Acids, Bases, and the Curve with a Cliff in It

A few questions and answers about pH and titration.

What does pH actually measure?

It measures how many free hydrogen ions are floating around in a solution, but on a compressed scale. Hydrogen ion concentrations span an enormous range, from about one mole per liter in a strong acid down to a ten-trillionth of that in a strong base, and writing those numbers out is unwieldy. So chemists use pH, defined as the negative base-ten logarithm of the hydrogen ion concentration. The logarithm does two things. It turns those tiny, awkward numbers into a tidy range from roughly 0 to 14, and it means each whole step on the scale is a factor of ten in concentration. A solution at pH 4 has ten times more hydrogen ions than one at pH 5 and a hundred times more than one at pH 6. In pure water at room temperature the concentration works out to a pH of 7, which we call neutral.

What makes something an acid or a base?

The useful definition is the one from Brønsted and Lowry: an acid is a substance that donates hydrogen ions, and a base is one that accepts them. Hydrochloric acid dumps its hydrogen ions completely into solution, which is what makes it a strong acid. Acetic acid, the acid in vinegar, only lets go of a small fraction of its hydrogen ions at any moment, which makes it a weak acid. Weak does not mean dilute; it means reluctant to fully dissociate.

What is a titration for?

It is a method for finding out how much acid or base is in a solution whose concentration you do not know. The trick is to add a second solution whose concentration you do know, a little at a time, until the two exactly neutralize each other. Suppose you have an acid of unknown strength. You slowly add a base of known concentration from a calibrated tube, tracking the pH as you go. At the point where you have added exactly enough base to react with all the acid, called the equivalence point, the moles of base you have added equal the moles of acid you started with. Since you know the concentration and volume of base used, you can calculate backward to the amount of acid. The classic signal is a color-changing indicator, though a pH meter is more precise.

Why is the titration curve shaped so strangely?

Because the pH barely moves for most of the process and then leaps. Here is a strong acid being titrated with a strong base:

 pH
 14 +                                 _____________
    |                                /
    |                               |
 10 +                               |
    |                               |
  7 +- - - - - - - - - - - - - - - -* equivalence point
    |                              |
  4 +                              |
    |              ________________/
  1 +_____________/
    +----+----+----+----+----+----+----+----  base added (mL)

For a long stretch, each drop of base is swallowed up by the large reservoir of remaining acid and the pH creeps along almost flat. But near the equivalence point the remaining acid is nearly gone, so each additional drop has a huge proportional effect, and the pH shoots almost vertically through several units in the space of a drop or two. Then, once the acid is exhausted and you are just adding excess base, the curve flattens again high on the scale. That steep cliff in the middle is what makes the endpoint easy to detect, because a single drop tips you across it.

Does it matter if the acid is weak?

Yes, and the curve tells you. When you titrate a weak acid with a strong base, the equivalence point lands above pH 7 rather than at it, because the salt left behind is mildly basic. The curve also shows a gentle plateau early on, called the buffer region, where the solution resists pH change because it contains a mix of the weak acid and its conjugate base. Right at the halfway point of that plateau, where exactly half the acid has been neutralized, the pH equals a characteristic constant of the acid called its pKa. So a titration does double duty: it tells you how much weak acid is present and, from the shape of the buffer region, how strong that acid is.

So the curve is the whole experiment in one picture. The flat parts tell you the solution is buffered and changing slowly; the cliff tells you that you have hit the point of exact neutralization; and where the cliff sits on the pH axis tells you whether you were dealing with a strong acid or a weak one.