Acid–Base Titrations
A titration is a controlled way to find the concentration of an unknown acid or base. You add a solution of known concentration (the titrant) from a burette, a little at a time, to a measured volume of the unknown (the analyte) until the reaction is complete.
The Key Terms
- Equivalence point: the point where the moles of titrant added exactly equal the moles of analyte — the reaction is stoichiometrically complete.
- Endpoint: the point where the indicator changes colour. You want it as close to the equivalence point as possible.
- Indicator: a weak acid or base whose colour depends on pH, so it signals when you are near the equivalence point.
At the equivalence point, $M_a V_a = M_b V_b$ for a 1:1 reaction — the moles of acid equal the moles of base.
Strong Acid–Strong Base Titration
Titrating HCl with NaOH gives the classic S-shaped curve. The pH starts low, rises slowly, then jumps sharply through the equivalence point, where the pH is exactly 7.00 — the solution contains only NaCl and water. After the equivalence point, excess OH− makes the pH climb toward that of the titrant.
After adding 10.0 mL of NaOH (1.00 mmol of OH−), the remaining H+ is $2.50 - 1.00 = 1.50$ mmol in a total volume of 35.0 mL:
$$[\text{H}^+] = \frac{1.50\ \text{mmol}}{35.0\ \text{mL}} = 0.0429\ \text{M} \;\Rightarrow\; \text{pH} = -\log(0.0429) = 1.37$$At the equivalence point, 25.0 mL of NaOH has been added and the solution is neutral: pH = 7.00.
After adding 30.0 mL of NaOH, the excess OH− is $3.00 - 2.50 = 0.50$ mmol in 55.0 mL:
$$[\text{OH}^-] = \frac{0.50\ \text{mmol}}{55.0\ \text{mL}} = 0.00909\ \text{M} \;\Rightarrow\; \text{pOH} = 2.04 \;\Rightarrow\; \text{pH} = 11.96$$Weak Acid–Strong Base Titration
Titrating acetic acid with NaOH looks different in two ways. First, the equivalence-point pH is above 7, because the conjugate base CH3COO− left behind reacts with water to make OH−. Second, the curve has a buffer region, and at the half-equivalence point — when exactly half the acid has been neutralized — $[\text{HA}] = [\text{A}^-]$ and the Henderson–Hasselbalch equation gives pH = p$K_a$.
At the half-equivalence point, 12.5 mL of NaOH has been added, so $[\text{HA}] = [\text{A}^-]$ and:
$$\text{pH} = \text{p}K_a = -\log(1.8 \times 10^{-5}) = 4.74$$At the equivalence point, 25.0 mL of NaOH has been added. The solution is 0.0500 M CH3COO− (2.50 mmol in 50.0 mL), with $K_b = \frac{K_w}{K_a} = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.6 \times 10^{-10}$:
$$[\text{OH}^-] = \sqrt{K_b C} = \sqrt{(5.6 \times 10^{-10})(0.0500)} = 5.3 \times 10^{-6}\ \text{M} \;\Rightarrow\; \text{pOH} = 5.28 \;\Rightarrow\; \text{pH} = 8.72$$Choosing an Indicator
Pick an indicator whose colour-change range brackets the equivalence-point pH. For a strong acid–strong base titration, almost any indicator works because the pH jumps several units with a single drop — phenolphthalein (8.2–10.0) is the usual choice. For a weak acid–strong base titration, you need an indicator that changes above pH 7, so phenolphthalein works but methyl orange (3.1–4.4) does not — it would change colour long before the equivalence point. For a weak base titrated with a strong acid, the equivalence pH is below 7, so methyl orange or methyl red is the right pick.
Polyprotic Acids
An acid with more than one acidic proton has one equivalence point per proton, and each step is weaker than the last. Phosphoric acid, H3PO4, has three equivalence points ($K_{a1} = 7.5 \times 10^{-3}$, $K_{a2} = 6.2 \times 10^{-8}$, $K_{a3} = 4.8 \times 10^{-13}$); the first jump is sharp, the second is smaller, and the third is usually too weak to see. Sulfuric acid, H2SO4, has two: the first proton is strong and the second is weak ($K_{a2} = 1.2 \times 10^{-2}$). Carbonic acid, H2CO3, also has two equivalence points, and its titration curve shows two distinct rises — the first near pH 8 (HCO3− formed) and the second near pH 11 (CO32− formed) — which is why bicarbonate is such a useful buffer in blood.
Practice Problems
- What volume of 0.100 M NaOH is needed to neutralize 20.0 mL of 0.150 M HCl?
- What is the pH after adding 5.0 mL of 0.100 M NaOH to 25.0 mL of 0.100 M HCl?
- A weak acid has Ka = 4.0 × 10−5. What is the pH at its half-equivalence point when titrated with NaOH?
- Which indicator is better for titrating acetic acid with NaOH: methyl orange (range 3.1–4.4) or phenolphthalein (range 8.2–10.0)? Explain.
Answers: 1. 30.0 mL 2. 1.18 3. 4.40 4. Phenolphthalein — the equivalence pH is above 7, inside its range; methyl orange would change colour far too early