Measuring Acidity: the pH scale
The proper function of biological systems depends on the correct concentration of hydrogen ions (H+ or more correctly H3O+) in an aqueous solution. The concentration of H+ in water can range from higher than 1.0 M (extremely acidic), to lower than 0.00000000000001 or 10-14 M (extremely basic). The pH scale was devised by Soren Sorenson to simplify dealing with the wide range of hydrogen ion concentrations (labelled [H+]) in aqueous solutions. The pH is defined as the negative logarithm of the hydrogen ion concentration:
pH = – log[H+] and [H+] = 10 -pH
An example of an extremely acidic solution is one for which [H+] =1 M (=100M) or pH = 0
An example of an extremely basic solution is one for which [H+] = 10-14 M or pH = 14
Notice that Sorenson chose to drop the minus sign, so our extreme base has a pH of 14, not -14. This is nice because we avoid negative numbers, but a bit tricky, since it means that the BIGGER the pH, the LOWER the concentration of H+.
The concentration of H+ in pure water is 10-7M, as is the concentration of OH– ions. H2O is itself a weak acid and dissociates into H+ and OH –. The equilibrium constant for this dissociation is:
K = [H+][OH–] / [H2O]
The value of K is 1.8 x 10-16 M at 25 0C. This can be simplified by realizing that there is a large excess of water which has a molar concentration of 55.56 M and can be assumed to be constant. The equation simplifies to:
K [H2O] = [H+] [OH–] = 1.8 x 10-16 x 55.56 = 1 x 10 -14 M2.
This is known as the ionic product of water, Kw:
Kw= [H+] [OH–] = 10-7 x 10-7 = 10 -14 M2
If the pH of the solution is less than 7 it means that the [H+] is greater than 10-7 M and the solution is acidic. If the pH is greater than 7, [H+] is less than 10-7 M and the solution is basic. A solution of pH 7 is neutral.
Every time we go one “step” up (or down) on the pH scale, we increase (or decrease) the concentration of hydrogen ions by a factor of 10. This is an important characteristic of using logs: adding 1 to the log, or subtracting 1 from the log, changes the original number by a factor of 10 (multiplies or divides by 10). Hence:
Increasing/decreasing by 1 on a log scale corresponds to multiplying/dividing by 10 on the original scale
Increasing/decreasing by 2 on a log scale corresponds to multiplying/dividing by 100 on the original scale
Increasing/decreasing by 3 on a log scale corresponds to multiplying/dividing by 1000 on the original scale
and so on…
It works a little differently for pH, because pH is the negative log of concentration. So, every time we SUBTRACT a single pH unit (like going from 2 to 1), we multiply H+ by 10.