Anal Bioanal Chem (2002) 374 : 787–795 DOI 10.1007/s00216-002-1453-1

S P E C I A L I S S U E PA P E R

Petra Spitzer · Barbara Werner

Improved reliability of pH measurements

Received: 9 April 2002 / Revised: 24 June 2002 / Accepted: 24 June 2002 / Published online: 6 September 2002 © Springer-Verlag 2002

Abstract 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. Keywords Metrology · pH measurement · Primary standard · Traceability

P. Spitzer (✉) Physikalisch Technische Bundesanstalt (PTB), Bundesallee 100, 38116 Braunschweig, Germany e-mail: [email protected] B. Werner Zentrum für Messen und Kalibrieren GmbH Sachsen-Anhalt, Areal A, Filmstraße Nr. 7, Chemiepark Bitterfeld-Wolfen, 06766 Wolfen, Germany

Introduction pH is among the most frequently measured physicochemical properties in many areas of application; health care and safety, biochemistry, and environmental monitoring are among the most important. Recent research in environmental science and biochemistry has revealed that the measurement uncertainty in pH makes a major contribution to the uncertainty of thermodynamic data and geochemical transport models [1]. Statements of measurement uncertainty based on traceability to internationally recognised references are required by regulatory bodies, and by international quality assurance standards (ISO EN 17025 [2]) in general. Confidence in the reliability of analytical data requires complete knowledge of the chain of traceability linking the measured value of the quantity in the sample to a unit in the International System of Units (SI) or, when that is not possible, to internationally agreed and stated references [3]. A special feature of pH is that traceability does not extend to the SI at the uncertainty level necessary for practical pH measurements. Internationally recognised primary pH standards related as closely as possible to the thermodynamic definition of pH and provisions for sample pH to be traceable to the primary references are needed. The IUPAC (International Union on Pure and Applied Chemistry) recommendation [4] has formed the basis of the standardisation of pH measurements since 1985. The IUPAC recommended two different approaches for assignment of values to pH standard buffer solutions. The use of these yields two different pH values for the same buffer solution [5] and was not sufficient to establish confidence in the measurement results. The need for mutual acceptance of analytical data on the basis of demonstrated traceability and the confusion resulting from the ambiguous IUPAC recommendation led the IUPAC Analytical Chemistry Division (V) and the Division on Physical and Biophysical Chemistry (I) to form a working party on pH to develop a new concept of pH. The measurement procedures described in the recently

788

published provisional recommendation [6] are applied by national metrology institutes and by accredited calibration laboratories to determine the pH of a restricted number of primary and secondary pH reference materials with stated uncertainty. These pH standard reference materials form the basis of national and international measurement infrastructures for pH. Because they must maintain their pH even when contaminated with small amounts of acids or bases pH standards are buffer solutions.

The traceability chain for pH The definition of pH More than a hundred years ago, in 1909, Soerensen [7] defined pH in terms of concentration with a scale of 0–14 (at 25 °C) derived from the ionic product of water (KW= 10–14 mol L–1). Some years later the concept of activity was introduced by Lewis and in 1923 Debye and Hückel published their theory for strong electrolyte solutions. On the basis of this knowledge Soerensen and LinderstroemLang [8] suggested a new definition of pH in terms of the activity of hydrogen ions in solution:
 pH = − lg aH /m 0 = − lg m H γH /m 0 (1) where aH is the activity and γH the molal activity coefficient of the hydrogen ion H+ at molality mH, and m0 is the standard molality, 1 mol kg–1. The definition expressed by Eq. (1) involves the single ion activity coefficient of the hydrogen ion and takes into account ionic interactions in the solution. Activity coefficients of individual ions cannot be measured without nonthermodynamic assumptions being made. The primary measurement procedure for pH pH is determined by measuring the potential difference of the electrochemical cell depicted by cell (I), below, often called a Harned cell, which contains a selected buffer, the hydrogen-ion-sensing platinum hydrogen electrode, and the silver–silver chloride reference electrode. −

Pt |H2 | buffer, Cl |AgCl| Ag

(Cell I)

