Bates-Guggenheim convention

The pH value is defined for an aqueous solution in an operational (arbitrary but reproducible) manner according to the Bates-Guggenheim convention ... 

The important question arises of the actual precision of pH measurement in analytical control. In this connection, it has become common practice to standardize pH determinations, on standard buffer solutions with pH regions where the pH of the solution under test is to be expected. As currently commercially available pH meters, pH electrodes and buffer solutions are of outstanding quality, the reliability of the pH measurement becomes shifted to the performance of the measuring electrochemical cell here as first principle the same cell should be used for the test solution and the standard solution, so that according to the Bates-Guggenheim convention... 

It has been emphasized repeatedly that the individual activity coefficients cannot be measured experimentally. However, these values are required for a number of purposes, e.g. for calibration of ion-selective electrodes. Thus, a conventional scale of ionic activities must be defined on the basis of suitably selected standards. In addition, this definition must be consistent with the definition of the conventional activity scale for the oxonium ion, i.e. the definition of the practical pH scale. Similarly, the individual scales for the various ions must be mutually consistent, i.e. they must satisfy the relationship between the experimentally measurable mean activity of the electrolyte and the defined activities of the cation and anion in view of Eq. (1.1.11). Thus, by using galvanic cells without transport, e.g. a sodium-ion-selective glass electrode and a Cl -selective electrode in a NaCl solution, a series of (NaCl) is obtained from which the individual ion activity aNa+ is determined on the basis of the Bates-Guggenheim convention for acr (page 37). Table 6.1 lists three such standard solutions, where pNa = -logflNa+, etc. 

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 mci of added alkali chloride. In a subsequent step, the value of the acidity function at zero chloride molality, lg(flHyci)°, is determined by linear extrapolation. The activity of chloride is immeasurable. The activity coefficient of the chloride ion at zero chloride molality, yci, is calculated using the Bates-Guggenheim convention (Eq. 5) which is based on the Debye-Hiickel theory. The convention assumes that the product of constant B and ion size parameter a are equal to 1.5 (kg mol1)1/2 in a temperature range 5 to 50 °C and in all selected buffers at low ionic strength (I < 0.1 mol kg-1). 

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 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. 

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 [10], which uses a virial... 

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... 

The Bates-Guggenheim convention (7) assumes that the trace activity coefficient of the chloride ion ffciis given by... 

Ionic strength <0.1 mol kg to permit applicability of Bates-Guggenheim convention. 

The palladised-platinum hydrogen electrode is used to reduce the catalytised chemical reduction of the phthalate by hydrogen gas. The calculation involves a non-thermodynamic assumption, the Bates-Guggenheim Convention, for the single ion activity of the chloride ion - as... 

In order to obtain the pH of a solution from Ig(aHrci) independent way for getting the value of xci is needed. It is done by extrapolating Ig(flHyci) to zero chloride molality (lg(af]yci)°) and using the Bates-Guggenheim convention [34]. The convention proposes that die trace activity coefficient of the chloride ions (y°) can be caleulated on the basis of Debye-Hiickel theory, that is,... 

This expression, however, involves the activity coefficient of an individual ion, that cannot be measured but is assigned conventionally (the Bates-Guggenheim convention) as ... 

The quantity p(%Yci) = Ig (%YciX on the left hand side of (4), is called the acidity function (5). To obtain the quantity pH according to eqn. (2) from the acidity function, it is necessary to evaluate Ig g,- independently. This is done in two steps (i) the value of Ig (OhYci) t zero chloride molality, Ig (%Yci)°> is evaluated and (ii) a value for the activity of the chloride ion y°ci > nt zero chloride molality (sometimes referred to as the limiting or trace activity coefficient) is calculated using the Bates-Guggenheim convention (7). The value of Ig (anYa) corresponding to zero chloride molality is determined by linear extrapolation of measurements using Hamed cells with at least three added molalities of sodium or potassium chloride (/< 0.1 mol kg" ). 

The required attributes listed above effectively limit the range of primary buffers available to between pH 3 and 10 (at 25 C). Calcium hydroxide and potassium tetraoxalate are 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 piperazine phosphate) and the zwitterionic buffers (e.g. HEPES and MOPS (10)). These do not comply because either the Bates-Guggenheim convention is not applicable, or the liquid junction potentials 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. The uncertainties (11) associated with Hamed cell measurements are calculated (1) to be 0.004 in pH at NMIs, with typical variation between batches of primary standard buffers of0.003. 

The most illustrative examples of UP minimization and optimization can be found in the traditional area of pH measurements [42, 72]. It forms an important part of Bates-Guggenheim convention [21]. However, one should note that this convention also assumes an extrathermodynamic assumption, in which unknown accuracy is partly compensated by numerous calibrations. The example of later attempts to further improve UP aspects of the glass electrode can be found in ref. [73]. 

Bates-Guggenheim convention is restricted to solutions of low ionic strength, I < 0.1 mol kg . Values of pH that include all sources of uncertainty excepting that of the Bates-Guggenheim convention, as is the common practice, are considered conventional pH values, which is sufficient for most applications [18],... 

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