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Pure Appl. Chem., Vol. 74, No. 11, pp. 2169­2200, 2002. © 2002 IUPAC INTERNATIONAL UNION OF PURE AND APPLIED CHEMISTRY

MEASUREMENT OF pH. DEFINITION, STANDARDS, AND PROCEDURES
(IUPAC Recommendations 2002)
Working Party on pH R. P. BUCK (CHAIRMAN)1, S. RONDININI (SECRETARY)2,, A. K. COVINGTON (EDITOR)3, F. G. K. BAUCKE4, C. M. A. BRETT5, M. F. CAMóES6, M. J. T. MILTON7, T. MUSSINI8, R. NAUMANN9, K. W. PRATT10, P. SPITZER11, AND G. S. WILSON12 101 Creekview Circle, Carrboro, NC 27510, USA; 2Dipartimento di Chimica Fisica ed Elettrochimica, UniversitÞ di Milano, Via Golgi 19, I-20133 Milano, Italy; 3Department of Chemistry, The University, Bedson Building, Newcastle Upon Tyne, NE1 7RU, UK; 4Schott Glasswerke, P.O. Box 2480, D-55014 Mainz, Germany; 5Departamento de QuÌmica, Universidade de Coimbra, P-3004-535 Coimbra, Portugal; 6Departamento de QuÌmica e Bioquimica, University of Lisbon (SPQ/DQBFCUL), Faculdade de Ciencias, Edificio CI-5 Piso, P-1700 Lisboa, Portugal; 7National Physical Laboratory, Centre for Optical and Environmental Metrology, Queen's Road, Teddington, Middlesex TW11 0LW, UK; 8Dipartimento di Chimica Fisica ed Elettrochimica, UniversitÞ di Milano, Via Golgi 19, I-20133 Milano, Italy; 9MPI for Polymer Research, Ackermannweg 10, D-55128 Mainz, Germany; 10Chemistry B324, Stop 8393, National Institute of Standards and Technology, 100 Bureau Drive, ACSL, Room A349, Gaithersburg, MD 20899-8393, USA; 11Physikalisch-Technische Bundesanstalt (PTB), Postfach 33 45, D-38023 Braunschweig, Germany; 12Department of Chemistry, University of Kansas, Lawrence, KS 66045, USA
1



Corresponding author

Republication or reproduction of this report or its storage and/or dissemination by electronic means is permitted without the need for formal IUPAC permission on condition that an acknowledgment, with full reference to the source, along with use of the copyright symbol ©, the name IUPAC, and the year of publication, are prominently visible. Publication of a translation into another language is subject to the additional condition of prior approval from the relevant IUPAC National Adhering Organization.

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Measurement of pH. Definition, standards, and procedures
(IUPAC Recommendations 2002)
Abstract: The definition of a "primary method of measurement" [1] has permitted a full consideration of the definition of primary standards for pH, determined by a primary method (cell without transference, Harned cell), of the definition of secondary standards by secondary methods, and of the question whether pH, as a conventional quantity, can be incorporated within the internationally accepted system of measurement, the International System of Units (SI, SystÕme International d'UnitÈs). This approach has enabled resolution of the previous compromise IUPAC 1985 Recommendations [2]. Furthermore, incorporation of the uncertainties for the primary method, and for all subsequent measurements, permits the uncertainties for all procedures to be linked to the primary standards by an unbroken chain of comparisons. Thus, a rational choice can be made by the analyst of the appropriate procedure to achieve the target uncertainty of sample pH. Accordingly, this document explains IUPAC recommended definitions, procedures, and terminology relating to pH measurements in dilute aqueous solutions in the temperature range 5­50 °C. Details are given of the primary and secondary methods for measuring pH and the rationale for the assignment of pH values with appropriate uncertainties to selected primary and secondary substances. CONTENTS 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. INTRODUCTION AND SCOPE ACTIVITY AND THE DEFINITION OF pH TRACEABILITY AND PRIMARY METHODS OF MEASUREMENT HARNED CELL AS A PRIMARY METHOD FOR ABSOLUTE MEASUREMENT OF pH SOURCES OF UNCERTAINTY IN THE USE OF THE HARNED CELL PRIMARY BUFFER SOLUTIONS AND THEIR REQUIRED PROPERTIES CONSISTENCY OF PRIMARY BUFFER SOLUTIONS SECONDARY STANDARDS AND SECONDARY METHODS OF MEASUREMENT CONSISTENCY OF SECONDARY BUFFER SOLUTIONS ESTABLISHED WITH RESPECT TO PRIMARY STANDARDS TARGET UNCERTAINTIES FOR MEASUREMENT OF SECONDARY BUFFER SOLUTIONS CALIBRATION OF pH METER-ELECTRODE ASSEMBLIES AND TARGET UNCERTAINTIES FOR UNKNOWNS GLOSSARY ANNEX: MEASUREMENT UNCERTAINTY SUMMARY OF RECOMMENDATIONS REFERENCES

