Petra
Traceable
Spitzer
Received: Accepted:
14 June 2000 22 August 2000
Presented Conference Applications Laboratories, Israel
at the International on Metrology in Calibration 16-18 May
P. Spitzer Physikalisch-Technische Bundesallee 100, 38116 Germany e-mail:
[email protected] Tel.: + 49-53-5923322 Fax: + 49-53-5923015
The primary method for pH is based on the measurement of the potential difference of an electrochemical cell containing a platinum hydrogen electrode and a silver/silver chloride reference electrode, often called a Harned cell. Assumptions must be made to relate the operation of this cell to the thermodynamic definition of pH. National metrology institutes use the primary method to assign pH values to a limited number of primary standards (PS). The required comparability of pH can be ensured only if the buffers used for the calibration of pH meter-electrode assemblies are traceable to Abstract
- Trends and and Testing 2000, Jerusalem,
Bundesanstalt, Braunschweig,
measurements
Introduction
pH is the chemical parameter most frequently measured. Accurate pH measurements are needed in many areas, among which public health care, environmental protection and biotechnology are the most important ones. Thus, there is a huge demand for traceable measurement results for pH to ensure quality control and comply with the technical requirements. The users of pH meters thus need calibration solutions of long-time stability which are traceable to primary pH standards pH(PS) related as closely as possible to the definition of pH. Although pH measurements are carried out on a large scale, the problems posed by the traceability of pH have not yet been adequately solved. A hundred years ago, in 1909, Soerensen of the Carlsberg Laboratory in Copenhagen [l] defined pH in terms of the concentration with a scale of O-14 (at
of pH
these primary pH standards. To assess the degree of equivalence, comparisons of primary measurement procedures for pH were organized in co-operation with EUROMET. Typical results will be presented. In 1998, the Consultative Committee for Amount of Substance (CCQM) decided to include the field of pH in its working programme. The first key comparison for this quantity was recently carried out on two phosphate buffer solutions. Keywords
Traceability comparison
Metrology in chemistry * pH * Key
*
25 “C) which he derived from the ionic product of water (Kw = lo-l4 mol x dmp3). Some years later, Lewis introduced the concept of activity, and in 1923 Debye and Hiickel published their theory for strong electrolyte solutions. On the basis of this knowledge, Soerensen and Linderstroem-Lang [2] suggested a new pH definition in terms of the relative activity of hydrogen ions in solution: pH = - lgaH = - lg (rnH~~/rno)
(1)
where an is the relative (molality-based) activity, ?/H the molal activity coefficient of the hydrogen ion H + at the molality mn in mol kg-l, and m” a standard state chosen equal to 1 mol kg-’ of hydrogen ions. Equation (1) involves the single ion activity of the hydrogen ion, and it might be said that thus the problems commenced. Activities of individual ions can never be measured without non-thermodynamic assumptions being made.
56
The traceability
Pt I H2 I buffer S, Cl - I AgCl I Ag
of pH measurements
The International Union of Pure and Applied Chemistry (IUPAC) recommendation [3] for the definition of pH scales has formed the basis for the standardisation of pH measurements since 1985. IUPAC recommended two different approaches to derive the pH values of pH standard buffer solutions. They yield two different pH values for one solution [4]. The prerequisite for the mutual acceptance of analytical data such as pH is comparability. Comparability requires the complete evaluation of the measurement uncertainties which in turn are based on traceability to recognised references. The need for traceable pH measurements and the confusion resulting from the ambiguous IUPAC recommendation led to various international initiatives being taken. In 1997, IUPAC formed a Working Party on pH to develop a new pH concept. This work is now in its final stages and the final draft is just being reviewed. There is hope that the new recommendation will soon be accessible to the parties interested. Numerous national and international standards on pH are still applicable. Following increasing demands for quality assurance in laboratories, a European standard 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). The standard relates to requirements for how to establish traceability between pH measurements performed by the user and the primary reference method using hydrogen electrodes. The revised IUPAC draft for pH is intended to serve as a basis for the new European standard on pH. It has been clearly stated that this standardisation work will not duplicate the work already completed by IUPAC or by the International Electrotechnical Commission (IEC). The primary method for the measurement
of pH
After extensive studies of buffer solutions and suitable electrochemical cells, Bates and his co-workers [5] suggested a conventional procedure, the Bates-Guggenheim convention [6], to assign pH values to standards. If this convention is used with an estimate of its uncertainty, traceability to the SI can also be established for PH. The primary method for pH is based on the measurement of the potential difference of the electrochemical cell without a liquid junction involving a selected buffer solution, a platinum hydrogen gas electrode and a silver/silver chloride reference electrode, often also referred to as a Harned cell.
