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.     

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

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.     

Derived measurement standards of reduced uncertainty – A contradiction?

 If the value of a derived measurement standard is assigned by comparison with a reference standard of the same quantity, the uncertainty is increased by the additional uncertainty on the difference measurement. This basic fact has lead to the general belief that the uncertainty of derived standards is always larger than that of the reference standards. However, if the value of a derived standard is assigned by comparison with several independent reference standards using an appropriate average, the increase of uncertainty due to the uncertainty on difference measurement may be counterbalanced by the the well-known decrease of uncertainty through averaging. The gain of accuracy made possible by this mechanism is restricted to second-generation standards. Further gain through iteration is prevented by correlation between standards derived from the same set of reference standards. As a consequence, the concept of metrological hierarchy levels, relating to traceability chains, becomes questionable for traceability networks.     

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.     

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.     

Determination of pH values over the temperature range –60°C for some operational reference standard solutins and values of the conventional residual liquid-junction potentials

Direct measurements of the pH of six new operational standard solutions for the British Standard pH scale are reported from measurements with hydrogen gas electrodes in cells with liquid junctions reproducibly formed in vertical capillary tubes (1 mm internal diameter). Comparison with assigned pH values from cells without liquid junction enables values of the conventional residual liquid-junction potential to be calculated.     

Estimation of uncertainty in routine pH measurement

A procedure for estimation of measurement uncertainty of routine pH measurement (pH meter with two-point calibration, with or without automatic temperature compensation, combination glass electrode) based on the ISO method is presented. It is based on a mathematical model of pH measurement that involves nine input parameters. Altogether 14 components of uncertainty are identified and quantified. No single uncertainty estimate can be ascribed to a pH measurement procedure: the uncertainty of pH strongly depends on changes in experimental details and on the pH value itself. The uncertainty is the lowest near the isopotential point and in the center of the calibration line and can increase by a factor of 2 (depending on the details of the measurement procedure) when moving from around pH 7 to around pH 2 or 11. Therefore it is necessary to estimate the uncertainty separately for each measurement. For routine pH measurement the uncertainty cannot be significantly reduced by using more accurate standard solutions than ±0.02 pH units – the uncertainty improvement is small. A major problem in estimating the uncertainty of pH is the residual junction potential, which is almost impossible to take rigorously into account in the framework of a routine pH measurement.¹ Received: 11 August 2001 Accepted: 22 February 2002     

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.     

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.     

The Japanese traceability system and the role of uncertainty evaluation in measurement

 The new traceability system of measurement standards based on the Japanese Measurement Law has been established since November 1993. Some reference materials such as metal standard solutions, pH standard solutions and standard gas mixtures are included in the system together with relevant physical quantities. In this system, primary measurement standard instruments or primary reference materials are designated by the regulation for each quantity. For the practical dissemination of each quantity, accreditation of calibration bodies is recognized by the steering committee under the supervision of the government. In the course of assessment of a candidate calibration body, the concepts of ISO/IEC Guide 25 and ISO/IEC Guide 58 are effectively introduced. For the estimation of reliability, the concept of how to introduce the statistical approach is effectively considered. The method of uncertainty evaluation described in the ISO document entitled "Guide to the expression of uncertainty in measurement" is adopted.     

Development of metrology for pH measurement in Thailand

It has not been long that metrology is well accepted as an important part in analytical chemistry since it helps the chemists to receive the best measurement and accurate results with traceability. The National Institute of Metrology Thailand (NIMT), which is a public agency under the supervision of the Ministry of Science and Technology, not only focuses on physical standards but also provides and maintains standards in chemical field. pH measurement is one of the most widely used in the laboratories including industries and medical area in Thailand. The chemical laboratory starts working on the project with the objective of disseminating an accurate result in routine pH measurement. In 2002, the laboratory provided a service in calibration of pH meter and organized the first local interlaboratory comparison program (NIMT–C-ILC-1: pH buffer) in pH measurement. There were three buffer solution samples in the range of acid, neutral, and base. A total of 44 laboratories participated in this program. The NIMT chemical laboratory also participated in the proficiency testing program that was conducted by PSB Corporation Testing Group in Singapore. In 2003, NIMT started research in preparation of secondary buffers by using highly accurate pH meters with glass electrode systems. The laboratory produced three secondary buffers, which were pH 4.01, 6.86, and 9.18 with uncertainty 0.020 pH at 25°C. The competence of the laboratory was shown by the measurement results of the pilot study (APMP.QM-P06), which was organized by the APMP electrochemical analysis working group (EAWG/TCQM) in 2005. The title of this study was “pH determination of two phosphate buffers by Harned cell method and glass electrode method”. NIMT aims to achieve for establishment of the primary method for pH measurement in the near future. Presented at -- “BERM-10” -- April 2006, Charleston, SC, USA     