Because a liquid junction potential is avoided, the cell potential consists merely of the electrode potentials. Chloride ions are added to the chloride free buffer at several chloride molalities to stabilize the potential of the silver–silver chloride electrode. The primary method for pH now also recommended by the IUPAC [6] is based on the Bates–Guggenheim approach [9]; for low ionic strength (I≤0.1 mol kg–1) Bates and Guggenheim suggested an approximation for the single ion activity coefficient of the chloride ion on the basis of the Debye–Hückel theory of strong electrolytes. The convention they formulated assumed that the product of the mean distance of closest approach of the ions (ion size parameter) and a constant in the Debye–Hückel equation

of chloride ions is 1.5 at every temperature and in all selected buffers. For measurement of pH with cell (I) to be traceable to the SI the uncertainty in the Bates–Guggenheim convention must be estimated. One possibility is to estimate a reasonable uncertainty contribution as a result of variation of the ion size parameter. An uncertainty contribution of 0.01 (expanded uncertainty, U=0.01) [10] in pH should cover the entire variation. When this contribution is included in the uncertainty budget of a primary pH standard, the uncertainty at the top of the traceability chain is inappropriately high to enable derivation of the secondary standards used to calibrate pH meter–electrode assemblies. For most measurements the contribution resulting from the Bates–Guggenheim convention will therefore not be taken into account. Primary pH values stated without this contribution will be considered conventional. Determination of the pH (PS) of a primary standard buffer solution involves extrapolation of the measured potential difference to zero chloride molality. The potential difference E of cell (I) (corrected to 101325 Pa partial pressure of hydrogen) depends on the hydrogen-ion activity, aH, the quantity to be measured, in the following way:

 E = E 0 − [(RT /F ) ln 10] lg a H /m 0 m Cl γCl /m 0 (2) where E0 is the standard potential of the Ag/AgCl reference electrode, γCl the activity coefficient of the chloride ion, R the molar gas constant, F the Faraday constant, T the thermodynamic temperature, and p0 the standard pressure, 101325 Pa. Measurement of the pH of a buffer solution using cell (I) usually involves several different steps: 1. The standard potential difference E0 is determined by use of a Harned cell filled with hydrochloric acid of fixed molality, by use of Eq. (3). The mean activity coefficient of HCl, γ±HCl, at a variety of temperatures is best known at the molality 0.01 mol kg–1 [11]: E 0 =E + [(2RT /F ) ln 10]


lg m/m 0 + lg γ±(HCl) + 0.25 lg p0 /p 

(3)

The last term corrects E to 101325 Pa. The partial pressure of hydrogen, p, is defined as the difference between atmospheric pressure and the pressure of saturated water at the measurement temperature. The vapour pressure of water is calculated by use of the Claussius–Clapeyron equation, assuming the behaviour of the buffer solution is the same as that of water. In addition to the atmospheric pressure there is a hydrostatic pressure, which depends on the depth of immersion of the hydrogen inlet of the electrode [12]. 2. Equation (2) can be rearranged to give the acidity function, pa, so that the right hand side of Eq. (4) measurable quantities only and pa is measured as a function of mCl: 

pa = − lg a H + γCl − /m 0 = E − E 0 /

 (4) [(RT /F ) ln 10] + lg m Cl /m 0 + 0.5 lg p 0 / p

789

3. Extrapolation of the acidity function to zero chloride molality. The acidity function: 
pa0 = − lg aH γCl /m 0 m Cl→0 (5) corresponding to zero chloride molality is determined by linear extrapolation according to Eq. (6), which expresses pa as a function of the chloride molality, using measurements at at least three values of mCl in the range 0.005 to 0.02 mol kg–1. It is assumed that linear extrapolation is appropriate if the change in ionic strength produced by the addition of chloride is restricted to less than 20%. pa = pa0 + bm Cl

(6)

where b is an empirical, temperature-dependent constant. 4. The activity coefficient γCl at the ionic strength, I, of the buffer is obtained by adopting the Bates–Guggenheim proposal. Here, the activity coefficient γCl is given by Eq. (7):
1 /2 
1 /2  lg γCl = − A I /m 0 / 1 + 1.5 I /m 0 (7) where A is the Debye–Hückel temperature-dependent limiting slope [13] and I the ionic strength of the buffer solution. 5. Calculation of the pH (PS) value – from Eqs. (3), (4), (6), (7) and the definition of pH, pH=–lgaH, the pH value is obtained from Eq. (8): pH = pa0 + lg γCl

