The pH of pure water

In fact, pure water only has a pH of 7 at a particular temperature 25^oC - the temperature at which the K_w value is 1.00 x 10^-14 mol² dm^-6.

This is how it comes about:

To find the pH you need first to find the hydrogen ion concentration (or hydroxonium ion concentration - it's the same thing). Then you convert it to pH.

In pure water at room temperature the K_w value tells you that:

[H⁺] [OH^-] = 1.00 · 10^-14

But in pure water, the hydrogen ion (hydroxonium ion) concentration must be equal to the hydroxide ion concentration. For every hydrogen ion formed, there is a hydroxide ion formed as well.

That means that you can replace the [OH^-] term in the K_w expression by another [H⁺].

[H⁺]² = 1.00 x 10^-14

Taking the square root of each side gives:

[H⁺] = 1.00 · 10^-7 mol dm^-3

Converting that into pH:

pH = - lg[H⁺]

pH = 7

That's where the familiar value of 7 comes from.