Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25.degree.C

Rard, Joseph A.; Miller, Donald G.

doi:10.1021/je00047a025

Cited by 44 publications

(18 citation statements)

References 22 publications

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“…It is unclear to us why Platford's (1968) parameterization of the Scatchard model (using his isopiestic data for NaCl(aq) + MgCl 2 (aq) mixtures) yields results that are close to the Rard and Miller values for γ NaCl but not those for γ MgCl 2 . Essentially opposite behaviour is observed for the Harned-rule model of Wu et al (1968), which is close to Rard and Miller's (1987) prediction for γ MgCl 2 but not for γ NaCl . Pitzer (1991) has emphasised the importance of solubility data as a means of anchoring isothermal activity and osmotic coefficients to a single well-defined point.…”

Section: (Crosses)contrasting

confidence: 50%

“…Several mean activity coefficient models are compared with experimental data (Lanier, 1965) in reported by Miller (1981, 1987) is in good agreement with Lanier's (1965) potentiometric data for γ NaCl , but is distinctly different from the other models, including Rard and Miller's own calculations using both Pitzer (θ = ψ = 0) and Scatchard models (Rard and Miller, 1987). It is unclear to us why Platford's (1968) parameterization of the Scatchard model (using his isopiestic data for NaCl(aq) + MgCl 2 (aq) mixtures) yields results that are close to the Rard and Miller values for γ NaCl but not those for γ MgCl 2 .…”

Section: (Crosses)mentioning

confidence: 57%

“…9b). (Platford, 1968) (squares), Scatchard (Platford, 1968) (circles), Pitzer (θ = ψ = 0) (Rard and Miller, 1987) (triangles), Scatchard (Rard and Miller, 1987) …”

Section: Case Study D: General Regression Of Disparate Literature Datmentioning

confidence: 99%

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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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Section: (Crosses)contrasting

confidence: 50%

Section: (Crosses)mentioning

confidence: 57%

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Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

Rowland

Königsberger

Hefter

et al. 2015

Applied Geochemistry

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“…Thus the constancy of f S and a w at S i n i m i = (5.9632 2 0.0036) mol·kg −1 should break down somewhere in the acid-deficient region. Very few other ternary systems have been studied over a sufficiently large molality range at constant z to establish whether or not the f S curves undergo crossovers like those observed for {zH 2 SO 4 + (1 − z)MgSO 4 }(aq) at T = 298.15 K. Examination of the isopiestic results of Rard and Miller (26) for {zNaCl + (1 − z)MgCl 2 }(aq) at T = 298.15 K indicates that the f S curves undergo an inversion centered around S i n i m i 1 1.25 mol·kg −1 . However, for that system there is no single crossover value for S i n i m i but rather the crossovers occur over a range of S i n i m i values.…”

Section: Calculation Of Osmotic Coefficients and Relations Among Varimentioning

confidence: 99%

Isopiestic determination of the osmotic and activity coefficients of {zH2SO4+(1−z) MgSO4}(aq) at the temperatureT=298.15 K. I. Results forz=(0.85811, 0.71539, and 0.57353)

Rard

1997

The Journal of Chemical Thermodynamics

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“…In contrast to Pitzer et al 9 , who estimated the second virial coefficients based mainly on the experimental data of the osmotic and activity coefficients recommended by Robson and Stokes [11][12][13][14][15] , which were obtained in the 1960s, this study also includes newer published data for the osmotic coefficients, e.g. 16,17,18,19,20,21,22,23 as well as data from some secondary sources, such as Goldberg et al [24][25][26][27] and Hamer et al 28 . These sources are secondary sources in the sense that their work includes tables of recommended values rather than experimental data.…”

Section: Re-estimating the Second Virial Coefficients In The Pitzer Ementioning

confidence: 99%

Estimation of the Pitzer Parameters for 1–1, 2–1, 3–1, 4–1, and 2–2 Single Electrolytes at 25 °C

et al. 2016

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The Pitzer model is one of the most important thermodynamic models to predict the behavior of aqueous electrolyte solutions, especially at high ionic strengths. However, most of the parameters in the Pitzer equations have to be obtained experimentally and this represents an important drawback to this model. Therefore, in order to make the Pitzer equations less dependent on experimental data and more dependent on the properties of the solution, new equations that correlate the Pitzer equations with the properties of the solution have been successfully developed for 1-1, 2-1, 3-1, 4-1 and 2-2 electrolytes. In particular, these equations were developed for two cases: (i) considers the original Pitzer equations and (ii) considers some simplifications to the Pitzer equation (assuming C  B and  ). In particular, for case (ii), the second virial coefficients B and Bof the Pitzer equations were re-estimated using published experimental data of the osmotic coefficient obtained from the literature. As a conclusion, both the simplified and the original Pitzer equations presented a very good match with this published experimental data for the osmotic coefficients.Additionally, the second virial coefficients B and B for both cases were successfully correlated with the ionic radius and the ionic charge, and this is confirmed by the very high coefficients of determination achieved (R 2 >0.96). However, these new equations are valid only to cases in which no significant ion association occurs, which is also the basic premise of the original Pitzer model.

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Isopiestic determination of the osmotic and activity coefficients of aqueous mixtures of sodium chloride and magnesium chloride at 25.degree.C

Cited by 44 publications

References 22 publications

Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

Isopiestic determination of the osmotic and activity coefficients of {zH2SO4+(1−z) MgSO4}(aq) at the temperatureT=298.15 K. I. Results forz=(0.85811, 0.71539, and 0.57353)

Estimation of the Pitzer Parameters for 1–1, 2–1, 3–1, 4–1, and 2–2 Single Electrolytes at 25 °C

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