Acid-Base Titrations and Endpoints

An acid-base titration measures the concentration of an acid or base by adding a solution of known concentration (the titrant) from a burette until the reaction is complete; the equivalence point is where the amounts of acid and base are exactly equal, and the endpoint is where the indicator changes color. In brief: if 25.00 mL of HCl needs 18.62 mL of 0.1000 mol/L NaOH, then n(HCl) = 0.01862 × 0.1000 = 1.862 × 10⁻³ mol and the acid concentration is 0.09310 mol/L.

Titration is among the most accurate and widely used analytical methods. This article describes the apparatus and procedure, how to choose an indicator, how to standardize a solution with a primary standard, how to calculate results, lists common primary standards, works through examples including vinegar analysis and polyprotic acids, discusses errors and gives some history.

What are the key terms?

• Titrant: the solution of known concentration in the burette.
• Analyte: the solution of unknown concentration in the flask, measured with a pipette.
• Equivalence point: stoichiometrically equal amounts of acid and base have reacted.
• Endpoint: the observed signal (color change or pH jump). The difference between endpoint and equivalence point is the titration error and should be small.
• Titre: the volume of titrant used.

What is the procedure?

1. Rinse the burette with the titrant and fill it, removing air bubbles from the tip. Record the initial reading.
2. Pipette a known volume of analyte into a conical flask and add 2 to 3 drops of indicator.
3. Run in titrant while swirling. Slow down to drops near the end.
4. Stop at a permanent color change and record the final reading.
5. Repeat until three titres agree within 0.10 mL (concordant titres) and average them.
6. Calculate: n(titrant) = c × V, then use the mole ratio to find n(analyte), then c = n ÷ V.

How do you choose the indicator?

The indicator should change color within the steep part of the titration curve around the equivalence point.

What are primary standards?

A primary standard is a pure, stable, non-hygroscopic compound with a high molar mass, which can be weighed accurately to prepare a solution of known concentration. NaOH and HCl are not primary standards (NaOH absorbs CO₂ and water; HCl is a gas), so their solutions are standardized against a primary standard.

Worked examples

1. Standardizing NaOH. 0.5105 g of KHP (1 : 1 with NaOH) is titrated with 24.82 mL of NaOH. n(KHP) = 0.5105 ÷ 204.22 = 2.500 × 10⁻³ mol. c(NaOH) = 2.500 × 10⁻³ ÷ 0.02482 = 0.1007 mol/L.
2. Strong acid. 25.00 mL of H₂SO₄ needs 31.45 mL of 0.1000 mol/L NaOH. n(NaOH) = 3.145 × 10⁻³ mol; n(H₂SO₄) = 1.5725 × 10⁻³ mol; c = 0.06290 mol/L.
3. Vinegar. 10.00 mL of vinegar needs 41.7 mL of 0.1000 mol/L NaOH. n = 4.17 × 10⁻³ mol of CH₃COOH, c = 0.417 mol/L, which is 0.417 × 60.05 = 25.0 g/L, or 2.50% (m/v). (Commercial vinegar usually has 4 to 8%, so the sample was dilute or the vinegar was diluted before titrating.)
4. Percent purity of an acid. 0.500 g of impure oxalic acid dihydrate needs 76.2 mL of 0.1000 mol/L NaOH (2 : 1): n(acid) = 3.81 × 10⁻³ mol, mass = 0.480 g, purity 96.1%.
5. Back titration. A 0.500 g antacid tablet is dissolved in 50.00 mL of 0.1000 mol/L HCl (5.000 mmol). The excess acid needs 12.40 mL of 0.1000 mol/L NaOH (1.240 mmol). Acid consumed = 5.000 − 1.240 = 3.760 mmol. If the base is CaCO₃ (2 H⁺ each): 1.880 mmol = 0.188 g, or 37.6% of the tablet.

6. Average of concordant titres. Titres 22.45, 22.50, 22.40 mL: mean = 22.45 mL. A titre of 23.10 mL (a rough first run) is discarded.

What causes errors?

• Air bubble in the burette tip, which gives a false volume.
• Rinsing the flask with solution instead of water, or leaving water in the burette or pipette.
• Reading the meniscus from the wrong angle.
• Overshooting the endpoint (a strong pink with phenolphthalein).
• Too much indicator, since indicators are acids or bases.
• Carbon dioxide absorbed by NaOH solutions, which lowers their concentration over time.

How did titration develop?

François Descroizilles invented the burette in about 1791 for bleach analysis, and Gay-Lussac improved it and named the method titration in 1824. Karl Friedrich Mohr’s textbook of 1855 and his burette with a pinch clamp made the method common. Electronic pH meters and automatic titrators replaced indicators in many laboratories in the 20th century.

Which mistakes are common?

Mistake 1: Using the wrong mole ratio

H₂SO₄ needs 2 NaOH per molecule. Check the equation.

Mistake 2: Mixing up endpoint and equivalence point

They are close but not identical. Choose an indicator that keeps the gap small.

Mistake 3: Using a rough titre in the average

Only concordant titres are averaged.

Mistake 4: Rinsing the conical flask with the analyte

Extra analyte would be included. Rinsing with water is fine, since it does not change the moles.