Least-Squares Analysis of Osmotic Coefficient Data at 25 .degree.C According to Pitzer's Equation. 1. 1:1 Electrolytes

Marshall, Stephanie Pace; May, Peter M.; Hefter, Glenn

doi:10.1021/je00021a003

Cited by 47 publications

(53 citation statements)

References 15 publications

(31 reference statements)

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“…Even though widely used, only a single study dealing with Pitzer coefficient uncertainty is available [31]. The possibility that activity coefficients calculated on basis of the Pitzer equations, at least in certain circumstances, might give unreliable results, has not occurred.…”

Section: The Role Of Statistics In Chemistrymentioning

confidence: 99%

“…In several instances the electrolyte data (commonly osmotic coefficients, φ) are smoothed or selected from a larger amount of available data before interpretation [37]. It has, furthermore, been observed that the fitting criteria have a considerable effect on the optimum value of a value obtained from such a fitting exercise [31].…”

Section: The Role Of Statistics In Chemistrymentioning

confidence: 99%

“…Appendix) seems to make assessment of uncertainty prohibitively demanding. In a pioneering effort, however, Marshall et al [31] have performed statistical analysis on Pitzer coefficients by ordinary linear regression (OLS) based on the observation that Pitzer's equations are linear.…”

Section: Analysis Of the Uncertainty In Binary Pitzer Coefficientsmentioning

confidence: 99%

“…(these terms are defined in the Appendix). The cumulative distribution functions (CDF) are compared with the normal distributions of Marshall, May and Hefter [31] (MMH) and mean values reported by Kim and Frederick [33] (KF). For the bootstrap analysis two different CDF have been obtained.…”

Section: Analysis Of the Uncertainty In Binary Pitzer Coefficientsmentioning

confidence: 99%

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Extended traceability of pH: an evaluation of the role of Pitzer's equations

Meinrath

2002

Analytical and Bioanalytical Chemistry

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The 2002 IUPAC recommendation on pH (provisional) has taken its own philosophy to provide a basis for comparable and traceable assignment of a value, from a measurement, to the quantity pH. Whereas the substituted 1983 IUPAC recommendation relied heavily on precisely prescribed experimental techniques and procedures, the current recommendation defines a hierarchical relationship between references for comparison (primary and secondary standards) and objective criteria on the comparison of measurements with these standards. The recommendation aims at a traceability chain from the national metrological institution (NMI) level down to field and laboratory measurements. Currently, however, the traceability chain is developed to the level of certified reference materials (CRM), namely the above mentioned primary and secondary standards. To complete the traceability chain, several theoretical and practical aspects have to be pondered. In part, the methods for comparative assessment of different options have yet to be developed. As an illustrating example of the complexity of issues to be considered in a further extension of the traceability chain is estimation of the doubt associated with Pitzer coefficients. The Pitzer equations for activity coefficient modelling are explicitly mentioned in the 2002 IUPAC recommendation on pH (provisional) as enabling possible improvement in the ionic strength extrapolations to zero ionic strength. An assessment of uncertainty of ternary Pitzer coefficients is given for the first time.

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Section: The Role Of Statistics In Chemistrymentioning

confidence: 99%

Section: The Role Of Statistics In Chemistrymentioning

confidence: 99%

Section: Analysis Of the Uncertainty In Binary Pitzer Coefficientsmentioning

confidence: 99%

Section: Analysis Of the Uncertainty In Binary Pitzer Coefficientsmentioning

confidence: 99%

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Extended traceability of pH: an evaluation of the role of Pitzer's equations

Meinrath

2002

Analytical and Bioanalytical Chemistry

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“…Some of the reasons why the thermodynamics of aqueous electrolyte solutions has remained intractable are well known: the strong departure of ionic solutions from ideality due to short-and long-range electrostatic interactions (Grenthe et al, 1997, p. 327); the empirical nature of, and associated parameter correlation in, the extended Debye-Hückel modelling functions currently available (Marshall et al, 1995), including Pitzer; and the need to rely on approximate methods for making temperature corrections to thermodynamic data (Puigdomenech et al, 1997). More subtle difficulties have also started to become apparent.…”