Cell I
As a liquid junction potential is avoided, the cell potential consists merely of the electrode potentials of the hydrogen and the silver/silver chloride reference electrode. Chloride at known concentrations, mcl, must be added to the (chloride-free) buffer solution to use the silver-silver chloride electrode in cells without transference as a reference. This is different from silver/silver chloride reference systems with fixed potentials used for example as standard references in single-rod glass electrodes. The application of the Nernst equation for the reaction of cell (I) yields the potential difference Er (corrected to 101325 Pa - partial pressure of hydrogen gas) given by Eq. (2). Er can be rearranged to give the socalled acidity function so that there are only measurable quantities on the right side of Eq. (3). El = E0 - k lg (mHyHmcl3/cl)
(2)
- lg (a~ya) = (~3 - E”)/k + lg (ma)
(3)
E” is the standard potential in V of the silver/silver chloride electrode and ycl the activity coefficient of the chloride ion. The Nernstian slope k in V is given by Eq. (4): k = R T 1nlOIF
(4)
where R is the molar gas constant in J mol-1 K-l, F the Faraday constant in As mall1 and T the thermodynamic temperature in K. The standard potential difference of the Ag/AgCl reference electrode E” is determined in cell (I) filled with HCl at a fixed molality. For the molality of 0.01 mol kg-l, the values for the mean activity coefficient of the HCl are given in [7] at various temperatures. The measurements to get the cell potential El, of cell I filled with HCl and Er of cell I filled with buffer are performed simultaneously. The difference AE = EI - EI, is therefore independent of the standard potential difference. To obtain the pH, it is necessary to evaluate the activity coefficient of the chloride ion. So the acidity function is determined for at least three different molalities mcl of added alkali chloride. In a subsequent step, the value of the acidity function at zero chloride molality, The k(43YCl) O, is determined by linear extrapolation. activity of chloride is immeasurable. The activity coefficient of the chloride ion at zero chloride molality, #r, is calculated using the Bates-Guggenheim convention (Eq. 5) which is based on the Debye-Huckel theory. The convention assumes that the product of constant B and ion size parameter a are equal to 1.5 (kg mol11)1’2 in a temperature range 5 to 50°C and in all selected buffers at low ionic strength (I
57
- lg &
= -A11’2/(
1 + BaI”2);
Ba
=
1.5 (kg mol -‘) 1’2 (5)
is the Debey-Htickel constant (limiting slope) in (kg mall’) 1’2 and I the ionic strength of the buffer solution in mol kg-l. The various steps for the assignment of pH(PS) to the primary pH reference buffer are summarised in Fig. 1. In this figure also the main sources of uncertainty for the primary method for pH are mentioned. The extrapolation to zero chloride molality is assumed to be linear provided the change in ionic strength on addition of chloride is less than 20%. For a measurement of pH with cell (I) to be traceable to the SI, an uncertainty for the Bates-Guggenheim convention must be estimated. One possibility is to estimate a reasonable uncertainty contribution due to a variation of the ion size parameter. An uncertainty contribution of f 0.01 in pH should cover the entire variation. When this contribution is included in the