Chemistry · Analytical and physical chemistry · Year 2

Qualitative analysis and gravimetry

Which ions are in an ore or mineral water, and how many milligrams of sulfate?

The situation

A solution of ore from the Almalyk Mining and Metallurgical Combine and a sample of Chortoq mineral water have arrived at the analytical laboratory: “what does it contain, and how much?” Qualitative analysis tells you which ions are present — with group reagents in test tubes, a centrifuge and a burner flame. Quantitative analysis is gravimetry: sulfate is precipitated as barium sulfate, ignited in a crucible to constant mass and weighed on an analytical balance to 0.1 mg; the derivatograph in the corner records how the mass of a heated substance decreases. How can you “read” the composition of an ore from a few drops of solution?

Topic

Qualitative analysis and gravimetry. A sample of Chortoq mineral water and Almalyk ore has arrived at the analytical laboratory: “what does it contain, and how much?” A rack of test tubes, a centrifuge, a burner…

Key ideas

Cation groups
Solubility product
Gravimetry

Formulas

K_{s} (BaSO_{4}) = [Ba^{2 +}] [SO_{4}^{2 -}], s = \sqrt{K_{s}}, s |_{Ba^{2 +} excess} = \frac{K_{s}}{[Ba^{2 +}]}

Solubility product and solubility; a common ion decreases solubility.

I = \frac{1}{2} \sum c_{i} z_{i}^{2}, \lg γ = - 0.51 z^{2} (\frac{\sqrt{I}}{1 + \sqrt{I}} - 0.3 I)

Ionic strength and activity coefficient (Debye–Hückel, Davies form): $a = γ c$ , $K_{s}^{\circ} = a (Ba^{2 +}) a (SO_{4}^{2 -})$ — the salt effect.

m (SO_{4}^{2 -}) = m (BaSO_{4}) \cdot F, F = \frac{M (SO_{4}^{2 -})}{M (BaSO_{4})} = 0.4116

Gravimetric (analytical) factor: conversion from the weighed form to the substance being determined.

ω (H_{2} O) = \frac{m_{1} - m_{2}}{m_{1} - m_{0}} \cdot 100 %

Water of crystallisation: $m_{0}$ — empty crucible, $m_{1}$ — crucible + hydrate, $m_{2}$ — after heating to constant mass.

\frac{[I^{-}]}{[Cl^{-}]} = \frac{K_{s} (AgI)}{K_{s} (AgCl)} \approx 5 \cdot 10^{- 7}

Fractional precipitation: when AgCl begins to precipitate, almost no iodide ions are left in the solution.

Theory

Analytical chemistry and the systematic scheme

Analytical chemistry determines the composition of water, soil, air, alloys, ores, and biological and environmental samples: qualitative analysis — which ions are present, quantitative analysis — how much. The stages of analysis are sampling, decomposition of the sample (dissolving an ore in $HNO_{3}$ or “aqua regia”, fusing with $Na_{2} CO_{3}$ ), determination, and calculation of the result. In the acid–base classification the cations fall into six groups: I — $K^{+}, Na^{+}, NH_{4}^{+}$ (no group reagent); II — $Ag^{+}, Pb^{2 +}, Hg_{2}^{2 +}$ (2 M HCl, chlorides); III — $Ba^{2 +}, Sr^{2 +}, Ca^{2 +}$ (1 M $H_{2} SO_{4}$ + alcohol, sulfates); IV — $Al^{3 +}, Cr^{3 +}, Zn^{2 +}, Sn^{2 +}, Sn^{4 +}$ (amphoteric hydroxides that dissolve in excess NaOH; $H_{2} O_{2}$ oxidises $Cr^{3 +}$ to yellow $CrO_{4}^{2 -}$ ); V — $Fe^{2 +}, Fe^{3 +}, Mn^{2 +}, Bi^{3 +}, Mg^{2 +}, Sb^{3 +}, Sb^{5 +}$ (insoluble in excess alkali); VI — $Cu^{2 +}, Ni^{2 +}, Co^{2 +}, Cd^{2 +}, Hg^{2 +}$ (ammine complexes in excess $NH_{3}$ ). In systematic analysis the groups are separated one after another (reagent → centrifuge → the solution goes into the next test tube); in fractional analysis an ion is detected in a separate portion by a reaction that the other ions do not interfere with ( $NH_{4}^{+}$ , $Fe^{2 +}$ , $Fe^{3 +}$ , $Sn^{2 +}$ — from the original solution, because their oxidation states change in the scheme). Working rules: never point the mouth of a test tube at yourself, load the centrifuge balanced, smell by wafting the vapour towards you with your hand, and never taste anything.