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Measurement of pH ABBREVIATIONS USED BIPM CRMs EUROMET NBS NIST NMIs PS LJP RLJP SS Bureau International des Poids et Mesures, France certified reference materials European Collaboration in Metrology (Measurement Standards) National Bureau of Standards, USA, now NIST National Institute of Science and Technology, USA national metrological institutes primary standard liquid junction potential residual liquid junction potential secondary standard

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1 INTRODUCTION AND SCOPE 1.1 pH, a single ion quantity The concept of pH is unique among the commonly encountered physicochemical quantities listed in the IUPAC Green Book [3] in that, in terms of its definition [4], pH = -lg aH it involves a single ion quantity, the activity of the hydrogen ion, which is immeasurable by any thermodynamically valid method and requires a convention for its evaluation. 1.2 Cells without transference, Harned cells As will be shown in Section 4, primary pH standard values can be determined from electrochemical data from the cell without transference using the hydrogen gas electrode, known as the Harned cell. These primary standards have good reproducibility and low uncertainty. Cells involving glass electrodes and liquid junctions have considerably higher uncertainties, as will be discussed later (Sections 5.1, 10.1). Using evaluated uncertainties, it is possible to rank reference materials as primary or secondary in terms of the methods used for assigning pH values to them. This ranking of primary (PS) or secondary (SS) standards is consistent with the metrological requirement that measurements are traceable with stated uncertainties to national, or international, standards by an unbroken chain of comparisons each with its own stated uncertainty. The accepted definition of traceability is given in Section 12.4. If the uncertainty of such measurements is calculated to include the hydrogen ion activity convention (Section 4.6), then the result can also be traceable to the internationally accepted SI system of units. 1.3 Primary pH standards In Section 4 of this document, the procedure used to assign primary standard [pH(PS)] values to primary standards is described. The only method that meets the stringent criteria of a primary method of measurement for measuring pH is based on the Harned cell (Cell I). This method, extensively developed by R. G. Bates [5] and collaborators at NBS (later NIST), is now adopted in national metrological institutes (NMIs) worldwide, and the procedure is approved in this document with slight modifications (Section 3.2) to comply with the requirements of a primary method.

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1.4 Secondary standards derived from measurements on the Harned cell (Cell I) Values assigned by Harned cell measurements to substances that do not entirely fulfill the criteria for primary standard status are secondary standards (SS), with pH(SS) values, and are discussed in Section 8.1. 1.5 Secondary standards derived from primary standards by measuring differences in pH Methods that can be used to obtain the difference in pH between buffer solutions are discussed in Sections 8.2­8.5 of these Recommendations. These methods involve cells that are practically more convenient than the Harned cell, but have greater uncertainties associated with the results. They enable the pH of other buffers to be compared with primary standard buffers that have been measured with a Harned cell. It is recommended that these are secondary methods, and buffers measured in this way are secondary standards (SS), with pH(SS) values. 1.6 Traceability This hierarchical approach to primary and secondary measurements facilitates the availability of traceable buffers for laboratory calibrations. Recommended procedures for carrying out these calibrations to achieve specified uncertainties are given in Section 11. 1.7 Scope The recommendations in this Report relate to analytical laboratory determinations of pH of dilute aqueous solutions (0.1 mol kg­1). Systems including partially aqueous mixed solvents, biological measurements, heavy water solvent, natural waters, and high-temperature measurements are excluded from this Report. 1.8 Uncertainty estimates The Annex (Section 13) includes typical uncertainty estimates for the use of the cells and measurements described. 2 ACTIVITY AND THE DEFINITION OF pH 2.1 Hydrogen ion activity pH was originally defined by SÜrensen in 1909 [6] in terms of the concentration of hydrogen ions (in modern nomenclature) as pH = -lg(cH/c°) where cH is the hydrogen ion concentration in mol dm­3, and c° = 1 mol dm­3 is the standard amount concentration. Subsequently [4], it has been accepted that it is more satisfactory to define pH in terms of the relative activity of hydrogen ions in solution pH = -lg aH = -lg(mHH/m°) (1) where aH is the relative (molality basis) activity and H is the molal activity coefficient of the hydrogen ion H+ at the molality mH, and m° is the standard molality. The quantity pH is intended to be a measure of the activity of hydrogen ions in solution. However, since it is defined in terms of a quantity that cannot be measured by a thermodynamically valid method, eq. 1 can be only a notional definition of pH.