uncertainty budget, the uncertainty at the top of the traceability chain is too high to derive secondary standards as used to calibrate pH meter-electrode assemblies. For most measurements the contribution from the Bates-Guggenheim convention will therefore not be allowed for. Primary pH values stated without this contribution will be considered conventional. The primary method is applied by national metrology institutes to assign conventional pH values to a limited number of primary standard (PS) buffer solutions in dilute aqueous solutions. The experimental details are given in [S, 91 where national standard measurement devices for pH in Denmark and Germany are described. In order to improve the primary method for pH, investigations into solution theory and into the concept of single ion activity are necessary. A model of electrolyte solutions which takes into account both electrostatic and specific interactions for individual solutions would be an improvement over the Bates-Guggenheim convention. It is hoped that the Pitzer model of electrolytes [lo], which uses a virial A
Table
1
Values
of pH
primary
Primary
standard
(PS)
Potassium Potassium Potassium Disodium Disodium Sodium Sodium
hydrogen dihydrogen hydrogen hydrogen hydrogen tetraborate hydrogen
tartrate citrate, phthalate, phosphate, phosphate, decahydrate, carbonate,
standards
(PSs)
for
primary
Cell
with
Pt 1 H, [ buffer
PS,
buffer
PS
Cr (m,,)
I AgCl
1 Ag
Acidity function for m,, (1) . . . m,, (3)
1 Extrapolation -k
vzc,+,, (a, ya)
Calculation
pH
pH=-lg(u,y,,)o+lg(y~,)
Fig.
1
Summary
of the
primary
method
for
pH
measurement
equation approach, will provide such an improvement. Until now, sufficient and reliable data are not available in the literature, so calculations for all buffer solutions of interest cannot be carried out. First limited work is being carried out on phosphate and carbonate buffers [ll]. For the Pitzer approach an uncertainty must be estimated too. Primary pH reference materials were chosen, see Table 1, which can be easily prepared and have a reproducible purity of preparation. Batch-to-batch differences in purity, however cannot be avoided. The
standards
(sat. at 25 “C) 0.005 mol kg-l 0.005 mol kg-l 0.025 mol kg-’ + potassium dihydrogen 0.03043 mol kg-’ + potassium dihydrogen 0.01 mol kg-’ 0.025 mol kg-’ + sodium carbonate, 0.025
at 2.5 “C
(PTB
phosphate, phosphate, mol
kg-l
materials
0.025 mol 0.008695
are
kg-’ mol
chosen
kg-’
as an
example)
PTB Primary reference material
PH-(PS)
PTB-TA 00 PTB-CIT 00 PTB-PHT 00 PTB-PHOA 00 PTB-PHOB 00 PTBBO OOb PTBCAR 00
3.557 3.775 4.008 6.865 7.416 9.182 10.014
58
\
pH(PS) values are valid, therefore, only with provision of a certificate for the specific batch. The pH reference materials were selected also to cause small liquid junction potential
3 years), except solid borax buffer material. Borax buffer (0.1 mol kg-‘) has a restricted stability of about 2 years only [14]. The pH(PS) values listed in Table 1 are examples derived from Physikalisch-Technische Bundesanstalt (PTB) certificates for primary pH reference materials. The typical measurement uncertainty for the determination of pH(PS) using cell(I) is U= 0.003 (k = 2) at
-
9,187
9,185
I
-
9,183
I g ,8, p ’ : 9,179
9,177
9,175 OMH
Fig. rate
GUM
2 EUROMET decahydrate,
NIST
comparison 0.01 mol kg-’
PTB
424 [19]. Buffer: (T = 25 “C)
DPL
sodium
tetrabo-
10,018
25 “C.
