Abstract. The determination of pH values suffers from two sources of error. One is the method of calibration of glass electrode cells. Multiple point calibration with.
Fresenius J Anal Chem (1994) 349:603-606
Fresenius' Journal of
© Springer-Verlag 1994
The standardization of pH measurements R. Naumann 1, Ch. Alexander-Weber 1, E G . K . Baucke 2 1AnalytischesZentrallabor,Fa. E. Merck OHG, D-64271 Darmstadt, Germany 2Schott Glaswerke,D-55122 Mainz, Germany Received: 28 September 1993/Accepted: 3 January 1994 Abstract. The determination of pH values suffers from two sources of error. One is the method of calibration of glass electrode cells. Multiple point calibration with linear regression is highly recommended instead of the usual bracketing procedure in cases where a precision of A pH < +_0.02 is required. Advantages of this method are discussed, particularly regarding the contribution of the liquid junction potentials to the cell emf. The second uncertainty is caused by batch to batch variations of Standard Reference Materials and their respective standard pH(S), actual values of which are part of the data set of microprocessor-controlled pH meters. Differential potentiometry is proposed as the method of choice to avoid these differences. It results in pH(S) independent of a particular material. Experimental data of the restandardization of pH reference materials are also presented.
Introduction The pH value is one of the most frequently used quantities in chemistry. Its measurement and calibration, however, have not been sufficiently standardized. This becomes apparent when high precision pH values (with ApH = < +0.02) are required (i.e. for pH related thermodynamic quantities such as pK values and complexation constants). The pH is a critical parameter in biochemistry and hence in biotechnology and in some medical applications and also in water chemistry. Limitations to the precision of pH measurements are the methods of calibration (e.g. of commercial glass electrode cells) and the accuracy of standard pH values. Recommendations for the standardization of pH measurements; current status and future prospects The discussion regarding pH standardization concentrates on two problems: The first is the notional definiCorrespondence to: R. Naumann
tion of pH which includes a single ion activity and, therefore, is not according to straightforward thermodynamics. The second refers to the contribution of the liquid junction potential to the overall emf of a cell with transference. There are mainly two groups contributing to the discussion: One is related to the National Institute of Standards and Technology, NIST in USA [1, 2] and the other to the British Standards Institution, BSI [3]. While, with regard to the first problem, both groups agreed to use the same convention, they follow different philosophies with respect to the second [1, 2, 3]. The result is: there are two different sets of pH standards and hence two different pH scales currently recommended by IUPAC [4]. The use of the so-called bracketing procedure is recommended by IUPAC [4] for calibration purposes of practical (e.g. glass electrode) cells according to which the unknown pH(X) is calculated by pH(X) = pH(S 1)- [E(x)- E(S 1)]/k'
(1)
where k' is the practical slope of the E versus pH function: k' =
E(S2)-E(S1) pH (S2)-pH(SI)
(2)
and pH(S 1) and pH(S 2) and E(S 1) and E(S2) are pH values and emfs, respectively, of the standard buffers bracketing the unknown pH(X). The consequences of these recommendations were recently discussed by the authors [5]. The final result of a pH measurement will depend not only on the choice of the pH scale but also on the choice of the two standard buffers used for the calibration. In order to avoid difficulties with different pairs of buffers, it is recommended by the German Industrial Standard DIN 19268 [6], in cases where a precision A pH < + 0.02 is required, to replace the bracketing procedure by a multiple point calibration. The calibration function E(S) = E ° ' - k' pH(S)
(3)
is calculated by linear regression with ~c' (i.e. the practical
604 average slope) and E °' the standard potential. The pH values of unknown solutions are then obtained by pH(X) = [ E ° ' - E ( X ) ] / k '
(4)
Provided the type and number of standard buffers is agreed upon, the final result from pH determination no longer depends on their choice and the uncertainties are minimized. Further information may be obtained by the linear regression procedure regarding liquid junction potentials. This was shown [5] on the basis of measurements in practical cells with transference. Additional data to this work are presented in [7], in which, apart from E °' and k', deviations of actually measured potentials from the regression line are calculated and transferred into A pH. These A pH values represent the residual liquid junction errors of single standard buffers, already determined by Bates [1, 2] in the case of Standard Reference Materials (SRM) from NIST; however the work was carried out in a cell equipped with a free diffusion liquid junction device. In contrast to this, the authors employed liquid junction devices of commercial design, such as ceramic or platinum or ground glass sleeve junctions [5] since these are nearer to the practical situation in an industrial laboratory. A pH have been shown to be of the same order of magnitude as those in the data of Bates [1, 2]. The sleeve junction appeared to be the best alternative to the free diffusion liquid junction. The average A pH used to quantitatively characterize the internal consistency of the calibration function and hence the particular cell in use have also been calculated. Contributions of the liquid junction potential to the overall emf can also be deduced from differences between practical and theoretical values (E ° ' - E °) and ( k ' - k ) , obtained from measurements in a cell containing a Pt/hydrogen-electrode. The practical slope k' of a Pt/hydrogen-electrode cell with transference is always smaller than the theoretical or Nernst slope k, by a f a c t o r / / < 1 . / / d e notes the electromotive efficiency of the cell [5]. With a glass electrode replacing the Pt/hydrogen-electrode, the
slope of the E versus p H function is reduced to still smaller values. From this the electromotive efficiency of the glass electrode itself can be evaluated [7]. Commercial pH meters such as the pH-meter 713 from Metrohm (Herisau, Switzerland) or the Delta 350 from Mettler-Toledo (Giegen, Germany) recently became available providing the possibility to perform multiple point calibration, in the Metrohm case also including the option to calculate residual liquid junction potentials A pH. Hence with these pH meters, together with the ease of automation provided by microprocessor technology, the necessity to measure more than two standard buffer solutions should not be an obstacle to the proposed method of calibration. Data thus obtained may be useful for a further discussion about the two different pH scales.
Standard pH values Accuracy and precision of a pH measurement are limited also by the accuracy of standard p H values. The uncertainty of pH(S) values given in certificates from NIST is ApH+0.005. Provided the purity of the materials measured is sufficiently high, pH(S) as a function of temperature should be independent of the particular batch. Unfortunately this is not always true. Batch to batch differences can be easily detected by differential potentiometry, a method already recommended in 1984 by IUPAC [4] but described in detail only recently [8]. It is designed to restandardize buffer materials with respect to an SRM from NIST in a cell with two identical Pt,H 2 electrodes. Pt,H2(pH2)/buffer S (pH)// buffer S (pH + A pH)/Pt,H2(PH2)
(I)
The two P t / H 2 electrodes are in contact with quasiidentical buffer solutions (i.e. identical with respect to concentration and type of material) but with small differ-
Table 1. Restandardization of potassium dihydrogen p h o s p h a t e / d i s o d i u m hydrogen phosphate, 0 . 0 0 9 m o l / k g and 0.03 m o l / k g , respectively, against SRM 186-I-e/186-II-e of NIST
T/°C
p H (S) a
SRM
Restandardized material
Eap H (gV)
ApH
pH(RS) b
25 25 30 35 40 45 50 20 20 15 10 5 0
6.863 6.863 6.852 6.844 6.840 6.837 6.836 6.879 6.879 6.899 6.924 6.950 6.984
NIST NIST NIST NIST NIST NIST NIST NIST NIST NI ST NIST NIST NIST
NIST MERCK MERCK MERCK MERCK MERCK MERCK NIST MERCK MERCK MERCK MERCK MERCK
+ + + + + +
< 0.001
