5.1.3 (e,f) The Ionic Product of Water, Kw

Syllabus

(e) use of the expression for the ionic product of water, Kw

(f) calculations of pH, or related quantities, for:

(i) strong monobasic acids

(ii) strong bases, using Kw

What does this mean?

What is Kw?

Water can dissociate into ions, although it is not good at doing so.

The concentrations of ions formed are very small.

If we wrote a Kc for the dissociation it would be:

But, instead, we use the similar expression:

Sometimes examiners ask why Kw drops the [H2O] term.

DON'T say that you can't measure the concentration of water in water.

It's perfectly possible to work out how many moles of water molecules are in 1 dm3.

So the concentration of water exists but it is a very high number, and both [H+] & [OH-] are very small.

So if we included [H2O] we would have an exceptionally low number for Kw.

At hotter temperatures water dissociates a little more.

So, [H+] & [OH-] increase in a measurable way.

But so little water would be used up that [H2O] would remain almost constant.

Since it is constant dropping it is not a problem, and it makes the value of Kw more useful since it will change more markedly.

Even without [H2O] in Kw the value is 1 x 10-14 at 25oC (298K)

This is the only value you might be expected to remember.

Usually people recall it because it explains why the pH is generally said to go up to 14 (not strictly true).

If, Kw = 1 x 10-14 for pure water at 25oC then [H+] & [OH-] must both be 1 x 10-7 since the dissociation of water ( H2O ⇌ H+ + OH-) cannot avoid producing equal amounts of both ions.

And if [H+] = 1 x 10-7, pH = -log10(1 x 10-7) = 7.

So the reason you were told at age 11 that neutral pH = 7 is that this is true under standard conditions.

Since it is generally not 25oC, neutral pH is generally not exactly 7 but it is so close that it makes little difference.