Realisation of the primary measurement procedure For certification of the pH (PS) of primary standard reference buffers the primary method for pH was set up at the Physikalisch-Technische Bundesanstalt (PTB), the German metrology institute, in 1993. The basic structure of the primary measurement device is illustrated in Fig. 2. The set-up includes twelve Harned cells. Each cell consists of five compartments, one for the platinum electrode, one for the silver–silver chloride reference electrode and three for humidifying the hydrogen gas. Experimental details, including electrode preparation, are described elsewhere [14, 15]. pH is measured between 5 and 50 °C, at temperature intervals of 5 K and at 37°C. The Harned cells are mounted in a thermostatted water bath connected to a refrigeration unit (Lauda, LSC1067/UKT 600). The temperature is constant within 0.005 K. Three of the cells are filled with hydrochloric acid at 0.01 mol kg–1 for determination of the standard potential of the silver–silver chloride electrodes. The molality of the hydrochloric acid is determined by high-precision controlled-current coulometry with an standard uncertainty <1×10–5 mol kg–1. Controlled-current coulometry is a primary method of measurement with a direct link to the SI [16].

(8)

The flowchart in Fig. 1 summarizes the steps of the procedure for primary measurement of pH.

Fig. 1 Procedure for primary measurement of pH

Fig. 2 Basic structure of the primary measurement device for pH set up at PTB, Germany

790

The other Harned cells are divided into three groups of three cells, each filled with primary buffer solution containing fixed amounts of sodium chloride (0.005 mol kg–1, 0.01 mol kg–1, and 0.015 mol kg–1). The whole measurement set-up is computer controlled. The validated software for measurement control and evaluation is written in C++(Borland). Two Pt-100 temperature sensors and the electrodes are connected to a scanner (Keithley 7001) which in turn is connected to a temperature meter and to a digital voltmeter (DVM) (Keithley). The DVM is controlled by means of an IEEE interface. The atmospheric pressure is transferred from the pressure sensor (Setra 370 M) to the computer via a serial interface.

N 

The uncertainty budget for the pH (PS) of a primary standard reference buffer

s2 =

Neglecting the uncertainties, u, associated with the Bates– Guggenheim approsch, (u(lg(γCl–)≡0), and regarding the small uncertainty in the ionic strength, I, as insignificant, the standard measurement uncertainty, u, of pH is: u (pH) = u (pa0 )

and u(pa0 ) =



(9)

u 2 (pam=0.005 ) + u 2 (intercept)

(10)

The uncertainty, u (pam=0.005), in the acidity function for the smallest amount of added chloride, where mCl=0.005 mol kg–1, is usually the largest contribution to the standard uncertainty. If the scatter around the regression line is large, the uncertainty of the intercept can become the major contribution to the overall uncertainty. The standard uncertainty u(intercept) of the extrapolation of the acidity function, pa, to zero chloride molality by a linear least squares fit at the pa values obtained at the different chloride molalities is obtained according to Eq. (11), where s is the residual standard deviation, N the number of measureTable 1 Standard uncertainty of the acidity function at mCl=0.005 mol kg–1

Table 2 Standard uncertainty in the standard potential of the silver–silver chloride electrode (E0) from measurements in hydrochloric acid (mHCl=0.01 mol kg–1)

ments used to obtain pa at different chloride molalities, and b the slope of the regression line (Eq. 6). Estimation of the uncertainty of the acidity function requires knowledge of the uncertainty contributions from determination of the standard potential E0 according to Eq. (3). The uncertainty in the molality of HCl has been identified as the main component contributing to the uncertainty in E0. The small uncertainties of F and R do not contribute significantly to the budget and are omitted.       2  1 m¯ Cl  u (i ntercept) = s  + N ,     N (m Cl − m¯ Cl )2 (11) i =1 pam Cl − (pa0 + b · m Cl )

