Acids and bases

What the exam asks

Expect a titration curve, a buffer, or a table of pKa values, and expect the question to be answerable by comparison rather than calculation. The commonest items are: read pKa off a curve at half-equivalence, identify whether the acid was strong or weak from the pH at equivalence, predict which way a buffer moves when a strong acid or base is added, and say which form of a species dominates at a stated pH. The trap that catches most candidates is assuming equivalence means pH 7. It means the moles match, nothing more, and for a weak acid titrated with strong base the equivalence pH is above 7 because what is sitting in the flask at that moment is a solution of the conjugate base. If a curve's equivalence pH is 8.7, the question has already told you the acid was weak.

This topic is about one equilibrium, HA releasing a proton to water, and about reading what a solution does when you push on that equilibrium. Everything else here is bookkeeping: pH is a log scale for how much free proton there is, Ka is how willing the acid is to let go, and pKa puts Ka on the same log scale so the two can be compared by eye.

The exam almost always arrives as a titration curve or a buffer. A curve is not a picture to admire, it is three readings: the flat part in the middle where the buffer is working, the point halfway to equivalence where pH equals pKa, and the pH at equivalence, which tells you what kind of acid you were titrating. Learn to take those three readings off any curve and most items in this topic answer themselves.

The reasoning that transfers is comparative, not computational. Henderson-Hasselbalch is a ratio statement: pH sits at pKa when acid and conjugate base are equal, and every pH unit away from pKa is another factor of ten in that ratio. You rarely need to calculate anything. You need to say which side of pKa the solution is on, and therefore which form dominates.

What to hold

• pH is a log scale, so one pH unit is a tenfold change in hydronium concentration and a pH of 3 is a hundred times more acidic than a pH of 5.
• At 25 degrees Celsius, pH plus pOH is 14, because the ion product of water is fixed at that temperature.
• A larger Ka means a stronger acid, and because pKa is the negative log, a smaller pKa means a stronger acid. The sign flip catches people every time.
• Strong and concentrated are unrelated. Strong describes how completely the acid dissociates; concentrated describes how much of it is in the bottle.
• Henderson-Hasselbalch says pH = pKa + log([A-]/[HA]), so pH equals pKa exactly when the acid and its conjugate base are present in equal amounts.
• One pH unit above pKa is a 10:1 ratio of conjugate base to acid; one unit below is 10:1 the other way. Below its pKa a group is protonated.
• A buffer resists pH change because it holds a reservoir of both forms, and it is strongest when pH equals pKa, working usefully for roughly one pH unit either side.
• Diluting a buffer barely moves its pH, because dilution divides both the acid and the base by the same factor and the ratio is what sets pH.
• At the half-equivalence point of a weak acid titration, exactly half the acid has been converted, so [HA] equals [A-] and pH equals pKa. This is where the curve is flattest.
• The equivalence point is where moles of added base equal moles of acid, which is a stoichiometric statement and not a claim about pH 7.
• A weak acid titrated with a strong base has an equivalence pH above 7, because the conjugate base left in the flask hydrolyses water. A weak base titrated with strong acid lands below 7.
• The volume of titrant needed to reach equivalence depends only on the moles of acid present, not on how strong the acid is. Ka moves the shape of the curve, not the endpoint volume.
• A useful indicator is one whose own pKa is close to the pH at equivalence, so its colour change coincides with the steep part of the curve.
• For a polyprotic acid, each successive proton is harder to remove than the last, because pulling a positive charge off an increasingly negative species costs more.