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Physical Chemistry 76

is sufficiently small that their activity coefficients can be approximated to 1 (see Topic
C1) and .
+
From this equation it can be calculated that in pure water the concentrations of H 3O
−
−3
−7
and OH are both equal and are 1.00×10 mol dm at 298 K.
The pH scale

The equation:
pK w=14.00=pH+pOH

is obtained by taking the negative logarithm to the base 10 of the autoprotolysis equation,
where

In general pX denotes −log 10 of any given variable, X, so that an increase in X results in a
decrease in pX. This equation applies in all aqueous solutions, and it allows the definition
of the pH scale for water acidity. From the pH of a solution, pOH can always be found
from this equation, and the balance of these terms determines the water acidity. For
example, when pH=7, then pOH=7 and the water solution is neutral, as the activities of
−7
−
+
both H 3O and of OH are equal at 10 . When pH<7 and pOH>7, the solution has an
+
excess of H 3O and is described as an acidic solution. When pH>7 and pOH<7, the
−
solution has an excess of OH and is described as a basic solution. It must be
remembered that an increase of one unit in pH corresponds to a ten-fold decrease in the
hydronium ion activity and a ten-fold increase in the hydroxide ion activity.
In terms of concentration (see Topics C1, E1 and E2):

where γ i is the activity coefficient of species i.
Often, at low ionic strength (see Topic E2), the log 10γ terms are sufficiently small to
enable a reasonable estimate of the concentration of the hydronium and hydroxide ions
from the pH value: