There is a formula linking the values of pH and pOH which allows determining the pH or pOH based on one another.
It is derived from the expression of water ionization, Kw = [H+][OH–].
To get the pH and pOH correlation, we take a negative log of both sides of the equation:
-log [H+] + (- log [OH–]) = – log 10-14
Notice that the terms on the left represent the pH and pOH of the solution (-log [H+] = pH, – log [OH–] = pOH). Therefore, we can write that:
pH + pOH = 14
Let’s see how this can be used to calculate, for example, the pH from pOH.
For example, determine the pH of a 0.850 M NaOH.
The strategy here is to calculate the pOH and then, using the pH + pOH = 14 relationship, determine the pH.
NaOH is a strong base, so [OH–] = [NaOH], and therefore, the pOH is:
pOH = -log 0.850 = 0.0706
The pH then is equal to:
pH = 14 – pOH = 14 – 0.0706 = 13.9
As expected, the pH is very high because it is a solution of a strong base.