pH buffer assessment and Pitzer��s equations

Traceable measurement of the quantity pH in media outside the limits of the recent IUPAC recommendation requires an alternative to the Bates?CGuggenheim convention. The Pitzer??s approach to ion interactions is widely appraised and offers a suitable approach to the estimation of single-ion activity coefficients. For this purpose, the underlying electrolyte data need to be consistent and the uncertainty in existing Pitzer??s data needs to be assessed. Such an assessment is attempted in this study for pH in potassium acetate buffer medium. The re-evaluation of Pitzer??s data from potassium nitrate data revealed inconsistencies and wide uncertainty margins. The uncertainty contribution from binary Pitzer??s parameters to an assessment of pH in seawater resulted in an uncertainty in pH of about 0.03 (95% confidence interval). This contribution has to be taken into account in the overall uncertainty budget. Lack of appropriate data for other pH buffer systems (e.g., phosphate buffers) is noted.     

A pitzer mixed electrolyte solution theory approach to assignment of pH to standard buffer solutions

The IUPAC recommendations for the pH scale for aqueous solutions are based on the Bates-Guggenheim (B-G) convention (1961) for the single ion activity coefficient of the chloride ion in the standard buffer(s). This convention was adopted as a reasonable estimate based on the Debye-Huckel theory and is limited in its application to ionic strengths less than 0.1 mol-kg^–1. This approach ignores the results of many workers over the years on the properties of mixed electrolyte solutions and their prediction on the basis of the theories of Harned, Scatchard, Guggenheim and more recently of Pitzer. The literature data of EMF measurements on appropriate weak acid systems have been reexamined to determine both the pK_a values and values of appropriate Pitzer interaction coefficients. The latter are used to calculate single chloride ion activity coefficients for the chosen compositions of pH standard buffers, and compared with the B-G convention values. Calculations were made to check the consistency of the pH values with determined pK_a values using the Pitzer treatment for all the required single ion activity coefficients. The overall aim was to remove the ionic strength restriction of the B-G convention and rationalize the approach to pH standardization for such diverse aqueous media as sea water, blood and acid-rain water.An account of this work was presented at the 12^th International Conference on Chemical Thermodynamics, Snowbird, Utah, August 1992.     

Equations for calculation of the pH of buffer solutions containing sodium or potassium dihydrogen phosphate, sodium hydrogen phosphate, and sodium chloride at 25°C

Published thermodynamic data measured in aqueous mixtures of sodium or potassium dihydrogen phosphate with hydrogen phosphate and chloride at 25°C were used to test recently developed methods for calculation of the pH of phosphate buffer solutions. Equations for ionic activity coefficients are used in these methods. It is shown that all data used in the tests up to an ionic strength of about 0.5 mol-kg^-1 can be accurately predicted by the two methods recommended. In one of these methods, equations of the Hückel type are used for ionic activity coefficients and in the other equations of the Pitzer type. Several sets of phosphate buffer solutions are recommended,e.g., for calibrations of glass electrode cells. In the recommended sets, the pH of the buffer solutions can be calculated either by the Hückel or Pitzer method, and the pH predictions of these methods agree in most cases within 0.005 at least up to ionic strengths of about 0.2 mol-kg^-1. The pH values of the two primary pH standards endorsed by IUPAC based on aqueous mixtures of KH₂PO₄ and Na₂HPO₄,i.e., pH values of 6.865 and 7.413, can also be accurately predicted by the equations recommended in this study.     

