydroxide solids, gases such as CO2, water, and principal aqueous solute species, such as Na+, Ca2+, Cl
, SO2
4 , and H. The need for an accurate and consistent set of key reference data was recognized by CODATA (Committee on Thermodynamic Data) and addressed in six interim reports (CODATA, 1971, 1972, 1975, 1976, 1977, 1978) and a final report (Cox et al., 1989). The NEA TDB volumes on thermodynamic data adopted the final CODATA recommendations (see Grenthe et al., 1992) and added reference data for additional key species, all of which are relevant to nuclear waste disposal. Although these efforts address data for many key species of geochemical interest, they do not address all. Also, the CODATA results are now somewhat dated and in need of revision (examples will be noted later in this paper). Despite the influence of CODATA and NEA TDB, many existing thermodynamic data are based on older key values, a fact that in many instances may not be readily apparent. Combining sets of thermodynamic data often results in inconsistencies due to the use of inconsistent key reference values. Some older works may not have used a consistent set of key reference values, leading to internal inconsistency (we will note examples in the present paper and subsequent papers in this series). In some instances, it may be difficult to identify with certainty the key reference values that may have been used. However, if the key data that were used can be identified, corrections can be made.

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The quest to achieve an internally consistent thermodynamic database for geochemical use was advanced by Helgeson et al. (1978), who developed set of thermodynamic data for the common rock-forming minerals by analyzing phase equilibrium and other data. This spawned subsequent efforts to develop internally consistent mineralogic/petrologic (‘‘minpet”) databases using global optimization techniques (see for example Berman et al., 1985; Berman, 1988; Holland and Powell, 1985, 1990, 1998, 2011; Saxena et al., 1993; Olbricht et al., 1994; Chatterjee et al., 1994; and Gottschalk, 1997). Most of these ‘‘minpet” models focused on minerals, largely ignoring aqueous species other than water (in contrast to Helgeson et al., 1978, who used a number of reactions involving aqueous species in their development). More recently, emphasis has been placed on integrating ‘‘minpet” databases with data for aqueous species (see for example Holland and Powell, 1998, 2011; Heinrich et al., 1996; Dolejsˇ and Baker, 2004; Dolejsˇ and Wagner, 2008; Zimmer et al., 2016; and Miron et al., 2016). Although progress has been made in this area, problems remain in achieving large-scale consistency. Also, some questions have arisen about the accuracy of certain key reference data. For example, Miron et al. (2016) found that there may be a problem with the CODATA (Cox et al., 1989) recommendations for Na+ and K+. It seems appropriate at this time to review present and past practices of treating key reference data, and to review relevant aspects of the history of its development. This is perhaps especially pertinent to database development focused on ‘‘low temperature geochemistry.” Here the scope of needed chemical species (addressing for example problems radioactive waste disposal and environmental contamination) exceeds that commonly needed for ‘‘minpet” work. Without some knowledge of the history of major sources of thermodynamic data (especially ‘‘standard” compilations), one might easily make inferior selection choices and/or fail to make needed corrections. Engi (1992) and Oelkers et al. (2009) each covered a number of useful points regarding thermodynamic database development. However, the present series is focused on points not specifically addressed by either of these works. In Part 2 of this series, we will address how to modify SUPCRT92 and other codes that use equation of state (EOS) models for water to be consistent with the standard thermochemical properties of water recommended by Cox et al. (1989), the last CODATA report. We will address the Haar et al. (1984) EOS presently in SUPCRT92 and also the more recent IAPWS-95 EOS (Wagner and Pruss, 2002). In Part 3, we will illustrate the principles and methods described here by analyzing the Helgeson et al. (1978) mineral database, and showing how different results can be obtained using different assumptions about key reference data. We will also discuss ‘‘sequential” versus ‘‘optimization” approaches. This paper has two Electronic Annexes. The first is a spreadsheet which contains data and calculations and is intended to aid users as a research tool. It underlies all tables presented in this paper. The second Electronic Annex includes discussions that are not included in the main

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paper, but which readers may find useful and which support certain observations made in the main text.

Df Goi ¼ Df H oi
T Df S oi

2. THERMODYNAMIC FRAMEWORK The equilibrium constant for the r-th reaction (K r ) is related to the corresponding standard partial molar Gibbs energy of reaction Dr Go by the familiar relation Dr Go ¼
lnð10ÞRTlogK r

ð1Þ

where R is the gas constant and T is the absolute temperature. The standard partial molar Gibbs energy of reaction is related to the standard partial molar Gibbs energy of formation of the i-th species appearing in the reaction (Df Goi ) by X mir Df Goi ð2Þ Dr Go ¼ i

where mir is the coefficient of the i-th species in the r-th reaction, defined as positive for products and negative for reactants. Most major works addressing thermodynamic data (see for example Helgeson et al., 1978; Robie et al., 1978; Wagman et al., 1982; Berman, 1988; Grenthe et al., 1992; Barin, 1995; and Robie and Hemingway, 1995) present the data in common ‘‘G-H-S” format, in which the data include the standard partial molar Gibbs energy of formation, the standard partial molar enthalpy of formation (Df H oi ), and standard partial molar entropy (S oi ), all at 298.15 K and standard pressure (now 1 bar). Some works omit the Gibbs energy of formation, using an ‘‘H-S” format (see for example Holland and Powell, 1985, 1990, 1998, 2011; Saxena et al., 1993; and Binnewies and Milke, 1999). With this format, one can use the data provided to first calculate the standard enthalpy of reaction (Dr H o ) and the standard entropy of reaction (Dr S o ) according to X Dr H o ¼ mir Df H oi ð3Þ i

X mir S oi Dr S ¼ o

ð4Þ

i

The standard Gibbs energy of reaction is then obtained from Dr Go ¼ Dr H o
T Dr S o

chemical element reference form. The Gibbs energy of formation can then be obtained from

ð5Þ

There is no need in this approach to calculate a standard Gibbs energy for an individual chemical species, as chemical equilibrium calculations can be fully supported by standard Gibbs energies of reaction. If the standard Gibbs energy of formation is desired, it must be calculated from the entropy of formation, which is the entropy for a reaction in which one mole of the species of interest is formed from the chemical elements in their reference forms. This takes the form X Df S oi ¼ S oi þ mei S oe ð6Þ e

where mei is the reaction coefficient for the e-th chemical element reference form (defined as negative, since these would be reactants) and S oe is the partial molar entropy of the same

ð7Þ

Eq. (6) requires a set of values for the entropies of the chemical elements in their reference forms. This is most convenient for the standard reference temperature and pressure of 298.15 K and 1 bar, as only one datum per chemical element is required. Thermodynamic databases generally contain ‘‘G-H-S” or ‘‘H-S” data only for 298.15 K and 1 bar pressure. These data are extrapolated (usually in software) using data for corresponding thermodynamic functions such as heat capacities, phase transitions (where applicable), molar volumes, and compressibilities, or an equivalent equation of state parameters. For discussion of such models and associated data, see Helgeson et al. (1978, 1981), Helgeson and Kirkham (1974a,b, 1976), Berman (1988), Johnson et al. (1992), Saxena et al. (1993), Gottschalk (1997), Holland and Powell (1985, 1990, 1998, 2011), Shock and Helgeson (1988), Shock et al. (1989), Anderson (2005), Heinrich et al. (1996), Shock et al. (1997), Dolejsˇ and Baker (2004), Dolejsˇ and Wagner (2008), Oelkers et al. (2009), Walther (2009), and Dolejsˇ (2013). In contrast, the same models may be used to extrapolate experimental data at elevated temperature and pressure to 298.15 K and 1 bar (see for example Helgeson et al., 1978; Holland and Powell, 1985; Berman, 1988). It is also possible to obtain thermodynamic data at 298.15 K and 1 bar from fitting data over a wide range of temperature and pressure including 298.15 K and 1 bar (see for example the model for Al3+ developed by Tagirov and Schott, 2001, which will be discussed later in this paper). There is sometimes concern about ‘‘model dependency” of the resulting data values for 298.15 K and 1 bar. However, the means to avoid such dependency is often limited. Although the present paper mainly addresses ‘‘G-H-S” data at 298.15 K and 1 bar, we note some issues with the definition of the standard Gibbs energy and enthalpy of an individual chemical species at other temperatures and pressures. These issues come about because multiple definitions are currently extant. It is often necessary to identify which definition a data source might be using. See the second Electronic Annex, Section 2 for discussion of treatment of standard Gibbs energies and standard enthalpies of individual chemical species at temperature and pressures other than 298.15 K and 1 bar. 3. METHODS/APPROACH/PHILOSOPHY In this paper we will begin by briefly reviewing the issues that come into play in obtaining and using key reference data (which in the present context pertain to 298.15 K and 1 bar). We propose a somewhat formal approach to assessing consistency with regard to such data and correcting thermodynamic data to achieve such consistency. In theory there should be nothing new here, but mistakes and omissions in developing thermodynamic data are not uncommon. We will point out examples later in this paper and in following papers in the series. In many instances,

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these inconsistencies are small. However, they may propagate if the data are used to calculate still other data, as is the case with the use of key reference data. Some basic knowledge of the history of thermodynamic data development is necessary to provide a firm footing for thermodynamic database development, particularly if this is to be done for a wide range of chemical species. We will review this history through the lens of major compilations and other influential works, focusing on key reference data of importance to geochemistry. We will note various key facts that potential users of such sources should be aware of. Much of what will be discussed is primarily aimed at investigators of ‘‘low temperature geochemistry.” We do not accept a ‘‘roll-up” view of the development of thermodynamic data that would carry the notion that past mistakes have been corrected and only the latest summary of the ‘‘best” data is relevant to ongoing and future work. Many older data values (particularly key reference values) that should be corrected or discarded remain embedded in currently used data values for other chemical species. We will note examples later in this paper and in following papers in the series. In this paper we will present G-H-S data for 298.15 K and 1 bar for a selection of key species of common (including geochemical) interest, taken from various major sources and compilations that are (a) illustrative of the history of thermodynamic data development and (b) thought to have been influential in the development. We will discuss pertinent information that is helpful to essential in understanding the data given by these sources. In the present paper we will largely defer discussion of the ‘‘minpet” databases and the works of Helgeson and co-workers (citations for both given previously) to Part 3 of this series. These works primarily use key reference data taken from one or more of the sources noted here. Holland and Powell (1998, 2011) do not hold constant what we consider to be key reference data in their global optimization fitting. Thus for example, the output values for such data do not precisely match the input values. This is also true for some key reference data in the work of Miron et al. (2016), although their study was more exploratory in nature. The chosen set of species in this paper includes 35 aqueous species, 3 alternate aqueous species, 4 gases, and 25 solids. This set is likely to be useful in future efforts to analyze thermodynamic data and build better data sets. One the one hand, it provides a quick summary of how thermodynamic data values have evolved. On the other, it may facilitate making corrections to other data. Data not originally given in Joule units (kJ mol
1, J mol
1 K
1) for 1 bar pressure have been corrected in the tables presented here. The spreadsheet Electronic Annex contains all the data concerned here, including the data as originally captured from the sources. While users may find the spreadsheet useful, we recommend that they also consult the original sources if engaged in database evaluation or development. In capturing data from any given source, we focused on the main table or tables provided. We account for corrections only if the value in a main table is incorrect, as by a transposition of digits, and the source itself gives the intended correct value in text, table, or table footnote, or

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if a later issue within a series gives a correction. Such corrections are noted in the table footnotes of the present paper. Some sources give data to different precision in different parts of the works, typically giving a more precise value in text and a less precise (rounded) value in a summary table. Uncertainties are given by some of the sources we examined. The uncertainty for a thermochemical quantity is usually defined as twice the standard deviation, or 2r (see for example Robie and Waldbaum, 1968, p. 9; Cox et al., 1989, p. 14). This corresponds to about the 95% confidence level (see for example Cox et al., 1989, p. 12; Grenthe et al., 1992, Appendix C). The means of estimating uncertainties in thermodynamic data are generally not statistically rigorous, relying more on elements of expert judgment. For a general overview of the treatment of uncertainties, particularly in regard to estimation and calculation of propagation, see Grenthe et al. (1992), Appendix C. For this paper, we only captured uncertainties from the final CODATA report (Cox et al., 1989) and the NEA TDB volumes (see for example Grenthe et al.; a full list of these volumes will be given later in this paper). For other sources examined, we will note those that include uncertainties. Although we will present a large quantity of G-H-S data, only a limited analysis is possible in the present paper. Our main goal here is to discuss the major sources, summarize the data, and point out some important issues. Later in this paper we will present more detailed analysis for a few chemical species to provide illustration and a start to a larger effort. For some species, the major sources and compilations used here do not capture recent thinking and data for certain key species of geochemical interest, such as aqueous silica and Al(III) species (see for example Tagirov and Schott, 2001; Tutolo et al., 2014; Sverjensky et al., 2014; Miron et al., 2016) and the aqueous sulfate ion (Nordstrom, 2013). In such cases, additional data from more recent sources should be factored into analyses. In order to improve the readability of this paper, the following conventions will be used. The ‘‘standard partial molar Gibbs energy” will be abbreviated in some instances to ‘‘standard Gibbs energy,” ‘‘Gibbs energy”, or simply ‘‘G.” The corresponding enthalpy and entropy functions will be treated analogously. Except for instances otherwise explicitly noted or implied by context, such references will pertain to data for 298.15 K and 1 bar. 4. LINKS TO THE CHEMICAL ELEMENTS: A NEW(?) CONCEPT Standard thermochemical convention (see for example Rossini et al., 1952; Wagman et al., 1982; Cox et al., 1989) defines the standard Gibbs energy and enthalpy of an individual chemical species in terms of formation from the chemical elements in their reference forms. The development of such data for a chemical species is usually the result of a series of steps described as a ‘‘thermodynamic cycle.” Each step involves the usage of associated data. The steps include chemical reactions, but also represent various corrections, as of temperature and pressure, or to correct non-standard state thermochemical data to standard states.

