pH, pOH and the Ionization of Water

So what?  What does pOH have to do with pH?  Or come to think of it, how can a solution of a 0.1 M NaOH solution have a pH?  After all, there are only Na⁺ and OH^- that result from NaOH dissolving in solution, right?

Well to see how pH and pOH tie together and why the concept of pH is so important in defining where the water balance lies, take a closer look at the ionization of water equilibrium.  (What follows is a somewhat simplified equation for the ionization of water and the equilibrium constant for this equilibrium.)

H2O(l) ⇆ H⁺(aq) + OH^-(aq)                Kw = [H⁺] * [OH^-] = 1 X 10^-14

This equation points out that whenever there is a water solution, you will always find both H⁺ and OH^- ions present.  The equilibrium constant implies that there will not be very many H⁺ or OH^- ions present.  This is true for all water solutions . . . whether it is a latex paint solution, blood, ground water, lemon juice, soap solutions,  . . . Any water solution.  Recalling LeChatelier's principle, check out the implications for these various solutions.

A distilled water solution.  Looking at the equilibrium constant expression, we can calculate the [H⁺] and the [OH^-] for the water solution.  Since the [H⁺] and [OH^-] should be the same . . .
[H⁺] and [OH^-] = 1 x 10^-14
[H⁺]² = 1 x 10^-14
[H⁺] = 1 x 10^-7 M
[OH^-] = 1 x 10^-7 M
This means that the pH = 7 and the pOH = 7 for neutral distilled water.

An acidic solution.  If we have an acid that has a pH of 5, we can conclude that the [H⁺] = 1 x 10^-5 M.  Using the equilibrium constant expression, we can determine the [OH^-].
[H⁺] * [OH^-] = 1 x 10^-14
10^-5 * [OH^-] = 10^-14
[OH-] = 10^-14/10^-5 = 10^-9M
This implies that the pOH = 9

A basic solution.  If we have a base that has a pH of 10, we can conclude that the [H⁺] = 1 x 10 ^-10 M = 10^-10M.  Using the equilibrium constant expression, we can determine the [OH^-].
[H⁺] * [OH^-] = 1 x 10^-14
10-10 * [OH^-] = 10^-14
[OH^-] = 10^-14/10^-10 = 10^-4M
This implies that the pOH = 4.

Summarizing the findings...

Hopefully you can induce a very important relationship that applies to all water solutions.  Notice what pH + pOH always equals.  This leads us to state these relationships.

All water solutions have H⁺ and OH^- in them.  There is only one situation where the H⁺ and OH^- are equal.  That is a neutral solution.  [H⁺] = [OH^-] = 10^-7M.  Acids have [H⁺] >10^-7M.  Bases have [H⁺] < 10^-7M and [OH^-] > 10^-7M.

Picture this like this...

Relative Concentration of H⁺ and OH^- in Water Solutions

If you know either [H⁺] or [OH^-], the other concentration can be determined.

For example, determine the pH of a 0.0045M NaOH solution.

[OH^-] = 4.5 x 10^-3M
pOH = - log(4.5 x 10^-3) = 2.3
pH = 14 - pOH = 11.7
[H⁺] = (1 x 10^-14)/(4.5 x 10^-3) = 2 x 10^-12M