Secondary pH standards and their uncertainty in the context of the problem of two pH scales

Establishing a traceability route with all measurement and uncertainty relationships determined is an important aspect of traceability, and seems to be particularly striking in pH measurement. In this paper the issue of evaluation of secondary pH standards measured with reference to a primary standard in a differential cell with free diffusion type liquid junctions is considered. Relatively high uncertainty, U=0.015, has been assigned to such standards in the recent IUPAC Recommendations on pH (2001), because of a specific residual liquid-junction potential treated statistically as a contribution to the combined uncertainty. Close inspection of the problem leads to the conclusion that a correction for the residual liquid-junction potential should be applied to the measured value of a secondary pH standard. This can be considered as a correction for a known systematic effect on the traceability route. With available experimental data it is demonstrated that such a correction can reasonably be made for well-studied standard buffer systems. In this way the uncertainty associated with secondary pH standards is kept to a low level, and, what is more, the problem of two pH scales, a multi-standard scale and a single-standard scale, gains a proper solution. The need for different treatment of residual liquid-junction potentials at different levels in the measurement hierarchy is noted. Much attention is also given to rational categorization of pH standards in the hierarchy.     

New IUPAC (International Union of Pure and Applied Chemistry) recommendations on the measurement of pH - background and essentials

The IUPAC Recommendations on pH (1985) have serious metrological deficiencies (recommendation of two pH scales and of several pH definitions and procedures to measure pH). Background and essential features of new recommendations, which replace the 1985 document, are reported in this paper. The new document is strictly based on metrological principles. pH is defined (notionally) by the negative logarithm of the hydrogen ion activity according to S?rensen and Linderstr?m-Lang (1924), that is pH=-lg a(H). Because pH is a single ion quantity it is immeasurable and is therefore experimentally verified, with stated uncertainties, by pH(PS) values of primary standard buffer solutions. The assignment of pH(PS) is carried out in a Harned cell (without transference), which is defined as a primary method of measurement, and involves the Bates-Guggenheim convention. pH(PS) is thus a conventional quantity. Consideration of the uncertainty of the Bates-Guggenhein convention, however, permits its incorporation into the internationally accepted SI system of measurement. Comparison of the pH of secondary buffer solutions with pH(PS) values in recommended cells with transference yields secondary standards, whose pH(SS) can be traced back to pH(PS) and consequently to the definition of pH. The traceability chain is continued "downwards" by practical cells with transference containing glass electrodes for the measurement of pH(X) values of unknown solutions, for which three calibration procedures are recommended. The measurement of pH is thus represented by the traceability chain pH(X)-->pH(SS)-->pH(PS)-->pH as defined, each step having stated uncertainties. This hierarchical system of measurement excludes any pH 'scale'. Tabulated pH(PS) values are given as examples, and it is recommended that actual pH(PS) and pH(SS) be taken from certificates, which are to accompany each lot of certified reference material (CRM). Target uncertainties and examples of their calculation, a sign convention for pH cells and conventions for presenting cell schemes are given in the new document.     

Improved reliability of pH measurements

Measurements of pH are performed on a large scale at laboratory level, and in industry. To meet the quality-control requirements and other technical specifications there is a need for traceability in measurement results.The prerequisite for the international acceptance of analytical data is reliability. To measure means to compare. Comparability entails use of recognised references to which the standard buffer solutions used for calibration of pH meter-electrode assemblies can be traced.The new recommendation on the measurement of pH recently published as a provisional document by the International Union on Pure and Applied Chemistry (IUPAC) enables traceability for measured pH values to a conventional reference frame which is recognised world-wide. The primary method for pH will be described.If analytical data are to be accepted internationally it is necessary to demonstrate the equivalence of the national traceability structures, including national measurement standards. For the first time key comparisons for pH have been performed by the Consultative Committee for Amount of Substance (CCQM, set up by the International Bureau of Weights and Measures, BIPM) to assess the equivalence of the national measurement procedures used to determine the pH of primary standard buffer solutions. The results of the first key comparison on pH CCQM-K9, and other international initiatives to improve the consistency of the results of measurement for pH, are reported.     

