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Lesson 6 · 25 min

Gravimetric analysis

An “absolute” method with no calibration curve: control supersaturation for a good precipitate, digest, wash, ignite to constant mass, and use gravimetric factors for sulfate and nickel.

In this lesson

  • List the steps of a gravimetric analysis: precipitate, digest, filter, wash, dry or ignite, and weigh to constant mass
  • Use relative supersaturation to explain why precipitation is done hot, dilute and slowly, and what homogeneous precipitation gains
  • Calculate results from precipitate masses with gravimetric factors
  • Recognise coprecipitation errors (surface adsorption, occlusion, mixed crystals) and their remedies: digestion, reprecipitation and washing with an electrolyte

In 1914 Theodore Richards won the Nobel Prize in Chemistry for accurate atomic weights. His main tools were not exotic instruments but a balance and beakers: precipitate the chloride of a sample quantitatively as AgCl, wash it, dry it, weigh it. Gravimetry is the oldest quantitative method and one of the few “absolute” ones that need no calibration curve — if the precipitate is pure and complete, its mass is the answer.

Predict first

To obtain large, easily filtered, pure crystals of BaSO₄, how should the BaCl₂ be added?

Pick an answer and lock it in before you look. A wrong guess teaches more than no guess.

From solution to weighing form

  1. Precipitate with a slight excess of reagent (the common-ion effect cuts solubility losses). Von Weimarn’s rule: the smaller the relative supersaturation (Q − S)/S, the larger the crystals. Homogeneous precipitation goes further — the precipitant is generated slowly inside the solution (heating urea raises the pH gradually, for example), so the supersaturation stays low throughout.
  2. Digest: leave the precipitate in the hot mother liquor for a while. Small particles dissolve and large ones grow (Ostwald ripening), releasing trapped impurities.
  3. Filter and wash, through ashless paper or a sintered-glass crucible. Use several small portions of wash liquid; for precipitates that peptise easily (AgCl), wash with a volatile electrolyte such as dilute HNO₃ rather than pure water.
  4. Dry or ignite: Ni(DMG)₂ and AgCl are dried at 110–120 °C; BaSO₄ is ignited with its paper at about 800 °C to burn the paper to ash.
  5. Weigh to constant mass: heat, cool in a desiccator, weigh, and repeat until two successive weighings agree within 0.3 mg.
wA=mP⋅Fmsample,F=a MAb MPw_\text{A} = \frac{m_\text{P}\cdot F}{m_\text{sample}},\qquad F = \frac{a\,M_\text{A}}{b\,M_\text{P}}
SO₄²⁻/BaSO₄: F = 96.06/233.39 = 0.4116; Ni/Ni(C₄H₇N₂O₂)₂: F = 58.693/288.92 = 0.2031; 2Fe/Fe₂O₃: F = 0.6994.
wAw_\text{A}
mass fraction of the analyte
mPm_\text{P}
mass of the weighing form (precipitate)
FF
gravimetric factor
a,ba, b
coefficients that balance the key atom between analyte and weighing form

Coprecipitation is the biggest source of error in gravimetry: ions that should stay in solution come down with the precipitate.

  • Surface adsorption: colloidal particles have enormous surfaces that hold the ions of their charged layer. Digestion and washing with an electrolyte reduce it.
  • Occlusion: crystals that grow too fast wrap up mother liquor and impurities that no washing can reach. BaSO₄ precipitated quickly from solutions containing NO₃⁻ or Cl⁻ occludes Ba(NO₃)₂ or BaCl₂ and reads high. Remedies: precipitate slowly, digest, and if needed dissolve and reprecipitate.
  • Mixed crystals: ions of similar size and charge take lattice sites (Pb²⁺ or Sr²⁺ in BaSO₄); they must be removed beforehand.