Section: Introductionmentioning

confidence: 99%

Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

Rowland

Königsberger

Hefter

et al. 2015

Applied Geochemistry

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Despite intense efforts, general thermodynamic modelling of aqueous electrolyte solutions still presents a difficult challenge, with no obvious method of choice. Even though the Pitzer equations seemingly provide a well-established theoretical framework applicable to many chemical systems over a wide range of temperatures and pressures, they are not as widely adopted as their early promise might have suggested. This is strikingly illustrated by the simultaneous appearance in the literature of numerous, different (and potentially incompatible) Pitzer models alongside a proliferation of alternative theoretical approaches with inferior capabilities.To better understand this problem, the ability of the Pitzer equations to represent the physicochemical properties of aqueous solutions has been systematically investigated for exemplar electrolyte systems. Pitzer ion-interaction parameters have been calculated for selected systems by least-squares regression analysis of published solution data for activity coefficients, osmotic coefficients, relative enthalpies, heat capacities, volumes and densities to high temperatures and pressures. Although satisfactory fits can be achieved when the ranges of conditions are carefully chosen and when sufficient data are available to constrain the regression, the fits obtained tend otherwise to be unsatisfactory. The Pitzer equations do not cope well with gaps and other deficiencies in the regressed data. Profound difficulties, poorly recognized hitherto, can also arise because of variation in the sensitivity of the Pitzer functions to values for different physicochemical properties when these are combined. Given the dimensionality of numerous related thermodynamic properties, all changing as functions of composition, temperature and pressure, these problems are difficult to detect, let alone address, especially in multicomponent systems. The growing practice of improving fits simply by adding basis functions (thereby increasing the number of adjustable parameters) should be deprecated because it increases the likelihood of error propagation, introduces subjectivity, makes independent verification difficult and has deleterious implications for both automated data processing and for consistency between thermodynamic models.

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Prediction of Activity Coefficients for Uni‐univalent Electrolytes in Pure Aqueous Solution

et al. 2010

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Parameter-free activity coefficient equations were tested in addition to those containing one, two, three or four electrolyte-dependent parameters with the experimental activity coefficients obtained from the literature data for aqueous solutions of the following electrolytes at 298.15 K: KCl, NaCl, RbCl, KBr, RbBr, CsBr, KI, RbI, KNO 3 , and KH 2 PO 4 . The experimental activity coefficients of each electrolyte considered can be reproduced within the uncertainty of the measurements up to the molality of the saturated solution by using a three-parameter equation of the extended Hückel type. The best Hückel equations are given for all electrolytes in question. The results from the present studies reveal that the parameterfree equations can be reliably used in thermodynamic studies only for very dilute electrolyte solutions. On the other hand, in most cases, a good agreement with the experimental data is obtained with the one-parameter equations of Bromley [14] and Kusik and Meissner [13], with the two-parameter equation of Bretti et al. [15], and with the three-or four-parameter equation of Hamer and Wu [19] in addition to the three-parameter Pitzer equation [23], with almost all parameter values suggested in the literature. In several cases, these equations seem to apply to much higher molalities than those used in the parameter estimations. Therefore, the best of these equations may have important applications in calculations associated with the dissolution and crystallization processes of these salts.

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Least-Squares Analysis of Osmotic Coefficient Data at 25 .degree.C According to Pitzer's Equation. 1. 1:1 Electrolytes

Cited by 47 publications

References 15 publications

Extended traceability of pH: an evaluation of the role of Pitzer's equations

Extended traceability of pH: an evaluation of the role of Pitzer's equations

Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

Prediction of Activity Coefficients for Uni‐univalent Electrolytes in Pure Aqueous Solution

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