2

i=1

N −2 where N (the number of measurements)=9. The uncertainty budget estimated according to the Guide to the Expression of Uncertainty in Measurement [17], taking into account all known components which affect the measurement result, is given in Tables 1 and 2 for a representative example, phosphate buffer (potassium dihydrogen phosphate–disodium hydrogen phosphate, approximately 0.025 mol kg–1 each) at a measurement temperature of 25 °C. The measurement equation is Eq. (2) (above). As a first step the uncertainty in the determination of the acidity function at a chloride molality mCl=0.005 mol kg–1 is estimated according to Eq. (12): 

pamCl=0.05 = − lg aH+ γCl− /m 0 = E − E 0 /
 (12) [(RT /F ) ln 10] + lg m Clm=0.05 /m 0
0  + 0.5 lg p / p

The standard uncertainty associated with the output quantity pa, denoted u(pa), is determined from the estimate xi

Quantity

Value xi

Standard uncertainty u(xi)

Sensitivity coefficient |ci|

Uncertainty contribution ui (pa)

Relative contribution ui (pa) (%)

E (V) E0 (V) (see Table 2) T (K) mCl (mol kg–1) P H2 (Pa)

0.772 0.222 298.15 0.005 1.01×105

2×10–5 5.5×10–5 8×10–3 2.2×10–6 3

16.9 16.9 0.033 86.9 2.2×10–6

3×10–4 1×10–3 2.5×10–4 1.9×10–4 1×10–5

17.14 57.14 14.29 10.86 0.57

Quantity

Value xi

Standard uncertainty u(xi)

Sensitivity coefficient |ci|

Uncertainty contribution ui (pa)

Relative contribution ui (pa) (%)

E (V) T (K) mHCl (mol kg–1) PH2 (Pa)

0.464 298.15 0.01 1.01×105

2×10–5 8×10–3 1×10–5 3

1 8×10–4 5.1 1.3×10–7

2×10–5 6.4×10–6 5.1×10–5 4.2×10–7

26.03 8.33 65.09 0.55

791

of the input quantities (E, E0, T, mCl, p) and their associated standard uncertainties, u(xi):
 pa = f E , E 0 , m Cl , T , p For the uncorrelated input quantities, xi, the square of the standard uncertainty, u (the variance), associated with pa is: N  ∂f u 2 ( pa) = ci2 u 2 (x i ) with ci = ∂ xi i =1 The sensitivity coefficient, ci, describes the extent to which the acidity function is affected by variations of the input quantities, xi. u(pa)=0.001 Example of the calculation of an single uncertainty contribution: xi=xp Partial pressure of hydrogen ci, derived from Eq. (12), ci = 10−6 Pa−1

∂ pa ∂p

=

−.5 p ln(10)

= −2.17×

u(p): The pressure sensor is calibrated. In the calibration certificate the expanded uncertainty (k=2) is given: U=6 Pa. Divided by two the standard uncertainty u(p)=3 Pa.
 u E 0 = 5.5 · 10−5 V According to Eq. (11), u (the intercept)=3.6×10–4. The combined standard uncertainty for the pH (PS) value is therefore:  u (pa0 ) = u (pH (PS)) = 0.0011 2 + 0.00036 2 = 0.0012 U (pH (PS)) = 0.0024

The expanded uncertainty, U, of the measurement is stated as the standard uncertainty of measurement multiplied by the coverage factor k=2 which for a normal distribution corresponds to a coverage probability of approximately 95% [18].

Primary pH standard reference buffers National metrology institutes (NMI) use the primary method to assign pH (PS) values to a restricted number of primary standards in dilute aqueous solutions between pH 3 and 10 and in a temperature range from 5 to 50 °C. The primary pH standard buffer materials selected are available at high purity, have long-term stability, and can Table 3 Typical values of pH (PS) for primary standards at 25 °C. These figures should not be used in place of the certified value for a specific batch of buffer material

