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

Abstract

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.

A Generic and Updatable Pitzer Characterization of Aqueous Binary Electrolyte Solutions at 1 bar and 25 °C

“…For example, Pitzer and Mayorga used mainly osmotic coefficient data from Robinson and Stokes to evaluate their parameters; Kim and Frederick obtained Pitzer parameters from smoothed osmotic coefficient data evaluated by Hamer and Wu and other authorities. As Meinrath has pointed out, non-normal distributions of residuals arise when preprocessed and smoothed experimental data are used to fit Pitzer equations. Moreover, the largest deviations from a normal distribution are found in β (1) , probably because this parameter depends strongly on osmotic coefficient data at low concentrations where the experimental uncertainty is usually largest.…”

“…As Meinrath 31 has pointed out, non-normal distributions of residuals arise when preprocessed and smoothed experimental data are used to fit Pitzer equations. Moreover, the largest deviations from a normal distribution are found 31 in β (1) , probably because this parameter depends strongly on osmotic coefficient data at low concentrations where the experimental uncertainty is usually largest. It is reasonable to expect that the systematic bias arising in such cases will be reduced when the regressed data are obtained from diverse sources.…”

Aqueous electrolyte solution modelling: Some limitations of the Pitzer equations

“…Given the real uncertainties in solubility measurements (Hefter, 2013;Hefter and Tomkins, 2003) it is completely unsatisfactory to assess the quality of a model in such a self-referencing manner. Meinrath and colleagues (Meinrath, 2002;Spitzer et al, 2011) claim, with good justification, that many mixing interactions in electrolyte solutions are not statistically significant. While some researchers contest this view, there can be little doubt that the experimental uncertainties are considerably greater than are commonly assumed.…”

Modeling Multicomponent Ion Exchange: Application of the Single-Parameter Binary System Model

“…13 In fact, there has been some discussion in the literature regarding whether all values of θ and ψ for univalentunivalent electrolyte mixtures should actually be set to zero, with all calculated nonzero values simply representing noise in experimental data. 23 Equation 4 is a matrix formulation for the exchangerphase model in the general multicomponent case. 10,14,15 Here, species 0 is the solvent, and summation over dummy index Q includes all exchanging species as well as the solvent.…”

“…This has been shown to have only a minor impact on the accuracy of activity coefficients calculated at the moderate concentrations used in this study . In fact, there has been some discussion in the literature regarding whether all values of θ and ψ for univalent−univalent electrolyte mixtures should actually be set to zero, with all calculated nonzero values simply representing noise in experimental data 2 Single Electrolyte Pitzer Model Parameters M X Ca 2+ Cl - 0.3159 a 1.614 a −0.00017 a SO 4 2- 0.2000 b 3.7762 b NO 3 - 0.2108 a 1.409 a −0.01007 a Na + Cl - 0.0765 a 0.2664 a 0.00127 a SO 4 2- 0.019575 a 1.113 a 0.00249 a NO 3 - 0.0068 a 0.1783 a −0.00072 a H + Cl - 0.1775 a 0.2945 a 0.00080 a SO 4 2- 0.2103 a 0.4711 a −0.00237 b NO 3 - 0.1168 a 0.3456 a −0.00539 a K + Cl - 0.04835 a 0.2122 a −0.00084 a Mg 2+ Cl - 0.3524 a 1.6815 a 0.002596 a a Ref .…”