What is pH?

When teaching and consulting about pH and buffers, I often get asked if the pH can be measured in some solvent (other than water) and if it can, what does it mean? In fact, it is a good bet that the commonly employed glass electrode will work (I’ll address the definition of “work” later) to measure pH in most situations and that the values displayed on the meter can be used to make quantitative comparison of the acidity of most places a pH probe can be stuck. Samples as diverse as concrete, LC solvents (1), chicken breasts, armpits, blood and dirt are measured routinely for practical purposes.

There are practical issues with measuring pH. A curious chemist will stick a pH probe into a sample; he or she will observe what appears to be an unusual reading on the meter, conclude the measurement is not working and give up. A lack of understanding of pH leads to this false conclusion. In school, we are taught that pH is the negative log of the hydrogen ion concentration. Indeed, this was the first definition proposed by Sørensen when the concept of pH was conceived in 1909. Though this definition makes solving test problems in the academic environment easy, the definition is of no practical utility. And no pH-measuring device is capable of measuring hydrogen ion concentration.

A more sophisticated definition is that pH is the negative log of hydrogen ion activity. But this gives us another problem: how do we prepare calibration standards of known hydrogen ion activity in the sample matrix of interest? It took nearly 100 years to solve this problem for dilute aqueous solutions in the midrange of pH (2). Standards of estimated hydrogen ion activity for a few partially aqueous solutions have also been developed (3).

But commerce demanded the world’s standardization organizations establish a consistent definition for pH that could support manufacturing, trade, research, and so on, in all sorts of samples. The result was a definition for pH unlike most we encounter in science – it has a value resulting from a series of distinct operations; so, it’s an “operation definition”. The pH-measuring device is calibrated by some disclosed procedure, the sample is measured, and pH is the resulting measurement. We would be hard pressed to figure out hydrogen ion activity from these pH measurement, but this limitation does not diminish in the slightest our ability to put the measurement to practical use.

There is one case where the pH measurement does yield a value for negative log of hydrogen ion activity. Primary Standard aqueous pH standards are dilute, aqueous and cover the midrange of pH values. The hydrogen ion activity of these standards has been measured/calculated to three significant figures (2). If a pH electrode is calibrated with these standards and then used to measure sample that is dilute (low ionic strength), aqueous and in the midrange of pH, the value measured is the hydrogen ion activity in the solution. This value can be reliably used to calculate species activities in equilibrium, if the equilibrium constant is known.

Interpretation problems arise when pH electrodes are stuck in places other than dilute aqueous solutions. How can we interpret the reading in a solvent other than water or a mixture of solvent and water, for example an LC mobile phase? The glass electrode responds in a predictable way to changes in hydrogen ion activity in many solvents and solvent mixtures – alcohols, glycols, acetic acid, acetonitrile, to name a few. A successful approach is to calibrate the electrode with aqueous standards and take the measurement in the solvent or solvent mixture. It may take minutes for the electrode to equilibrate in this new environment so be patient. If the measurement is stable and the value seems to correlate with the solution’s acidity, it is likely that it can be used to quantitatively compare the acidities among samples of this solvent composition.

The pH measured will be proportional to the solutions hydrogen ion activity but the measurement will offer no clue as to the absolute acidity or basicity. Do not make the mistake of interpreting the number based on a pH scale in water. For some thermodynamic reasons involving standard state and some electrochemical details (such as a change in junction potential), pH 7 will not be the neutral pH of some solvent other than water. A measured pH of 7 in this or that solvent could even be strongly acidic or basic. There is no way to know from the measurement. But that does not make the measurement meaningless or useless.

In summary, only in rare cases does a pH measurement yield an absolute measure of a solution’s hydrogen ion activity. However, in most cases the pH measurement will provide a quantitative comparison of solution acidity/basicity – providing the solutions being compared have essentially the same solvent composition.