It took me a while to knock up a bit of a not too mathematical explanation of pH during the thread on the acids wiki. In that thread it has aroused no comment so I post it here in case anyone is still interested, and had given up following that thread.
S
Spamlet says:
Some of the confusion comes from the way we tend to label acids as 'corrosive: causes burns', and alkalis as 'caustic: causes burns'...
The negative log gets you a nice round figure for one particular ion instead of having to quote for H+ *&* OH-, but it is by no means an easy concept to explain.
Let's have a go...
You could just say that: "Extremes of acidity or alkalinity are highly reactive and can cause serious burns": but how to indicate just how reactive they are? A useful way to make a scale of reactivity is to imagine a series of concentrations where each step is ten times stronger than the last. Such is the pH scale.
[You can think, similarly when you are heating solutions: a 10C rise in temperature approximately doubles the rate of reaction.]The 'H' in pH stands for hydrogen ion (H+). Positive ions like H+, are reactive atoms from which an electron has been removed: this is what *makes* them reactive in solution: they 'want' to get their electrons back, from other substances, to become neutral again. The more concentrated these ions are, the more strongly they will be able to attract electrons back and the more vigorous the reaction will be. The pH scale *only* deals with the concentration of the H+ ion: the concentration of the chemicals that will produce a solution of a particular pH varies with the chemical, so speaking of Strong Acid, is not the same as speaking of concentrated acid.
When the chemist says Strong acid, he means that it is a substance that forms these H+ ions easily *in water*. Water is what is termed a 'polar' solvent, because its molecules are arranged such that the O atom has a bigger attraction for the molecule's electrons than the two H atoms. This makes each molecule like a little magnet with slightly positive poles at the H end, and slightly negative poles at the O end. This is what makes water such a good solvent: its slightly charged molecules can surround ions like H+ and keep them free in solution to make them available for chemical reactions.
Each step in the pH scale from 7 down to 1 indicates a tenfold increase in strength in the *acid* direction, with pH1 being ten million times as H+ ion concentrated as pH7. Each step in the scale from pH7 up to pH14 indicates a tenfold increase in the *alkaline* direction, with pH14 being ten million times stronger than pH7. [This may seem an awkward way of looking at things, but it saves having to have separate scales for H+ and its counterpart, OH-. For the DIYer it might have been more intuitive to call it a pOH scale, so then we would have a scale where the numbers went up with the concentration instead of down, but we are stuck with it I'm afraid!]
The concentration of the H+ ion is not directly related to the concentration of the acid that produces it. Weak acids with a capital W do not so readily form H+ ions in water, and so can still have a moderate pH even when quite concentrated. Solubility is also important: HCl is a gas that won't dissolve in water to give highly concentrated solutions, whereas H2SO4 will concentrate almost to treacle like consistency, and is so attracted to water that the pure acid is only found in space. In concentrated form it is extremely dangerous, but, because it is so lacking in the water the H+ ion needs to become mobilised, the term pH is no longer much use to indicate just how dangerous it is. Remember, the pH only refers to the concentration of H+ : not of the acid itself.
We normally make solutions of chemicals with water as the solvent. Everyone knows that the 'formula' of water is H2O, but if you want to imagine a bit more about pH, it is better to think of it as 'HOH'. This is a neutral structure in which the electrons are shared between the three atoms, though, as above, the O attracts them more strongly than the H, so it could be said to behave like a little magnet. Despite its general stability, in a volume of water containing billions of these molecules, a small percentage break up into ions: the H+ that we have already seen, has its counterpart in the negative OH- ion. This ion still has the electron attached which has been 'lost' by H to make the H+ ion. So, in the case of the OH- ion, it wants to 'give away' or share its extra electron to become neutral again, and, as in the case of H+, the more concentrated OH- becomes, the more strongly will be reactions, as it seeks to share its extra electron to become neutral again. The fact that water is thus slightly ionised itself allows us to quote a pH for it even when nothing is dissolved in it.
As, in pure water, there are always the same number of H+ ions as OH- ions, it is neutral over all, and should have a pH of 7 but will often be a little lower in practice. Once acids or alkalis are dispersed in the water, the pH changes dramatically as extra H+ or OH- ions are mobilised. Acids are, thus chemicals which break up in water to greatly increase the proportion of H+ ions relative to OH- ions. Alkalis have the opposite effect: increasing the concentration of OH- relative to H+.
Hope this gives a reasonable insight without having to go into the maths. Wikipedia proper will give the full picture, for the mathematically inclined: