Lesson 1 · 25 min
Volumetric analysis: primary standards and standardisation
The 0.1 M on the label is never 0.1000 M. Standardise titrants against primary standards such as KHP, master burettes and pipettes, and see where the uncertainty comes from.
In this lesson
- Distinguish primary from secondary standards and list what makes a good primary standard
- Standardise a titrant against a primary standard and compute its concentration from mass and volume
- Use burettes, pipettes and volumetric flasks correctly, knowing class A tolerances and how to read them
- Plan direct, back and displacement titrations and estimate the uncertainty of the result
The bottle says “0.1 mol/L NaOH”, but it is never 0.1000 mol/L. Solid NaOH picks up water and CO₂ from the air, and the solution drifts over a few days. Titrations reach an accuracy of one part in a thousand not because of labels but because of a strict routine: a substance of very high purity and exactly known composition — a primary standard — is used to standardise the titrant, and the standardised titrant then measures the unknowns.
Predict first
Titrating with about 0.1 M NaOH, you want to use about 40 mL. Which of these primary standards gives the smallest relative weighing error? (The analytical balance reads ±0.1 mg.)
Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.
Primary and secondary standards
A good primary standard is at least 99.9 % pure with a certificate; matches its formula exactly (water of crystallisation included); is stable in air, not hygroscopic and easy to dry; has a large molar mass; reacts quickly with a definite stoichiometry; and is affordable. The usual ones:
- for bases, potassium hydrogen phthalate (KHP); for acids, anhydrous sodium carbonate and borax;
- for redox, potassium dichromate (weighed straight into a standard solution), sodium oxalate (for KMnO₄), potassium iodate (for Na₂S₂O₃);
- for EDTA, calcium carbonate or zinc metal; for AgNO₃, sodium chloride.
NaOH, HCl, KMnO₄ and Na₂S₂O₃ cannot be weighed into standard solutions; they are made up roughly and then standardised — they are secondary standards.
- titrant concentration, mol/L
- mass and molar mass of the standard
- moles of titrant per mole of standard
- volume of titrant at the endpoint, L
Volumetric glassware and technique
Class A tolerances at 20 °C: 50 mL burette ±0.05 mL, 25 mL pipette ±0.03 mL, 250 mL volumetric flask ±0.12 mL. Key points:
- Rinse burettes and pipettes three times with small portions of the solution they will hold, and clear the air bubble from the tip; the titration flask needs only distilled water and may stay wet — the amount of analyte inside does not change.
- Read the bottom of the meniscus at eye level to 0.01 mL; a drop is about 0.05 mL, and near the endpoint you can add half drops (let a drop hang on the tip and rinse it in).
- Start near 0.00, read both the initial and final levels; their difference is the volume.
- The endpoint differs from the equivalence point by the indicator error; subtract a blank titration when needed.
Besides direct titration there is back titration — add a known excess of reagent and titrate what is left, useful when the reaction is slow, the endpoint poor or the sample insoluble (calcium carbonate, the Volhard method); displacement titration — the analyte releases an equivalent amount of another species, which is titrated (calcium via Mg–EDTA); and indirect titration — titrating a product quantitatively related to the analyte (iodometry).
Worked example
Standardise NaOH, then a back titration of an antacid
(a) 0.8154 g of KHP (M = 204.22 g/mol) needs 39.62 mL of NaOH; find c(NaOH). (b) 0.2500 g of antacid powder reacts with 50.00 mL of 0.1000 M HCl, and the excess acid takes 12.40 mL of 0.1000 M NaOH. Find the mass fraction of CaCO₃.
Concept check
You fill a burette that still has distilled water on its walls (not rinsed with titrant) with standard NaOH and titrate an acid. The acid concentration you calculate will be:
Try the calculation
0.4912 g of anhydrous Na₂CO₃ (M = 105.99 g/mol) is titrated to its second equivalence point with 45.26 mL of HCl. What is c(HCl)?
Key takeaways
- Primary standards are pure, of exact composition, stable, non-hygroscopic and of large molar mass; NaOH, HCl, KMnO₄ and Na₂S₂O₃ are secondary standards that must be standardised.
- c_T = (m/M)·ν/V: choose a mass that uses most of the burette so that both weighing and reading errors stay small.
- Rinse burettes and pipettes with the solution they will hold; the flask only with water; read to 0.01 mL.
- Besides direct titration there are back, displacement and indirect titrations.
Data and references
- D. C. Harris, Quantitative Chemical Analysis, 9th ed., W. H. Freeman (2016), ch. 2 (glassware, calibration) and ch. 7, 10–11 (titrations, primary standards).
- D. A. Skoog, D. M. West, F. J. Holler, S. R. Crouch, Fundamentals of Analytical Chemistry, 9th ed. (2014), ch. 13–14.
- ASTM E287/E288/E969 class A tolerances, as tabulated in Harris, Tables 2-2 to 2-4.