Volumetric and gravimetric analysis

What you'll learn

Volumetric and gravimetric analysis are the classical quantitative methods of chemistry — techniques used in laboratories across the Caribbean to check the quality of water, food, fertilisers, rum and pharmaceuticals. Volumetric analysis measures volumes of solutions in titrations; gravimetric analysis measures masses, usually of a precipitate or a residue after heating. This guide covers primary standards and preparing standard solutions, the apparatus and techniques of accurate titration, acid–base, redox and back titrations, the principles and steps of gravimetric analysis, analysis of hydrated salts and precipitates, calculations, and the evaluation of errors and uncertainty.

CAPE Unit 2 Paper 2 and the practical components rely heavily on these skills. You must be able to describe procedures precisely, perform multi-step calculations, and evaluate results in terms of accuracy and precision.

Key terms and definitions

Volumetric analysis — Quantitative analysis based on measuring volumes of solutions of known concentration.

Gravimetric analysis — Quantitative analysis based on measuring masses.

Standard solution — A solution of accurately known concentration.

Primary standard — A substance pure enough and stable enough to be weighed directly to prepare a standard solution.

Titre — The volume of solution added from the burette to reach the end point.

Concordant titres — Titres that agree closely, typically within 0.10 cm³.

End point — The point at which the indicator changes colour.

Equivalence point — The point at which reactants have reacted in exact stoichiometric proportions.

Back titration — A titration in which excess reagent is added and the amount remaining is determined, to find the amount that reacted.

Constant mass — Repeated heating and weighing until the mass no longer changes, showing a reaction or drying is complete.

Precision — How close repeated measurements are to each other.

Accuracy — How close a measurement is to the true value.

Core concepts

Primary standards

A primary standard must be:

• available in high purity;
• stable in air (not absorbing water or carbon dioxide, not oxidised);
• soluble in water;
• of high molar mass, to reduce weighing errors;
• reactive in a known, complete reaction.

Examples: anhydrous sodium carbonate (for standardising acids), potassium hydrogen phthalate (for standardising alkalis), potassium dichromate(VI) and potassium iodate(V) (for redox titrations).

Sodium hydroxide is not a primary standard because it absorbs water and carbon dioxide from the air; its solutions must be standardised. Potassium manganate(VII) is also not a primary standard because it slowly decomposes.

Preparing a standard solution

1. Weigh accurately (to 0.001 g or better) the required mass of the primary standard in a weighing bottle; reweigh the empty bottle to find the exact mass transferred (weighing by difference).
2. Dissolve the solid in a beaker with distilled water.
3. Transfer the solution to a volumetric flask using a funnel, rinsing the beaker and funnel into the flask.
4. Add distilled water until the bottom of the meniscus reaches the graduation mark, at eye level.
5. Stopper and invert several times to mix thoroughly.

Titration technique

1. Rinse the pipette with the solution it will contain, then transfer an exact volume (e.g. 25.0 cm³) to a conical flask using a pipette filler.
2. Rinse the burette with the titrant, fill it, remove air bubbles from the tip and record the initial reading to 0.05 cm³.
3. Add a few drops of a suitable indicator.
4. Add titrant while swirling; add dropwise near the end point.
5. Record the final reading; carry out a rough titration, then accurate titrations until concordant results are obtained.
6. Calculate the mean titre of concordant results only.

Using a white tile under the flask makes the colour change easier to see.

Types of titration

Acid–base titrations — e.g. standardising HCl with sodium carbonate, or finding the concentration of ethanoic acid in vinegar.

Redox titrations — e.g. potassium manganate(VII) with iron(II) or ethanedioate ions, or iodine–thiosulfate titrations for oxidising agents.

Back titrations — used when a substance is insoluble or reacts slowly. For example, the calcium carbonate in limestone or an antacid tablet can be found by reacting it with a known excess of hydrochloric acid, then titrating the unreacted acid with sodium hydroxide.

Gravimetric analysis

By precipitation:

1. Dissolve an accurately weighed sample in water.
2. Add an excess of precipitating reagent to ensure complete precipitation (e.g. barium chloride to precipitate sulfate as BaSO₄; silver nitrate to precipitate chloride as AgCl).
3. Digest the precipitate (keep it warm) to form larger, more easily filtered crystals.
4. Filter through a pre-weighed sintered glass crucible or ashless filter paper.
5. Wash the precipitate with distilled water to remove soluble impurities.
6. Dry or ignite to constant mass and weigh.
7. Calculate the mass of the ion of interest from the mass of precipitate.

By volatilisation (heating): heating a hydrated salt drives off water of crystallisation; heating a carbonate drives off carbon dioxide. The mass loss gives the amount of volatile component.

Water of crystallisation

To find x in a hydrated salt such as CuSO₄·xH₂O:

1. Weigh the hydrated salt.
2. Heat until it becomes anhydrous (blue crystals become white powder), cool in a desiccator and weigh; repeat to constant mass.
3. Calculate moles of anhydrous salt and moles of water lost.
4. x = moles of water ÷ moles of anhydrous salt.

Errors and uncertainty

Systematic errors affect accuracy in one direction (e.g. a balance reading consistently high, heat loss, incomplete reaction, impure reagents). Random errors affect precision (e.g. judging the end point, reading scales).

Percentage uncertainty = (uncertainty ÷ measured value) × 100. For a burette reading with ±0.05 cm³ uncertainty, each titre involves two readings, so the uncertainty is ±0.10 cm³. A larger titre reduces percentage uncertainty.

Common sources of error:

• Titration: parallax errors, air bubbles in the burette, not rinsing apparatus correctly, overshooting the end point.
• Gravimetric: incomplete precipitation, loss of precipitate during filtering, not drying to constant mass, absorption of moisture after heating, decomposition of the anhydrous salt if overheated.

Worked examples

Example 1: Standardising acid

1.325 g of anhydrous sodium carbonate was dissolved and made up to 250.0 cm³. 25.0 cm³ of this solution required 24.80 cm³ of HCl. Find [HCl]. (Mᵣ Na₂CO₃ = 106)

Moles Na₂CO₃ in 250 cm³ = 1.325 ÷ 106 = 0.01250 mol; in 25.0 cm³ = 0.001250 mol. Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂, so moles HCl = 0.002500 mol. [HCl] = 0.002500 ÷ 0.02480 = 0.101 mol dm⁻³.

Example 2: Back titration

A 0.500 g antacid tablet (containing CaCO₃) was added to 50.0 cm³ of 0.200 mol dm⁻³ HCl. The excess acid required 15.0 cm³ of 0.100 mol dm⁻³ NaOH. Find the percentage of CaCO₃ in the tablet. (Mᵣ CaCO₃ = 100)

Initial HCl = 0.200 × 0.0500 = 0.0100 mol. Excess HCl = moles NaOH = 0.100 × 0.0150 = 0.00150 mol. HCl reacted = 0.00850 mol. CaCO₃ + 2HCl → CaCl₂ + H₂O + CO₂, so moles CaCO₃ = 0.00425 mol; mass = 0.425 g. Percentage = 0.425 ÷ 0.500 × 100 = 85.0%.

Example 3: Gravimetric sulfate

A fertiliser sample of mass 2.00 g gave 2.33 g of BaSO₄. Find the percentage of sulfate (SO₄²⁻) in the fertiliser. (Mᵣ BaSO₄ = 233; SO₄ = 96)

Moles BaSO₄ = 2.33 ÷ 233 = 0.0100 mol = moles SO₄²⁻. Mass SO₄²⁻ = 0.0100 × 96 = 0.960 g. Percentage = 0.960 ÷ 2.00 × 100 = 48.0%.

Example 4: Water of crystallisation

2.50 g of hydrated copper(II) sulfate, CuSO₄·xH₂O, was heated to constant mass, leaving 1.60 g of anhydrous CuSO₄. Find x. (Mᵣ CuSO₄ = 159.6, H₂O = 18.0)

Moles CuSO₄ = 1.60 ÷ 159.6 = 0.01003. Mass of water = 0.90 g; moles = 0.90 ÷ 18.0 = 0.0500. x = 0.0500 ÷ 0.01003 = 4.99 ≈ 5, so the formula is CuSO₄·5H₂O.

Example 5: Iron in a tablet by redox titration

An iron tablet was dissolved in dilute sulfuric acid and made up to 100.0 cm³. 25.0 cm³ portions required a mean titre of 22.50 cm³ of 0.0200 mol dm⁻³ potassium dichromate(VI). Calculate the concentration of Fe²⁺ in the solution.

Cr₂O₇²⁻ + 14H⁺ + 6Fe²⁺ → 2Cr³⁺ + 6Fe³⁺ + 7H₂O

Moles Cr₂O₇²⁻ = 0.0200 × 0.02250 = 4.50 × 10⁻⁴ mol. Moles Fe²⁺ in 25.0 cm³ = 6 × 4.50 × 10⁻⁴ = 2.70 × 10⁻³ mol. [Fe²⁺] = 2.70 × 10⁻³ ÷ 0.0250 = 0.108 mol dm⁻³.