Activity coefficients in mixed-electrolyte solutions at 25°C: Na-formate + NaCl system

Activity coefficients for NaCl in aqueous mixtures with Na-Formate were determined at 25°C from emf measurements for different total ionic strengths. At each total ionic strength studied, the measurements were carried out at different ratios of the Na-Formate to NaCl ionic strengths. The experimental activity coefficients were fitted using the Harned equation and the treatments of Scatchard et al. and Pitzer et al. Finally, the excess Gibbs energy of these mixtures was also calculated.     

pH measurements in non-aqueous and aqueous–organic solvents – definition of standard procedures

pH standardisation procedures in non-aqueous and aqueous-organic solvents are discussed in the light of the newly prepared IUPAC recommendation on measurement of pH in dilute aqueous solutions. Both scientific and metrological aspects are considered, as required by the definitions of primary and secondary methods of measurements recently endorsed by BIPM (Bureau International de Poids et de Mesures, France).     

273.15K时LiCl-Li2SO4-H2O体系热力学性质的等压研究

0℃下用改进的等压设备和改进的实验方法测定了纯水溶液(LiCl 0.5～9.2mol·kg-1,Li2SO40.3～2.5mol·kg-1)以及混合水溶液(离子强度0.5～9.5mol·kg-1)的水活度和渗透系数.该体系的等水活度线与Zdanovskii规则非理想混合溶液表达式的标准偏差为0.0088,当Li2SO4溶液达到饱和后,用Zdanovskii规则扩展式计算,标准偏差为0.0027.根据Pitzer离子相互作用模型对实验数据进行了理论分析,用本文和不同来源的文献数据拟合求取了0℃下该体系的Pitzer纯盐参数和混合参数,计算值与实验值相吻合.     

Compatibility of activity coefficients estimated experimentally and by Pitzer equations for the assessment of seawater pH

Calibration of pH meters is usually performed with reference pH buffer solutions of low ionic strength, I ≤ 0.1 mol kg^?1. For seawater pH measurements (I ≈ 0.7 mol kg^?1), calibration buffers in high ionic strength matrix are required. The Harned cell, in association with the Nernst equation and a model for estimating the chloride ion activity coefficient, \(\gamma_{{{\text{Cl}}^{ - } }} ,\) is the basis of the primary method for pH assignment to reference pH buffers. The semi-empirical Pitzer model is, in principle, adequate to estimate \(\gamma_{{{\text{Cl}}^{ - } }}\) of complex solutions, namely seawater. Nevertheless, no assessment of the validity of the model for this matrix is known to the authors. This work aims at estimating the adequacy of the Pitzer model by assessing the metrological compatibility of mean activity coefficients, in this case \(\gamma_{ \pm } = \sqrt {\gamma_{{{\text{H}}^{ + } }} \gamma_{{{\text{Cl}}^{ - } }} }\) estimated experimentally with the Harned cell, \(\gamma_{ \pm }^{\text{Exp}} ,\) and using the Pitzer model, \(\gamma_{ \pm }^{\text{Ptz}}\). The measurement uncertainty considered in the compatibility test was estimated using the bottom-up approach, where components were combined by the numerical Kragten method after checking its adequacy. The compatibility of the estimated \(\gamma_{ \pm }\) was assessed for solutions with increasing complexity and an ionic strength of 0.67 mol kg^–1. \(\gamma_{ \pm }^{\text{Exp}}\) and \(\gamma_{ \pm }^{Ptz}\) are metrologically compatible for a confidence level of 95 % where the relative standard uncertainty of their difference ranged from 1.1 % to 3.1 % in all chloride solutions to approximately 6.3 % when sodium sulfate was also present. This led to assume the validity of the Pitzer model equations to estimate \(\gamma_{{{\text{Cl}}^{ - } }} ,\) required to define reference pH values of buffer solutions with high ionic strength.     

