You can never know too much chemistry: Part 3: pH

I remember asking students when I first came to the UTC: "what does the 'p' stand for in pH?" I was surprised at the answers: proportion? percentage? part? Not unreasonable guesses if you haven't been taught the origins of the scale used to measure the precise level of acidity or alkalinity of a solution. This question came hot on the heels of my first (in retrospect) more challenging question: can pH be greater than 14 or less than 1? It was clear that pH needed explaining properly. But before I move on, the p is thought by some to refer to the "power" as in force of the hydrogen ion in solution, but is formally defined as the decimal logarithm (log base 10) of the reciprocal hydrogen ion activity. Before I confuse you completely the term activity is often used synonymously with concentration, and at this stage in your studies I shall not burden you with the difference, but I will write about activity and concentration separately in respect of the buffers we use in Biological experiments. If you want to read more about p then there is a further comment here. Mathematically, pH  is written as follows:

The consequence of this logarithmic relationship, is that pH has no units (or it is said to be dimensionless). (I will not dwell on the use of logs here since we have covered this in lab classes last year, but again, it is a topic for the future and for now, you can find a basic explanation here). The use of the term pH was pioneered by the Danish Physical Chemist Soren Sorensen (pictured top left).

There are a few simple consequences of the above relationship. First as the pH increases, the concentration of H+ ions (sorry sometimes superscripting seems too many mouse clicks away) decreases, or alternatively, as the pH decreases, the concentration of H+ ions increases and consequently acidity increases. Secondly, the range of pH that we tend to work with in the laboratory is between a strong acid (pH3) and a strong base (or alkali) at pH11. However, in vivo, apart from localised exceptions, we maintain our net intracellular and body fluid pH at around 7. The problem with pHs beyond 3 (or 11) are related to the instrument used to measure pH (and more importantly the Nernst equation, relating pH and electrode potential) utilises an ion selective glass electrode, and the properties of glass electrodes become non-Nernstian at extremes of pH. It is worth noting that absolute measurements of Tris buffers require a dedicated Tris electrode (see here for an explanation). However, in principle pH can exceed the boundaries of 1-14, it just isn't commonly observed in most laboratories.

The ionization of water (and in fact we refer to pH more precisely in terms of the hydronium ion) is given as follows:

K_eq = [H+][OH-]/[H₂O], which is 1.0 * 10⁻¹⁴ at 25°C.

Therefore, a few simple things follow:

The pH of pure water is 7. Why? Can you work this out for yourselves?

The basic elements of acids (proton donors) and bases (as proton acceptors) is covered very concisely at this Chemguide site. 

Look up a definition for the term Ka and consider the form of the Henderson- Hasselbalch equation which is given below (and explained in full at the Chemwiki site). 

I will use the splendid Excel resources provided by Professor Scott Sinex, to illustrate the value of the H-H equation and I would encourage you to take a look yourselves, in advance (and after). 

Let me give you an indication of the value of this relationship in respect of amino acids. Take an amino acid such as glycine or histidine. IBoth have an acidic group (COO-) and a basic group (NH3+): these define the amino acid nature of these two molecules. In addition, it whilst Gly has two protons, one of which is referred to as the R group or the side chain, His has what is referred to as an imidazole side chain. For each of the ionizable protons, we can re-arrange the H-H equation, and produce a value for pKa, which is given by:

pKa = pH + log [HA] / [A^-]

(note the inversion of the acid (HA) and its conjugate base (A-). Hence the values of the pKas of the amino acid side chains gives an indication of their potential role in acid base catalysis. See here for more details and a list of values.

Why is this relationship useful?

• It tells us that when the pH = pKa then log [HA] / [A^-] = 0 therefore [HA] = [A^-]   i.e. equal amounts of the two forms, the acid and the conjugate base.

• If we make the solution more acidic, i.e. lower the pH, so pH < pKa, then log [HA] / [A^-] has to be > 0 so [HA] > [A^-]. This makes sense as it tells us that a stronger acid will cause the formation of HA, the protonated form.

• If instead we make the solution more basic, ie raise the pH, so pH > pKa and log [HA] / [A^-] has to be < 0 so [HA] < [A^-]. This makes sense as it tells us that a stronger base will cause the formation of A^- , the deprotonated form.

These features of amino acid side chains (shown in the figure left), are thought to be a key element of the mechanism of catalysis in a number of enzymes. In the example shown, two His residues of Ribonuclease A, perform a pincer movement on the RNA substrate, an example of amino acid side chains participating in acid base catalysis. You can see a detailed series of images here. The ability of the "ring nitrogens" to act as acid or base provides one of the pathways for removing the activation energy in this and a number of other enzymes.