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In general, there will be a step in which each chemical element reference form is converted to a corresponding primary key species Such species, noted earlier in this paper, represent a chemical element in a particular oxidation state. They include simple oxides and hydroxides and simple or relatively simple aqueous ions. Primary key species usually consist of no more than three chemical elements. Thus MgO (periclase), Mg2+, and Mg(OH)2 (brucite) might be used as primary key species for Mg(II). Additional discussion of primary key species and primary key reference data is given in the second Electronic Annex, Section 3. We consider a step or chain of steps leading back from a chemical species to the elemental reference forms as a ‘‘link.” We define a valid link as one which provides not only an associated reference value for Gibbs energy and/ or enthalpy value, but which also includes the path (the steps leading back to the elemental reference forms), the data for all of the steps, including corrections, and complete documentation. The key thermodynamic reference data given by Cox et al. (1989) generally correspond as valid links. An incomplete link would be missing one or more of the necessary components defined above. The thermochemical data for key chemical species given by Wagman et al. (1968) or Wagman et al. (1982) correspond to incomplete links because the data are given without references. We include elemental reference forms at 298.15 K and 1 bar as links, as their associated entropies are required to relate the standard Gibbs energy of formation of a chemical species to the corresponding enthalpy of formation through Eq. (7) (Df Goi ¼ Df H oi
T Df S oi ). As noted earlier, it is possible to avoid the standard Gibbs energy of formation entirely, as standard Gibbs energies of reaction are sufficient to support calculations of chemical equilibrium, and those can be calculated from standard enthalpies and entropies of reaction. However, that is less common in dealing with thermochemical data. Also, the elemental reference forms may be species of direct interest in equilibrium calculations. It seems appropriate and useful at this time to formalize the concept of valid links as a part of evaluating thermodynamic data and constructing thermodynamic databases. This will be helpful in the context of any regulatory environment, such as application of thermodynamic data in analyses and simulations that fall under regulatory requirements of bodies such as the U.S. Nuclear Regulatory Commission and the U.S. Environmental Protection Agency. From a scientific point of view, there should be nothing new here. The conceptual basis is already part of the framework of chemical thermodynamics and thermodynamic database development. What we are proposing here is a formalized approach with strict attention to the state of key reference data, particularly primary key reference data, emphasizing complete documentation of the origin of the data. Thermochemical data are significant to both science and technology. From the technology side, thermodynamic data can be viewed as ‘‘accepted engineering data” that can be compiled and published without sufficient documentation. Thus for example Wagman et al. (1968) and Wagman et al. (1982) do not give specific references for the data they present. Such works have nonetheless influ-

enced the science side. For example, Helgeson et al. (1978) used key reference data from Wagman et al. (1968) in their scientific study of mineral thermodynamics. Although links are associated most strongly with primary key species, they can be associated with more complex species. For example, chrysotile (Mg3Si2O5(OH)4) can be associated with a higher level link used in the thermochemical cycle for say enstatite (MgSiO3) or talc (Mg3Si4O10(OH)2). Higher level links can be utilized in a ‘‘sequential” approach to developing thermodynamic data. Helgeson et al. (1978) is considered an example of such a development, in which data (mostly primary key reference data) are adopted, and then phase equilibria (which may include solubility equilibria) for a set of reactions are evaluated. For each such reaction, data are extracted for one more chemical species to add to the dataset. In this approach, many higher-level links may be developed. A purely sequential approach requires only a minimal set of data. Common multiple values for say a Gibbs energy of reaction can be dealt with by averaging before starting. This is analogous to the averaging done by Cox et al. (1989) in deriving primary key thermochemical data. However, more complex situations may arise in which multiplicity of data is not so easily resolved, and in which the data to be used span some range of temperature and pressure. For example, one might have calorimetric data for talc along with one or more phase equilibria and/or solubility equilibria data that would provide independent means to determine the thermochemical data for talc. This problem has been addressed by various optimization techniques. Such techniques have been applied in the mineralogic/petrologic context by Berman et al. (1985), Holland and Powell (1985, 1990, 1998, 2011), Berman (1988), Saxena et al. (1993), Olbricht et al. (1994), Chatterjee et al. (1994), Gottschalk (1997), and others, up to the present (see for example Miron et al., 2016, and references cited therein). We also note the work of Ruscic et al. (2004, 2005), and Burcat and Ruscic (2015), which has been mainly in the context of applications in the areas of combustion and air pollution. Chatterjee (1991, Chapter 2) reviews a number of optimization methods that have been used in the ‘‘minpet” literature. Optimization is a simultaneous-solution process with a set of outputs determined from a larger, overlapping set of inputs. There is internal linkage or structure; however, it is more complex than in a purely sequential process. Holland and Powell (1985) emphasized the existence of structure and presented a table of correlation coefficients describing the dependence of outputs on inputs. Chatterjee et al. (1994) also examined correlations. Active Thermochemical Tables or ‘‘ATcT” (Ruscic et al., 2004, 2005; Burcat and Ruscic, 2005) has an explicit focus on linkage through a Thermochemical Network (TN) approach. Most primary key reference data now are based only on measurements near 298.15 K and 1 bar (see for example Cox et al., 1989). Most optimization methods use such primary key reference data in the input. In most cases, these data are held constant. However, in the method used by Holland and Powell (1998, 2011) to derive thermochemical

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data for minerals, the primary key reference data are optimized along with other data, using high temperature data in the process. Thus, the output values for quartz and other primary key species are not the same as the input values. This is a somewhat problematic, in that primary key reference data for aqueous species tend to be based on such data. Thus, mixing of the Holland and Powell (2011) data for minerals with commonly available data for aqueous species should result in some inconsistency. As discussed previously, Miron et al. (2016) explored this issue by optimizing some primary key data for aqueous species along with the mineral data. ATcT (Ruscic et al., 2004, 2005) works a bit differently. Instead of refining existing key primary data, it determines its own by taking the analysis down to the level of CODATA (Cox et al., 1989). It is not always clear when primary key data are optimized if the corresponding inputs are at the level of the CODATA (Cox et al., 1989) recommendations, most of which are averages of two to three values for any thermochemical function treated, or at the level of the underlying data used by CODATA. If they are at the CODATA recommendation level, then as averages, they should be given appropriately higher weighting. We will further address ‘‘sequential” and ‘‘optimization” approaches in Part 3 of this series. 5. THE HISTORICAL DEVELOPMENT OF KEY REFERENCE DATA Chemical thermodynamic data have been measured and collected for well over a century (see for example Wagman, 1992). Many of the currently extant thermodynamic data are based on measurements that were made and first reported long ago. To our knowledge, the tables to be presented here summarizing the historical development of data for entropies of the elemental reference forms and the formation properties and entropies of other key chemical species are the first of their kind to be assembled. Only some of the more important tables are included in the body of this paper. A more complete set is contained in the spreadsheet Electronic Annex, which is a Microsoft Excel spreadsheet. We hope that these tables will serve readers in two ways: first, by giving a sense of how the data have changed over the years, and second, by providing a convenient resource to aid in making corrections to other data that may have been developed using obsolete or uncorrected (as from 1 atm pressure to 1 bar) key reference data. Some of the data noted here would qualify as associated with the concept of valid links; other data would not. We cannot present a detailed history of the development of key reference data in this paper. Here we focus on data from sources thought to be influential in the development of thermodynamic data. These are primarily major compilations. Widespread availability of works is one criterion. For example, we discuss data from the JANAF Tables, including the JANAF Tables 2nd edition (Stull and Prophet, 1971), the 3rd edition (Chase et al., 1985), and the 4th edition (Chase, 1998). We exclude the 1st edition because it was a loose-leaf product with restricted distribution to U.S. government agencies. For a brief history of the

641

JANAF Tables, see Chase (1998). A second criterion is common citation by other works (we did not conduct a study of citation frequency). It is not uncommon for many of the sources discussed here to cite data one from another. The reputation of source organizations is an important consideration. For example, works from CODATA, the U.S. National Bureau of Standards (now the National Institute of Science and Technology), the United States Geological Survey (U.S.G.S.), and the U.S. Bureau of Mines (U.S.B. M) are given attention in addition to the JANAF Tables. We do not give much attention to sources from the old Soviet Union, apart from Gurvich et al. (1989, 1991, 1993), which provide a late overview. We include data from the NEA TDB volumes, as these are among the most recent. Still other sources are included based on historical significance. In examining the tables to be presented showing the historical development of data as seen through the lens of major compilations, the reader is cautioned about interpreting trends. It is reassuring on the one hand to see convergence through time to a narrow range of values, as this may reflect the use of better samples and measurement techniques. On the other hand, too much agreement may reflect repetition of values. Thus, a lack of significant variation may be a cause for concern. Joule units (for example, J mol
1, J mol
1 K
1) are generally used in modern work, in part due to the influence of recommendations by the International Union of Pure and Applied Chemistry (see IUPAC, 1979, 1982). Calorie units (1 cal = 4.184 J) are common in the older literature. The calorie is now considered obsolete (see for example IUPAC, 1979, 1982). However, calorie units are still used by geochemists (see for example Tutolo et al., 2014; Sverjensky et al., 2014), in large part due to the influence of the code SUPCRT92 (Johnson et al., 1992) and closely related papers by H.C. Helgeson and associates (see the review by Oelkers et al., 2009). All results in the main paper here will be given in Joule units (corrected by us; see the spreadsheet Electronic Annex). An issue of some significance is the move from 1 atmosphere (1.01325 bar) to 1 bar (105 Pa) as the standard pressure. This was also driven by recommendations of IUPAC (1979, 1982). The shift to 1 bar in the literature was largely coincident with the shift from calorie to Joule units. There are rare instances in which Joule units have been used with 1 atm. These include Rodebush and Rodebush (1929) and the six interim recommendations of CODATA (1971, 1972, 1975, 1976, 1977, 1978). The consequences of shifting the standard pressure from 1 atmosphere to 1 bar have been discussed in various works (Robie et al., 1978; IUPAC, 1979, 1982; Wagman et al., 1982; Robie and Hemingway, 1995). The pressure shift has no significant effect on the absolute properties of condensed phases. However, it does indirectly affect the Gibbs energies of formation of such phases if any of the relevant elemental reference forms are gases. For gas phases, the standard entropy is changed by a constant amount (regardless of the gas), the enthalpy is unchanged, and the Gibbs energy is changed because of the entropy change. For gases that are not elemental reference forms, the Gibbs energies

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may be additionally affected in the same indirect manner as those of condensed phases. This would be the case, for example, with carbon dioxide and methane. The relevant entropy change for a gas is given with various precision as 0.11 J mol
1 K
1 (IUPAC, 1982; Robie and Hemingway, 1995), 0.109 J mol
1 K
1 (Cox et al., 1989), 0.1094 J mol
1 K
1 (Wagman et al. (1982), and 0.109442 J mol
1 K
1 (Chase et al., 1985). For our purposes, the 0.1094 J mol
1 K
1 value is sufficient. We use this in calculations to be presented and round results appropriately (as discussed below). Another notable historical factor is the change from red phosphorus (the stable form) to white phosphorus as the elemental reference form for this element. We will note this in the tables to be presented. As will be shown, earlier works addressing thermodynamic data usually present data values to the number of figures thought to be significant. In later works, data are generally tabulated to three decimal places for data given in kcal mol
1, cal mol
1 K
1, kJ mol
1, or J mol
1 K
1. We will follow this practice in the calculations to be presented (where for example we change from calorie to Joule units or convert to a standard pressure of 1 bar). In taking data from the cited sources for inclusion in our spreadsheet Electronic Annex, we used text mode to avoid the loss of trailing zeros. The captured data is thus exactly that given by the source. There is one exception, in that some sources such as Robie and Waldbaum (1968) and Robie et al. (1978) give standard Gibbs energies and enthalpies in units of cal mol
1 or J mol
1. In such cases, we captured the data in units of kcal mol
1 or kJ mol
1, as appropriate, but preserved the original number of figures. It is not uncommon for calculated thermodynamic data and the corresponding uncertainties to be rounded to reflect uncertainty (see for example Grenthe et al., 1992, Appendix C). We avoid rounding other than to three decimal places for quantities in kcal mol
1, cal mol
1 K
1, kJ mol
1, and J mol
1 K
1. Robie and Waldbaum (1968, p. 9) pointed out that rounding to express uncertainty works against the maintenance of internal consistency and may obscure small differences of importance in calculations of geological interest. Also, Coufal et al. (2005) noted that rounding to express uncertainty means that a less probable value is preferred to a more probable value. In addition, small differences due to rounding may be significant to estimating degree of disequilibrium and hence rates of approach to equilibrium. Analyses of complex behavior in geochemical systems (see for example that of Maher et al., 2009, on reaction affinity and weathering, and Zhu and Lu, 2009, on alkali feldspar dissolution and secondary mineral precipitation) require that such small differences be respected. Similar arguments about rounding could be made in regard to uncertainties. The best way to represent uncertainty in thermodynamic data is to assign uncertainty values. A small over-precision in the representation of thermochemical data and corresponding uncertainties retains maximum fidelity to the original data, and causes no harm. The spreadsheet Electronic Annex contains all data captured from the sources, in the original units and for the original standard pressure. We have included there such

unit conversions and pressure corrections as are needed to facilitate comparison and usage of the data. In all instances, the spreadsheet includes the data in both Joule and calorie units for a standard pressure of 1 bar. For purposes of discussion (particularly when addressing elemental entropies), we define works using a standard pressure of 1 atm as belonging to the ‘‘Historical” group and those using 1 bar as belonging to the ‘‘Modern” group. These groups overlap somewhat time-wise, largely in the 1970s and 1980s. Robie et al. (1978) is the earliest notable compilation we found that uses 1 bar as the standard pressure (it is also made the leap to Joule units). Pankratz et al. (1984) is the last one we found that uses 1 atm (it also uses calorie units). Cox et al. (1989) give data for both 1 atm and 1 bar. In referring to certain works (usually those appearing in series), to enhance readability we will often use short ‘‘handles” instead of the full formal references. For example, the JANAF Tables 2nd edition (Stull and Prophet, 1971) will be referred to as JANAF 2, and other versions of the JANAF Tables will be referred to similarly. U.S. Bureau of Mines Report 350 (Kelley, 1932) will be referred to as USBM 350, and other U.S.B.M. reports will be treated analogously. U.S. National Bureau of Standards reports and U.S. Geological Survey reports will be treated in similar fashion. For example, NBS 500 refers to the famous ‘‘Circular 500” (Rossini et al., 1952), while USGS 1259 refers to ‘‘Geological Survey Bulletin 1259” (Robie and Waldbaum, 1968). 5.1. Entropies of the chemical elements in their reference forms Here we address the first 96 chemical elements (hydrogen through curium). The 22 major compilations we look at in the present paper do not extend to higher known elements, which consist of short-lived isotopes. Sample purity is likely better represented in later works. We only focus on the entropy data as reported. The underlying raw data and methods of analysis are not considered here. Table 1 gives the data reported by 11 notable works in the Historical group. All of these sources used calorie units and a standard pressure of 1 atm, here converted to Joule units and corrected to a pressure of 1 bar. The table starts with data from Lewis and Gibson (1917), whose paper covered 46 elements. This was followed by a later paper (Lewis et al., 1922) that covered 50 elements and provided a number of updated values. In these papers, the data were given for one mole of element, rather than for one mole of reference species, as is the general custom in later works. This is an issue for the diatomic reference species (including as Cl2 (g), H2(g), and O2(g)). Although we captured the as-given data in the spreadsheet Electronic Annex, we converted it to the more customary format for comparison with other data. USBM 350 (Kelley, 1932) is an early report on thermodynamic data from the U.S. Bureau of Mines. In capturing data from this work, we took the data in the report’s Table 1, in the column marked ‘‘Value recommended” (entropy values also appear in other columns). NBS 500

Table 1 Reference values of elemental entropies from the Historical group. Data are calculated from data given by the sources. Units are J mol
1 K
1, for 1 bar standard pressure. Elem. Ref. Form

Lewis et al. (1922)

USBM 350 Kelley (1932)

NBS 500 Rossini et al. (1952)

ACS 18 Stull and Sinke (1956)

USBM 592 Kelley and King (1961)

USGS 1259 Robie and Waldbaum (1968)

NBS 270 NBS 270 Parts 3–8 1968–1981

JANAF 2 Stull and Prophet (1971)

Hultgren et al. (1973)

42.677 28.870

42.886 28.535

42.677 28.242

42.702 28.321

62.760 42.677 28.326

62.760 42.677 28.326

42.677 28.326

56.484 42.551 28.326

28.321

42.677 28.326

152.407

153.662

154.876 35.146

154.846 35.146

154.843 35.146

45.606 8.954 57.739 153.134 5.439 41.631 51.463 57.739 221.861

47.698 6.527 66.944 9.540 56.902 152.298 5.694 41.631 51.463 57.739 223.058

154.834 35.146 121.336 47.321 5.870 66.944 9.540 56.484 152.298 5.690 41.631 51.756 69.454 223.075

35.146

47.698

154.834 35.146 121.336 47.363 5.858 64.852 9.540 56.819 151.670 5.732 41.631 51.756 69.622 223.075

47.321 5.870 66.944 9.540 56.735 152.231 5.740 41.631 51.798 64.015 223.066

47.405 5.858 62.760 9.498 56.735 152.231 5.740 41.422 51.756 71.965 223.066

28.451 23.765 82.843 33.305

30.041 23.765 84.098 33.346 74.894 73.220 71.128 202.992 27.154 94.140 40.878 67.781 31.087 130.692 126.173 45.647 76.023 75.312 116.148 58.158 35.480

30.041 23.640

203.452 27.154

30.041 23.849 84.349 33.346 74.768 73.136 71.128 202.824 27.154 94.140 41.087 65.982 31.087 130.692 126.173 45.647 76.107 74.350 116.734 57.823 36.401

30.041 23.765 85.228 33.150 74.768 73.178 77.781 202.782 27.280 95.395 40.878 68.074 31.087 130.684 126.150 43.555 76.023 75.312 116.135 57.823 35.480

