In pure water the concentrations of these ions have been worked out and are known to both be found at 1×10^ -7 moles each. The dissociation constant is something used to describe the rate at which the dissociation to give these ions occurs. I'm not going to explain what this means now but you can look it up if you're interested.
The formula for working out the dissociation constant is:
We known that the concentration of pure water (H2O) is 55.6M and we know that the concentrations of H+ and OH- are both 1×10^ -7M, so lets put that into the equation:
Ka = 1×10^ -7 × 1×10^ -7 / 55.6^2
If we look back at the equation above we can rearrange it:
Ka × 55.6^ 2 = 1×10^ -7 × 1×10^ -7
The first part is known as Kw to simplify it. It will always be equal to 1×10^ -7 × 1×10^ -7, or 1×10^ -14
Now, in a solution that isn't pure water, the concentrations of H+ and OH- will differ. In a strong acid, the concentration of H+ ions is high while in a very basic solution there are very little free H+ ions. While the concentrations of H+ and OH- can differ, the product ([H+] × [OH-]) will always be 1×10^ -14 (as Kw is always 1×10^ -14).
Remember the formula for pH is: pH = -log [H+]? We can also use the same formula for pOH (the concentrations of OH- ions): pOH = -log [OH-]
If: [H+] [OH-] = 1×10^ -14, we can use the rules of multiplying logarithms to rearrange to give:
pH + pOH = 14
You can't have a negative concentration so the maximum pH can only ever be 14 when pOH is 0.
Rules of logarithms:
Log(a × b) = Log(a) + Log(b)
Log(a ÷ b ) = Log(a) - Log(b)
Log(a^b) = b × Log(a)