© 2002 IUPAC, Pure and Applied Chemistry 74, 2169­2200


Measurement of pH 3 TRACEABILITY AND PRIMARY METHODS OF MEASUREMENT 3.1 Relation to SI

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Since pH, a single ion quantity, is not determinable in terms of a fundamental (or base) unit of any measurement system, there was some difficulty previously in providing a proper basis for the traceability of pH measurements. A satisfactory approach is now available in that pH determinations can be incorporated into the SI if they can be traced to measurements made using a method that fulfills the definition of a "primary method of measurement" [1]. 3.2 Primary method of measurement The accepted definition of a primary method of measurement is given in Section 12.1. The essential feature of such a method is that it must operate according to a well-defined measurement equation in which all of the variables can be determined experimentally in terms of SI units. Any limitation in the determination of the experimental variables, or in the theory, must be included within the estimated uncertainty of the method if traceability to the SI is to be established. If a convention is used without an estimate of its uncertainty, true traceability to the SI would not be established. In the following section, it is shown that the Harned cell fulfills the definition of a primary method for the measurement of the acidity function, p(aHCl), and subsequently of the pH of buffer solutions. 4 HARNED CELL AS A PRIMARY METHOD FOR THE ABSOLUTE MEASUREMENT OF pH 4.1 Harned cell The cell without transference defined by Pt | H2 | buffer S, Cl­ | AgCl | Ag Cell I known as the Harned cell [7], and containing standard buffer, S, and chloride ions, in the form of potassium or sodium chloride, which are added in order to use the silver­silver chloride electrode. The application of the Nernst equation to the spontaneous cell reaction:
1

/2H2 + AgCl Ag(s) + H+ + Cl­

yields the potential difference EI of the cell [corrected to 1 atm (101.325 kPa), the partial pressure of hydrogen gas used in electrochemistry in preference to 100 kPa] as EI = E° ­ [(RT/F)ln 10] lg[(mHH/m°)(mClCl/m°)] which can be rearranged, since aH = mHH/m°, to give the acidity function p(aHCl) = -lg(aHCl) = (EI ­ E°)/[(RT/F)ln 10] + lg(mCl/m°) (2) (2)

where E° is the standard potential difference of the cell, and hence of the silver­silver chloride electrode, and Cl is the activity coefficient of the chloride ion. Note 1: The sign of the standard electrode potential of an electrochemical reaction is that displayed on a high-impedance voltmeter when the lead attached to standard hydrogen electrode is connected to the minus pole of the voltmeter. The steps in the use of the cell are summarized in Fig. 1 and described in the following paragraphs.

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Fig. 1 Operation of the Harned cell as a primary method for the measurement of absolute pH.

The standard potential difference of the silver­silver chloride electrode, E°, is determined from a Harned cell in which only HCl is present at a fixed molality (e.g., m = 0.01 mol kg­1). The application of the Nernst equation to the HCl cell Pt | H2 | HCl(m) | AgCl | Ag gives Cell Ia

EIa = E° ­ [(2RT/F)ln 10] lg[(mHCl/m°)(±HCl)] (3) where EIa has been corrected to 1 atmosphere partial pressure of hydrogen gas (101.325 kPa) and ±HCl is the mean ionic activity coefficient of HCl. 4.2 Activity coefficient of HCl The values of the activity coefficient (±HCl) at molality 0.01 mol kg­1 and various temperatures are given by Bates and Robinson [8]. The standard potential difference depends in some not entirely understood way on the method of preparation of the electrodes, but individual determinations of the activity coefficient of HCl at 0.01 mol kg­1 are more uniform than values of E°. Hence, the practical determination of the potential difference of the cell with HCl at 0.01 mol kg­1 is recommended at 298.15 K at which the mean ionic activity coefficient is 0.904. Dickson [9] concluded that it is not necessary to © 2002 IUPAC, Pure and Applied Chemistry 74, 2169­2200