46.024

46.024

30.543

30.543

154.808 5.439 46.024 48.534 57.739 215.167

136.398 5.439 44.518 49.371 57.739 220.188

30.125 24.267

30.125 24.267

33.472

34.225

28.451 23.430 79.496 33.054

27.614

28.075

27.196 42.677

133.161 122.282

123.286 124.918

40.585 130.776 126.173

74.475

74.475

77.404

42.677 58.576 42.426 130.696 126.157 54.810 77.404

131.378

111.294

36.401

36.401

116.734 60.668 36.401

116.734 52.300 36.401

33.346

202.782 27.280

130.684 43.555 76.023 116.135

154.842 35.690

5.870 9.540 152.231 5.686 41.555

223.071 30.041 85.149 33.108

202.812 27.317

130.684

76.027 116.139

47.488 5.858 62.417 9.498 56.735 5.732 41.422 51.798 69.454 223.083 30.041 23.640 85.061 33.150 74.894 73.178 80.793 202.774 27.280

USBM 672 Pankratz (1982) 42.551 28.351 54.488 154.846 35.706 47.405 5.899 62.417 9.498 56.735 152.210 5.740 41.589 51.798 71.965 223.075 71.965 30.041 23.640 85.228 33.154 74.894 73.178 77.822 202.795 27.280

40.827 40.827 67.948 67.948 31.087 31.087 130.684 130.679 126.148 126.152 43.555 43.555 75.898 75.898 75.019 75.019 116.148 116.139 57.823 57.823 35.505 35.485 (continued on next page)

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Ac Ag Al Am Ar As At2 Au B Ba Be Bi Br2 C Ca Cd Ce Cl2 Cm Co Cr Cs Cu Dy Er Eu F2 Fe Fr Ga Gd Ge H2 He Hf Hg Ho I2 In Ir

Lewis and Gibson (1917)

643

644

Table 1 (continued) Lewis and Gibson (1917)

Lewis et al. (1922)

USBM 350 Kelley (1932)

NBS 500 Rossini et al. (1952)

ACS 18 Stull and Sinke (1956)

USBM 592 Kelley and King (1961)

USGS 1259 Robie and Waldbaum (1968)

NBS 270 NBS 270 Parts 3–8 1968–1981

JANAF 2 Stull and Prophet (1971)

K Kr La Li Lu Mg Mn Mo N2 Na Nb Nd Ne Ni Np O2 Os P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rh Rn Ru S Sb Sc Se Si Sm Sn Sr Ta Tb

82.425

63.597 163.997 57.321 31.798

63.597 164.080 57.321 28.033

34.727 30.543 31.380 190.900 51.045

32.635 30.543 28.451 191.737 51.045

32.510 31.757 28.577 191.599 51.045 34.727

30.125

145.127 30.125

146.382 29.706

146.332 30.125

64.183 164.080 56.902 28.033 49.371 32.677 31.966 28.535 191.611 51.212 37.656 73.220 146.340 29.874

64.183 164.082 56.902 29.121 50.961 32.677 32.008 28.660 191.611 51.212 36.401 71.546 146.328 29.874

64.672

34.727 30.543 31.380 190.900 51.045

64.392 164.080 56.902 28.242 49.162 32.677 32.008 28.577 191.611 51.087 36.526 73.220 146.340 29.874

64.768

57.321 31.798

69.454 162.783 57.321 31.798

201.778 32.635

200.941 32.635

205.251 32.635

205.138 32.635 44.350

205.167 32.635 22.845 51.882 64.810 37.865 72.007 62.760 73.011 41.840

205.167 32.635 41.003 51.882 64.810 37.907 71.965 62.760 73.638 41.631

71.128 76.232 37.196 31.798 176.256 28.870 31.882 45.689 37.656 42.468 18.954 68.116 51.421 52.300 41.422 73.053

71.128 75.730 37.196 31.506 176.256 28.535 31.882 45.689 37.656 42.426 18.870 68.199 51.421 52.300 41.505 73.220

64.434 37.238

64.978 37.238

65.270 37.238

64.894 37.238

41.840

41.840

53.137 41.840

41.840

28.870 31.798

31.798 175.042 28.870 31.798

31.798 176.256 28.870 31.798 43.932

71.128 69.454 41.840 31.798 176.256 28.870 31.882 43.932

19.665

19.665

18.828

41.840 18.702

48.116

46.735

51.463

71.965 31.798

39.330

51.463 54.392 41.422

29.079 32.677 32.008 28.660 191.611 51.212 36.401

29.874 205.109 22.803 65.061

41.631

31.798 45.689 42.442 18.828 51.547 52.300

205.138 32.635 41.087 51.882 64.810 37.572

29.096 32.694 28.606 191.611 51.455

205.142 22.803 64.785

73.220 41.631 71.128 76.776 36.861 31.506 176.214 28.535 31.798 45.689 34.644 42.442 18.828 69.580 51.547 52.300 41.505 73.220

31.928

18.820

Hultgren et al. (1973) 64.685 164.085 56.902 29.275 50.961 32.677 32.008 28.660 191.611 51.170 36.401 71.086 146.328 29.874

USBM 672 Pankratz (1982)

65.061 37.823

64.672 164.085 56.902 29.096 50.961 32.677 32.008 28.660 191.611 51.455 36.401 71.546 146.328 29.874 50.459 205.146 32.635 41.087 51.882 64.810 37.710

73.931 41.631 51.463

73.931 41.631 56.149

76.776 36.526 31.506 176.231 28.535 31.798 45.522 34.644 41.966 18.828 69.496 51.195 52.300 41.505 73.304

76.776 36.526 31.556

205.142 32.635 41.003

28.614 32.054 45.522 34.644 42.442 18.828 69.580 51.195 52.300 41.505 73.304

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Elem. Ref. Form

38.970 29 Red 41.631 38.953 50 Red

50.208 28.911 32.635

41.631 38.409 73 White

35.146 168.432

41.129 39.748 50 –

35.146

41.003 39.748 46 –

41.631 39.748 62 –

50.334 29.497 33.472 169.687 46.442 46.442

46.442 27.196 33.472 169.603

56.902 27.614 61.086

Tc Te Th Ti Tl Tm U V W Xe Y Yb Zn Zr Count P Ref.

56.902 27.614 61.086

56.902 27.614 64.852

37.656 49.706 56.902 30.292 64.434

33.472 49.706 53.388 30.669 64.224 71.379 50.334 29.330 33.639 169.687 46.024 62.760 41.631 38.869 92 Red

33.472 49.706 53.555 30.543 64.224 71.546 50.334 29.372 32.635 169.687 46.024 62.760 41.631 38.995 92 –

49.706 53.388 30.627

49.706 53.388 30.627 64.183 74.015 50.208 28.911 32.635 169.683 44.434 59.873 41.631 38.995 88 White

30.648

32.660

33.472 49.497 53.388 30.627 64.183 74.015 50.292 28.911 32.635 169.641 44.434 59.831 41.631 38.995 85 –

49.706 53.388 30.627 64.183 74.015 50.208 28.932 32.635 169.687 44.434 59.831 41.631 38.995 88 White

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(Rossini et al., 1952) represents the first major compilation of thermodynamic data in ‘‘G-H-S” form. It covered 73 elements. ACS 18 (Stull and Sinke, 1956) is a book that addresses only chemical elements. It is a prequel of sorts to the JANAF Tables. It includes data for 92 chemical elements. ACS 18 is notable for the use of a computer to generate tables of thermodynamic properties as a function of temperature. USBM 592 (Kelley and King, 1961), is a later U.S.B.M. report that included data for 92 chemical elements. USGS 1259 (Robie and Waldbaum, 1968) is the first major thermodynamic data compilation from the U.S.G.S. It only covers 50 chemical elements, but provides G-H-S data for many chemical species of interest in geochemistry. NBS 270 is a series of National Bureau of Standards reports that superseded NBS 500. It starts with 270-3 (Wagman et al., 1968), including 270-4 (Wagman et al., 1969), 270-5 (Wagman et al., 1971), 270-6 (Parker et al., 1971), and 270-7 (Schumm et al., 1973), concluding with 270-8 (Wagman et al., 1981). The N.B.S. produced two earlier reports 270-1 (Wagman et al., 1965) and 270-2 (Wagman et al., 1966). These were quickly superseded by 270-3 and appear to have had little influence on other works. NBS 270 covered 88 chemical elements. It was highly influential on work related to geochemistry, being drawn on for example by Helgeson et al. (1978) in the construction of their thermodynamic database for minerals. As noted previously, NBS 270 does not include references for the data. JANAF 2 (Stull and Prophet, 1971) was the first generally circulated version of the JANAF Tables. The JANAF Tables were aimed at supporting the development of rocket engines. JANAF 2 covered only 29 chemical elements. Despite that, it had some influence outside rocketry. It is cited for example in the Helgeson et al. (1978) mineral thermodynamics paper. Hultgren et al. (1973) is book that is notable for the detailed information regarding the development of the data included in the volume. USBM 672 (Pankratz, 1982) is one of the last reports on thermodynamic data from the U.S. Bureau of Mines, which was closed in 1996. The same data are included in USBM 677 (Pankratz et al., 1984), which is a more general compilation of thermodynamic data. Table 1 omits one work that might have been included here. Rodebush and Rodebush (1929) gave a compilation of thermodynamic data for elemental species as part of the International Critical Tables. This work covers only 23 elements and does not appear to have been influential on other works. However, the data are included in the spreadsheet Electronic Annex. Table 1 shows that, for most elements, the given entropy values for the elemental reference forms have been fairly comparable among the sources represented in the Historical group. An issue in making comparisons for this group is the absence of data for many elements, especially in the earlier works. In a number of instances, the values repeat several times, though they may be given with varying precision. Some sources in the Historical group use red phosphorus as the reference form, while others use the white allotrope (see the bottom of Table 1).

646

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The following sources from the Historical group do not tabulate uncertainty values: Lewis and Gibson (1917), Lewis et al. (1922), Rodebush and Rodebush (1929), NBS 500, ACS 18, NBS 270, and JANAF 2. These may include general discussion of the nature and magnitude of uncertainty, as well as occasional discussion of uncertainty in the development and discussion of certain of the data, but regularly tabulated uncertainty values are not provided. The following sources do tabulate uncertainty values: USBM 350, USBM 592, USGS 1259, Hultgren et al. (1973), and USB 672. We have not captured or analyzed uncertainty values from these sources. Table 2 summarizes the data from eleven major sources in the Modern group. All of these sources give the data in Joule units for a standard pressure of 1 bar. USGS 1452 (Robie et al., 1978) is the second major thermodynamic compilation issued by the U.S. Geological Survey. It is the only source in this group to use red phosphorus as the reference form for that element. NBS 82 (Wagman et al., 1982) superseded NBS 270. Although this is one of the most comprehensive compilations of thermodynamic data ever produced, it continued the problematic practice of not including references. It was also the last major work covering the thermodynamics of inorganic species produced by the National Bureau of Standards (renamed the National Institute of Standards and Technology in 1988). JANAF 3 (Chase et al., 1985) superseded JANAF 2. CODATA 89 (Cox et al., 1989) is a seminal work in addressing key thermodynamic reference data. It only covers 37 chemical elements, but it provides brief though mostly adequate discussion of the origin of the data chosen. It also addresses uncertainties. CODATA had earlier issued a series of interim recommendations (CODATA, 1972, 1975, 1976, 1977, 1978). We will not address the elemental entropy data recommendations from these in the present paper. However, they did have some influence on other works, so we have included them in the spreadsheet Electronic Annex. Gurvich 4 represents a series of volumes (Gurvich et al., 1989, 1991, 1993) that appeared as an internationalized updated translation of earlier work by Gurvich and others in the former Soviet Union. This was referred to by the publisher as the ‘‘fourth” edition. Work on this edition was apparently terminated before the intended scope could be completed. It covers only 37 chemical elements, but contains much detailed information. [Note: there appears to be a ‘‘1994” issuance of the same 1993 work.] The volume collection Thermal Constants of Substances edited by Yungman (1999) contains a comprehensive compilation of data related to these efforts. The NEA TDB series on thermochemical data began in 1992 with the publication of Volume 1 (Grenthe et al., 1992), which focused on uranium. The series generally addresses radionuclide elements and other elements that are associated with radioactive waste disposal. Although the series is organized around elements of interest, the scope addresses a significant range of associated chemical species. The series is continuing, and has produced a number of additional volumes (Vol. 2, Americium: Silva et al., 1995; Vol. 3, Technetium: Rard et al., 1999; Vol. 4, Neptunium

and Plutonium, Lemire et al., 2001; Vol. 5, Update on U, Np, Pu, Am, and Tc: Guillaumont et al., 2003; Vol. 6, Nickel: Gamsja¨ger et al., 2005; Vol. 7, Selenium: Olin et al., 2005; Vol. 8, Zirconium: Brown et al., 2005; Vol. 9, Compounds and complexes of U, Np, Pu, Am, Tc, Se, Ni, and Zr with selected organic ligands: Hummel et al., 2005; Vol 10, Solid solutions: Bruno et al., 2007; Vol. 11, Thorium: Rand et al., 2007; Vol. 12, Tin: Gamsja¨ger et al., 2012; and Vol. 13a, Iron, part 1: Lemire et al., 2013). Other volumes are in preparation or planned. For a current list of available volumes, see https://www.oecdnea.org/dbtdb/info/publications/. The NEA TDB series adopted the key reference data from CODATA 89 (Cox et al., 1989). This is the source of most of what the NEA calls the ‘‘auxiliary data” (data covering various elemental reference forms, liquid water, the principle common aqueous species, common oxides and other simple solid phases, and various common gas species). The series continues the attention to developing uncertainties that was present in CODATA 89. Barin (1995) is a compilation aimed principally at metallurgy and materials science. JANAF 4 (Chase, 1998) is the last volume in the JANAF Tables series. The elemental entropy data from it are unchanged from those in JANAF 3. USGS 2131 (Robie and Hemingway, 1995) is the last major thermodynamic data compilation from the U.S. Geological Survey. NASA 3287 (McBride et al., 2001) is one of a number of NASA compilations of thermodynamic data (see previous works cited in NASA 3287). Lange 05 is the 2005 edition of ‘‘Lange’s Handbook.” It is included here because it is relatively recent and the fact that it does not simply present a summary of data from one of the standard compilations such as NBS 82 or JANAF 4. The actual origin of the data is undocumented. Lange 05 covers 93 elements, one more than ACS 18 or USBM 592 (which are from the Historical group). The following sources from the Modern group do not tabulate uncertainty values: NBS 82, JANAF 3, Barin 95, JANAF 4, NASA 3287, and Lange 05. As with corresponding sources in the Historical group, these may include general discussion of the nature and magnitude of uncertainties, was well as occasional discussion of uncertainty in the development and discussion of certain data, but regularly tabulated uncertainties are not given. The following sources do tabulate uncertainty values: USGS 1452, CODATA 89, NEA TDB, and USGS 2131. We have captured uncertainty values only from CODATA 89 and NEA TDB. These will be addressed later in the present paper. Tables 1 and 2 allow a direct comparison of data for elemental reference entropies that have appeared over much of the past century. Capture of the data in the spreadsheet Electronic Annex facilitates a variety of possible analyses, more than can be addressed in the present paper. Some oddities are apparent in examining the data in Tables 1 and 2. NBS 500 gave an entropy value of 10.6 cal mol
1 K
1 (44.350 J mol
1 K
1) for P(white), which is notably higher than the values given by other sources (see Tables 1 and 2). For example, the successor report NBS 270-3 gives 9.82 cal mol
1 K
1 (41.087 J mol
1 K
1). Another notable

Table 2 Reference values of elemental entropies from the Modern group. Data are as given by the sources. Units are J mol
1 K
1, for 1 bar standard pressure. Elem. Ref. Form

NBS 82 Wagman et al. (1982)

JANAF 3 Chase et al. (1985)

CODATA 89 Cox et al. (1989)

