So pH literally stands for power of hydrogen, and was introduced in the early 20th century by the Danish chemist, Soren Sorenson.
Normally, we use it to measure the concentration of hydrogen ion in aqueous solution............
And by definition, pH=−log10[H3O+].
[H3O+] is a conceptual species, and could also be represented as H+. It is the characteristic cation of the water solvent; and the characteristic anion of water is designated as hydroxide, −OH.
By careful measurement of pure water, [H3O+] and [HO−], were found to be present in some (small) quantity at equilibrium dependent on temperature:
2H2O⇌H3O++HO−
Kw=[H3O+][HO−]=10−14 at 298⋅K (NB [H2O] does not appear in the equilibrium expression, because it is so large it is effectively constant.) So in an acid solution, the relationship tells us that [−OH] is low, and vice versa for an alkaline solution.
Now back in the day (only 30-40 years ago in fact), before the advent of cheap electronic calculators, division and multiplication of large and small numbers was fairly difficult. Scientists, students and teachers, and engineers would routinely use logarithmic tables (to the base 10 or base e for multiplication and division.)
And thus the product a×b≡10log10a+log10b. It was easier to find logs and antilogs of the given product, than it was to do the long multiplication/division. Of course these days we would simply plug the numbers into a hand-held calculator.
But if we take log10 of Kw=[H3O+][HO−]=10−14, we gets.....
log10Kw=log10[H3O+]+log10[HO−]=log1010−14
But since logaab=b by definition, then, log1010−14=−14.
And so −14=log10[H3O+]+log10[−OH]
OR
14=−log10[H3O+]−log10[−OH]
And given our definition,
14=pH+pOH
And thus a low or negative pH characterizes a STRONGLY acidic solution, and a high pH (approaching 14) characterizes a STRONGLY alkaline solution.
I have gone on for a bit about nothing to the power of less. Look at the examples of pH in your text to consolidate your understanding.