(The tablet contained 4 × 2.70 × 10⁻³ = 0.0108 mol Fe²⁺, or 0.0108 × 55.8 = 0.603 g of iron.)

Example 6: Percentage uncertainty

A titre of 24.50 cm³ was measured with a burette reading to ±0.05 cm³, and a 25.0 cm³ pipette has an uncertainty of ±0.06 cm³. Calculate the percentage uncertainty in each measurement.

The titre involves two burette readings, so the uncertainty is ±0.10 cm³. Titre: 0.10 ÷ 24.50 × 100 = 0.41%. Pipette: 0.06 ÷ 25.0 × 100 = 0.24%.

The total percentage uncertainty in a calculated concentration is approximately the sum of the individual percentage uncertainties. Using larger volumes or more concentrated solutions that give larger titres reduces percentage uncertainty.

Example 7: Gravimetric analysis by mass loss

A 5.00 g sample of limestone was heated strongly to constant mass. The mass decreased by 1.98 g. Assuming only calcium carbonate decomposes, calculate the percentage of CaCO₃ in the limestone. (Mᵣ CaCO₃ = 100, CO₂ = 44)

CaCO₃ → CaO + CO₂. The mass lost is CO₂: 1.98 ÷ 44 = 0.0450 mol. Moles CaCO₃ = 0.0450 mol; mass = 4.50 g. Percentage = 4.50 ÷ 5.00 × 100 = 90.0%.

Precision and accuracy illustrated

Systematic errors (such as an incorrectly calibrated pipette) shift all results in the same direction and are not removed by repeating; random errors are reduced by repeating and averaging.

Common mistakes and how to avoid them

• Averaging non-concordant titres, including the rough titre.
• Forgetting the scaling factor when an aliquot is taken from a larger volume.
• Wrong mole ratios — always write the balanced equation.
• Not heating to constant mass, leading to underestimated water content.
• Using NaOH as a primary standard.
• Reading the burette at the top of the meniscus or at an angle.

Self-test questions

1. 0.530 g of anhydrous Na₂CO₃ is made up to 100.0 cm³. What volume of 0.100 mol dm⁻³ HCl would neutralise a 10.0 cm³ portion? (Mᵣ = 106) Answer: Moles Na₂CO₃ in 10.0 cm³ = (0.530 ÷ 106) ÷ 10 = 5.00 × 10⁻⁴ mol; moles HCl = 1.00 × 10⁻³ mol; volume = 10.0 cm³.
2. Why is the pipette rinsed with the solution it will contain, but the conical flask rinsed only with distilled water? Answer: Rinsing the pipette with distilled water would dilute the solution measured; the conical flask can contain water because only the number of moles transferred into it matters.
3. Why must a precipitate be washed before drying and weighing? Answer: To remove soluble impurities that would otherwise remain and make the mass too high.
4. Give one reason why the calculated value of x in CuSO₄·xH₂O might be too low. Answer: The sample was not heated to constant mass, so some water of crystallisation remained.

How this links to your Internal Assessment

These are core SBA skills. Typical investigations include determining the calcium carbonate content of local limestone or eggshells by back titration, the ethanoic acid content of vinegar, the water of crystallisation in a hydrated salt, or the sulfate content of a fertiliser gravimetrically. Moderators look for precise measurements recorded to the correct number of decimal places, concordant titres, clear calculations, and thoughtful evaluation of errors with realistic improvements (for example, using a larger sample to reduce percentage uncertainty).

Exam technique for Volumetric and gravimetric analysis

• When describing procedures, give apparatus, quantities and reasons for each step.
• Set out calculations step by step: moles of known → ratio → moles of unknown → concentration or mass.
• State the number of significant figures consistent with the data.
• In evaluation questions, distinguish accuracy from precision and systematic from random errors.

Quick revision summary

• Primary standards are pure, stable, soluble, high-Mᵣ (Na₂CO₃, KH phthalate, K₂Cr₂O₇).
• Standard solutions: weigh by difference, dissolve, transfer quantitatively, make up to the mark, mix.
• Titration: rinse correctly, read to 0.05 cm³, obtain concordant titres, average them.
• Acid–base, redox and back titrations.
• Gravimetric: precipitate with excess reagent, filter, wash, dry to constant mass, weigh; or heat to drive off volatile components.
• x in hydrates = moles of water ÷ moles of anhydrous salt.
• Evaluate accuracy, precision, systematic and random errors; percentage uncertainty.