42.55 28.35

56.5 42.55 28.33

154.84 35.69

154.843 35.1

47.49 5.90 62.42 9.54 56.74

47.40 5.86 62.8 9.50 56.74

28.275

42.55 28.30

28.300

154.845

154.846

154.845

152.32 5.74 41.63 51.80 69.46

152.231 5.740 41.42 51.76 72.0

152.206 5.740 41.588

223.08

223.066

223.079

30.04 23.64 85.23 33.15 74.89 73.18

30.04 23.77 85.23 33.150 74.77 73.18

30.067 23.618 85.147 33.164

80.79 202.79 27.28

77.78 202.78 27.28

40.83 68.45 31.09 130.68 126.15 43.56

95.4 40.88 68.07 31.09 130.684 126.150 43.56

5.834 62.475 9.440

202.789 27.321

NEA TDB NEA TDB Series 1992–2013

Barin 95 Barin (1995)

42.550 28.300 55.400 154.846 35.100

42.677 28.275 54.488 154.845 35.706

5.900 62.500 9.500

5.900 62.420 9.500 56.740

47.497 5.830 62.417 9.440 56.735

152.21 5.74 41.59 51.80

152.210 5.740 41.590

152.210 5.740 41.590 51.800

152.210 5.740 41.422 51.798 69.454

152.206 5.740 41.588

152.20 5.74 42.90 51.80 72.0

152.210 5.734 42.536 51.800

152.21 5.74 41.59 51.80 72.0

223.081

223.079

223.081

223.117

223.079

223.08

223.082

233.08b

85.230 33.150

30.041 23.640 85.147 33.164 74.894 73.178

30.067 23.618 85.147 33.164

30.04 23.62 85.23 33.14

30.067 23.618 85.230 33.150

30.0 23.8 85.23 33.15 75.6 73.18

202.789 27.321

202.79 27.09

202.792 27.321

31.09 130.68

95.40 40.8 68.07 31.090 31.09 130.681 130.680 126.154 126.153 43.56 (continued on next page)

5.90 9.50

85.23 33.15

202.791

40.838

130.680 126.152 43.560

Gurvich 4 Gurvich et al. (1989–1993)

202.790

202.791 27.085

41.220 31.09 130.680 126.153

31.090 130.680 126.152

31.090 130.680 126.153

77.822 202.795 27.280

40.828 67.948 31.087 130.680 126.148 43.555

JANAF 4 Chase (ed.) 1998

28.275

USGS 2131 Robie and Hemingway (1995)

NASA7 3287 McBride et al., 2001

42.55 28.30

42.550 28.300

154.845

154.847 35.69

5.834 62.475 9.440

47.49 5.83 62.42 9.50 56.74

40.838

130.680 126.152 43.560

5.834 62.352 9.503

Lange 05 Lange’s Handbook (2005) 56.5 42.55 28.30 62.7 154.846 35.1 121.3a 47.4 5.90 62.48 9.50 56.7

77.78 202.791 27.32

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Ac Ag Al Am Ar As At2 Au B Ba Be Bi Bk Br2 C Ca Cd Ce Cf Cl2 Cm Co Cr Cs Cu Dy Er Es Eu F2 Fe Fm Fr Ga Gd Ge H2 He Hf

USGS 1452 Robie et al. (1978)

647

648

Table 2 (continued) Elem. Ref. Form

NBS 82 Wagman et al. (1982)

JANAF 3 Chase et al. (1985)

CODATA 89 Cox et al. (1989)

75.90 75.02 116.15 57.84 35.48 64.68 164.08 56.90 29.12

76.02 75.3 116.135 57.82 35.48 64.18 164.082 56.9 29.12

76.028

75.90

116.142

116.14

64.670 164.084

64.68 164.085

29.085

29.12

50.96

50.96

32.68 32.01 28.66 191.61 51.30 36.40 71.09 146.32 29.87

32.68 32.01 28.66 191.61 51.21 36.40 71.5 146.328 29.87

32.671 32.010 28.605 191.609 51.455 36.464

32.67

32.680

32.670

191.609 51.30

191.607

191.609 51.300

146.327 29.870

146.328

146.327

146.328 29.870

205.15 32.64 22.85

205.138 32.6 41.09 51.9 64.81 37.57

205.147

205.152

205.148

50.460 205.152

41.077

41.09

41.090

41.090

64.785

64.80

64.800

64.800

65.06 37.82

73.93 41.63 51.46 76.78 36.53 31.54 176.23 28.53 31.80

Gurvich 4 Gurvich et al. (1989–1993)

116.140 57.650

164.084

NEA TDB NEA TDB Series 1992–2013

Barin 95 Barin (1995)

JANAF 4 Chase (ed.) 1998

USGS 2131 Robie and Hemingway (1995)

NASA7 3287 McBride et al., 2001

Lange 05 Lange’s Handbook (2005)

75.900

75.898 75.019 116.142 57.823 35.505 64.670 164.085 56.902 29.080

76.028

75.90

76.028

116.142

116.14

116.139

64.670 164.084

64.67

64.680 164.086

29.085

29.09

29.120

75.90 75.3 116.14 57.8 35.48 64.68 164.085 56.9 29.12

116.140

64.680 164.085 29.120

50.961

73.2 41.63 54.460 71. 76.78 36.86 31.51 176.21 28.53 31.80

76.778

76.78

176.235 32.056

76.780

176.235 32.054

32.070

32.054

32.677 32.008 28.593 191.609 51.455 36.401 71.086 146.324 29.874 50.459 205.147 32.635 41.070 51.882 64.785 37.823

50.96 32.671 32.010 28.605 191.609 51.455 36.464

32.535 32.010 28.605 191.610 51.300 36.464

146.327 29.870

29.87

146.330 29.870

205.147

205.15

205.149

41.077

41.09

41.090

64.785

64.8

64.800

73.931 41.631 51.463 76.780 36.526 31.505 176.231 28.535 32.056

32.67 32.01 28.66 191.61 51.46

41.63

76.778

76.780

176.235 32.056

32.05

32.070

32.67 32.01 28.71 191.609 51.30 36.4 71.6 146.328 29.87

205.152 32.6 41.09 51.8 64.80 37.61 62.8 73.2 41.63c 51.5 71 76.78 36.9 31.51 176.235 28.53 32.054

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Hg Ho I2 In Ir K Kr La Li Lr Lu Md Mg Mn Mo N2 Na Nb Nd Ne Ni No Np O2 Os P Pa Pb Pd Pm Po Pr Pt Pu Ra Rb Re Rh Rn Ru S

USGS 1452 Robie et al. (1978)

a b c d e

45.52 34.64 42.27 18.81 69.50 51.20 55.40 41.51 73.30

45.69 34.64 42.442 18.83 69.58 51.55 52.3 41.51 73.22

49.50 53.39 30.63 64.18 74.01 50.29 28.91 32.64 169.68 44.43 59.83 41.63 38.99 85 Red

49.71 53.39 30.63 64.18 74.01 50.21 28.91 32.64 169.683 44.43 59.87 41.63 38.99 88 White

45.520

18.820

18.81

18.810

42.090 18.810

51.18

51.180 55.700

51.180 55.700

55.694 41.471

30.759

32.506d 49.221 52.640e 30.720

51.8 30.72 64.300 50.20

28.936 32.660 169.684

41.717 38.869 47 White

169.685

50.200

169.685

169.685

30 White

41.630 39.080 51 White

41.63 37 White

45.522 34.644 42.258 18.820 69.496 51.195 55.690 41.505 73.304 33.472 49.497 53.388 30.759 64.183 74.015 50.292 28.911 32.660 169.683 44.434 59.831 41.631 38.869 89 White

45.52

18.820

55.694 41.471

30.759

28.936 32.660 169.684

41.717 38.869 47 White

Lange 05 gives the At reference form as ‘‘At” but surely means ‘‘At2”. The Lange 05 value of 233.08 J mol
1 K
1 for Cl2 likely contains a typographical error and should be 223.08 J mol
1 K
1. Lange 05 has the value of 41.63 J mol
1 K
1 for Pt in the wrong column. NEA TDB changed the Tc entropy value from 32.500 J mol
1 K
1 in the 1999 Tc volume to 32.506 J mol
1 K
1 in the 2003 Update volume. NEA TDB changed the Th entropy value from 51.800 J mol
1 K
1 in earlier volumes to 52.640 J mol
1 K
1 in the 2009 Th volume.

42.27 18.81 51.18 55.69

49.71 51.83 30.76

18.810 51.180 54.999 41.471

51.830 30.720

50.2 28.94 32.65

50.200 28.936 32.660 169.686

41.63 38.87 50 White

41.630 38.869 50 White

45.7 34.64 41.97 18.81 69.58 51.08 55.0 41.47 73.22 33.47 49.70 51.8 30.72 64.18 74.01 50.20 28.94 32.6 169.685 44.4 59.87 41.63 39.0 93 White

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Sb Sc Se Si Sm Sn Sr Ta Tb Tc Te Th Ti Tl Tm U V W Xe Y Yb Zn Zr Count P Ref.

649

650

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

case concerns Ge, for which NBS 500 gives the entropy as 10.14 cal mol
1 K
1 (42.426 J mol
1 K
1), while for example NBS 270-3 gives 7.43 cal mol
1 K
1 (31.087 J mol
1 K
1), which is fairly consistent with other sources. Table 3 shows data along with corresponding estimated actual uncertainties (2r) from CODATA 89 and NEA TDB. As noted previously, NEA TDB initially adopted the rec-

ommended values of CODATA 89 covering 37 elements and then extended the data set to include more elements, bringing to total to 51 (as of Vol. 13a, Iron, part 1: Lemire et al., 2013). NEA TDB changed the data for Th from 51.800 ± 0.500 J mol
1 K
1 (the CODATA 89 data, with higher precision) to 52.640 ± 0.500 J mol
1 K
1 in the 2009 Th volume (Vol. 11: Rand et al., 2007). It also

Table 3 Elemental entropy data with uncertainties (2r) from CODATA 89 and NEA TDB. Units are J mol
1 K
1, for 1 bar pressure. Elemental reference form

Ag Al Am Ar As B Ba Be Bi Br2 C Ca Cd Cl2 Cs Cu F2 Fe Ge H2 He Hg I2 K Kr Li Mg N2 Na Ne Ni Np O2 P Pb Pu Rb S Sb Se Si Sn Sr Tc Te Th Ti U Xe Zn Zr

CODATA 89

NEA TDB

Entropy value

Uncertainty (2r)

Entropy value

Uncertainty (2r)

42.55 28.30

0.20 0.10

154.846

0.003

5.90

0.08

9.50

0.08

152.21 5.74 41.59 51.80 223.081 85.23 33.15 202.791

0.30 0.10 0.40 0.15 0.010 0.40 0.08 0.005

31.09 130.680 126.153 75.90 116.14 64.68 164.085 29.12 32.67 191.609 51.30 146.328

0.15 0.003 0.002 0.12 0.30 0.20 0.003 0.20 0.10 0.004 0.20 0.003

205.152 41.09 64.80

0.005 0.25 0.30

76.78 32.054

0.30 0.050

18.81 51.18

0.08 0.08

51.8 30.72 50.20 169.685 41.63

0.5 0.100 0.20 0.003 0.15

42.550 28.300 55.400 154.846 35.100 5.900 62.420 9.500 56.740 152.210 5.740 41.590 51.800 223.081 85.230 33.150 202.791 27.085 31.090 130.680 126.153 75.900 116.140 64.680 164.085 29.120 32.670 191.609 51.300 146.328 29.870 50.460 205.152 41.090 64.800 54.460 76.780 32.054 45.520 42.090 18.810 51.180 55.700 32.506 49.221 52.640 30.720 50.200 169.685 41.630 39.080

0.200 0.100 2.000 0.003 0.600 0.080 0.840 0.080 0.420 0.300 0.100 0.400 0.150 0.010 0.400 0.080 0.005 0.160 0.150 0.003 0.002 0.120 0.300 0.200 0.003 0.200 0.100 0.004 0.200 0.003 0.200 0.800 0.005 0.250 0.300 0.800 0.300 0.050 0.210 0.330 0.080 0.080 0.210 0.700 0.050 0.500 0.100 0.200 0.003 0.150 0.100

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

changed the Tc entropy value of 32.500 ± 0.700 J mol
1 K
1 in the 1999 Tc volume (Vol. 3: Rard et al., 1999) to 32.506 ± 0.700 J mol
1 K
1 in the 2003 Update volume (Vol. 5: Guillaumont et al., 2003). 5.2. Gibbs Energies, Enthalpies, and Entropies of Key Chemical Species We now address the development of ‘‘G-H-S” data for key chemical species other than chemical element reference forms. Most of the sources to be considered here have been introduced previously in the section on elemental entropies. About half of the sources from that section only addressed the thermodynamic properties of the chemical elements, so only those sources with greater scope will be addressed here. Although we were able to include elemental entropy data for the vast majority of chemical elements, we are here only able to deal with a limited number of aqueous, gas, and solid species that can be considered key chemical species. We believe that the set of species chosen is sufficiently extensive to support many investigations of thermodynamic data that might be of interest to geochemists. In order to develop a consistent set of tables, it was necessary to standardize the form of some of the aqueous species. For dissolved silica, we chose H4SiO4(aq) as the ‘‘primary” form and SiO2(aq) as the ‘‘alternate” form and present data for both, with data for one calculated from data for the other as needed using only data from the cited source. For dissolved borate, we chose B(OH)
4 as primary
and BO
2 as alternate. For aluminate, we chose Al(OH)4 as
primary and AlO2 as alternate. The two forms of aqueous silica for example are related by the pseudo-reaction H4SiO4(aq) = SiO2(aq) + 2 H2O, which itself has defined zero reaction properties. The forms we chose as primary are merely those more often given by the sources considered here. In one instance (NBS 500, Rossini et al., 1952), borate was represented by a third form, H2BO
3 . In another (USGS 1259, Robie and Waldbaum, 1968), aqueous silica was represented by H2SiO3(aq). We do not include the original data for these two instances in the tables, but they are given in the spreadsheet Electronic Annex. We include data for the solids AlCl36H2O and P4O10 (hexagonal). These are not of direct geochemical interest. However, AlCl36H2O appears in certain thermochemical cycles leading to thermodynamic properties for the aqueous aluminum ion, Al3+ (see for example Cox et al., 1989, p. 46). Similarly, P4O10 appears in some thermochemical cycles leading to the thermodynamic properties of aqueous phosphate ions (see for example Rard and Wolery, 2007). In many of the sources cited, P4O10 is represented by the formula (P2O5)2. Data for AlCl36H2O have been controversial in the past (see for example Helgeson et al., 1978, p. 110–112, and sources cited therein). We note that there have also been questions about data for P4O10 (see for example Rard and Wolery, 2007). The shift in reference form for elemental phosphorus has caused some confusion in G-H-S data for phosphorusbearing species. For example, Robie and Hemingway (1995) give the same thermodynamic data for PO3
4 (within precision) as the earlier U.S.G.S compilation of Robie et al.