10,016
Consistency
of primary
pH
buffer
solutions
For the measurement results to be recognised at the international level, it is necessary to demonstrate the equivalence of the national traceability structures, including national measurement standards, with the aim of a mutual recognition of national measurement standards and certificates. To evaluate the degree of equivalence of the national primary measurement procedures for pH, the first key comparison for this quantity was recently carried out by the CCQM on two phosphate buffer solutions. These experiments were piloted by the PTB Germany and involved another ten metrology institutes. A first evaluation of the results obtained shows that the majority of the results agree within the uncertainty stated by the participants. The draft B for this comparison will be available soon. In the past, comparisons of primary measurement procedures for pH were carried out in co-operation with EUROMET [15-171, with the aim of improving the uniformity of pH measurements in Europe. The results obtained in the measurement of five different buffers demonstrated a high degree of comparability for the measurements carried out at different laboratories. At 25 “C the pH value of the respective buffer agreed within U= 0.005 (k = 2). The evaluation of the results did not furnish evidence for significant effects of the cell design. Typical results are presented in Figs. 2-4. The uncertainties stated by the participants were evaluated according to the Guide to the Expression of Uncertainty in Measurement (GUM) [ 181. The participants were: GUM; Central Office of Measures, Poland; National Office of Measures (OMH), Hungary; Physikalisch-Technische Bundesan-
10,008
10,006
L GUM
Fig. gen
3 EUROMET carbonate,
0.025
OMH
PTB
comparison mol kg-’
424 [19]. + sodium
DPL
NET
Buffer: sodium hydrocarbonate, 0.025 mol
kg-’ (T=25”C) 7,396
7,394
Ip
7,392
-
7,39
-
7,388
t 0
t
1
GUM
DPL
PTB
7,386
7,384
Fig. 4 EUROMET drogen phosphate, phosphate, 0.008695
comparison 370 [18]. 0.03043 mol kg-’ + mol kg-l (T=37 “C)
Buffer: potassium
OMH
disodium dihydrogen
hy-
stalt (PTB), Germany; Danish Primary Laboratory for pH Measurement (DPL) c/o Radiometer Medical A/S, Denmark; National Institute of Standards and Technology (NIST), USA.
59
Secondary for
pH
standards
and
secondary
methods
measurement
In most applications, the use of a high-accuracy PS for pH measurement will not be justified if a traceable secondary standard of sufficient accuracy is available. It is therefore recommended to derive secondary pH standards, pH(SS), from the pH(PS) buffer solutions. Deviating from the primary method for pH, measurements for deriving SSs are carried out in cells, separating the solutions by a diffusion-limiting or liquid junction device. Liquid junction potentials forming as a result cannot be determined directly and vary with the composition of the solution forming the junction and the geometry of the junction device. The uncertainty due to the liquid junction potential can be estimated from independent measurements or from theoretical assumptions. Secondary pH reference materials can be derived from the PS buffer solutions by different measurement procedures, which provide results for: pH(SS) of the same nominal composition as pH(PS) pH(SS) of different composition pH(SS) not compatible with platinum hydrogen electrodes. To achieve highest metrological quality, it is strongly recommended to derive SSs from PSs of nominally the same chemical composition. Liquid junction potentials are largely minimised when buffer solutions of nominally the same chemical composition are separated from one another in a strictly isothermal cell (II) containing two platinum hydrogen cells at exactly the same hydrogen pressure [ 191. Pt I H2 I primary
The primary rated by a liquid of fine porosity. tion of the liquid very small. The small.
SSs
derived
from
buffer (PS) secondary
II buffer
(SS) I Pt I H2
cell II
and the secondary buffers are sepajunction device, preferably a glass disk Under these conditions, the contribujunction potential to the cell voltage is increase in uncertainty is also very
measurements
in cell
ions to the ionic strength is significant. Also, the zwitterionic buffers [20] (e.g. HEPES and MOPSO) and the nitrogen bases of the type BH + (e.g., tri-hydroxymethy1 aminomethane, TRIS) are excluded as primary pH reference materials because either the Bates-Guggenheim convention is not applicable, or the liquid junction potentials are high.