Establishment of traceability of ammonium nitrogen determination in wastewater

A case study is presented for the establishment of traceability for ammonium nitrogen determination in wastewater in a routine laboratory in order to fulfil the requirements of ISO/IEC standard 17025. The necessary relevant information was obtained from the method validation data, the quality control data and equipment calibration certificates. The method of measurement is described together with the measurement equation, selected traceable reference standards and the associated measurement uncertainty. The major sources of uncertainty of the result of measurement were identified and the combined uncertainty was calculated. Identification of the main uncertainty sources represents the basis for target operations for reducing the measurement uncertainty of this determination.     

Lifetime of the traceability chain in chemical measurement

Since the uncertainty of each link in the traceability chain (measuring analytical instrument, reference material or other measurement standard) changes over the course of time, the chain lifetime is limited. The lifetime in chemical analysis is dependent on the calibration intervals of the measuring equipment and the shelf-life of the certified reference materials (CRMs) used for the calibration of the equipment. It is shown that the ordinary least squares technique, used for treatment of the calibration data, is correct only when uncertainties in the certified values of the measurement standards or CRMs are negligible. If these uncertainties increase (for example, close to the end of the calibration interval or shelf-life), they are able to influence significantly the calibration and measurement results. In such cases regression analysis of the calibration data should take into account that not only the response values are subjects to errors, but also the certified values. As an end-point criterion of the traceability chain destruction, the requirement that the uncertainty of a measurement standard should be a source of less then one-third of the uncertainty in the measurement result is applicable. An example from analytical practice based on the data of interlaboratory comparisons of ethanol determination in beer is discussed. Received: 5 October 2000 Accepted: 3 December 2000     

Basic equations and uncertainties in isotope-dilution mass spectrometry for traceability to SI of values obtained by this primary method

A current interest in chemistry concerns traceability of analytical measurements to the International System of Units (SI) and the estimation of their uncertainties in accordance with principles of metrology, that is, measurement science. “Primary methods of measurement” achieve traceability to SI directly without intermediate reference standards or materials and without significant empirical correction factors. Isotope-dilution mass spectrometry should be regarded as such a method. It has the potential of smallest presently achievable uncertainties for analytical measurements directly or for the certification of reference materials including those with abnormal isotopic composition. A simple explanation of the method including its basic equations is given. Full uncertainty estimation is emphasized in terms of these equations. The wider use of concepts of metrology in chemistry is discussed.     

Meeting the measurement uncertainty and traceability requirements of ISO/IEC standard 17025 in chemical analysis

The new laboratory accreditation standard, ISO/IEC 17025, reflects current thinking on good measurement practice by requiring more explicit and more demanding attention to a number of activities. These include client interactions, method validation, traceability, and measurement uncertainty. Since the publication of the standard in 1999 there has been extensive debate about its interpretation. It is the author's view that if good quality practices are already in place and if the new requirements are introduced in a manner that is fit for purpose, the additional work required to comply with the new requirements can be expected to be modest. The paper argues that the rigour required in addressing the issues should be driven by customer requirements and the factors that need to be considered in this regard are discussed. The issues addressed include the benefits, interim arrangements, specifying the analytical requirement, establishing traceability, evaluating the uncertainty and reporting the information.     

Traceability system for elemental analysis

A complete metrological traceability system for measurement results of chemical analysis was set up. Core components are pure substances (national standards) characterised at the highest metrological level, primary solutions prepared from these pure substances and secondary solutions deduced from the primary solutions and intended for sale. The relative uncertainty of the element mass fraction of the primary substances and solutions is < 0.01 and < 0.05%, respectively. For the certification of transfer solutions and for stability testing, a precision measurement method for element contents has been developed by means of optical emission spectrometry (ICP OES) by which uncertainties between 0.1 and 0.05% can be achieved. The dissemination to field laboratories is effected with the aid of a calibration laboratory of the German Calibration Service (DKD) which certifies the element content of the secondary solutions with an uncertainty ≤ 0.3%. Calibration with these solutions enables the user to establish traceability of his measurement results to the International System of Units (SI). Currently, the system comprises Cu, Fe, Bi, Ga, Si, Na, K, Sn, W, and Pb.     

