A few points on pH

In another article, I broke down a misleading chart taken from a health-food store, that contained all kinds of mistakes about the pH of foods and waters.  In this post, I take some time to explain what pH means and how it is obtained.

A very brief chart of pH range.

First, let us establish what is meant by pH – and note that it is not written “Ph” or “PH” or “ph”.  The “H” represents hydrogen ions (H+), but that could be any ion – pOH for hydroxide (OH-) ions, pCa for calcium (Ca2+) ions, pMg for magnesium (Mg2+) ions, and so on.  The “p” is said to stand for potential (as in electric potential – what we often call “voltage”), since pH is normally calculated from a voltage measurement; but to chemists, “p” is taken to mean the negative of the base-10 logarithm of the concentration of the ion.  Therefore, a solution with pH 7 has a concentration of 10-7 (0.0000001) mol/L of H+, which works out to approximately 0.1 ug/L.  A solution with pH 6 has a concentration of 10-6 (0.000001) mol/L, or ~1 ug/L of H+, which is ten times more.  In fact, a one-unit decrease in pH represents a tenfold increase in concentration of H+.  Using p-values makes calculations much easier when working with solution concentrations that well below 1 mol/L; instead of working with tiny numbers like 10-7, we can work with small positive numbers like 7.  (Chemistry experts will note that this description is not strictly true – the measured pH is actually based not on concentration, but on activity of the H+ ion, and the activity can vary from the concentration if the ion interacts with other ions in the solution.  At low concentrations, the difference is negligible.)

 

Another important feature of water is tied to the fact that “pure” water has a pH of 7.  In fact, there is no such thing as completely pure, ion-free water; even what we call “pure” water has 10-7 mol/L, or ~0.1 ug/L, of H+.  The atoms in a water molecule are bonded in the order H-O-H; like many compounds with a terminal hydrogen, they will tend to dissociate slightly – that is, the end hydrogen separates from the rest of the molecule, leaving behind its one electron.  For water, this results in the hydrogen ion (H+) and the hydroxide ion (OH-).  In “pure” water, these two will be the same concentration; this means that the pOH of pure water is also 7.

 

Note that the sum of pH and pOH in pure water is 14; this is true for any solution made in water at 25°C.  If we multiplied these molar concentrations of H+ and OH-, we get 10-7 x 10-7 = 10-14; that product is known as the dissociation constant of water at 25°C.  The product of their concentrations will always give 10-14 at 25°C, since these ions exist in equilibrium.  The “p-value” of the dissociation constant is therefore 14 at 25°C.

 

Also note that this ability of water to dissociate is not uncommon – in fact, by definition, any acid dissociates in solution to form H+, along with the rest of the molecule as a negative ion.  For example, acetic acid (CH3COOH) dissociates to form H+ and the acetate ion (CH3COO-) in solution.  Only a fraction of acetic acid molecules are dissociated at any time, which makes it a weak acid.  Citric acid, found in citrus fruit, is also a weak acid but tends to dissociate a bit more than acetic acid.  The relative weakness of acids can be determined quantitatively by looking at the acid dissociation constant; the larger the constant, the stronger the acid.  (Note that some compounds, such as citric acid, have several terminal hydrogens that can dissociate; in their case, each hydrogen has its own acid dissociation constant.)  A strong acid, such as hydrochloric acid, is dissociated at 100% at all times, and would have an extremely large acid dissociation constant.  This also means that water itself can act as a weak acid, since at any time, a fraction of its molecules are dissociated and leave behind H+.

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