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repeat the measurement of E° at other temperatures, but that it is satisfactory to correct published smoothed values by the observed difference in E° at 298.15 K. 4.3 Acidity function In NMIs, measurements of Cells I and Ia are often done simultaneously in a thermostat bath. Subtracting eq. 3 from eq. 2 gives E = EI ­ EIa = -[(RT/F)ln 10]{lg[(mHH/m°)(mClCl/m°)] - lg[(mHCl/m°)2 2±HCl]}, (4) which is independent of the standard potential difference. Therefore, the subsequently calculated pH does not depend on the standard potential difference and hence does not depend on the assumption that the standard potential of the hydrogen electrode, E°(H+|H2) = 0 at all temperatures. Therefore, the Harned cell can give an exact comparison between hydrogen ion activities at two different temperatures (in contrast to statements found elsewhere, see, for example, ref. [5]). The quantity p(aHCl) = -lg(aHCl), on the left-hand side of eq. 2, is called the acidity function [5]. To obtain the quantity pH (according to eq. 1), from the acidity function, it is necessary to evaluate lg Cl by independent means. This is done in two steps: (i) the value of lg(aHCl) at zero chloride molality, lg(aHCl)°, is evaluated and (ii) a value for the activity of the chloride ion °Cl , at zero chloride molality (sometimes referred to as the limiting or "trace" activity coefficient [9]) is calculated using the Bates­Guggenheim convention [10]. These two steps are described in the following paragraphs. 4.4 Extrapolation of acidity function to zero chloride molality The value of lg(aHCl)° corresponding to zero chloride molality is determined by linear extrapolation of measurements using Harned cells with at least three added molalities of sodium or potassium chloride (I < 0.1 mol kg­1, see Sections 4.5 and 12.6) -lg(aHCl) = -lg(aHCl)° + SmCl, (5) where S is an empirical, temperature-dependent constant. The extrapolation is linear, which is expected from BrÜnsted's observations [11] that specific ion interactions between oppositely charged ions are dominant in mixed strong electrolyte systems at constant molality or ionic strength. However, these acidity function measurements are made on mixtures of weak and strong electrolytes at constant buffer molality, but not constant total molality. It can be shown [12] that provided the change in ionic strength on addition of chloride is less than 20 %, the extrapolation will be linear without detectable curvature. If the latter, less-convenient method of preparation of constant total molality solutions is used, Bates [5] has reported that, for equimolal phosphate buffer, the two methods extrapolate to the same intercept. In an alternative procedure, often useful for partially aqueous mixed solvents where the above extrapolation appears to be curved, multiple application of the Bates­Guggenheim convention to each solution composition gives identical results within the estimated uncertainty of the two intercepts. 4.5 Bates­Guggenheim convention The activity coefficient of chloride (like the activity coefficient of the hydrogen ion) is an immeasurable quantity. However, in solutions of low ionic strength (I < 0.1 mol kg­1), it is possible to calculate the activity coefficient of chloride ion using the Debye­HÝckel theory. This is done by adopting the Bates­Guggenheim convention, which assumes the trace activity coefficient of the chloride ion °Cl is given by the expression [10]. lg °Cl = -A I / /(1 + Ba I / )
1 2 1 2

(6)

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where A is the Debye­HÝckel temperature-dependent constant (limiting slope), a is the mean distance of closest approach of the ions (ion size parameter), Ba is set equal to 1.5 (mol kg­1)­1/2 at all temperatures in the range 5­50 °C, and I is the ionic strength of the buffer (which, for its evaluation requires knowledge of appropriate acid dissociation constants). Values of A as a function of temperature can be found in Table A-6 and of B, which is effectively unaffected by revision of dielectric constant data, in Bates [5]. When the numerical value of Ba = 1.5 (i.e., without units) is introduced into eq. 6 it should be written as lg °Cl = -AI / /[1 + 1.5 (I/m°) / ] (6) The various stages in the assignment of primary standard pH values are combined in eq. 7, which is derived from eqs. 2, 5, 6,
1 2 1 2

pH(PS) = lim mCl0 {(EI ­ E°)/[(RT/F)ln 10] + lg(mCl/m°)} - AI / /[1 + 1.5 (I/m°) / ], and the steps are summarized schematically in Fig. 1.
1 2 1 2

(7)

