Quick Notes Ionic Product of Water, Kw

  • The ionic product of water, Kw, is a constant that links the concentration of OH-(aq) ions in solution to the concentration of H+(aq) ions in solution.
    Kw = [H+][OH-] Kw expression pH ionic product of water
  • To find the pH of an alkaline solution, the concentration of H+(aq) ions in solution can be found using the ionic product of water, Kw.
    [H+] = Kw divided by [OH-] finding H+ concentration using Kw
  • At 298K, Kw has a fixed value (1 x 10-14).

Full Notes Ionic Product of Water, Kw

Up until now, we have just linked pH to H+ ion concentration in a solution. This is fine for calculating the pH of an acidic solution, as it is only the concentration of H+(aq) ions we need to worry about.

If we only have an alkaline solution, however, there is no H+ ion concentration to use for a pH calculation – this concentration needs to be found based upon the concentration of hydroxide (OH-(aq)) ions present. For example, if you have a solution of 1.0 mol dm-3 sodium hydroxide, NaOH, there is no H+ ion concentration to use for calculating pH. Instead, we need to find the H+(aq) concentration based on the hydroxide ion concentration.

Kw, Ionic Product of Water

In water, a very small percentage of molecules dissociate to release H+ and OH- ions. It’s only a small percentage that dissociate but, because the number of water molecules present in a solution is so high, there is still a concentration of H+ ions. There is an equilibrium between the water, the hydroxide ions and protons present.

dissociation of water as a weak acid

Here, the water is acting as a weak acid and, even though the position of equilibrium massively favours the backward reaction, a Ka expression can still be applied.

Ka expression acid dissociation constant for water weak acid

As already mentioned, the actual number of water molecules dissociating is so small the overall concentration of water molecules remains effectively the same – this means we can consider it to be ‘constant’.

rearranging Ka expression acid dissociation constant for water weak acid

The Ka of a weak acid is also constant (at a given temperature), this means Ka and [H2O] can be treated as two constants that are never going to change at a particular temperature. These are multiplied together to give a new ‘combined’ constant, Kw. This constant is called the ionic product of water and has a value of 1x10-14 at 298K.

Ka x [H2O] = Kw ionic product of water from acid dissociation constant of water

This gives us a new expression:

Kw = [H+][OH-]

When dealing with alkaline solutions, the concentration of the alkali can be used to find the concentration of H+ ions present by using the above Kw expression. The concentration of H+ ions can then be used to find the pH (pH = -log10[H+(aq)]).

finding H+ concentration from Kw and concentration of OH-