be prepared with high reproducibility [19]. Apart from the applicability of the Bates–Guggenheim convention (ionic strength ≤0.1 mol kg–1) buffer solutions between pH 3 and 10 prepared from these materials have small dependence on temperature – 0.001–0.01 K–1. The pH (PS) values do not include any diffusion (liquid junction) potentials. The primary buffer solutions have been selected such that only small diffusion potentials occur in measurements made with commercial pH electrodes incorporating liquid junctions. The order of the residual liquid junction potential also depends on the kind of liquid junction device used, of course. Further attributes of the primary pH standards are high buffer capacity and a small dilution effect [20]. Figures are given in the German standard DIN 19266 [21]. Each batch of material must be individually certified. The pH and the associated uncertainty are given in a certificate for every measurement temperature. Typical values of the pH (PS) of primary standard reference buffer solutions are listed in Table 3. These are examples from DIN 19266 [21]. The figures should not be used instead of the certified value for a specific batch of buffer material. Calcium hydroxide and potassium tetraoxalate also listed in DIN 19266 [21] are not recommended by IUPAC as primary buffers because the contribution of the hydroxyl or hydrogen ion to the ionic strength is significant. For calcium hydroxide preparation of the standard reference material is also extremely time-consuming and consists of several steps [19]. A typical expanded uncertainty for determination of pH (PS) by use of cell (I) is U=0.003 (coverage factor, k=2) at 25 °C. The batch-to-batch variations are of the same order.

The first international key comparison on the primary method for pH The extent of equivalence of primary standards for pH measured at different NMI is established by the Mutual Recognition Arrangement (MRA) [22] for national measurement standards and for calibration and measurement certificates issued by national metrology institutes in 1999. To support the MRA the first key comparison for pH, CCQM-K9 [23], was organised by the CCQM (Consultative Committee for Amount of Substance of the BIPM in Paris) in 2000 on two phosphate buffer solutions. A sec-

Primary pH standard reference buffers

Molality (mol kg–1)

pH (PS), typical values at 25 °C [21]

Potassium hydrogen tartrate Potassium dihydrogen citrate Potassium hydrogen phthalate Potassium dihydrogen phosphate– disodium hydrogen phosphate Sodium tetraborate decahydrate Sodium bicarbonate–sodium carbonate

Saturated at 25 °C 0.05 0.05 0.025/0.025 0.008695/0.03043 0.01 0.025/0.025

3.557 3.775 4.008 6.865 7.416 9.182 10.014

792

ond key comparison on a phthalate buffer solution (CCQMK17) started in 2001. The designation ‘key comparison’ emphasises that it is only possible to organize international comparisons in the field of chemistry in so-called priority areas representative of a wider field of analytes [24]. The key comparison CCQM-K9 was co-ordinated by the CCQM Working Group on Electrochemical Analysis and piloted by the Physikalisch-Technische Bundesanstalt (PTB) with assistance from the Slovak Institute of Metrology (SMU) and the National Institute of Standards and Technology (NIST) The substantial agreement of the measurement results of the NMI is evident. Most of the results obtained agree within the uncertainty stated by the ten participants. Two phosphate buffers, both containing potassium dihydrogen phosphate (KH2PO4) and disodium hydrogen phosphate (Na2HPO4) at different molalites were chosen as transfer standards. The molality (mol kg–1) was known to the participants for sample (1) only. The buffer solution was prepared and tested for homogeneity by the laboratory of the German Calibration Service (DKD) Zentrum für Messen und Kalibrieren GmbH Sachsen-Anhalt, Germany (ZMK) in co-operation with the pilot laboratory PTB. Sample (1): 0.025 mol kg–1 KH2PO4+0.025 mol kg–1 Na2HPO4 Sample (2): 0.02 mol kg–1 KH2PO4+0.02 mol kg–1 Na2HPO4 It was recommended that the participants in CCQMK9 performed measurements between 5 and 50 °C in steps of 5 K, and at 37 °C, but at least at 15 °C, 25 °C and 37 °C, because not all were able to measure over the whole temperature range. Controlled-current coulometry was recommended as a primary method of choice for determination of the molality of HCl. The CCQM-K9 evaluation confirmed the results obtained in comparisons performed under EUROMET cooperation, which have demonstrated the comparability of measurements within ∆pH=0.005 in different laboratories by use of samples from a single batch [25, 26, 27]. The uniformity of the results obtained for sample (1), of known molality, was negligibly better than the unifor-

Fig. 3 Results for sample (2) in the CCQM-K9 key comparison on pH

mity for sample (2), of unknown composition. This confirmed the competence of the participants. As an example the results for sample (2) at 25 °C are given in Table 4 and illustrated in Fig. 3.