651

(1978). However, the earlier work uses red phosphorus as the reference form (entropy of 22.85 J mol
1 K
1), while the later work uses the white form (entropy of 41.09 J mol
1 K
1). The earlier work (Robie et al., 1978) took the data for this species from Wagman et al. (1968), who actually claimed white phosphorus as the reference. Some discussion is required concerning correction of Gibbs energy of formation data from 1 atm to 1 bar pressure. Increasing the entropy of an elemental reference form that is a gas species by 0.1094 J mol
1 K
1 increases the Gibbs energy of a substance formed from that species by (0.1094 J mol
1 K
1)  (298.15 K)  (0.001 kJ J
1) = 0.0326 kJ mol
1 for each mole consumed. Letting d represent the total number of moles of reference form gas consumed in the formation of the i-th species (here a condensed phase), the correction in Joule units can be written as: DGo1bar;T r ;i ¼ DGo1atm;T r ;i þ d 0:0326

ð8Þ

A convenient form that is applicable to a species of any type is:  z DGo1bar;T r ;i ¼ DGo1atm;T r ;i þ d
n
0:0326 ð9Þ 2 where n is 1 if the i-th species is itself a gas (as its entropy will also be changed) and 0 otherwise, and z is the charge number of the i-th species if it is an ion. This equation can be applied to a half reaction such as C þ 1:5O2ðgÞ þ 2e
¼ CO2
3

ð10Þ

Here d = 1.5 and z =
2. It can be shown that Eq. (28) is consistent with the standard convention regarding the Gibbs energy of formation of the hydrogen ion. Previous works addressing the pressure correction (such as NBS 82, Wagman et al., 1982) use Eq. (8) with the effects of n and z folded into a differently defined d that is equivalent to the quantity in parentheses in Eq. (9). The uncertainty in the standard Gibbs energy of formation of a species generally exceeds the magnitude of the change resulting from correcting the pressure from 1 atm to 1 bar. For example, CODATA 89 (Cox et al., 1989) gives the 2r uncertainty in the Gibbs energy of formation of quartz (SiO2) as 1.002 kJ mol
1, while d = 1 for the formation reaction and the pressure correction is only 0.033 kJ mol
1. They also give an uncertainty of 1.675 kJ mol
1 for AlCl36H2O, for which d = 10.5 and the pressure correction is 0.342 kJ mol
1. The correction is again small compared with the uncertainty, but it is relatively larger than was the case for quartz. Though often relatively small, this pressure correction should not be ignored, because doing so introduces a systematic error. Helgeson et al. (1978, p. 13) in their study of phase equilibrium data found that in a number of cases the calculated standard Gibbs energy of reaction was constrained to within 50 cal mol
1 (0.209 kJ mol
1). This is often comparable to the magnitude of 1 atm to 1 bar pressure corrections. In presenting data for solids, all forms are crystalline. P4O10 is the crystalline (hexagonal) form as noted earlier. SiO2 is alpha-quartz, Al2O3 is corundum, Al(OH)3 is gibbsite, Al2SiO5 is andalusite, Fe2O3 is hematite, Fe3O4 is mag-

652

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

netite, MgO is periclase, Mg(OH)2 is brucite, MgCO3 is magnesite, and Mg2SiO4 is forsterite, CaO is lime, Ca (OH)2 is portlandite, CaCO3 is calcite, and CaSiO3 is wollastonite. The identification of other solids should be obvious. Some sources only give chemical formulas, which in certain instances may add an element of ambiguity. We believe that we have made the correct identifications, but cannot completely rule out any misidentification. Table 4 shows G-H-S data for the chosen set of species taken from the three principal works on thermodynamic data issued by the U. S. National Bureau of Standards. The first was NBS 500 (Rossini et al., 1952). This 1268 page volume was a pioneering work in the development of thermodynamic data. The earlier work by Bichowsky and Rossini (1936) is also notable, but that work is largely limited in scope to various kinds of enthalpy data. The second is NBS 270, which denotes a series of reports beginning with NBS 270-3 (Wagman et al., 1968; other reports in the series have been cited previously). The third and last work is NBS 82 (Wagman et al., 1982). NBS 500 and NBS 270 gave the data in calorie units for 1 atm pressure. The data from these sources have been corrected by us to Joule units for 1 bar. All members in the NBS series use white phosphorus as the reference form for P. NBS 500 includes references for the data, but not uncertainties. NBS 270 and NBS 82 provide neither references nor uncertainties. The Gibbs energy and enthalpy of formation values for the aqueous phosphate species (represented here by HPO2
4 and H2PO
4 ) given by NBS 270 and NBS 82 differ sharply from the corresponding values given by NBS 500. The NBS 270 and NBS 82 values for aqueous phosphate species also differ sharply from the corresponding values given by other recent sources, notably CODATA 89 (Cox et al., 1989; see Table 8 in the present paper). Rard and Wolery (2007) confirmed that the CODATA 89 values were consistent with the body of relevant information. The enthalpy of formation value for P4O10 in NBS 500 (
3012.480 kJ mol
1) is quite different from the corresponding values in NBS 270 (
2984.029 kJ mol
1) and NBS 82 (
2984.0 kJ mol
1). This may have to do with the ‘‘phosphate” problem noted above. The G-H-S values for AlCl36H2O in NBS 500 differ notably from the corresponding data in NBS 270 and NBS 82. The G-H data for Mg2SiO4 and CaSiO3 in NBS 500 also differ notably from the corresponding data in the two later works. Table 5 shows the corresponding G-H-S data from the three principal works on thermodynamic data produced by the U.S. Geological Survey. The first of these works is USGS 1259 (Robie and Waldbaum, 1968). As the table shows, it was missing enthalpy and entropy data for many of the aqueous species. This situation was rectified by the second member in the series, USGS 1452 (Robie et al., 1978). The final member of the series was Robie and Hemingway (1995). The first report, USGS 1259, gave the data in calorie units for 1 atm pressure (converted here to Joule units and 1 bar). The two later works gave the data in Joule units for 1 bar. The first two members of the series used red phosphorus as the reference form for P, while the last one used the white form. The U.S.G.S. works noted

here include references. They also include uncertainties, although we have not noted them in the present paper. The P4O10 H-S data from USGS 1452 (Robie et al., 1978) closely match those of NBS 270 and NBS 82. However, those works claim white phosphorus for the elemental reference form, not the red form claimed by USGS 1452. Later in the present paper, we will show that the misidentification error is in NBS 270 and NBS 82. The P4O10 G-H values in the earlier USGS 1259 differ considerably from those in USGS 1452, despite the fact that both claimed red phosphorus as the reference form. The data from the latter report, converted for consistency with white phosphorus using data for P(red) from JANAF 4 (Chase, 1998), appear consistent with data from USGS 2131 and other sources (as will be shown later in this paper). The USGS 1259 P4O10 G-H values appear to be erroneous. They are taken from NBS 270-1 (Wagman et al., 1965), which gives no references. The G-H data for H4SiO4 (aq) given by NBS 270 and NBS 82 are erroneously low. A credible explanation involving misinterpretation of the enthalpy data has been provided by Hemingway et al. (1978). The problem noted here has nothing to do with the issue of the solubility of quartz at low temperature (see for example Rimstidt, 1997), which will be discussed later in the present paper. The Gibbs energies of formation for Cs+ given by USGS 1452 and USGS 2131 differ significantly even though these two sources give nearly identical H-S data for this ion. The data given by USGS 1452 are in error, as they do not satisfy Eq. (7). Table 6 shows G-H-S data from the JANAF Tables and USBM 677 (Pankratz et al., 1984). The JANAF Tables are represented by JANAF 2 (Stull and Prophet, 1971), JANAF 3 (Chase et al., 1985), and JANAF 4 (Chase, 1998). For the species considered here, JANAF 3 and JANAF 4 give the same data values, and these are combined in the table under ‘‘JANAF 3/4.” Liquid water is the only aqueous species for which data are given by these sources. The JANAF Tables give detailed notes including references. Uncertainties are not tabulated, but are sometimes included in the notes. USBM 677 gives references, but not uncertainties. JANAF 2 was influential in the development of thermodynamic databases for geochemistry (see for example Helgeson et al., 1978). In Table 6, the only differences between the values for JANAF 2 on the one hand and JANAF 3 and JANAF 4 on the other pertain to small changes in the GH data for B2O3 and Al2O3. For most species in the table, the G-H-S data from USBM 677 are generally close to the corresponding data from the JANAF Tables. However, the K2O data from USBM 677 are very different. These data appear to apply to the liquid (molten) phase. Table 7 shows corresponding G-H-S data along with uncertainties (for 1 bar pressure) from CODATA 89 (Cox et al., 1989). This source does not tabulate Gibbs energies of formation and corresponding uncertainties. We calculated values for these using Eq. (7) and standard uncertainty propagation. Details may be found in the spreadsheet Electronic Annex. We include some data from the source that is not tabulated in the main table of recommendations but rather are found in its ‘‘Notes” section,

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 4 G-H-S data for representative aqueous, gas, and solid key species from the three principal works of the NBS on thermodynamic data. All data are given in Joule units and for 1 bar pressure. The NBS 500 and NBS 270 data shown are corrected by us. They were originally given in calorie units for 1 atm pressure. The original data are given in the electronic supplement. All three works here use white phosphorus as the elemental reference form for P.

Notes: An errata report to NBS 82 was published by Wagman et al. (1989). The only data affected here
1 concerns NO
and the DfG° was changed to
111.25 kJ mol
1. 3 .The DfH° was changed to
207.36 kJ mol NBS 270 and NBS 82 give data for gibbsite having the formula Al2O33H2O. Here we have corrected their data to be consistent with the more conventional formula Al(OH)3. Rose background marks problematic values that are discussed in the text.

653

654

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 5 G-H-S data for representative aqueous, gas, and solid species, from the three principal works of the USGS on thermodynamic data. All data are given in Joule units and for 1 bar pressure. The USGS 1259 data shown are corrected by us. They were originally given in calorie units for 1 atm pressure. The original data are included in the electronic supplement. USGS 1259 and USGS 1452 use red phosphorus as the reference form for P, while USGS 2131 uses the white form.

Notes: Rose background marks problematic values that are addressed below or discussed in the text. USGS
1 1259 gives theGibbs energy of formation of SO2
4 as
117.970 kcal mol . This is a typographical error. The intended value (from the cited source, NBS 270-1) was
177.97 kcal mol
1. This becomes
744.529 kJ mol
1 at 1 bar. Also in USGS 1259, the Gibbs energy of formation of HS
contains a sign error from the same source, NBS 207-1. USGS 2141 gives the enthalpy of formation of HS
with the wrong sign, and the corresponding Gibbs energy of formation is incorrect. USGS 1259 gave data for aqueous silica in the unusual form of H2SiO3(aq). We corrected this to obtain data for the more standard form H4SiO4(aq).

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

655

Table 6 G-H-S data for representative aqueous, gas, and solid species, from JANAF 2, JANAF 3/4, and USBM 677. All data are given in Joule units and for 1 bar pressure. The JANAF 2 and USBM 677 data shown are corrected by us. They were originally given in calorie units for 1 atm pressure. The original data are included in the electronic supplement. JANAF 2 uses red phosphorus as the elemental reference form for P. The other sources use the white form. For the species considered here, JANAF 3 and JANAF 4 give the same values. The sources represented in this table only include data for one aqueous species, liquid water.

Note: Rose background marks problematic values that are discussed in the text.

which includes descriptions of how the data were obtained and the pertinent references. As noted previously, CODATA 89 is one of the best sources on which to build links for future database development, though some caution is advised. Anyone using CODATA 89 should consult the relevant entries in the ‘‘Notes” section before taking data from the main table. We point out one potential problem. The tabulated data include values for Al3+ and Al2O3. Without delving deeper, one might assume that one could take independent solubility data for gibbsite (Al(OH)3) along with the CODATA 89 data for Al3+ and OH
(or Al3+, H+, and H2O) and calculate the Gibbs energy of formation of this solid. However, CODATA 89 itself adopted data for gibbsite in the notes (see pp. 46–47) that they used (in part) to develop their recommended data for Al3+. They similarly adopted data for Ca(OH)2 (portlandite) and CaCO3 (calcite) in developing their recommended data for Ca2+. They did not, however, include these mineral phases in their main table. We previously noted the existence of six interim CODATA recommendations (CODATA, 1971, 1972,

1975, 1976, 1977, 1978). These reports include H-S data and were used by others (including Helgeson et al., 1978). We will not further address these interim reports in the present paper. We have included full workups of the data from CODATA (1977) and CODATA (1978) in the spreadsheet Electronic Annex. The earlier interim reports are of rather limited scope and do not appear to have been very influential. Table 8 gives the corresponding G-H-S data from the NEA TDB series (the relevant sources have been noted previously). The NEA TDB series subsumes data from the main table from CODATA 89, but does note the additional data appearing in the ‘‘Notes” section of that work. The NEA TDB dataset includes values for the standard Gibbs energies of formation and corresponding uncertainties for all species covered, including those from CODATA 89. The Gibbs energy values we calculated for CODATA 89 (Table 7) differ from those in Table 8 by no more than 0.001 kJ mol
1, the limit of precision used by us and NEA TDB. The agreement is sufficient for accurate database development. As noted earlier, the NEA TDB data appears to be one of the best existing works to build on in future

656

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 7 G-H-S data with uncertainties for representative aqueous, gas, and solid species, from CODATA 89. All data are given in Joule units and for 1 bar pressure. The Gibbs energy of formation data (including uncertainties) were calculated by us. The original and calculated data are included in the electronic supplement. P(white) is the reference form for P.

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

657

Table 7 (continued)

Note: Enthalpy and entropy data in cells with a yellow background are found only in the notes section of CODATA 89. Enthalpy and entropy data in cells with an orange background were calculated by us from such data.

data base development, as it includes detailed descriptions of how the data were developed and includes full references. We cannot fully analyze the G-H-S data presented here due to its rather extensive scope. However, we have noted some issues associated with the data in the sources discussed above. We will analyze data for a few specific species both to illustrate what can be done and also to provide a starting point for more extensive future analyses. We reiterate that for some species, the data covered by the sources addressed above are insufficient for complete modern analysis. Data from additional sources (typically individual papers and topical reports, and especially any pertinent later literature) must also be addressed. Table 9 summarizes the G-H-S data for liquid water, H2O(g), and CO2(g) taken from the ten major data sources represented in Tables 4–8. These three species are of major importance in geochemistry. They are also key species in interpreting phase equilibrium data in building thermodynamic databases for application in the earth sciences (see for example Helgeson et al., 1978; Berman, 1988; Holland and Powell, 1985, 1990, 1998, 2011; Olbricht et al., 1994; Chatterjee et al., 1994; Gottschalk, 1997). The G and H values shown in Table 9 all fall within the corresponding ranges defined by the CODATA 89 values and corresponding uncertainties. This condition is not quite

true for the S values, but most of the source values for entropies do fall in the CODATA 89 range and those that do not are not far outside. This suggests that the properties of all three species (at least at 298.15 K and 1 bar) have been well-known for some time. The same can be said of the corresponding data for the ‘‘redox” gases H2(g) and O2(g) (see data in Tables 4–8). As elemental reference forms, their G-H values are by definition zero, hence the corresponding uncertainties are zero. The entropies of these species are also quite well known. Table 10 summarizes the G-H-S data for SiO2 (quartz), Al2O3 (corundum), Al(OH)3 (gibbsite), MgO (periclase), CaO (lime), and CaCO3 (calcite) taken from the ten major data sources represented in Tables 4–8. These mineral phases are often used as primary key species in developing thermodynamic databases (see for example Helgeson et al., 1978 or Berman, 1988). The G-H values for quartz lie within the corresponding CODATA 89 ranges, while the S values are still relatively consistent. The G-H-S values for corundum, with the exception of those from NBS 500, all lie within the corresponding CODATA 89 ranges. Despite the good agreement among the later sources, the data for corundum have been the subject of some controversy (see Helgeson et al., 1978, pp. 110–112, and references cited therein). We will address that later in the present paper.

658

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

The G-H data for gibbsite each show differences of about 10 kJ mol
1 due to the inclusion of values from NBS 270 and USGS 1259. The values from the later sources are quite consistent. Omitting the data from NBS 270 and USGS 1259, the G-H-S data for gibbsite all lie with the corresponding CODATA 89 ranges. The data for periclase, lime, and calcite shown in Table 10 do not show any notable outliers. Most of the G-H-S values for periclase lie within the respective CODATA 89 ranges, and the others are just outside. All of the G-H values for lime lie within the respective CODATA 89 ranges. Most of the S values do as well, with only minor deviations. All of the G-H values for calcite also lie within the respective CODATA 89 ranges. However, the S values are not very consistent. The 88.000 J mol
1 K
1

value from USGS 2131 is noticeably low compared to the other values shown in the table. Key solids of sodium and potassium are a bit problematic. In constructing geochemical databases, it is common to use a sodium aluminosilicate such as NaAlSiO3 (albite) (see for example Berman, 1988) or the aqueous ion Na+ (see for example Helgeson et al., 1978) as a link to elemental Na. Similarly, it is common to use a potassium aluminosilicate such as KAlSi3O8 (K-feldspar) (see for example Helgeson et al., 1978) or KAl2(Si3Al)O10(OH)2 (muscovite) (see for example Berman, 1988) as a link to elemental K. Na2O and K2O do not appear in phase equilibria of geochemical interest, and thus are typically not used as key species in building thermodynamic databases for geochemical applications. They do appear in phase equilibria of

Table 8 G-H-S data with uncertainties for representative aqueous, gas, and solid species, from NEA TDB. All data are given in Joule units and for 1 bar pressure. The data are included in the electronic supplement. P(white) is the reference form for P.

