system
Given the following post, respond as if you're commenting on Reddit:
human
Why is the pH scale 1 through 14 instead of 1-10 or 1-100?

Goodness, can't edit titles.

The lowest pH is 0 and not 1. So the title should read "Why is the pH scale 0-14 instead of 0-10 or 0-100?".
gpt
pH is defied as -log([ H^+ ]), where [ H^+ ] is the concentration of H^+ ions in mol/L.  

Water auto-dissociates into H^+ and OH^-.  The equilibrium equation is:

H_2O <-> H^+ + OH^-

so we can write the equilibrium expression for this as:

K_eq = [ H^+ ] * [ OH^- ]

At 25 deg C, K_eq = 1 x 10^-14.  If H^+ and OH^- are equal, as would be the case at neutral pH, then both would have concentrations of 1 x 10^-7 and this would be equivalent to a pH of 7, so that's where that number comes from.  Given a concentration of OH^- as 1 molar, then we'd get an H^+ concentration of 1 x 10^-14 and a resulting pH of 14.  The converse can be done with an H^+ concentration of 1 molar to show that the pH would be 0 in that case.  

Could you have an H^+ concentration of greater than 1 molar?  Yup.  You'd end up with a negative pH in that case, which is perfectly fine.  Same deal with a pH greater than 14.  These situations require a very powerful acid or base, but that's easy to come up with using a concentrated strong acid or base solution.  

There's one little cheat above - pH isn't really the negative log of the H^+ concentration, but rather the H^+ ion *activity*.  This is complicated and difficult to measure experimentally, but is actually important when talking about very concentrated acid or base solutions.  In these cases the actual pH isn't terribly accurate or useful, but rather reporting the concentration of the acid itself (ionized or no) is more useful since you rarely care what the pH is in the concentrated acid since you want to know what the pH is going to be when you dilute it.  For most cases pH works fine.

One weird quirk about the dissociation constant of water - like all equilibrium constants it changes with temperature.  That means that if you change the temperature you change the pH scale and what number corresponds to 'neutral' pH.  At high temperatures a neutral pH is actually closer to 6 than 7.