The key comparison reference value (KCRV) and its uncertainty Because of the substantial overlap of the uncertainties stated by the participants, the individual laboratory uncertainties play a major role in determining the uncertainty of the KCRV. Assuming all participants in CCQM-K9 are equally competent there is no reason to doubt their uncertainty statements, so these can be regarded as credible. Two different approaches to assigning the KCRV, and the uncertainty associated with it, were taken into consideration. The value provided by each laboratory is regarded as an unbiased estimate of the quantity of interest [28]. The maximum-likelihood estimator yields the KCRV, pHR, as the variance-based weighted mean [29, 30] according to Eqs. (13), (14), and (15): N

Table 4 pH values for sample (2) of the key comparison CCQMK9: 0.02 mol kg–1 KH2PO4+0.02 mol kg–1 Na2HPO4 at 25 °C Participant KRISS NRCCRM SMU GUM PTB DPL NIMC VNIIFTRI NIST CENAM

Country Korea China Slovakia Poland Germany Denmark Japan Russia United States Mexico

pH 6.8877 6.8886 6.8896 6.8903 6.8914 6.8923 6.8933 6.8936 6.8941 6.9066

Expanded uncertainty, U (k=2) 0.0016 0.0040 0.0018 0.0016 0.0022 0.0016 0.0084 0.0036 0.0042 0.0130

pH R =

i =1

wi p Hi

N i =1

(13) wi

where pHi represents the individual results and wi the individual weights, wi =

C u i2

(14)

C=

1 N 1

(15)

i =1

u i2

where the values of ui are the individual uncertainties and C is the variance.

793 Table 5 CCQM-K9. key comparison reference value for sample (2) 0.02 mol kg–1 KH2PO4+0.02 mol kg–1 Na2HPO4 at different temperatures Temperature (°C)

Number of laboratories

pHR

u′(pHR) (k=1)

15 25 37

10 10 10

6.9248 6.8905 6.8667

0.00086 0.00070 0.00078

The uncertainty of the KCRV, u(pHR), is completely given by the individual uncertainties, by use of Eq. (16) 2
u pHR = C (16) A problem with this classical method is that a laboratory that quotes an optimistically small uncertainty has a strong influence on the KCRV and makes the uncertainty of the latter unreasonably small [31]. A more reasonable estimate of the uncertainty for the KCRV is, therefore, that of the external consistency concept [30, 32] taking into account the individual uncertainties and the spread of the results according to Eq. (17): N 
2  wi pHi − pHR
2 i =1 u  pHR = (17) N wi (N − 1) ·

Secondary standards and secondary measurement procedure Secondary pH reference materials can be derived by use of different measurement procedures. By use of evaluated uncertainties it is possible to rank primary and secondary reference materials in terms of the methods used for their pH determination. The choice between the methods should be made according to the uncertainty required for the application. For the highest metrological quality it is strongly recommended that secondary standards are derived from primary standards of nominally the same chemical composition. Liquid junction potentials are largely minimised when buffer solutions of nominally the same chemical composition are separated from each other in a strictly isothermal cell (II) containing two platinum hydrogen cells at exactly the same hydrogen pressure [33]. Pt, H2 |primary buffer, pH (PS) secondary buffer, pH (SS), Pt, H2 cell (II)

The primary and the secondary buffers are separated by a liquid-junction device, preferably a glass disk of fine porosity. Under these conditions the contribution of the liquid junction potential to the cell voltage and, therefore, the increase in the uncertainty is very small for ∆pH≤0.02.

i =1

The key comparison reference value and its uncertainty are summarized in Table 5 for the measurement temperatures 15 °C, 25 °C, and 37 °C. Evaluation of equivalence between the participants of CCQM-K9 The degree of equivalence, Di, of each laboratory with regard to the key comparison reference value (KCRV) is estimated according to Appendix B of the MRA [23]:
 Di = pHi − pHR (18) Ui, the expanded uncertainty of Di (k=2), is calculated according to Eq. (19): 
2 Ui = 2 u i2 + u  pHR . (19) The degree of equivalence between two laboratories is given by Eq. (20): Di j = Di − D j

(20)

and Uij, the expanded uncertainty of Dij (k=2), is calculated according to Eq. (21):  Ui j = 2 u i2 + u 2j (21) The matrix of equivalence is part of the BIPM key comparison data basis [22]. Fig. 4 Traceability chain for pH in Germany