Calibration
of pH
meter-electrode
assemblies
Routine pH measurements are carried out using pH meter-glass electrode assemblies. If the platinum/hydrogen electrode is replaced by a glass electrode cell, often designed as single-rod or combination electrode, the measurements of pH are affected by various random and systematic effects producing uncertainties of unknown magnitude. Hence, the glass electrode cell must be calibrated against standard buffer solutions traceable to primary pH standards. The choice among the methods should be made according to the uncertainty required for the application. According to the number of standards used, the calibration procedures can be subdivided into: Single-point calibration Two-point calibration Multi-point calibration. In most routine applications, glass electrode cells are calibrated by the two-point or bracketing procedure, using two secondary (or primary) standards with values that “bracket” the range in which the unknown lies. Multi-point calibration will be recommended if minimum uncertainty and maximum consistency are required over a wide range of pH(X) values [21, 221. The calibration function of the electrode is then calculated by linear regression of the difference in cell voltage results from the standard pH values. This calibration procedure is also recommended for characterising the performance of electrode systems. For single-point calibration using one standard, the calibration function is assumed to be a straight line defined by the intercept and the theoretical slope factor of the cell. In order to obtain the overall uncertainty of measurement, uncertainties of the respective pH(PS) or pH(SS) values must be taken into account.
I
Buffer material that does not fulfil all the criteria for primary pH reference materials but to which pH values can be assigned using cell I are considered to be pH(SSs). An example of such a secondary buffer is acetic acid for which a consistent chemical quality is hard to achieve. Calcium hydroxide and potassium tetraoxalate do not fulfil the criteria for a primary pH reference material because the contribution of hydroxyl or hydrogen
Conclusion
The quantity pH is used to characterise the acidity of a system, but also in speciation [22] because of the importhe chemical tance of the species H+ for controlling equilibrium. The required comparability of pH can be ensured only if the buffers used for the calibration are traceable to primary pH reference materials. pH(PS) and pH(SS) values of primary and secondary reference
60
NM1 (e.g. PTB)
-
Hydrogen electrode system
Primary method u = 0,003
I
Calibration service (e.g. DKD)
-
User
-
Differential
Secondary method u = 0,004
cell
Glass electrode
system
-
Field method u= 0,Ol
I
Fig 5 Traceability chain for pH in Germany. The uncertainty stated is the expanded uncertainty with a coverage factor k =2. The uncertainty due to the Bates-Guggenheim convention is not taken into account
buffer solutions, respectively, were shown to be traced back as closely as possible to the thermodynamic definition of the pH. Future improvements of the concept of single ion activity, e.g. the Pitzer treatment will open up the possibility for pH values to be traceable to the SI with acceptable uncertainties for calibration purposes. The hierarchical approach to the traceability of pH measurements and pH reference materials is consistent with the agreed approach to traceability for metrology in chemistry [23]. Uncertainties stated for the primary method and for all subsequent measurements permit the uncertainties for all steps to be linked to the primary reference material. For several years a traceability chain for pH measurements has been available within the German metrological infrastructure. By the choice of buffer solutions certified by the German Calibration Service (DKD) for the calibration of the pH meter-electrode assembly, traceability to the national standard is guaranteed for the user in the way shown in Fig. 5. For the mutual recognition of measurement standards and certificates, it is necessary to demonstrate the equivalence of the national traceability structures, including national measurement standards. The first key comparison for pH took place in 1999 and the results will be available soon. Acknowledgements hardt for technical
The author assistance.
would
like
to
thank
Ralf
Eber-
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8. Kristensen HB, Salomon A, Kokholm G (1991) Anal Chem 63 : 885 9. Spitzer P, Eberhardt R, Schmidt I, Sudmeier U (1996) Fresenius J Anal Chem 356 : 178-181 10. Pitzer KS (1991) Activity coefficients in electrolyte solutions, 2nd edn. CRC Press, Boca Raton, Fla., p. 91 11. Covington AK, Ferra MIA (1994) J Solution Chem 23 : l-10 12. Naumann R, Alexander-Weber C, Baucke FGK (1994) Fresenius J Anal Chem 349 : 603-606 13. Bates RG (1973) Determination of pH. Theory and practice. 2nd edn. Wiley, p. 95 14. Naumann R, Alexander-Weber C, Baucke FGK (1994) Fresenius J Anal Chem 350 : 119-121 15. Spitzer P (1996) Metrologia 33:95-96
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