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

659

Table 8 (continued)

interest to ceramists and other materials scientists (see for example Alper, 1995, and references cited therein), and such equilibria have been noted in at least one work devoted to mineral phase equilibrium (Morey, 1964). Na2O and K2O could be used as key species if developers of ‘‘minpet” databases were to broaden the range of phase equilibria used in their models. Halite (NaCl) and sylvite (KCl) could conceivably be used as alternative key species to provide links to elemental Na and K, respectively. Another primary key species would have to be introduced to provide a link to Cl2(g). Thermochemical data for Na2O, K2O, halite, and sylvite are presented and discussed in the second Electronic Annex, Section 5.

Table 11 summarizes the G-H-S data for Fe2O3 (hematite) and Fe3O4 (magnetite) taken from the ten major data sources represented in Tables 4–8. CODATA 89 gives no data for either of these solids. NEA TDB, however, gives data for them, and these are included in the table. The GH-S data for hematite are generally consistent, but the NBS 500 data appear discrepant. The NEA TDB data also appear slightly discrepant. Omitting the NBS 500 data, the data are all within the corresponding NEA TDB ranges. The G-H-S data for magnetite are not in quite such good accord, however. Table 12 summarizes the G-H-S data for P4O10, P(red), and P(white) taken from the ten major data sources repre-

Notes: For a work published in series (NBS 270, NEA TDB), the year of publication refers to the year that publication commenced. All data are shown to three decimal places to assist with comparison. These notes also apply to subsequent tables of this type.

213.740 213.800 0.010
393.522
393.500 0.130
394.405
394.359 0.133 188.448 188.835 0.010
241.827
241.800 0.040 Minimum Maximum CODATA 89 2r

69.910 70.000 0.030
285.840
285.800 0.040
237.143
237.100 0.041


228.600
228.569 0.040


393.513
393.509
393.509
393.522
393.510
393.509
393.509
393.522
393.510
393.500
394.383
394.359
394.371
394.405
394.375
394.359
394.375
394.389
394.373
394.400 188.833 188.448 188.825 188.833 188.720 188.825 188.833 188.834 188.835 188.800
241.826
241.818
241.818
241.827
241.814
241.818
241.814
241.826
241.826
241.800 1952 1968 1968 1971 1978 1982 1984 1985 1989 1995 NBS 500 NBS 270 USGS 1259 JANAF2 USGS 1452 NBS 82 USBM 677 JANAF 3/4 CODATA 89 USGS 2131

69.940 69.915 69.915 – 69.950 69.910 69.948 69.950 69.950 70.000
285.840
285.830
285.830 –
285.830
285.830
285.830
285.830
285.830
285.800
237.143
237.129
237.134 –
237.141
237.129
237.142
237.141
237.140
237.100


228.579
228.572
228.577
228.581
228.569
228.572
228.572
228.582
228.582
228.600

S° J mol
1 K
1 DfH° kJ mol
1 DfG° kJ mol
1 DfG° kJ mol
1 S° J mol
1 K
1 DfH° kJ mol
1 DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1

CO2(g) H2O(g) H2O(liquid) Year Source

Table 9 G-H-S data for H2O(liquid), H2O(g), and CO2(g) at 298.15 K, 1 bar, from ten major sources, ordered by year of publication.

213.749 213.744 213.744 213.795 213.790 213.740 213.786 213.795 213.785 213.800

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660

sented in Tables 4–8. CODATA 89 gives no data for any of these solids (nor does NEA TDB). The G-H data for P4O10 are complicated by the fact that some of the sources give values that are based on red phosphorus as the reference form, while others give values based on the white form. Near the bottom of the table, the JANAF 2 data for P4O10 based on red phosphorus as the elemental reference form have been converted (using the JANAF 2 data for P (white)) to data consistent with the white form. These data are closely consistent with the corresponding white-based data from USGS 2131, JANAF 3/4, and USBM 677. The JANAF 2 G-H red-based data for P4O10 closely match the corresponding red-based USGS 1452 data. However, the entropy value of 231.000 J mol
1 K
1 is notably discrepant. The G-H data for P4O10 from NBS 270, USGS 1259, and NBS 82 are not consistent with values from other sources. As noted previously, the G-H data for NBS 270 and NBS 82 data for this phase and the corresponding data for the aqueous phosphate species were discredited by Rard and Wolery (2007) in favor of the data from CODATA 89. The enthalpy value for P(red) from NBS 500 and the entropy value for P(white) from the same source are outliers. Note the complementary relationship for G-H values for P(red) based on the white form with the corresponding values for P(white) based on the red form. Table 13 summarizes the G-H-S data for six aqueous cations (Li+, Na+, K+, Mg2+, Ca2+, and Al3+) taken from the relevant seven major data sources represented in Tables 4–8. JANAF 2, JANAF 3, JANAF 4, and USBM 677 do not give data for aqueous solute species, thus the number of source entries is decreased. CODATA 89 gives data for all of these species. Most of the data are fairly consistent. The NBS 500 H-S data for Na+ are slightly discordant with the corresponding data from later sources (though the G value is not). The NBS 500 G-H data for K+ are also slightly discordant, but the S value is not. The NBS 500 G-H-S data for both Mg2+ and Al3+ are noticeable outliers. The remaining G-H-S data for Li+, Na+, K+, and Mg2+ are fairly consistent, with most of the values falling within the respective CODATA 89 ranges. This is also true of the GH data for Ca2+, but less so for the corresponding S data. The G-H-S data for Al3+ are scattered, indicating problems in determining accurate values for this important species, as pointed out elsewhere (see for example Tagirov and Schott, 2001, and references cited therein). Table 14 summarizes the G-H-S data for three monova
lent aqueous anions (OH
, HCO
3 , and Cl ) taken from the relevant seven major data sources represented in Tables 4– 8. CODATA 89 gives data for all of these species. Looking at the data from all sources, in the case of the bicarbonate ion, the S data vary significantly, the H data vary less, and the G data are highly consistent. The CODATA 89 data were based on a combination of equilibrium and calorimetric references (see Cox et al., 1989, p. 40). The uncertainty in G shown in Tables 8 and 9 is a pro-forma value based on uncertainties in H and S. The data for all three anions are fairly consistent, with most values falling within the respective CODATA 89 ranges. Table 15 summarizes the G-H-S data for two divalent 2
aqueous anions (SO2
4 and CO3 ) taken from the relevant

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 10 G-H-S data for SiO2 (Quartz), Al2O3 (Corundum), Al(OH)3 (Gibbsite), MgO (Periclase), CaO (Lime), and CaCO3 (Calcite) at 298.15 K, 1 bar, from ten major sources, ordered by year of publication.

Note: The NBS 500 G-H values for Al2O3 are significant outliers. The corresponding S value is a slight outlier. The NBS 270 and USGS 1259 G-H-S values for gibbsite are also clear outliers. These outlier values (marked with gray background in the table) were omitted in determining the minimum and maximum values shown.

Table 11 G-H-S data for Fe2O3 (hematite) and Fe3O4 (magnetite) at 298.15 K, 1 bar, from ten major sources, ordered by year of publication.

Notes: The Fe2O3 G-H-S data from NBS 500 (gray background) constitute small but noticeable outliers. These values were omitted in determining the minimum and maximum values shown. The NEA TDB G-H data for this phase appear to constitute modest outliers, but were not omitted.

661

662

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 12 G-H-S data for P4O10, P(red), and P(white) at 298.15 K, 1 bar, from ten major sources, ordered by year of publication.

Notes: The truly discrepant data (see text) are marked by a gray background. No minimum and maximum values are given in this table owing to presenting data that involve two elemental reference forms.

Table 13 G-H-S data for Li+, Na+, K+, Mg2+, Ca2+, and Al3+ at 298.15 K, 1 bar, from seven major sources, ordered by year of publication.

Notes: The truly discrepant data (see text) are marked by a gray background. These data were omitted in calculating the minimum and maximum values shown.

seven major data sources represented in Tables 4–8. CODATA 89 gives data for both species. The NBS 500 G-H-S data for the sulfate ion are clear outliers. Otherwise, for this ion the G-H data are very consistent, though the corresponding S data vary somewhat. The NBS 500 G-HS data for the carbonate ion are slight outliers. The G data from the other sources are very consistent, while the corresponding H-S values vary somewhat. As was the case for 2
the HCO
3 data, the data for CO3 are based on a combination of equilibrium and calorimetric measurements (see

Cox et al., 1989, p. 39-40). The uncertainty in G shown in Tables 8 and 9 is again a pro-forma value that is somewhat too high. Table 16 summarizes the G-H-S data for three neutral aqueous species (H4SiO4(aq), H3BO3(aq), and CO2(aq)) taken from the relevant seven major data sources represented in Tables 4–8. CODATA 89 gives data for all of these species except H4SiO4(aq). The NBS 500 and NBS 270 G-H data for H4SiO4(aq) are erroneous as noted earlier, as is the USGS 1259 G value (which was taken from NBS

55.103 56.730 0.20
167.456
167.080 0.10 91.200 98.400 0.5
691.992
689.900 0.20
230.025
229.940 0.040
157.328
157.220 0.072 Minimum Maximum CODATA 89 2r

1952 1968 1968 1978 1982 1989 1995 NBS 500 NBS 270 USGS 1259 USGS 1452 NBS 82 CODATA 89 USGS 2131


10.900
10.539 0.20


10.710
10.750
10.900
10.700
230.025
229.994
230.015
230.000


586.975
586.766 0.251

91.200 91.200 98.400 98.400
691.990
691.990
689.930
689.900


131.270
131.136 0.116

56.730 56.500 56.600 56.600
167.080
167.159
167.080
167.100

55.103 56.484
167.456
167.159


131.136
131.228
131.228
131.270
131.228
131.218
131.200 94.977 91.211
10.539
10.753
229.940
229.994


157.249
157.244
157.244
157.328
157.244
157.220
157.300


586.975
586.766
586.766
586.850
586.770
586.845
586.800


691.113
691.992

DfG° kJ mol
1 S° J mol
1 K
1 DfH° kJ mol
1 DfG° kJ mol
1 DfH° kJ mol
1 DfG° kJ mol
1

S° J mol
1 K
1

HCO
3 OH
Year Source

Table 14
G-H-S data for OH
, HCO
3 , and Cl at 298.15 K, 1 bar, from seven major sources, ordered by year of publication.

Cl


DfH° kJ mol
1

S° J mol
1 K
1

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663

270-1). The remaining data for aqueous silica are closely consistent. We will discuss aqueous silica in more detail later in the present paper, where we will also note data recommended by NEA TDB (Grenthe et al., 1992). The NBS 500 G-H-S values for H3BO3(aq) and CO2(aq) are clear outliers. Excluding these, the G-H-S data are fairly consistent. 2
As was the case for the HCO
3 and CO3 data, the data for
CO2(aq) are based on a combination of equilibrium and calorimetric measurements (see Cox et al., 1989, p. 39). The uncertainty in G shown in Tables 8 and 9 is again a pro-forma value that is somewhat too high. As noted earlier, we are unable in the present paper to analyze the data for all of the species represented in Tables 4–8. The above analysis for selected species is somewhat rudimentary, but it provides a useful starting point for further work. In the case of some species, additional data sources must be addressed to provide a more complete and sometimes more accurate analysis. We remark on three important cases for geochemical thermodynamic database building where additional, generally more recent data are required to establish up-to-date understanding. The first case concerns liquid water, which plays a critical role as the solvent in aqueous solutions. The thermodynamic data for many other species depend on the data chosen for this species. The second case concerns quartz and aqueous silica. The third case concerns key Al(III) species, notably corundum, gibbsite, and Al3+. 5.2.1. Remarks on liquid water Table 9 showed a strong consistency among the sources considered for the G-H-S data for liquid water. Table 17 shows the data from five of the sources represented in Table 9, along with the corresponding data from Helgeson et al. (1978), and the computer program SUPCRT92 (Johnson et al., 1992). The values from Helgeson et al. (1978) are thought to represent what was present in the original SUPCRT program (see also Helgeson and Kirkham, 1974a). Helgeson et al. (1978) attribute their liquid water G-H-S data to NBS 270-3 (Wagman et al., 1968), a source which gives data for a standard pressure of 1 atm. These values had been adopted in an earlier work (Helgeson and Kirkham, 1974a). Helgeson and co-workers did not correct the Gibbs energy of formation for consistency with 1 bar as the standard reference pressure. In Table 17, the corrected NBS 270-3 Gibbs energy of formation differs from the corresponding Helgeson et al. (1978) value by 0.049 kJ mol
1 (1.5  0.0326 kJ mol
1). The standard G-H-S values for liquid water are hardcoded in SUPCRT92, as was the case for earlier SUPCRT versions. The original version of SUPCRT used an equation of state (EOS) model for water due to Keenan et al. (1969) to describe the temperature and pressure dependence of the thermodynamic properties of water. This EOS was replaced in SUPCRT92 by a combination of EOS models due to Haar et al. (1984) and Levelt Sengers et al. (1983) (see Johnson et al., 1992, for details). All of these EOS models use a non-thermochemical reference frame. It is necessary to supply a ‘‘translation” to link an EOS model to a standard thermochemical reference frame. Helgeson and

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T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 15 2
G-H-S data for SO2
4 and CO3 at 298.15 K, 1 bar, from seven major sources, ordered by year of publication.

Notes: The notably discrepant data (see text) are marked by a gray background. These data were omitted in determining the minimum and maximum values shown.

Table 16 G-H-S data for H4SiO4(aq), H3BO3(aq), and CO2(aq) at 298.15 K, 1 bar, from seven major sources, ordered by year of publication.

Notes: The notably discrepant data (see text) are marked by a gray background. These data were omitted in calculating the minimum and maximum values shown.

Kirkham (1974a) developed such a translation for the Keenan et al. (1969) model, using thermochemical data from NBS 270-3. This was retained without modification in SUPCRT92. The Gibbs energy of formation that we calculated for 1 bar using SUPCRT92 differs from that reported by Helgeson et al. (1978) by 1 cal mol
1 (5 J mol
1), the limit of precision for that code. A correction would be needed in SUPCRT92 owing to use in the original translation of a 1 atm value for the standard Gibbs energy of liquid water in place of one for 1 bar. The value from NBS 270-3 can be pressure-corrected, as we have done in Table 17. However, NBS 270-3 is not a suitable data source owing to its lack of references. Furthermore, the G-H-S data for liquid water from CODATA 89 (Cox et al., 1989) are preferred. Adopting the CODATA 89 data for liquid water results in a smaller numerical change in the Gibbs energy than would result from pressure-correcting the corresponding NBS 270-3 value (an increase of 38 J mol
1 versus one of 49 J mol
1). In Part 2 of this series we update the Helgeson and Kirkham (1974a) ‘‘translation” for consistency with the CODATA 89 data and the EOS models of Haar et al. (1984) (IAPS-

84) and Wagner and Pruss (2002) (IAPWS-95). Using the CODATA 89 data for liquid water has consequences for other species’ data that are developed using water data. To maintain consistency, corrections need to be made. We will note such corrections in the following remarks on (a) quartz and aqueous silica and (b) key Al(III) species. 5.2.2. Remarks on silica: quartz and aqueous silica Quartz (SiO2) is a key species in developing thermodynamic data for other silicates and for the aluminosilicate minerals. The data summarized in Table 10 showed that the G-H-S data for quartz have generally been in a tightly defined range. Table 18 compares data from Helgeson et al. (1978) and from Richet et al. (1982) with data from NBS 270-3, USGS 1452, CODATA 89 and USGS 2131 (from Table 10). The data adopted by Helgeson et al. (1978) were uncorrected 1 atm data taken from NBS 270-3 that were also used by Walther and Helgeson (1977) in developing data for aqueous silica (represented as SiO2(aq)). The corrected NBS 270 G value shown in Table 18 is greater by 0.033(1  0.0326) kJ mol
1 than the uncorrected value used by Walther and Helgeson (1977) and Helgeson et al. (1978).