794

In Germany laboratories accredited by the German Calibration Service (DKD) for the quantity pH use cell (II) to derive secondary pH standard reference buffers from the primary buffers. For several years a traceability chain for pH measurements has been established within the German measurement infrastructure. Calibration laboratories accredited by the DKD have an intermediate multiplier function in disseminating traceable references materials for calibration of pH meter electrode assemblies. The users could be sure that the reference buffers they buy are certified and traceable to standards recognised by the MRA [23] as international standards. Accreditation by the DKD is international, because of the mutual agreement between the members of the European Co-operation for Accreditation and bilateral agreements between specific countries. The traceability chain for pH established within the German measurement infrastructure is illustrated in Fig. 4. Secondary standards derived from measurements in cell (I) Buffer materials that do not fulfil all the criteria for primary pH reference materials but to which pH values can be assigned by use of cell (I) are considered to be secondary pH standards, pH (SS). An example of such a secondary buffer is ethanoic (acetic) acid, for which it is difficult to achieve consistent chemical quality. The zwitterionic buffers [34] (e.g. HEPES and MOPSO) and nitrogen bases of the type BH+ (e.g. tris-hydroxymethylaminomethane) are also excluded as primary pH reference materials because either the Bates–Guggenheim convention is not applicable, because the buffers contain Cl–, or the liquid junction potentials are high. It is possible to link pH (SS) values to the primary pH standards by comparison measurements using a cell with two free diffusion liquid junctions [35]. This cell is hard to realize. It will be a task of future work to link these standards with low uncertainty to the primary standards. The Bates–Guggenheim convention has limited validity for ionic strengths I≤0.1 mol kg–1. For applications in clinical chemistry and in environmental samples traceable pH standards with ionic strengths more similar to those of the samples would be lower than the liquid-junction potentials in practical measurement and improve the comparability of measurement results. To overcome current limitations of the primary pH standards and to extend the standards to higher ionic strength, investigations into solution theory and into the concept of single-ion activity are necessary. One approach is to investigate the potential of the Pitzer model of electrolytes [36, 37, 38], which uses a virial equation approach to provide an improvement in the primary method. For the Pitzer equation the uncertainty of all components must be estimated [37].

Conclusion The key to higher reliability of measurement standards is demonstrated traceability to internationally recognised references. The first key comparison on pH which was organised in the framework of CCQM demonstrated a high degree of equivalence of the national measurement standards for pH. Within the Mutual Recognition Arrangement, MRA, linking the NMI the measurement competence of the laboratories at the top of the traceability chain can be continuously demonstrated by key comparisons. Numerous national and international written standards on pH are still applicable. Because of increasing demands for quality assurance in laboratories, a European standard in this field is needed. In 1999 a working group on instrumentation in electrochemical analysis (WG 5) was created by the Technical Committee Laboratory Equipment of the European Committee for Standardisation (CEN/TC 332). It is clearly stated that this standardisation work will not duplicate the work already completed by IUPAC or by IEC (International Electrotechnical Commission). This European standard addresses on its first line the needs of manufacturers of pH meters, pH electrodes, and pH standards and of calibration laboratories and end-users such as test laboratories as a basis for performing pH measurements. The CEN standard will consist of three parts dealing with general aspects and terminology, certification of reference materials for pH measurements, and calibration of pH measuring equipment and practical pH measurements. There is hope that the concept of traceability for pH measurement will also influence the numerous application notes for pH measurements in different matrices. The traceability of pH measurements for application in fundamental and applied science must be disseminated to field laboratories. Because a pH value given without any uncertainty and without a measurement temperature is meaningless, it is necessary to include the uncertainty in pH measurements as a factor, e.g. in environmental prognosis. It has been demonstrated that the required comparability of pH and hence acceptance of measurement results can be improved if the certified reference solutions used for calibration of pH meter–electrode assemblies are traceable to recognised primary references. The uncertainty evaluation, must take into account the uncertainties of the certified reference buffer solutions used to calibrate the pH meter–electrode assembly, and the uncertainties in the operation of the measurement procedure. When uncertainty is evaluated according to the principles of the Guide to the Expression of Uncertainty in Measurement (GUM) [17] it is given as an interval around the result of the measurement. The interval expressing the uncertainty of the result enables the “fitness for purpose” of a result to be judged.