Practical estimation of the uncertainty of analytical measurement standards

Nowadays, a lot of time and resources are used to determine the quality of goods and services. As a consequence, the quality of measurements themselves, e.g., the metrological traceability of the measured quantity values is essential to allow a proper evaluation of the results with regard to specifications and regulatory limits. This requires knowledge of the measurement uncertainties of all quantity values involved in the measurement procedure, including measurement standards. This study shows how the uncertainties due to the preparation, as well as the chemical and compositional stability of a chemical measurement standard, or calibrator, can be estimated. The results show that the relative standard uncertainty of the concentration value of a typical analytical measurement standard runs up to 2.8% after 1 year. Of this, 1.9% originates from the preparation of the measurement standard, while 2.0 and 0.53% originate from the chemical and compositional stability during storage at −20 °C. The monthly preparation of working calibrators stored at 4 °C and used on a weekly basis, results in an additional standard uncertainty of the analyte concentration value of 0.35% per month due to compositional stability. While the preparation procedure is the major contributor to the total measurement uncertainty, the uncertainties introduced by the stability measurements are another important contributor, and therefore, the measurement procedure to evaluate stability is important to minimize the total measurement uncertainty.     

From total allowable error via metrological traceability to uncertainty of measurement of the unbiased result

The concept of "total allowable error", investigated by Westgard and co-workers over a quarter of a century for use in laboratory medicine, comprises bias as well as random elements. Yet, to minimize diagnostic misclassifications, it is necessary to have spatio-temporal comparability of results. This requires trueness obtained through metrological traceability based on a calibration hierarchy. Hereby, the result is associated with a final uncertainty of measurement purged of known biases of procedure and laboratory. The sources of bias are discussed and the importance of commutability of calibrators and analytical specificity of the measurement procedure is stressed. The practicability of traceability to various levels and the advantages of the GUM approach for estimating uncertainty are shown.     

Buffer Standards for the Physiological pH of the Zwitterionic Compound, ACES, from 5 to 55 °C

The values of the second dissociation constant, pK ₂, and related thermodynamic quantities of [N-(2-acetamido)-2-aminoethanesulfonic acid] (ACES) have already been reported over the temperature range 5 to 55 °C including 37 °C. This paper reports the pa _H values of four chloride ion free buffer solutions and eight buffer solutions with I=0.16 mol⋅kg⁻¹, matching closely that of the physiological sample. Conventional pa _H values for all twelve buffer solutions from 5 to 55 °C are reported. The residual liquid-junction potential correction for two widely used temperatures, 25 and 37 °C, has been made. The flowing-junction calomel cell method has been utilized to measure E _j , the liquid-junction potential. The operational pH values for four buffer solutions at 25 and 37 °C are calculated using the physiological phosphate buffer standard based on the NBS/NIST convention. These solutions are recommended as pH standards in the pH range of 6.8 to 7.2 for physiological fluids.     

Influence of buffer quality on pH measurement uncertainty: prediction and experimental evaluation

Dependence of the uncertainty of a pH measurement result on the quality of buffers (i.e. the uncertainty of their certified pH values) at different levels of instrumental uncertainty (pH-meter, etc.) was simulated using the Monte Carlo method and regression analysis. The contribution of the instrumental standard uncertainty (in the studied range from 0.1 to 1 mV) to the uncertainty of the pH measurement result is negligible, if the standard uncertainties of the pH buffers exceed 0.04 pH (e. g. for in-house buffers). It is shown how the choice of pH-meter and buffers should be correlated in order to meet the required uncertainty of a pH measurement result in a sample under analysis. The results of the simulation were compared with experimental data obtained from calibrations of a pH/ion-meter with a hydrogen working electrode (Radiometer PHM-240) and with a glass electrode (Metrohm 744). Buffers of different quality (National Institute for Standards and Technology standard reference materials, certified Radiometer buffers and Merck CertiPUR buffers) were used for the calibrations. The uncertainties of the experimental results are close to the predicted ones obtained by the simulation. Received: 16 June 2002 Accepted: 19 July 2002 Presented at the 14^th International Conference of the Israel Society for Quality, 18–21 November 2002, Jerusalem, Israel Correspondence to I. Kuselman