Characteristic reactions of cations

I: $K^{+}$ — yellow precipitate with $Na_{3} [Co (NO_{2})_{6}]$ ; $Na^{+}$ — white crystals with $K [Sb (OH)_{6}]$ ; $NH_{4}^{+}$ — $NH_{3}$ on heating with alkali (damp litmus paper turns blue), red-brown precipitate with Nessler's reagent. II: AgCl dissolves in $NH_{3}$ and is reprecipitated by $HNO_{3}$ ; $PbCl_{2}$ dissolves in hot water, yellow $PbI_{2}$ with KI; $Hg_{2} Cl_{2}$ turns black with ammonia. III: $Ba^{2 +}$ — yellow $BaCrO_{4}$ with $K_{2} Cr_{2} O_{7}$ ; $Sr^{2 +}$ — slow turbidity with gypsum water; $Ca^{2 +}$ — white $CaC_{2} O_{4}$ with oxalate. IV: $Al^{3 +}$ — red lake with alizarin; $CrO_{4}^{2 -}$ — blue $CrO_{5}$ with acidified $H_{2} O_{2}$ and ether; $Zn^{2 +}$ — white precipitate with $K_{4} [Fe (CN)_{6}]$ ; $Sn^{2 +}$ — reduces $HgCl_{2}$ to $Hg$ . V: $Fe^{2 +}$ — $K_{3} [Fe (CN)_{6}]$ (Turnbull's blue), $Fe^{3 +}$ — $K_{4} [Fe (CN)_{6}]$ (Prussian blue) and KSCN (blood-red); $Mn^{2 +}$ — violet $MnO_{4}^{-}$ with $NaBiO_{3}$ ; $Bi^{3 +}$ — black Bi with stannite; $Mg^{2 +}$ — $MgNH_{4} PO_{4}$ ; $Sb^{3 +}$ — red $Sb_{2} OS_{2}$ with thiosulfate, $Sb^{5 +}$ — rhodamine B. VI: $Cu^{2 +}$ — deep blue in ammonia, red-brown with $K_{4} [Fe (CN)_{6}]$ ; $Ni^{2 +}$ — raspberry-red with dimethylglyoxime; $Co^{2 +}$ — $NH_{4} SCN$ + amyl alcohol — blue layer; $Cd^{2 +}$ — yellow CdS; $Hg^{2 +}$ — red $HgI_{2}$ with KI. Flame: Na yellow (589 nm), K violet (766 nm, seen through cobalt glass), Li deep red (671 nm), Ca brick-red, Sr crimson, Ba yellowish-green, Cu blue-green.

Anions and dry-salt analysis

Group I ( $SO_{4}^{2 -}, SO_{3}^{2 -}, S_{2} O_{3}^{2 -}, CO_{3}^{2 -}, HPO_{4}^{2 -}, B_{4} O_{7}^{2 -}, SiO_{3}^{2 -}$ ) is precipitated by $BaCl_{2}$ in neutral or weakly alkaline medium; only $BaSO_{4}$ is insoluble in HCl. Group II ( $Cl^{-}, Br^{-}, I^{-}$ ) — $AgNO_{3}$ + $HNO_{3}$ : white AgCl, pale yellow AgBr, yellow AgI; AgCl dissolves in ammonium carbonate; $Br^{-}$ and $I^{-}$ with chlorine water colour chloroform orange/violet. Group III ( $NO_{3}^{-}, NO_{2}^{-}, CH_{3} COO^{-}$ ) has no group reagent: diphenylamine (blue), $NO_{2}^{-}$ liberates iodine from KI, acetate gives a red-brown colour with $FeCl_{3}$ . Characteristic tests: $SO_{3}^{2 -}$ and $S_{2} O_{3}^{2 -}$ decolourise iodine, thiosulfate gives a precipitate of S with acid, carbonate gives $CO_{2}$ (lime water turns cloudy), phosphate gives a yellow precipitate with molybdate, borate a green flame, silicate a gelatinous $H_{2} SiO_{3}$ . Fractional precipitation: if $AgNO_{3}$ is added dropwise to a mixture of $Cl^{-}$ and $I^{-}$ , AgI precipitates first, because its solubility product is reached first. Dry salt: examine its colour and solubility, do a flame test, then identify the cation and anion in solution.

Equilibrium, solubility and ionic strength

Law of mass action: $K = \prod [products] / \prod [reactants]$ . Analytical concentration is the total amount of a substance introduced into the solution; equilibrium concentration refers to a particular form ( $SO_{4}^{2 -}$ or $HSO_{4}^{-}$ ). Ions screen one another: activity $a = γ c$ ; ionic strength $I = \frac{1}{2} \sum c_{i} z_{i}^{2}$ , with $γ$ from the Debye–Hückel law (at small I, $\lg γ = - 0.51 z^{2} \sqrt{I}$ ). Constants are thermodynamic (in activities), concentration-based (dependent on I) or conditional (taking pH and side reactions into account). Solubility product $K_{s}$ (25 °C): $BaSO_{4}$ 1.1·10⁻¹⁰, AgCl 1.8·10⁻¹⁰, AgBr 5.4·10⁻¹³, AgI 8.5·10⁻¹⁷, $CaC_{2} O_{4}$ 2.3·10⁻⁹, $PbCl_{2}$ 1.7·10⁻⁵. Factors that affect solubility: a common ion (decreases it), the salt effect — a foreign electrolyte lowers $γ$ and so raises solubility, acidity ( $BaSO_{4}$ is more soluble in strong acid because $HSO_{4}^{-}$ forms: $K_{s}^{'} = K_{s} (1 + [H^{+}] / K_{a 2})$ , $K_{a 2}$ = 1.02·10⁻²), complex formation (AgCl in ammonia), and temperature. Hydrolysis also affects precipitation: when $BiCl_{3}$ and $SbCl_{3}$ are diluted, white $BiOCl$ and $SbOCl$ fall out — the degree and constant of hydrolysis are in the “Hydrolysis of salts and the medium” experiment.