795

References 1. Meinrath G, Spitzer P (2000) Microchim Acta 135:155 2. ISO/EN 17025 (1999) General requirements for the competence of testing and calibration laboratories. ISO, Geneva, Switzerland 3. De Bièvre P, Kaarls R, Peiser HS, Rasberry SD, Reed WP (1997) Accred Qual Assur 2:168 4. Covington AK, Bates RG, Durst RA (1985) Pure Appl Chem 57:531 5. Baucke FGK (1997) In: Spitzer P (ed) The definition of pH. Proposal of improved IUPAC recommendations, PTB Report W-68: Traceability of pH measurements. Braunschweig 6. Buck RP, Rondinini S, Baucke FGK, Brett CMA, Camoes MF, Covington AK, Milton MJT, Mussini T, Naumann R, Pratt KW, Spitzer P, Wilson GS (2001) The measurement of pH – definition, standards and procedures. Report of the Working Party on pH. IUPAC Provisional Recommendation. http://www.iupac.org/ reports/provisional/archives.html 7. Sørensen SPL (1909) Biochem Z 21:131 8. Sørensen SPL, Linderstroem-Lang K (1924) Compt Rend Lab Carlsberg 15,6:1 9. Bates RG, Guggenheim EA (1960) Pure Appl Chem 1:163 10. Bates RG (1981) Crit Rev Anal Chem 10:247–278 11. Bates RG, Robinson RA (1980) Solution Chem 9:455 12. Hills GJ, Ives DJ (1951) J Chem Soc 307 13. OIML: pH Scaale for Aqueous Solutions (1980) International Recommendation No 54 14. Kristensen HB, Salomaon A, Kokholm G (1991) Anal Chem 63:885 15. Spitzer P, Eberhardt R, Schmidt I, Sudmeier U (1996) Fresenius J Anal Chem 356:178 16. Mariassy M, Vyskocil L, Mathiasova A (2000) Accred Qual Assur 5:437

17. BIPM, IEC, IFCC, ISO, IUPAC, and OIML (1993) Guide to the expression of uncertainty in measurement. Published in the name of BIPM, IEC, IFCC, ISO, IUPAC, and OIML by ISO, Geneva, Switzerland 18. CITAC Eurachem (2000) Quantifying uncertainty in analytical measurement http://www.measurementuncertainty.org 19. Bates RG (1973) Determination of pH. Theory and Practice, 2nd edn. Wiley 20. DIN 19261(2001). Beuth Verlag, Berlin, Germany 21. DIN 19266 (1998). Beuth Verlag, Berlin, Germany 22. http://kcdb.bipm.org/BIPM-KCDB 23. http://kcdb.bipm.org/BIPM-KCDB/AppendixB 24. Richter W (1999) Fresenius J Anal Chem 365:569 25. Spitzer P (1996) Metrologia 33:95 26. Spitzer P (1996) Metrologia 34:37 27. Spitzer P (2000) Metrologia 37:85 28. Pauwels J, Lamberty A, Schimmel H (1993) Accred Qual Assur 3:180–184 29. DIN 1319-4 (1999) Beuth Verlag, Berlin, Germany 30. Dietrich CF (1991), Uncertainty, calibration and probability. The statistics of scientific and industrial measurement, sc edn. Adam Hilger, UK, pp 39–49, 295–298 31. Cox MG (1999) A discussion of approaches for determining a reference value in the analysis of key-comparison data. NPL Report CISE 42/99 32. Gränicher WHH (1994) Messung beendet-was nun? Teubner, p 6-2–6-9 33. Baucke FGK (1994) J Electroanal Chem 368:67–75 34. Good NE et al (1966) Biochem J 5:467 35. Covington AK, Rebelo MJF (1987) Anal Chim Acta 200:245 36. Pitzer KS (1991) Activity coefficients in electrolyte solutions. CRC Press 37. Meinrath G (2002) Anal Bioanal Chem (in press) 38. Covington AK, Ferra MIA (1994) J Solution Chem 23:1–10