pH - Have you ever thought what it really is?

Most of us should know that the pH of a substance determines its acidity (or alkalinity). We know that both acids and alkalies are opposites of each other. An acid will react with an alkaline to neutralise it. pH is measured on the pH scale, with water being 'neutral'. However, have you ever thought what pH actually is?
In a nutshell, the pH of a substance measures how much a substance will dissociate when put in water.
This is when a hydrogen atom, attached by a covalent bond (shared electron) to a compound in an acid, breaks  free of the bond. However, with it breaking free it leaves behind its only electron: it is now a single proton with a positive charge. This little proton then attaches itself to a nearby water molecule (as the acid/alkali is in water) and forms the compound H3O. This is just water (H2O) with an extra hydrogen (H). Although the proton has now lost its electron it is still considered a Hydrogen molecule. The H3O ion (as it is now a positively charged particle - extra proton, but no extra electron) is extremely important, to the extent it has a special name of its own: hydronium. It is the measure of hydronium in a solution of an acid or base (which is an alkali dissolved in water) is rated on the pH scale. A low pH indicates there is a lot of hydronium, whereas a high pH indicates there is a smaller and smaller amount. Here's an example of an acid and water reaction, you can clearly see that H3O is left behind:
H2SO4 + H2O → H3O+ + HSO4−
The pH scale isn't just limited between 0 and 14, those are just the values which are naturally available, it can go above and below that into the minus numbers! However, if you have pure water, as much as you might like to think it is almost never pure. In fact, pure water self-ionises naturally over time. This is when one proton (hydrogen atom without its electron) transfers itself from one water molecule to another. This produces two oppositely charged ions and here is the equation:
H2O + H2O  H3O+ + OH−
However, water does not go on like this for ever, otherwise its pH would just keep falling! Eventually enough of it has undergone chemical change for it to be considerably less likely to react - a kind of equilibrium - the pH of that equilibrium just happens to be pH 7. That's why we call pH 7 neutral - its the pH of stability, and we base the scale around that.
So, any acid will naturally be a very good electrolyte (a substance which contains free ions, making it a good electrical conductor). This also explains why they use battery acid inside of batteries, as when the protons leave the acidic compounds, they make the compounds positive ions. Since electricity is the flow of charge (not electrons! That is just a very common method of transmitting charge) this means electric current can pass through!
If you have any questions please feel free to post below.