pH = - log10 ( gammaH x mH)
gammaH = hydrogen ion single ion activity coefficient
mH = molality of the hydrogen ion.
As pH can not be directly measured, it is defined operationally according to the method used to determine it. IUPAC recommend several standardised methods for the determination of pH in solution in aqueous solutions. There are seven primary reference standards that can be used, including 0.05 mol/kg potassium hydrogen phthalate as the Reference Value Standard. There is an ongoing debate concerning the relative merits of having a multiple primary standard scale ( that defines pH using several primary standards, and their values are determined using a cell without a liquid junction ) or a single primary standard ( that requires a cell with a liquid junction ). Interested readers can obtain further information on the debate in . Bates , is a popular text covering both theory and practise of pH measurement.
The glass electrode consists of a glass shaft on which a bulb of a special glass is mounted. The inner is filled with KCl, most often at a concentration of 3 Mol/liter and sealed. Electrical contact is provided by the way of a silver wire immersed in the KCl.
Normally this glass electrode is surrounded by a concentric reference electrode. This reference electrode can consists of a silver wire in contact with the almost insoluble AgCl. The electrical contact with the meter is through the silver wire. The contact with the solution to be measured is by way of a KCl filling solution which is physically in contact with the solution to be measured. In order to minimise mixing of the solution to be measured and the filling solution, a porous sealing, the diaphragm, is used. Alternatively other devices which allow a slow mixing contact can also be used. Besides the "normal" KCl solutions, often solutions with an increased viscosity, and hence lower mixing rate are used. In stead of a liquid KCl filling, also gel filling is used. This eliminates the necessity of low mixing devices. The glass electrode in contact with some solution gives in respect to the reference electrode a voltage of about 0 mV at pH 7, increasing with 59 mV per pH above 7 or decreasing with 59 mV per pH unit below 7. Both the slope and the intercept of the curve between pH and generated potential are temperature dependent. In fact, the potential of the electrode is roughly given by the Nernst equation :
E = E0 - RT log [H+] = E0 + RT pH
In which E is de generated potential, E0 is a constant, R is universal gas constant and T is the temperature in degrees Kelvin. All pH dependent glasses are also susceptible to other ions, such as Na or K. This gives an correction on the above equation. By this reason the relation between pH and generated voltage becomes nonlinear at high pH values.
Also the slope tends to diminish as the electrode wears out. At high pH the slope tends also to diminish. As the electrode has a very high impedance, typically 250 Mega Ohms to 1 giga Ohm, it is absolutely necessary to use a very high impedance measuring apparatus.
The reference electrode has a potential that does normally not vary too much. However the potential is also temperature dependent and can also vary if the activity of the silver ions in the reference electrode would vary. This can be the case if a pollutant enters the reference electrode.
To adjust, one should take care not to work too fast, so as to be sure that the system is in equilibrium. Also the pH meter should be already powered on for some time so as to ensure that all components are in a thermal steady state. On should first use the buffer at pH 7 and adjust the zero (or the intercept). Thereafter, one should use the buffer at a different pH to adjust the slope. This cycle in repeated at least once or until no further adjustments are necessary. Note many modern pH meters have an automatic calibration feature. In this case one only needs to use each buffer only once.
A similar case can develop if the glass wall between the inner and the outer part of a combined electrode break. This is possible eg. in case the outer part is made of a plastic material, which is bent. The inner part can crack without any marks on the outside. The electrical resistivity is over the glass electrode itself intact, but actual measuring between both electrodes reveals as in previous case a low resistivity. The remedy is the same as in previous case : replace the electrode.
The glass can wear out. This gives slow response times as well as a lower slope of the mV versus pH curve. The first remedy possible is to put the electrode in a 3 Molar KCl solution at 55 degrees celsius for 5 hours. This should revitalise to some extend the electrode. If this does not help, one can refurbish the electrode by removing a layer of the glass. This is done by putting the electrode for two minutes in a (plastic!) container containing a mixture of HCl and KF (be careful, do not breath the fumes; wear gloves). Afterwards the electrode is put two more minutes in HCl, and rinsed thoroughly. As a part of the glass in physically removed, the new surface will be about as good as the original new surface. However because the glass is now less thick, this shortens the life of the electrode. After this remedy the first days, a very frequent recalibration is required. The glass can be dirty. If a film of some product lays on the glass, the glass still measures correctly but does not measure the pH in the solution to be measured but the pH in the layer of surrounding product instead. This is seen normally by very slow response times and obviously wrong pH values. Also the pH may vary according to the buffer capacity and/or the stirring rate in the solution to be measured. If one knows exactly what product it is, one should dissolve the product using an adequate solvent. In the general case one should normally first dip the affected electrode a few minutes in a strongly alcaline solution, followed by immersing it in a strong acid (HCl) solution. If this does not help, one should try pepsin in HCl. If still unsuccessful, one can use the HCl/KF method described in the previous paragraph.
There is no contact over the diaphragm, due to some air bubbles. This is seen exactly as if the diagram were blocked, except that the diaphragm has its normal color. In this case one should make sure that the liquid is at all times (slowly) flowing from the reference electrode towards the liquid to measure.
A polluting substance did enter the reference electrode. This is seen as unstable or wrong pH measurements. Often the pH at which the output of the system is 0 mV differs considerably from pH 7. The diaphragm has its normal color and the electrical resistivity is normal. However, quite often this case is combined with the previous case, which invalidates the previous statement. The remedy is to replace, eventually several times the reference liquid. In many cases, however, the electrode will be permanently damaged. One can prevent this to happen by choosing for gel filled reference electrodes, double junction electrodes or by making sure that there is at all times an net outflow of reference liquid towards the solution to be measured.
The electrode was filled with a wrong reference solution. This is seen as pH measurements which are shifted. Replace the reference liquid.