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 17 G-H-S data for H2O(liquid) at 298.15 K, 1 bar. Data from Helgeson et al. (1978), SUPCRT92 (Johnson et al., 1992), and Berman (1988) compared with corresponding data from NBS 270, USGS 1452, JANAF 3/4, CODATA 89, and USGS 2131. The data from USGS 2131 are overly rounded.

Notes: The SUPCRT92 data shown were calculated using the software, which follows a model described by Johnson et al. (1992) that is hard-codedinto the software. The data in light green background are recommended for future work. The data in light blue background are as taken from the sources, apart from conversion to Joule units. The Gibbs energy valuesso marked are actually for 1 atm, not 1 bar. See text.

Table 18 G-H-S data for SiO2 (quartz) at 298.15 K, 1 bar. Data from Richet et al. (1982) compared with corresponding data from NBS 270, USGS 1452, CODATA 89 and USGS 2131. The data from USGS 2131 are overly rounded.

Notes: The data in light green background are recommended for future work. The data in light blue background are as taken from the source apart from conversion to Joule units. The Gibbs energy value is from Helgeson et al. (1978) actually for 1 atm, not 1 bar. See text.

The Richet et al. data are in good accord with the corresponding data from other sources noted previously. For future work, we recommend the use of the CODATA 89 data (which are nearly identical to the USGS 1452 data), considering the Richet et al. data as closely confirming the CODATA 89 data. The standard Gibbs energy of formation of aqueous silica is obtained from the solubility of quartz, while the corresponding entropy is obtained from the temperature dependence of the solubility (see for example Morey et al., 1962; Walther and Helgeson, 1977; Rimstidt, 1997; Gunnarsson and Arno´rsson, 2000; Stefa´nsson, 2001; Apps and Spycher, 2004). The enthalpy of formation is then obtained through inversion of Eq. (7). CODATA 89 gives no recommendation for aqueous silica.

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The data for aqueous silica shown in Table 16 (but which were not excluded from the previous analysis owing to obvious large error) correspond to a quartz solubility of 10
4 molal at 298.15 K and 1 bar. Many geochemical thermodynamic databases contain data that are closely consistent with this. The HKF equation-of-state model developed by Walther and Helgeson (1977) for aqueous silica as SiO2ðaqÞ falls in this category. It has long been a part of SUPCRT and SUPCRT92 data files (including slop98.dat and sprons98.dat). Helgeson et al. (1978) used this model in developing their mineral database. The classic measurements supporting such a solubility of 10
4 molal were first reported by Fournier (1960) and Morey et al. (1962). However, early on there were a number of other reported experimental results that supported a higher solubility of 10
3.75 molal (see discussion of relevant references given by Rimstidt, 1997; Arno´rsson, 2000; Gunnarsson and Arno´rsson, 2000; Stefa´nsson, 2001; and Apps and Spycher, 2004). Rimstidt (1997) presented arguments for the higher solubility case that, taken as a whole, seem compelling, and this has gained wide acceptance (see for example Gunnarsson and Arno´rsson, 2000; Stefa´nsson, 2001; Apps and Spycher, 2004; Tutolo et al., 2014; and Sverjensky et al., 2014). Table 19 shows some more recent G-H-S data for aqueous silica that are consistent with the higher solubility paradigm. The sources represented here are Rimstidt (1997), Gunnarsson and Arno´rsson (2000), Stefa´nsson (2001), and Apps and Spycher (2004). Included in Table 19 to facilitate comparison are the corresponding results from USGS 1452, USGS 2131, Walther and Helgeson (1977), and NEA TDB (Grenthe et al., 1992) which are consistent with the lower-solubility paradigm. In this table, aqueous silica is represented by H 4 SiO4ðaqÞ . NEA TDB used Si(OH)4(aq) which is thermodynamically equivalent. Walther and Helgeson (1977) and Apps and Spycher (2004) both used SiO2ðaqÞ as the aqueous silica species. Here their data have been converted to apply to H 4 SiO4ðaqÞ using the matching data for liquid water from these works (NBS 270-3, uncorrected to 1 bar, for Walther and Helgeson, 1977, and SUPCRT92 for Apps and Spycher, 2004). The intent here is to obtain the data for H 4 SiO4ðaqÞ that these authors would have obtained themselves, had they chosen this as the aqueous silica species. In constructing Table 19, we have avoided making other corrections, including those involving 1 atm to 1 bar adjustments. We will make such corrections as needed later in this paper. One can see that the higher-solubility data show some variation, as do the lower-solubility data, but they form a cluster that is distinct (especially in the G and H values) from the lower-solubility data. The lower-solubility Gibbs energy data average about
1307.8 kJ mol
1, while the higher-solubility data average about
1309.2 kJ mol
1, a difference of about 1.5 kJ mol
1. The data from the two U.S.G.S. reports noted in Table 19 have identical H and S values (and identical values for the three relevant elemental entropies). The difference in the G values is problematic and not easily explained. It appears that USGS 2131 intended to give a revised G value (it cites additional sources) and simply failed to update the

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T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Table 19 G-H-S data for H4SiO4(aq) at 298.15 K, 1 bar. Higher-solubility paradigm data (bottom) from Rimstidt (1987), Gunnarsson and Arno´rsson (2000), Stefa´nsson (2001), and Apps and Spycher (2004) are compared with lower-solubility paradigm data (top) from USGS 1452, USGS 2131, Walther and Helgeson (1977), and NEA TDB (Grenthe et al., 1992). The SiO2(aq) data of Walther and Helgeson (1977) and Apps and Spycher (2004) have been recalculated for consistency with H4SiO4(aq) (see text). The data shown here are otherwise uncorrected (see text). The data from USGS 2131 are overly rounded. Source

Year

H4SiO4(aq) DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1

USGS 1452 USGS 2131 Walther and Helgeson (1977)

1978 1995 1977


1308.000
1307.500
1307.768


1460.000
1460.000
1453.338

180.000 180.000 201.752

NEA TDB (Grenthe et al., 1992) Rimstidt (1997) Gunnarsson and Arno´rsson (2000) Stefa´nsson (2001) Apps and Spycher (2004)

1992 1997 2000 2001 2004


1307.735
1309.231
1309.181
1309.257
1309.241


1456.60
1460.913
1461.722
1458.861
1459.433

189.974 180.87 178.85 188.70 186.406

Notes: The obvious inconsistency in the data from the two USGS reports is discussed in the text.

H value. Walther and Helgeson (1977) give a similar Gibbs energy, but the fitted entropy and the calculated enthalpy are notably unique. If we were to correct their Gibbs energy to a standard pressure of 1 bar, it would be increased by 4  0.0326 = 0.130 J mol
1. The magnitude of this correction is small compared to that of the difference between the two clusters based on solubility. In developing his data, Rimstidt (1997) used key reference data from Robie et al. (1978) for quartz, liquid water, and the chemical elements. If we were to use his data in future work, using the corresponding key reference data from CODATA 89, small corrections would be required. Rimstidt utilized a simple van’t Hoff temperature function to describe the solubility that extended to about 300 °C. Gunnarsson and Arno´rsson (2000) used key reference data from CODATA 89, except that for quartz they used the data of Richet et al. (1982). If we were to use only the requisite reference data from CODATA 89, a very small correction would be required. Gunnarsson and Arno´rsson used a more elaborate temperature function to describe the solubility and a corresponding function for the apparent standard Gibbs energy of formation. Stefa´nsson (2001) developed an HKF (after Helgeson, Kirkham, and Flowers, 1981) model for H 4 SiO4ðaqÞ after

the HKF equation-of-state model for SiO2ðaqÞ developed by Walther and Helgeson (1977) and later modified by Shock et al. (1989). Like those earlier models, Stefa´nsson’s model was intended to work in SUPCRT92. It was tied to the hard-coded water properties model that used the uncorrected NBS 270-3 data for liquid water. It also indirectly assumed quartz data from the same source. The elemental entropy data were taken from CODATA 89. Some corrections are required for consistency with the water and quartz data from CODATA 89. The data needed to make the corrections are given in Table 17 (water) and Table 18 (quartz). The uncorrected data for H 4 SiO4ðaqÞ are given in Table 19, the corrected data in Table 20. The Gibbs energy changed by 0.440 kJ mol
1, the enthalpy by 0.343 kJ mol
1, and the entropy by
0.326 J mol
1 K
1. Apps and Spycher (2004) developed an alternative SUPCRT92-based HKF model with aqueous silica represented as SiO2ðaqÞ . The quartz and other requisite data were again the uncorrected NBS 270-3 data adopted by Helgeson and co-workers (see for example Helgeson and Kirkham, 1974a, and Helgeson et al., 1978). Again, consistency with the requisite CODATA 89 reference data requires corrections, which are similar in magnitude to those obtained for the Stefa´nsson (2001) model (compare the corresponding data in Table 20 with those in Table 19).

Table 20 G-H-S data for H4SiO4(aq) and the alternative species SiO2(aq) at 298.15 K, 1 bar. The data of Rimstidt (1997), Gunnarsson and Arno´rsson (2000), Stefa´nsson (2001), and Apps and Spycher (2004) all have been corrected for consistency with the relevant key data of CODATA 89. Source

Rimstidt (1997) Gunnarsson and Arno´rsson (2000) Stefa´nsson (2001) Apps and Spycher (2004)

Year

1997 2000 2001 2004

H4SiO4(aq)

SiO2(aq)

DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1

DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1


1309.228
1309.187
1308.817
1308.801


1461.166
1461.721
1458.518
1459.186

180.870 178.871 188.374 186.080


834.948
834.907
834.537
834.521


889.506
890.061
886.858
887.526

40.970 38.971 48.474 46.180

Notes: For details of the calculation of these corrected values, see the spreadsheet Electronic Annex.

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

Sverjensky et al. (2014) have developed another ‘‘higher solubility” SUPCRT92-based HKF model representing aqueous silica as a combination of SiO2(aq) and its dimer Si2O4(aq). The dimer is not significant at 298.15 K and 1 bar, but becomes important at high temperature and pressure. Because of uncertainty in identifying the data used by Sverjensky et al. (2014) for quartz, water, and the relevant chemical elements, we did not show data based on Sverjensky et al. (2014) in Table 19, nor do we show the corresponding corrected data in Table 20. Calculations developed in the spreadsheet Electronic Annex (worksheet ‘‘Misc Aq Sp”) suggest negligible corrections, other than for enthalpy values. Table 20 shows the G-H-S data of Rimstidt (1997), Gunnarsson and Arno´rsson (2000), Stefa´nsson (2001), and Apps and Spycher (2004), all corrected for consistency with CODATA 89 data for quartz, liquid water (as needed), and the relevant elemental reference forms. The data given are for H 4 SiO4ðaqÞ and the alternative species SiO2ðaqÞ . For details of these calculations, see the spreadsheet Electronic Annex. The enthalpy values shown here were calculated by inverting Eq. (7). The corrected data in Table 20 show that the Rimstidt (1997) and Gunnarsson and Arno´rsson (2000) data are fairly similar to each other, while the Stefa´nsson (2001) and Apps and Spycher (2004) data are also close to each other, but form a somewhat distinct group. The exact reason for this is difficult to determine. However, we note that the latter two works use the HKF equation of state approach, which distinguishes the effects of temperature and pressure, whereas the former two works use temperature functions and thus do not distinguish the effect of pressure from that of temperature. In terms of just the G-H-S values at 298.15 K and 1 bar, the corrected data from any of the four sources represented in Table 20 would seem to be acceptable for use in database development. The Stefa´nsson (2001) and Apps and Spycher (2004) models appear advantageous due their usage of the HKF equation of state approach. In each case, the G-H-S data at standard reference temperature and pressure is supplemented by a description of thermodynamic properties over a wide range of temperature and pressure. Some investigators may prefer data that are not tied to such a model, as there is the potential for bias in the results. Choosing data obtained using a model such as the HKF should perhaps be conditional on adoption of the model itself in constructing a thermodynamic data base. When the HKF equation of state is fitted to develop the properties of a neutral solute species such as aqueous silica, the entropy at 298.15 K and 1 bar is generally one of the fitting parameters. In contrast, when an HKF model is developed for an aqueous ion, the entropy at 298.15 K and 1 bar is commonly fixed separately (see for example Helgeson and Kirkham, 1976; Helgeson, Kirkham, and Flowers, 1981; Shock and Helgeson, 1988; or Oelkers et al., 2009). That appears to be done mainly to maintain consistency with data for 298.15 K and 1 bar from other sources. In addition to the entropy, the Gibbs energy (or alternatively, the enthalpy) can be used in such fitting. For example,

667

Tagirov and Schott (2001) adjusted both G and S (and thus H) of Al3+ for their HKF model for this ion. 5.2.3. Remarks on Al(III) The primary key species of Al(III) are corundum (Al2O3), gibbsite (Al(OH)3), and Al3+. Table 10 shows a strong consistency in recommended G-H-S data for corundum starting with NBS 270 (specifically NBS 270-3, Wagman et al., 1968) and USGS 1259 (Robie and Waldbaum, 1968). The same table shows good consistency in the data for gibbsite only later, starting with USGS 1452 (Robie et al., 1978). Table 13 shows a problematic history of data for Al3+. Background on the history of Al(III) key reference data is given in the second Electronic Annex, Section 6. This primarily relates to data for gibbsite and Al3+. A notable issue derived from the work of Barany and Kelley (1961) to determine the standard enthalpy of formation of gibbsite, which they found to be
306.380 kcal mol
1
1 (
1281.894 kJ mol ). In contrast, Hemingway and Robie (1977) obtained a value of
309.065 kcal mol
1 (
1293.128 kJ mol
1). Barany and Kelley (1961) used the calorimetric data of Coughlin (1958) for a reaction involving the formation of AlCl36H2O from aluminum metal dissolved in hydrochloric acid. Hemingway and Robie (1977) used a path not involving AlCl36H2O. Helgeson et al. (1978) focused on Coughlin’s (1958) work as a likely source of error in the Barany and Kelley (1961) determination. They chose to accept the gibbsite data from Hemingway and Robie (1977). However, they could not use gibbsite as a link to interpret their set of phase equilibrium data, because it did not appear in any of the associated reactions. A logical approach would have been to use calorimetric results for corundum, such as those of Mah (1957). Instead, Helgeson et al. (1978) made a link from gibbsite to kaolinite (Al2Si2O5(OH)4) using the reaction kaolinite þ H 2 O ¼ 2gibbsite þ 2SiO2ðaqÞ . They assumed equilibrium between the two minerals in some bauxitic groundwaters and in obtained their result from the aqueous silica concentration. They then used kaolinite as a link to interpret phase equilibrium data. Arguments against this approach have been given by Hemingway et al. (1982) and Tutolo et al. (2014), and additional arguments are given in the second Electronic Annex, Section 6. Later investigators developing thermodynamic data for minerals from phase equilibrium data accepted and used the calorimetric data for corundum as the primary link to elemental Al (for example, Berman, 1988, and Holland and Powell, 1985). It is now clear that there is a significant inconsistency in the Helgeson et al. (1978) thermodynamic data between gibbsite and Al3+ on the one hand and kaolinite, corundum, and other Al-bearing minerals on the other. Table 21 compares gibbsite and corundum data from Helgeson et al. (1978) (without pressure corrections to the Gibbs energies) with data from other sources, including Berman (1988). To accommodate the shift to 1 bar, the Helgeson et al. (1978) G value for gibbsite should be increased by 3  0.0326 kJ mol
1 = 0.098 kJ mol
1. G and H values for corundum would require corresponding