Monitoring the traceability of the pH of a primary tetraborate buffer: comparison of results from primary and secondary apparatus

This paper reports evaluation of the behaviour of different combined glass electrodes applied to measurement of the pH of a primary, 0.01 mol kg⁻¹, tetraborate buffer. Measurements were first performed by use of a primary Harned cell (at 15, 25, and 37 °C); these results were then compared with those obtained for the same solution by use of three combined glass electrodes (25 °C) with different membranes and liquid-junction designs, calibrated by use of commercial pH-metric buffers. The pH of the same solution was also measured in terms of the molal concentration of hydrogen ions, using acid–base titration to evaluate the formal potential difference K of each cell at fixed ionic strength, I, adjusted by addition of KCl or Et₄NI (tetraethylammonium iodide). The reference value from primary measurement, paH = 9.171, was slightly closer to the mean value obtained by determination of concentration, rather than that obtained by direct measurement of activity; the differences were smaller than the extended uncertainty characteristics of the secondary measurements. The importance of evaluation of the ionic strength of the solution under study is emphasised. We verified that for tetraborate buffer slight modification of the value of I used to calculate γ _i (the activity coefficient of a single ion) in the calculation of paH from the acidity function at zero molality of chloride can significantly affect the reference value of the calibrator tool. This is true, in general, for low values of the ionic strength, such as those considered in this work; an approximate value of I can then cause distortions along the pH traceability chain. Application of the concepts of thermodynamics to this traceability chain is discussed.     

Thermodynamic Properties of {NaCl-CsCl-LiCl}(aq) at T=298.15 K: Water Activities, Osmotic and Activity Coefficients

A hygrometric method has been used to measure water activities for the quaternary aqueous system NaCl-CsCl-LiCl-H₂O as a function of the solutes concentrations at T=298.15 K. The measurements were performed by measuring the diameter of solution droplets as a function of the surrounding relative humidity. The total ionic strength range covered in this study was about 0.6 to 6 mol?kg^?1 for different ionic strength fractions y of one of the three solutes ranging from y=1/3 to 1/2, whereas the constant ratio r of molalities of the two other solutes was fixed at unity. The osmotic coefficients of these aqueous mixtures were calculated over this ionic strength range. The obtained data were treated by the ECA I and ECA II rules, and the Pitzer and Kim, and Pitzer-Dinane models. The solute activity coefficients of components in the studied mixtures were also determined for different ionic strength fractions of the different solutes.     

电动势法对LiCl-MgCl2-H2O体系热力学性质的研究

用自制的锂离子选择电极和经典的Ag-AgCl电极, 以电动势法测定了25 ℃时离子强度为0.05—6.0 mol·kg~(-1)范围的LiCl-MgCl_2-H_2O三元体系中LiCl的平均活度系数. 由实验数据, 求出了Pitzer方程、Harned方程和Scatchard方程的参数和系数. 用上述方程计算了LiCl 在该体系中的活度系数, 并与实验值进行比较, 标准偏差小于0.008. 与等压法测定的渗透系数拟合的Pitzer方程参数计算值比较在实验误差范围内. 同时计算了MgCl_2在该体系中的平均活度系数和混合溶液的渗透系数.     

Determination of thermodynamic properties of aqueous mixtures of RbCl and Rb2SO4 by the EMF method at T=298.15 K

The thermodynamic properties, including activity coefficients, osmotic coefficients and excess Gibbs free energy for RbCl and Rb₂SO₄ aqueous mixtures at T=298.15 K and in 0.01 mol · kg⁻¹ to 5 mol · kg⁻¹ ionic strength, were determined by emf measurements. The Rb–ISE and Ag–AgCl electrodes used in this work were prepared in our laboratory and had a reasonably good Nernst response. The experimental data were fitted by using the Harned rule and Pitzer model. The Harned coefficients and the Pitzer binary and ternary interaction parameters for the system have been evaluated. The experimental results obey the Harned rule. The Pitzer model can be used to describe this aqueous system satisfactorily.     

Uses of pH electrodes in nuclear chemistry

The determination and definition of pH is a controversial subject in many areas in chemistry. For these reasons the International Union of Pure and Applied Chemistry (IUPAC) has developed recommendations for pH measurement. These recommendations are currently (winter 2001) under revision - there will be increased emphasis on traceability of uncertainties in pH measurement. Here we describe how glass electrodes designed for measurement of pH are used in nuclear chemistry. The use of pH electrodes is then related to the IUPAC recommendations. In applied chemistry, e.g. nuclear chemistry, a pH is not sought as often as a hydrogen ion concentration or a simple equilibrium point during a titration. Ionic strengths are, moreover, often above the range in which the IUPAC recommendations apply. In these instances uncertainties must be assessed individually.     