5 SOURCES OF UNCERTAINTY IN THE USE OF THE HARNED CELL 5.1 Potential primary method and uncertainty evaluation The presentation of the procedure in Section 4 highlights the fact that assumptions based on electrolyte theories [7] are used at three points in the method: i. The Debye­HÝckel theory is the basis of the extrapolation procedure to calculate the value for the standard potential of the silver­silver chloride electrode, even though it is a published value of ±HCl at, e.g., m = 0.01 mol kg­1, that is recommended (Section 4.2) to facilitate E° determination. Specific ion interaction theory is the basis for using a linear extrapolation to zero chloride (but the change in ionic strength produced by addition of chloride should be restricted to no more than 20 %). The Debye­HÝckel theory is the basis for the Bates­Guggenheim convention used for the calculation of the trace activity coefficient, °Cl.

ii.

iii.

In the first two cases, the inadequacies of electrolyte theories are sources of uncertainty that limit the extent to which the measured pH is a true representation of lg aH. In the third case, the use of eq. 6 or 7 is a convention, since the value for Ba is not directly determinable experimentally. Previous recommendations have not included the uncertainty in Ba explicitly within the calculation of the uncertainty of the measurement. Since eq. 2 is derived from the Nernst equation applied to the thermodynamically well-behaved platinum­hydrogen and silver­silver chloride electrodes, it is recommended that, when used to measure ­lg(aHCl) in aqueous solutions, the Harned cell potentially meets the agreed definition of a primary method for the measurement. The word "potentially" has been included to emphasize that the method can only achieve primary status if it is operated with the highest metrological qualities (see Sections 6.1­6.2). Additionally, if the Bates­Guggenheim convention is used for the calculation of lg °Cl , the Harned cell potentially meets the agreed definition of a primary method for the measurement of pH, subject to this convention if a realistic estimate of its uncertainty is included. The uncertainty budget for the primary method of measurement by the Harned cell (Cell I) is given in the Annex, Section 13. Note 2: The experimental uncertainty for a typical primary pH(PS) measurement is of the order of 0.004 (see Table 4).

© 2002 IUPAC, Pure and Applied Chemistry 74, 2169­2200


Measurement of pH 5.2 Evaluation of uncertainty of the Bates­Guggenheim convention

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In order for a measurement of pH made with a Harned cell to be traceable to the SI system, an estimate of the uncertainty of each step must be included in the result. Hence, it is recommended that an estimate of the uncertainty of 0.01 (95% confidence interval) in pH associated with the Bates­Guggenheim convention is used. The extent to which the Bates­Guggenheim convention represents the "true" (but immeasurable) activity coefficient of the chloride ion can be calculated by varying the coefficient Ba between 1.0 and 2.0 (mol kg­1)1/2. This corresponds to varying the ion-size parameter between 0.3 and 0.6 nm, yielding a range of ±0.012 (at I = 0.1 mol kg­1) and ±0.007 (at I = 0.05 mol kg­1) for °Cl calculated using equation [7]. Hence, an uncertainty of 0.01 should cover the full extent of variation. This must be included in the uncertainty of pH values that are to be regarded as traceable to the SI. pH values stated without this contribution to their uncertainty cannot be considered to be traceable to the SI. 5.3 Hydrogen ion concentration It is rarely required to calculate hydrogen ion concentration from measured pH. Should such a calculation be required, the only consistent, logical way of doing it is to assume H = Cl and set the latter to the appropriate Bates­Guggenheim conventional value. The uncertainties are then those derived from the Bates­Guggenheim convention. 5.4 Possible future approaches Any model of electrolyte solutions that takes into account both electrostatic and specific interactions for individual solutions would be an improvement over use of the Bates­Guggenheim convention. It is hardly reasonable that a fixed value of the ion-size parameter should be appropriate for a diversity of selected buffer solutions. It is hoped that the Pitzer model of electrolytes [13], which uses a virial equation approach, will provide such an improvement, but data in the literature are insufficiently extensive to make these calculations at the present time. From limited work at 25 °C done on phosphate and carbonate buffers, it seems that changes to Bates­Guggenheim recommended values will be small [14]. It is possible that some anomalies attributed to liquid junction potentials (LJPs) may be resolved. 6 PRIMARY BUFFER SOLUTIONS AND THEIR REQUIRED PROPERTIES 6.1 Requisites for highest metrological quality In the previous sections, it has been shown that the Harned cell provides a primary method for the determination of pH. In order for a particular buffer solution to be considered a primary buffer solution, it must be of the "highest metrological" quality [15] in accordance with the definition of a primary standard. It is recommended that it have the following attributes [5: p. 95;16,17]: · · · · · · · · High buffer value in the range 0.016­0.07 (mol OH­)/pH Small dilution value at half concentration (change in pH with change in buffer concentration) in the range 0.01­0.20 Small dependence of pH on temperature less than ±0.01 K­1 Low residual LJP <0.01 in pH (see Section 7) Ionic strength 0.1 mol kg­1 to permit applicability of the Bates­Guggenheim convention NMI certificate for specific batch Reproducible purity of preparation (lot-to-lot differences of |pH(PS)| < 0.003) Long-term stability of stored solid material

