Gravimetric Analysis with Worked Examples

Before electronic instruments existed, chemists measured the composition of substances in one of the most reliable ways possible: they converted the thing they wanted to measure into a pure solid of known formula and weighed it. That’s gravimetric analysis. It’s slow and demanding, but when done carefully it’s among the most accurate analytical methods there is, and it’s still used to check other methods and to measure some substances today.

The principle

1. Convert the analyte (the substance being measured) into a pure compound of known formula.
2. Weigh that compound accurately.
3. Use the formula and molar masses to calculate the amount of analyte.

Because a good analytical balance can weigh to 0.0001 g, and stoichiometry is exact, gravimetric analysis can achieve accuracies better than 0.1%.

Two main types

Precipitation gravimetry

The analyte is precipitated from solution as an insoluble compound, which is filtered, washed, dried and weighed.

Examples:

• chloride ions precipitated as silver chloride: Ag⁺ + Cl⁻ → AgCl(s)
• sulfate ions precipitated as barium sulfate: Ba²⁺ + SO₄²⁻ → BaSO₄(s)
• nickel precipitated with the organic reagent dimethylglyoxime as a red complex

Volatilisation gravimetry

The analyte (or something that contains it) is driven off as a gas by heating, and the loss in mass is measured. Or the gas is absorbed and weighed.

Examples:

• water of crystallisation lost by heating a hydrate (see hydrates and water of crystallisation)
• carbon dioxide lost when a carbonate is heated or reacted with acid
• in combustion analysis, CO₂ and H₂O absorbed and weighed to find carbon and hydrogen content

The steps of precipitation gravimetry

1. Weigh the sample accurately and dissolve it.
2. Precipitate the analyte by adding an excess of reagent, slowly, usually to a hot solution with stirring. Slow addition and heating give larger, purer crystals that are easier to filter.
3. Digest the precipitate: leave it warm in contact with the solution for a while. Small particles dissolve and larger ones grow, making filtering easier and reducing impurities.
4. Check precipitation is complete by adding a drop more reagent to the clear liquid; no more precipitate should form.
5. Filter through a pre-weighed sintered glass crucible or ashless filter paper.
6. Wash the precipitate to remove soluble impurities.
7. Dry or ignite the precipitate (heat it strongly), converting it to a stable form of known formula.
8. Cool in a desiccator and weigh.
9. Repeat heating, cooling and weighing to constant mass. See using a balance.

What makes a good gravimetric precipitate?

• Very low solubility, so almost all the analyte is precipitated.
• Pure and of known, fixed composition.
• Easy to filter (large particles, not a colloid).
• Stable when dried or heated, and not absorbing water from the air.
• Ideally with a high molar mass relative to the analyte, so small errors in weighing cause small errors in the result.

Barium sulfate is a classic example: extremely insoluble, stable to strong heating, and heavy.

Worked example 1: chloride in a salt

0.500 g of an impure sample of sodium chloride is dissolved and treated with excess silver nitrate. The precipitate of silver chloride, washed and dried, has a mass of 1.183 g. Calculate the percentage of NaCl in the sample.

(Ar: Na 22.99, Cl 35.45, Ag 107.87)

• M(AgCl) = 107.87 + 35.45 = 143.32 g/mol
• n(AgCl) = 1.183 ÷ 143.32 = 8.254 × 10⁻³ mol
• NaCl : AgCl = 1 : 1, so n(NaCl) = 8.254 × 10⁻³ mol
• M(NaCl) = 58.44 g/mol
• mass NaCl = 8.254 × 10⁻³ × 58.44 = 0.4824 g
• % NaCl = 0.4824 ÷ 0.500 × 100 = 96.5%

Worked example 2: sulfate in a fertiliser

A 1.250 g sample of fertiliser is dissolved and excess barium chloride added. The BaSO₄ precipitate has a mass of 1.905 g. Calculate the percentage of sulfate (SO₄²⁻) in the fertiliser.