用电势法测定混合电解质NaCl-Me4NCl-H2O体系在298．15K的活度系数

用电势法测定混合电解质ＮａＣｌ－Ｍｅ_４ＮＣｌ－Ｈ_２Ｏ体系在２９８．１５Ｋ的活度系数阎卫东,姚加,韩世钧,徐奕瑾（浙江大学化学系,杭州,３１００２７）关键词含季铵盐混合电解质,活度系数,渗透系数作为电解质溶液热力学研究工作［１］的继续,本文选择了含季...     

The history and development of a rigorous metrological basis for pH measurements

This paper discusses the basis and historical development of the traceability chain for pH. The quantity pH, first introduced in 1909, is among the most frequently measured analytical quantities. The practical measurement of the pH value of a sample is inexpensive, easy to perform, and yields a rapid result. However, the problems posed by the traceability of pH are not easy to solve. Most pH measurements are performed by potentiometry, using a glass electrode as the pH sensor. Such pH electrodes must be calibrated at regular intervals. Confidence in the reliability of pH measurements requires establishment of a metrological hierarchy including an uncertainty budget for calibration that links the pH measured in the sample to an internationally agreed and stated reference. For pH, this reference is the primary measurement of pH. A traceability chain can be established that links field measurements of pH to primary buffer solutions that are certified using this primary method. This allows the user in the field to estimate the measurement uncertainty of the measured pH data. As the realization of the primary measurement is sophisticated and time-consuming, primary standards are generally realized at national metrology institutes. A number of potentiometric methods are suitable for the determination of the pH of reference buffer solutions by comparison with the primary standard buffers. The choice between the methods should be made according to the uncertainty required for the application. For reference buffer solutions that have the same nominal composition as the primary standard, the differential potentiometric cell, often called the Baucke cell, is recommended.     

Specific ionic interactions in the quaternary systems HCl−NaCl−KCl-water and HCl−NH4Cl−KCl-water at 25°C

Mean ionic activity coefficients of hydrochloric acid in the systems HCl–NaCl–KCl-water and HCl–NH₄Cl–KCl-water at constant total ionic strength of 1 mole-kg^–1 have been determined for various ratios of the added salts at 25°C. The electromotive force method was used. Both an extended form of the simple empirical Harned equations (see ref. 1) and the more complicated semiempirical Pitzer equations (see refs. 2–4) for multicomponent electrolyte systems were used in the treatment of the data. Specific ionic interaction parameters for both types of equations are reported. The effects of the added salts on the thermodynamic behavior of HCl in the two systems mentioned were compared by considering the variation of its trace activity coefficient with change in amounts of the added salts at constant total ionic strength of 1 mole-kg^–1.     

The protonation constant of triethanolamine in KBr and KNO3 solutions at 25°C

We determined the stoichiometric acid-base constants of triethanolamine at 25°C in KBr and KNO₃ at different ionic strengths by the potentiometric technique using glass electrodes sensitive to the H⁺ ion. By applying the Pitzer equations for the activity coefficients of the species present in the medium we obtained equations accounting for the dependency of pK on the ionic strength. The coefficients thus obtained are critically analyzed.     

Improved traceability of pH measurements

Traceability is a prerequisite for the comparability and uniformity of measurements. Although pH-measurements are carried out on a large scale in laboratory and industry, the problems involved in the traceability of pH values have not adequately been solved in the past. The comparability of pH measurements is limited, among other parameters, by the accuracy of the pH values of the standard buffer solutions used to calibrate the pH meter-electrode assemblies. The measured pH(X) value must be traceable to primary standard pH(PS) values through an unbroken chain of comparisons, all values having stated uncertainties. A new primary standard measurement device for pH is used to certify primary pH reference materials from which these secondary reference materials can be derived.