Acids, bases and pH

The workable definition of an acid is a proton donor and of a base a proton acceptor. In water this shows up as the concentration of hydrogen ions, and because that concentration ranges over more than fourteen powers of ten, it is reported on a logarithmic scale: pH = −log₁₀[H⁺]. Neutral water sits at 7, acids below, bases above.

The logarithm is where intuition goes wrong. pH 3 is not "twice as acidic" as pH 6 — the difference of three units means a factor of 10³, so it is a thousand times more acidic. Small-looking pH changes are large chemical changes, which is why blood is held between 7.35 and 7.45 and why a drop of one unit in ocean pH is a serious event rather than a minor one.

Strength and concentration are also routinely conflated, and they are independent. Strength describes how completely an acid dissociates: hydrochloric acid gives up essentially every proton and is strong, acetic acid gives up a small fraction and is weak, regardless of how much of either is present. Concentration describes how much is dissolved. A dilute strong acid can easily have a higher pH than a concentrated weak one. Finally, the 0–14 range is a convenience, not a rule: concentrated strong acids reach negative pH and concentrated bases exceed 14, since the definition is just a logarithm and nothing in it stops at either end.