Gravimetric analysis (laboratory)

In the direct method the substance to be determined is separated as a precipitate ( $SO_{4}^{2 -} \overset{}{\to} BaSO_{4}$ ); in the indirect method the part that escapes is found (water of crystallisation, $CO_{2}$ ). The precipitated form and the weighed form may differ ( $Fe (OH)_{3} \overset{}{\to} Fe_{2} O_{3}$ ). For a crystalline precipitate (BaSO₄) the relative supersaturation (Q − S)/S must be small: $BaCl_{2}$ is added slowly, with stirring, to a dilute, acidified, hot solution; for an amorphous precipitate (hydroxides) use a concentrated hot solution and coagulation with an electrolyte. Digestion (1–2 h on a water bath): small crystals dissolve and large ones grow. Co-precipitation: adsorption on the surface (removed by washing), occlusion inside, and mixed crystals — isomorphism ( $KMnO_{4}$ with $BaSO_{4}$ ). Use an ashless “blue ribbon” filter paper, wash with hot water until $Cl^{-}$ is gone (test the filtrate with $AgNO_{3}$ ), dry, ignite at 800 °C, cool in a desiccator and weigh to constant mass (two weighings differ by ≤ 0.2 mg). Analytical balance (d = 0.1 mg): the vessel must be at room temperature, handled with tongs and not by hand, with the doors closed. Water of crystallisation: $CuSO_{4} \cdot 5 H_{2} O$ — 36.08 %, $BaCl_{2} \cdot 2 H_{2} O$ — 14.75 %. Errors are systematic (solubility, occlusion, passing through the filter — the “error budget” in the log), random (weighing ±0.1 mg, pipette) or gross (spilling the precipitate); the difference between the result and the true value is the absolute error, and its ratio to the true value is the relative error (%); from parallel results you calculate the mean, the standard deviation and the confidence interval.

Thermal analysis, safety and the model

Thermogravimetry (TG): the sample is heated steadily in a furnace connected to a balance and the mass is recorded against temperature; DTG is the derivative of the mass (steps become peaks); DTA is the temperature difference between the sample and an inert reference ( $Al_{2} O_{3}$ ): an endothermic process (dehydration, decomposition, melting) points downwards, an exothermic one (combustion, crystallisation) upwards. $CaC_{2} O_{4} \cdot H_{2} O$ : at ≈ 200 °C −12.3 % ( $H_{2} O$ ), at ≈ 480 °C a further −19.2 % ( $CO$ ; in air the CO burns — an exothermic peak in DTA), at ≈ 750 °C −30.1 % ( $CO_{2}$ ), leaving 38.4 % CaO. If the heating rate rises, the peaks shift to higher temperature. Melting and crystallisation: tin gives an endothermic peak at 231.9 °C and, on cooling, supercools slightly before crystallising exothermically. Safety: salts of mercury, lead, barium and cadmium, and chromates, are poisonous — put the waste in a separate container; add acid to water; take the crucible out of the muffle furnace with long tongs and gloves; never leave alcohol or ether open near a flame. The model: the ions and reactions follow the textbook scheme and interferences are simplified; the bands in the flame spectrum are approximate; gravimetric errors (occlusion, passing through the filter, adsorption, washing) are a semi-quantitative model, while the solubility is exact from $K_{s}$ , the Davies equation and $K_{a 2}$ ; the sample compositions are typical; the thermal curves use mass losses from the literature and typical peak shapes; the furnace and derivatograph time is sped up.

Did you know?

By studying flame spectra in 1860–1861, R. Bunsen and G. Kirchhoff discovered two new elements — caesium (from its blue lines) and rubidium (from its red lines).
The derivatograph — an instrument that records the mass, its derivative and the heat effect at the same time — was created in the 1950s by the Hungarian chemists F. Paulik, J. Paulik and L. Erdey.

Inside the experiment

The experiment starts from a real-life situation: you predict the result, change the controls, run the experiment and draw a conclusion. Inside are missions, theory, a quiz and a guided tour in which the camera moves and explains the key points.

More experiments in this section

Thermochemistry and Gibbs energy — Year 1
Electrochemical analysis — Year 1
Titrimetric analysis — Year 2
Optical methods of analysis — Year 2
Extraction and chromatography — Year 2
Spectra: determining structure — Year 2
Alloys: phase diagrams — Year 2
Chemical kinetics and Arrhenius — Year 2
Catalysis and enzymes — Year 2
Colloids and adsorption — Year 2