Values for the above and other important parameters for the selected primary buffer materials (see Section 6.2) are given in Table 1. © 2002 IUPAC, Pure and Applied Chemistry 74, 2169­2200


Table 1 Summary of useful properties of some primary and secondary standard buffer substances and solutions [5].
Molecular formula Molality/ mol kg­1 Molar mass/ g mol­1 254.191 254.191 188.18 230.22 204.44 141.958 136.085 141.959 136.085 1.0075 1.0001 1.0013 0.9991 0.02025 0.04985 0.00998 0.02492 0.03032 1.179 1.0020 0.08665 4.302 0.07 3.3912 0.016 ­0.0028 1.0029 1.0017 1.0038 0.04958 0.04958 0.02492 11.41 10.12 3.5379 0.024 0.052 0.080 0.034 0.016 0.029 1.0032 1.0036 0.04965 0.034 12.620 6.4 0.186 0.049 0.070 0.027 1.0091 0.09875 25.101 0.001 ­0.0014 ­0.022 0.00012 ­0.0028 Density/ g dm­3 Amount conc. at 20 °C/ mol dm­3 Mass/g to make 1 dm3 Dilution value pH1/2 Buffer value ()/ mol OH­ dm­3 pH temperature coefficient/ K­1

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Salt or solid substance

Potassium tetroxalate dihydrate Potassium tetroxalate dihydrate
4O8·2H2O H4O6

C KHC4 0.05 0.05 0.025 0.025 0.03043 0.00869

KH3 KH3 0.05 0.0341

C4O8·2H2O

0.1

KH2C6H5O7 KHC8H4O4 Na2HPO4

KH2PO4

Na2HPO4

R. P. BUCK et al.

KH2PO4

Potassium hydrogen tartrate (sat. at 25 °C) Potassium dihydrogen citrate Potassium hydrogen phthalate Disodium hydrogen orthophosphate + potassium dihydrogen orthophosphate Disodium hydrogen orthophosphate + potassium dihydrogen orthophosphate Disodium tetraborate decahydrate Disodium tetraborate decahydrate Sodium hydrogen carbonate + sodium carbonate Calcium hydroxide (sat. at 25 °C) 0.05 0.01 0.025 0.025 0.0203 381.367 381.367 84.01 105.99 74.09 19.012 3.806 2.092 2.640 1.5 0.01 0.079 ­0.28 0.020 0.029 0.09

­0.0082 ­0.0096 ­0.033

© 2002 IUPAC, Pure and Applied Chemistry 74, 2169­2200

Na2B4O7·10H2O Na2B4O7·10H2O NaHCO3 Na2CO3 Ca(OH)2


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Note 3: The long-term stability of the solid compounds (>5 years) is a requirement not met by borax [16]. There are also doubts about the extent of polyborate formation in 0.05 mol kg­1 borax solutions, and hence this solution is not accorded primary status. 6.2 Primary standard buffers Since there can be significant variations in the purity of samples of a buffer of the same nominal chemical composition, it is essential that the primary buffer material used has been certified with values that have been measured with Cell I. The Harned cell has been used by many NMIs for accurate measurements of pH of buffer solutions. Comparisons of such measurements have been carried out under EUROMET collaboration [18], which have demonstrated the high comparability of measurements (0.005 in pH) in different laboratories of samples from the same batch of buffer material. Typical values of the pH(PS) of the seven solutions from the six accepted primary standard reference buffers, which meet the conditions stated in Section 6.1, are listed in Table 2. These listed pH(PS) values have been derived from certificates issued by NBS/NIST over the past 35 years. Batch-to-batch variations in purity can result in changes in the pH value of samples of at most 0.003. The typical values in Table 2 should not be used in place of the certified value (from a Harned cell measurement) for a specific batch of buffer material.
Table 2 Typical values of pH(PS) for primary standards at 0­50 °C (see Section 6.2).
Primary standards (PS) Sat. potassium hydrogen tartrate (at 25 °C) 0.05 mol kg­1 potassium dihydrogen citrate 0.05 mol kg­1 potassium hydrogen phthalate 0.025 mol kg­1 disodium hydrogen phosphate + 0.025 mol kg­1 potassium dihydrogen phosphate 3.863 3.840 3.820 3.802 3.788 0 5 10 15 20 Temp./oC 25 3.557 30 3.552 35 3.549 37 3.548 40 3.547 50 3.549

