Tuesday, 24 November 2009

Why do we measure hydrogen ions in pH?

Ever wondered why we measure the concentration of hydrogen ions as pH, rather than as mmols, by which so many other bodily substances are calibrated?

First up, what does pH mean? The ‘p’, by convention, stands for ‘-log’. Thus the pH scale is a negatively logarithmic one. The negative means that if the hydrogen ion concentration goes up, the pH is recorded as going down, and vice versa. In other words, a pH of 3 is much more acidic than a pH of 7. And as for why we use logarithms, this is simply a convenient calibration to use in certain circumstances, especially when the variability of the thing being measured (i.e. the variation in hydrogen ion concentration) covers several orders of magnitude.

But back to the question – why do we measure hydrogen ions by their negative logarithm, but not (say) sodium ions? One of the problems is that the concentration of hydrogen ions is truly tiny when compared with other ions. To use an example from my physiology textbook, the concentration of sodium in extracellular fluid (~140 mmol/L) is about 3.5 million times as great as the normal concentration of hydrogen – which averages only 0.0004 mmol/L! Therefore we’d need to move away from mmol/L anyway to prevent ourselves from eternally writing zeros when it comes to talking about hydrogen ion concentrations.

However, if this were the only concern, we could just shift from talking about millimoles to micromoles, as we do (at least here outside America!) with creatinine. (A normal value in a man might be 85 μmol/dL.) The even smaller scale of nanomoles might have been even better. There is another, truer reason, that we measure hydrogen ions in a logarithmic scale, and it turns out to be disappointingly capricious.

As I alluded to above, logarithmic scales are useful when the data you are measuring cover several orders of magnitude. Chemists did the first and most detailed work on hydrogen ion concentrations, and found that the concentrations in their experiments could rapidly vary by trillions of times. One minute the hydrogen ions might clock up a puny 0.000000005 mol/L, but then they added another chemical and found that this number jumped to 0.2 mol/L. In circumstances like these, they found it easier to track the changes in logarithmic form. The above jump, for instance would have been from 8.3 to 0.69 – much more manageably notated!

And we in medicine simply inherited this way of dealing with hydrogen ions – even though the total variability of hydrogen ions in a (living) human being is only about 15 fold. We could have used picomoles and been quite happy, had it not been for the chemists.

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