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

668

Table 21 G-H-S data for Al(OH)3 (Gibbsite), Al2O3 (Corundum), Al2Si2O5(OH)4 (Kaolinite), at 298.15 K, 1 bar. Data from Helgeson et al. (1978) (without potential pressure corrections) are compared with data from other sources. Source

USGS 1452 NBS 82 CODATA 89 USGS 2131 Berman 88 Hel 78

Year

1978 1982 1989 1995 1988 1978

Al(OH)3 (Gibbsite)

Al2O3 (Corundum)

DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1

DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1


1154.889
1155.105
1155.075
1154.900


1293.128
1293.335
1293.300
1293.100

68.440 68.450 68.440 68.400


1155.487


1293.128

70.082


1582.228
1582.300
1582.257
1582.300
1582.199
1568.264


1675.700
1675.700
1675.700
1675.700
1675.700 -1661.655

50.920 50.920 50.920 50.900 50.820 50.961

Notes: ‘‘Hel 78” denotes Helgeson et al. (1978). The values from this source shown here are converted to Joule units. No attempt has been made here to apply any 1 atm to 1 bar corrections (see text). ‘‘Berman 88” denotes Berman (1988). Berman used corundum as an anchor mineral, taking the H-S data from CODATA (1978). The appendix in Berman’s paper gives the entropy as 50.920 J mol
1 K
1, while his Table 2 gives 50.820 J mol
1 K
1. It is not clear if he intended to adjust the entropy value or if the Table 2 value is simply a misprint.

adjustments. These corrections would be small compared to the differences shown in Table 21. Thermodynamic data for Al3+ from various sources are shown in Table 22. These data are a mix of results based on both calorimetric measurement and the solubility of gibbsite. All sources noted here used the G-H-S data for gibbsite from Hemingway and Robie (1977), though the data are sometimes attributed to a secondary source, notably USGS 1452 (Robie et al., 1978). Pokrovskii and Helgeson (1995) conducted an extensive review and analysis of solubility data and produced and HKF equation-of-state model for Al3+. The corresponding G-H-S data for are shown in the table. In their fitting process, they assumed the H value for Al3+ from CODATA 89 (Cox et al., 1989) and fitted G and S. With H fixed, only one of G and S was an independent fitting parameter. Shock et al. (1997) obtained a notably different set of results. They used a different process, namely first fitting an HKF model for AlO
2 (as did Apps et al., 1988), then þ using data for the reaction Al3þ þ 2H 2 O ¼ AlO
2 þ 4H from Couturier et al. (1984) to develop a corresponding model for Al3+. Their G-H-S values for this ion are notably discrepant with other sets of recommended values.

Tagirov and Schott (2001) conducted another analysis of solubility data and produced an HKF model that is more like that of Pokrovskii and Helgeson (1995). Their fitting approach was a different in that they fitted G and S as independent parameters (obtaining H from G and S). The Al3+ data of Pokrovskii and Helgeson (1995) and Tagirov and Schott (2001) do not differ greatly from the corresponding CODATA 89 data. The G-H-S values for 298.15 K and 1 bar of Pokrovskii and Helgeson (1995) and those of Tagirov and Schott (2001) are fairly close, and probably either set would be a good choice. However, there are some differences between the two models at higher temperature and pressure, and in addition there is a difference in scope in regard to the aluminum aqueous species covered other than the aluminum ion itself. Tutolo et al. (2014) adopted the Tagirov and Schott (2001) model in their work. Both Pokrovskii and Helgeson (1995) and Tagirov and Schott (2001) used the SUPCRT92 data for water discussed previously, and in either case the G value for the aluminum ion must be corrected for that if we are to use the CODATA 89 water data. A further correction to the G value would be required were one to use the CODATA 89 data for gibbsite

Table 22 G-H-S data for Al3+ at 298.15 K, 1 bar, comparing data from newer sources with data from USGS 1452, CODATA 89, and USGS 2131.

Notes: The bottom three sources all used gibbsite data from Robie et al. (1978) in their fitting processes. None of the three used the same fitting approach (see text). Light orange background denotes values obtained directly from the polythermal fitting process. The data with gray background were obtained by an indirect process involving AlO
2 (see text) and are notably discrepant.

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

instead if that of Robie et al. (1978). As we noted above, for gibbsite, CODATA 89 averages the H value of Hemingway and Robie (1977) (which appears in Robie et al., 1978) with the slightly different H value of Gross et al. (1970), although both CODATA 89 and Robie et al. (1978) use the same S value for this mineral. All calorimetrically-based data for corundum reported by the compilations noted here are very similar. Pokrovskii and Helgeson (1995) adopted the CODATA 89 data. Tagirov and Schott (2001) included corundum in their model, but did not note the G-H-S data used for this mineral or its source. It seems likely that they used the data from Robie et al. (1978), as that is where they took their data for gibbsite. For future work, the data of Robie et al. (1978) for gibbsite and corundum seem to be best. The CODATA 89 recommendation for gibbsite was a step in determining a recommendation for the aluminum ion and was not included in the table of recommended data. Also, as noted in the second Electronic Annex, Section 6, CODATA 89 miscalculated the enthalpy of formation of gibbsite as reported by Gross and Hayman (1970a) and Gross et al. (1970), and their recommended value was determined by averaging their erroneous result with the value reported by Hemingway and Robie (1977). Although one could correct the CODATA 89 result, we choose not to do so. We simply consider the Gross and Hayman (1970a) result as confirmatory. The G-H-S values for corundum recommended by Robie et al. (1978) are the same as those recommended by CODATA 89. The data of either Pokrovskii and Helgeson (1995) or Tagirov and Schott (2001) for Al3þ could be used for future work, although again there is potential bias due to the use

669

of the HKF equation of state. Both models are consistent with the Robie et al. (1978) data for the two minerals. We find the CODATA 89 data for Al3þ (partially tied to the development of data for gibbsite) to be overly complex with too much tendency to include potential data in averaging, where perhaps culling would be more appropriate. Nevertheless, corrections are needed to maintain consistency with the CODATA 89 recommendations for liquid water and elemental entropies. For the two solids we accept the H-S data for gibbsite and corundum from USGS 1452 (Robie et al., 1978) and recompute the corresponding G values using the CODATA 89 elemental entropies. The results are shown in Table 23, which also shows the original results from USGS 1452 for comparison. The corrected G value for gibbsite is very close to the original USGS 1452 value. The corrected G value for corundum exactly matches the CODATA 89 data, as both USGS 1452 and CODATA 89 used the same H-S data. In the case of the aluminum ion, the objective is to preserve the Gibbs energy of reaction and the entropy of reaction obtained by Pokrovskii and Helgeson (1995) or Tagirov and Schott (2001), the relevant reaction being AlðOH Þ3ðcÞ þ 3H þ ¼ Al3þ þ 3H 2 O. The corrections for the aluminum ion involve not only gibbsite (whose G value has just been corrected) but also water. The SUPCRT92 water data must be replaced by the CODATA 89 data. The results of these corrections are shown in Table 24. Both the Pokrovskii and Helgeson (1995) and Tagirov and Schott (2001) models include data for a number of aqueous aluminum complexes, and the G-H-S data for those species would need to be similarly corrected (again to preserve the corresponding reaction data).

Table 23 G-H-S data for Al(OH)3 (Gibbsite) and Al2O3 (Corundum), at 298.15 K, 1 bar. Data from USGS 1452 (Robie et al., 1978) are shown, along with corrections (affecting only the Gibbs energies of formation) for consistency with other data from CODATA 89. See text for a description of the corrections. Source

USGS 1452 USGS 1452, corrected

Year

1978 This work

Al(OH)3 (Gibbsite)

Al2O3 (Corundum)

DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1

DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1


1154.889
1154.903


1293.128
1293.128

68.440 68.440


1582.228
1582.257


1675.700
1675.700

50.920 50.920

Notes: For details of the calculation of these corrected values, see the spreadsheet Electronic Annex.

Table 24 G-H-S data for Al3+ at 298.15 K, 1 bar. Data from Pokrovskii and Helgeson (1995) and Tagirov and Schott (2001) are shown along with corrections for consistency with other data from CODATA 89. See text for a description of the corrections. Source

Pokrovskii and Helgeson (1995) Pokrovskii and Helgeson (1995), corrected Tagirov and Schott (2001) Tagirov and Schott (2001), corrected

Year

1995 This work 2001 This work

Al3+ DfG° kJ mol
1

DfH° kJ mol
1

S° J mol
1 K
1


487.616
487.759
487.478
487.621


538.401
538.572
538.769
538.937


338.067
338.148
339.753
339.834

Notes: For details of the calculation of these corrected values, see the electronic supplement.

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T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676 Table 25 G-H-S data with uncertainties for Al3+ from CODATA 89 compared with updated data based only on calorimetry. All data are given in Joule units and for 1 bar pressure.

Notes: The CODATA 89 Gibbs energy and corresponding uncertainty were calculated by us. The updated data were created by including the enthalpy data of Zeng et al. (1994) (thus averaging three values) and by omitting the one discrepant entropy value that was included by CODATA 89, thus averaging the two remaining values used by that work.

Table 25 compares the data recommended by CODATA 89 (Cox et al., 1989) with an updated equivalent set of data we calculated using only calorimetric data. CODATA 89 averaged two enthalpy values and three entropy values. We added the later enthalpy value reported by Zeng et al. (1994) and culled the one entropy value (based on studies of CsAl(SO4)2.12H2O) that was not consistent with the other two (see the second Electronic Annex, Section 6).


1576.357 kJ mol
1 (converted to Joule units and corrected to 1 bar pressure). The atomic weight correction would lead to
1576.298 kJ mol
1, a difference of 0.059 kJ mol
1. This is larger than the 0.049 kJ mol
1 pressure correction, but much smaller than the CODATA 89 uncertainty of 1.302 kJ mol
1. Although the atomic weight correction is still relatively small, it is large enough to be of concern if one were going to use pre-1962 data in future work.

6. ATOMIC WEIGHTS 7. SUMMARY AND CONCLUSIONS The number of moles of a species depends on its molecular weight, which in turn depends on the atomic weights of the constituent elements. Recommended values for atomic weights have changed due to the adoption of new standards, changes in assumptions regarding isotopic representation in natural mixtures, and newer, more precise measurements. A general review of the history of atomic weights and analysis of how changes may affect thermochemical data is given in the second Electronic Annex, Section 6. Here we will summarize the major conclusions. It is highly likely that sources of chemical thermodynamic data produced between about 1904–1962 were tied to the O = 16 scale (see for example Clarke et al., 1907). Later sources such as NBS 270 (starting with NBS 270-3, Wagman et al., 1968) and USGS 1259 (Robie and Waldbaum, 1968) are tied to the modern 12C = 12 scale that was adopted in 1961 (Cameron and Wichers, 1962). We did not make corrections related to atomic weights to the older data presented in the present paper. The atomic weight of oxygen on the 12C = 12 scale is 15.9994 (Cameron and Wichers, 1962). The correction factor would then be 15.9994/16 = 0.9999625. The largest elemental entropy from NBS 500 (Rossini et al., 1952) is 223.058 J mol
1 K
1 for Cl2 (converted to Joule units and corrected to 1 bar pressure). Applying the atomic weight correction associated with the change from O = 16 to 12C = 12 would change this to 223.050 J mol
1 K
1, a difference of only 0.008 J mol
1 K
1. This is smaller than the pressure correction for a gas (0.1094 J mol
1 K
1). It is also smaller than the corresponding CODATA 89 uncertainty (0.010 J mol
1 K
1). Gibbs energies of formation and enthalpies of formation values often present larger numbers than entropies. The Gibbs energy of corundum from NBS 500 is

Key reference data play a critical role in developing and evaluating thermochemical data. The convention of defining standard Gibbs energies and enthalpies in terms of formation from the elements in their reference forms requires that the primary links to the elemental reference forms be well understood. We propose a formal concept of links to the elemental forms as a means of assuring that a thermodynamic dataset or database is internally consistent. We consider a link to be valid only if there is a full description of how a link (key species with a defined reference value) has been developed. Thus, some common sources of key reference data that do not provide the necessary references (notably NBS 270 and NBS 82) should be considered unsuitable for serious work. There are two categories of links. The first is comprised of the entropies of the elements in their reference forms at 298.15 K and 1 bar. The other consists of G-H-S values at 298.15 K and 1 bar of key, mostly chemically simple species of various types (mineral, gas, aqueous). For links to the same element developed independently (for example calorimetric data for both Mg2+ and MgO, portlandite), it is necessary to show close numerical consistency via analysis of some point of commonality. This can be done by various methods, including ones that would be characterized as ‘‘optimization.” The first task in developing a thermodynamic dataset or database should be to choose a consistent set of primary links, which should then be strictly adhered to in further development. In analyzing G-H-S data for a chemical species, dataset, or database, one should identify the links underlying the data. One should then be able to modify the data for consistency with a preferred set of links. In combining thermochemical data, correction to a common

T.J. Wolery, C.F. Jove´ Colo´n / Geochimica et Cosmochimica Acta 213 (2017) 635–676

set of links should remove a major source of inconsistency. Remaining differences would be due to factors such as choice of phase equilibrium data, different means of representing temperature and pressure dependence, and differences in regression techniques. We have reviewed the development of primary key reference data from important sources, mainly major compilations produced over decades, and looked at how recommended values have changed. We have noted how historical data may need to be corrected for consistency with modern standards such as a standard pressure of 1 bar in place of 1 atm. We have shown that for many data, the values, when corrected to modern standards, have varied little, while for others, they have changed significantly. For future development, the best compilation sources to consult first for primary key reference data seem to be CODATA 89 (Cox et al., 1989), the NEA TDB series, and Gurvich (1989, 1991, 1993). However, these sources all have limited scope, and in some instances better data may be available from the more recent general literature. Anyone using CODATA 89 should look beyond the main table to the ‘‘Notes” section. Data developed for some chemical species (including gibbsite and calcite) are not given in the main table. Also, some of the logic in the ‘‘Notes” is questionable (for example in the case of the entropy of Al3+). For liquid water, we note that the SUPCRT92 data (which are built into the software) are not consistent with CODATA 89 and should no longer be used. For aqueous silica, we recommend data consistent with the highersolubility of quartz paradigm (see for example Rimstidt, 1997). Two of the relevant models (Stefa´nsson, 2001, and Apps and Spycher, 2004) are developed with HKF equations of state. We have corrected these for consistency with CODATA 89 data for quartz, liquid water and elemental entropies. For Al(III) key species, the gibbsite and corundum data of Robie et al. (1978), and the Al3+ data of either Pokrovskii and Helgeson (1995) or Tagirov and Schott (2001) seem appropriate for future use. Both of these Al3+ models are consistent with the Robie et al. (1978) data for gibbsite and corundum. We corrected the Robie et al. (1978) Gibbs energy data for the two minerals, so that they are consistent with the CODATA 89 elemental entropies. We also corrected the Pokrovskii and Helgeson (1995) and Tagirov and Schott (2001) data for the aluminum ion for consistency with the corrected gibbsite data and the CODATA 89 data for liquid water and elemental entropies. In addition, we updated calorimetry-based estimates of the thermochemical data for Al3+. ACKNOWLEDGMENTS This research was supported by the Used Fuel Disposition Campaign, Office of Nuclear Energy, U.S. Department of Energy. We thank Ben Tutolo, Alexander Gysi, and two anonymous reviewers for comments that significantly improved the manuscript. Joseph Rard and John Apps also provided helpful reviews. We thank Prasad Nair (USDOE) and Mark Sutton (LLNL) for encouraging this work. Lawrence Livermore National Laboratory is a multi-program laboratory managed and operated by Lawrence Livermore National Security LLC for the U.S. Department of Energy’s

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National Nuclear Security Administration under contract DEAC52-07NA27344. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000.

APPENDIX A. SUPPLEMENTARY DATA Supplementary data associated with this article can be found, in the online version, at http://dx.doi.org/10.1016/ j.gca.2016.09.028.

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