(M(BaSO₄) = 233.39 g/mol; M(SO₄²⁻) = 96.06 g/mol)

• n(BaSO₄) = 1.905 ÷ 233.39 = 8.162 × 10⁻³ mol = n(SO₄²⁻)
• mass SO₄²⁻ = 8.162 × 10⁻³ × 96.06 = 0.7840 g
• % SO₄²⁻ = 0.7840 ÷ 1.250 × 100 = 62.7%

Using a gravimetric factor: chemists often combine these steps with a factor = M(analyte) ÷ M(precipitate) × (moles analyte per mole precipitate). For sulfate from BaSO₄: 96.06 ÷ 233.39 = 0.4116. Mass of sulfate = 1.905 × 0.4116 = 0.7841 g. Same answer, quicker.

Worked example 3: water of crystallisation

A 2.500 g sample of hydrated magnesium sulfate, MgSO₄·xH₂O, is heated to constant mass. The anhydrous residue weighs 1.221 g. Find x.

• mass of water lost = 2.500 − 1.221 = 1.279 g
• n(H₂O) = 1.279 ÷ 18.02 = 0.07098 mol
• n(MgSO₄) = 1.221 ÷ 120.37 = 0.01014 mol
• ratio H₂O : MgSO₄ = 0.07098 ÷ 0.01014 = 7.00
• x = 7, so the formula is MgSO₄·7H₂O (Epsom salts)

Worked example 4: a carbonate

1.000 g of a mixture of calcium carbonate and sand is heated strongly until all the CaCO₃ has decomposed: CaCO₃ → CaO + CO₂. The mass decreases by 0.352 g. Calculate the percentage of CaCO₃ in the mixture.

• mass lost = mass of CO₂ = 0.352 g
• n(CO₂) = 0.352 ÷ 44.01 = 8.00 × 10⁻³ mol = n(CaCO₃)
• mass CaCO₃ = 8.00 × 10⁻³ × 100.09 = 0.801 g
• % CaCO₃ = 80.1%

Worked example 5: iron as Fe₂O₃

Iron in a 0.850 g ore sample is converted to Fe³⁺, precipitated as hydrated iron(III) oxide, and ignited to Fe₂O₃. The Fe₂O₃ weighs 0.563 g. Calculate the percentage of iron in the ore.

(Ar: Fe 55.85; M(Fe₂O₃) = 159.69 g/mol)

• n(Fe₂O₃) = 0.563 ÷ 159.69 = 3.526 × 10⁻³ mol
• n(Fe) = 2 × 3.526 × 10⁻³ = 7.051 × 10⁻³ mol
• mass Fe = 7.051 × 10⁻³ × 55.85 = 0.3938 g
• % Fe = 0.3938 ÷ 0.850 × 100 = 46.3%

Note the factor of 2: each Fe₂O₃ contains two iron atoms.

Sources of error

Error	Effect on result
Precipitate slightly soluble, or precipitation incomplete	too low
Precipitate lost when filtering or transferring	too low
Impurities trapped in the precipitate (co-precipitation)	too high
Precipitate not dried fully	too high
Precipitate absorbs water from air before weighing	too high
Not heated to constant mass (hydrate not fully decomposed)	depends on method
Precipitate decomposes on over-heating	too low or wrong formula

Gravimetric analysis today

Although instrumental methods have replaced gravimetric analysis for most routine work, it hasn’t disappeared. National measurement laboratories use it to certify reference materials, because it depends only on mass and stoichiometry. Moisture and ash content in foods, animal feeds and coal are still measured by weighing before and after heating. And thermogravimetric analysis (TGA), which records a sample’s mass continuously as it’s heated, is a modern instrumental descendant used to study polymers, pharmaceuticals and minerals.

Advantages and disadvantages

Advantages:

• Very accurate and precise when done well.
• Needs no calibration against standards; it depends only on masses and molar masses (an “absolute” method).
• Simple, inexpensive equipment.

Disadvantages:

• Slow and labour-intensive.
• Needs relatively large amounts of analyte.
• Many ions can interfere by co-precipitating.

Key takeaways

• Gravimetric analysis converts the analyte into a pure compound of known formula and weighs it.
• Precipitation methods weigh an insoluble product; volatilisation methods measure mass lost or gained.
• Precipitate, digest, filter, wash, dry or ignite, then heat to constant mass.
• Calculate moles of the weighed compound, apply the formula ratio, then find the mass or percentage of analyte.
• It’s slow but highly accurate and needs no calibration standards.