3.776

3.766

3.759

3.756

3.754

3.749

4.000

3.998

3.997

3.998

4.000

4.005

4.011

4.018

4.022

4.027

4.050

6.984

6.951

6.923

6.900

6.881

6.865

6.853

6.844

6.841

6.838

6.833

0.03043 mol kg­1 disodium hydrogen phosphate + 0.008695 mol kg­1 potassium 7.534 dihydrogen phosphate 0.01 mol kg­1 disodium tetraborate 0.025 mol kg­1 sodium hydrogen carbonate + 0.025 mol kg­1 sodium carbonate 9.464

7.500

7.472

7.448

7.429

7.413

7.400

7.389

7.386

7.380

7.367

9.395

9.332

9.276

9.225

9.180

9.139

9.102

9.088

9.068

9.011

10.317

10.245

10.179 10.118 10.062

10.012

9.966

9.926

9.910

9.889

9.828

The required attributes listed in Section 6.1 effectively limit the range of primary buffers available to between pH 3 and 10 (at 25 °C). Calcium hydroxide and potassium tetroxalate have been excluded because the contribution of hydroxide or hydrogen ions to the ionic strength is significant. Also excluded are the nitrogen bases of the type BH+ [such as tris(hydroxymethyl)aminomethane and © 2002 IUPAC, Pure and Applied Chemistry 74, 2169­2200


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piperazine phosphate] and the zwitterionic buffers (e.g., HEPES and MOPS [19]). These do not comply because either the Bates­Guggenheim convention is not applicable, or the LJPs are high. This means the choice of primary standards is restricted to buffers derived from oxy-carbon, -phosphorus, -boron, and mono, di-, and tri-protic carboxylic acids. In the future, other buffer systems may fulfill the requirements listed in Section 6.1. 7 CONSISTENCY OF PRIMARY BUFFER SOLUTIONS 7.1 Consistency and the liquid junction potential Primary methods of measurement are made with cells without transference as described in Sections 1­6 (Cell I). Less-complex, secondary methods use cells with transference, which contain liquid junctions. A single LJP is immeasurable, but differences in LJP can be estimated. LJPs vary with the composition of the solutions forming the junction and the geometry of the junction. Equation 7 for Cell I applied successively to two primary standard buffers, PS1, PS2, gives pHI = pHI(PS2) - pHI(PS1) = lim mCl0 {EI(PS2)/k - EI(PS1)/k} ­ A{I(2) / /[1 + 1.5 (I(2)/m°) / ] - I(1) / /[1 + 1.5 (I(1)/m°) / ]}
1 2 1 2 1 2 1 2

(8)

where k = (RT/F)ln 10 and the last term is the ratio of trace chloride activity coefficients lg[ °Cl(2)/ °Cl(1)], conventionally evaluated via B-G eq. 6. Note 4: Since the convention may unevenly affect the °Cl(2) and °Cl(1) estimations, pHI differs from the true value by the unknown contribution: lg[ °Cl(2)/ °Cl(1)] ­ A{I(1) / /[1 + 1.5(I(1)/m°) / ] ­ I(2) / /[1 + 1.5(I(2)/m°) / ]}.
1 2 1 2 1 2 1 2

A second method of comparison is by measurement of Cell II in which there is a salt bridge with two free-diffusion liquid junctions Pt | H2 | PS2 ¦ KCl (3.5 mol dm­3) ¦ PS1 | H2 | Pt for which the spontaneous cell reaction is a dilution, H+(PS1) H+(PS2) which gives the pH difference from Cell II as pHII = pHII(PS2) - pHII(PS1) = EII/k ­ [(Ej2 ­ Ej1)/k] (9) where the subscript II is used to indicate