The modern concept of pH requires a primary method measurement in order to maintain validity as a definition. Specifically, some sort of method is required to calibrate standard buffer solutions, against which the pH of all substances can be measured. The experimental apparatus used by IUPAC to assign standard pH values to primary standard pH buffer solutions is based on the Harned cell.
The cell itself is composed of two half-cells, one with the standard platinum-hydrogen electrode and the other with a silver/silver chloride electrode (though originally the mercury-based calomel electrode was used, these days people have trended away from it, owing perhaps to the extreme toxicity of mercury compounds). A simplified diagram can be used to represent an idealised cell:
The two electrodes are immersed in the same reference buffer, the substance which is being evaluated as a reference standard.
The spontaneous cell reaction which takes place can be described by the following equation:
½ H2 + AgCl →Ag(s) + H+ + Cl-
This reaction generates a current E, which together with the known concentration variables can be plugged into the Nernst equation to arrive at the pH value. The precise equations which are used for this are clearly described in the IUPAC document (section 4.1, Harned cell as a primary method for the absolute measurement of pH).
The Danish National Metrology Institute hosts an image of their actual working Harned cell apparatus, which I have reproduced here without their permission, and with substantial modification, but with the best intentions.
IUPAC produce an extensive discussion of the uncertainties involved in using the Harned cell for the measurement of pH. Among the various objections raised, the following are interesting:
This level of accuracy is probably good enough for government work. The pragmatic intensivist will wave aside concerns regarding miniscule error and the influence of the inadequacies of electrolyte theories. The most important concern, from the point of view of bedisde medicine, is that a Harned cell takes hours to prepare, and a considerable level of skill to operate. Additionally, in order to arrive at measurements which meet some sort of international standard, one needs to perform them in a buffer with at least three different concentrations of added chloride.
In short, the potentiometric method of measurement is too cumbersome for bedside use.
Additionally, from an article by Susumu Nakamura for the National Metrology Institute of Japan I have discovered that the stabilization time for the Harned cell experiment is around 3 hours, which is too long to wait for an ABG result.
Fortunately, we have various metrology institutes whose skilled staff have the time and patience to produce commercially available reference buffer solutions. These can in turn be used to calibrate other methods of measurement, which are more convenient and which allow a rapid assesment of acid-base balance.
Such methods - of which the glass electrode is the undisputed king - merit a more detailed discussion.