Organic precipitants are often very selective: dimethylglyoxime in ammoniacal solution precipitates almost only Ni²⁺ (palladium comes down in acid) as red Ni(C₄H₇N₂O₂)₂. Its large molar mass gives nearly 5 mg of precipitate per milligram of nickel, so the weighing error is small.

Analytical balance 0.1 mg · constant mass within ±0.3 mg

Gravimetry: precipitate, digest, heat to constant mass

Sample # 2

NiX2++2 HX2DMG→Ni(HDMG)X2(s)+2 HX+\ce{Ni^2+ + 2H2DMG -> Ni(HDMG)2(s) + 2H+} · dimethylglyoxime in ethanol, ammonia buffer (pH 5–9)

30.6921gd = 0.1 mg
Sample weighed (by difference)
0.1012 g
Empty crucible (at constant mass)
30.6921 g
Ni(CX4HX7NX2OX2)X2\ce{Ni(C4H7N2O2)2} · sintered-glass crucible, dry at 110–120 °C to constant mass
GF = 0.2031
② Precipitation conditions
Computed: the ideal precipitate mass = moles of analyte in the sample × the precipitate’s molar mass (from its formula), and the gravimetric factor = molar mass of analyte ÷ molar mass of precipitate. The loss to the wash uses BaSO₄’s solubility in pure water, √Ksp (Ksp = 1.1 × 10⁻¹⁰), with the wash liquid half saturated; occlusion (cold, concentrated, fast +1.5 %; hot, dilute, slow +0.2 %) and fines passing the filter without digestion (−1.0 %) are illustrative magnitudes that show why technique matters. Each weighing after heating approaches constant mass (adsorbed water and filter-paper ash decrease cycle by cycle) with a deterministic balance repeatability of 0.05 mg. The sample’s content is set by its number.
Nickel dimethylglyoximate: precipitate, filter, then “heat and weigh” repeatedly until two weighings agree within 0.3 mg. Then return to barium sulfate, switch to “cold, concentrated, all at once” or skip the digestion, and after revealing the true value see how each error source contributes; raise the wash to 200 mL and watch the solubility loss grow.

Worked example

Sulfate as barium sulfate

0.4012 g of a soluble sulfate sample is dissolved and precipitated with BaCl₂; after ignition to constant mass the BaSO₄ weighs 0.4938 g. Find the mass fraction of SO₄²⁻.

Concept check

A quickly precipitated BaSO₄ has occluded some BaCl₂. The reported sulfate content will be:

Try the calculation

0.1165 g of a nickel alloy is dissolved and precipitated with dimethylglyoxime in ammoniacal solution; dried to constant mass, the Ni(C₄H₇N₂O₂)₂ weighs 0.2371 g (M = 288.92 g/mol; Ni 58.693 g/mol). What is the nickel content of the alloy, in %?

%

Key takeaways

  • Steps: precipitate → digest → filter and wash → dry or ignite → weigh to constant mass (two weighings within 0.3 mg).
  • The smaller the relative supersaturation (Q − S)/S, the larger the crystals: hot, dilute and slow, or homogeneous precipitation.
  • w = m_P·F/m_sample with F = aM_A/(bM_P); for BaSO₄ F(SO₄) = 0.4116, for Ni(DMG)₂ F(Ni) = 0.2031.
  • Coprecipitation (adsorption, occlusion, mixed crystals) is the main error; digestion, reprecipitation and electrolyte washes reduce it.
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Data and references

  1. D. C. Harris, Quantitative Chemical Analysis, 9th ed. (2016), ch. 27 (gravimetric analysis, relative supersaturation, coprecipitation, constant mass).
  2. D. A. Skoog, D. M. West, F. J. Holler, S. R. Crouch, Fundamentals of Analytical Chemistry, 9th ed. (2014), ch. 12.
  3. IUPAC/CIAAW standard atomic weights for all molar masses and gravimetric factors.
  4. The Nobel Prize in Chemistry 1914: Theodore William Richards, “in recognition of his accurate determinations of the atomic weight of a large number of chemical elements”.