Basic Analytical Chemistry BCH5T12

Syllabus topics (RTMNU)

• Classification of analytical techniques
• Qualitative and quantitative analysis
• Classical and instrumental methods
• Factors affecting choice of analytical method
• Errors in chemical analysis. Types of errors: Systematic and random, Absolute and relative, Additive and proportional
• Normal distribution of indeterminate errors
• Statistical parameters for data evaluation: Mean, median, average deviation, standard deviation, coefficient of variation, relative standard deviation
• Accuracy and precision of results
• Comparison of data using F and t-test, rejection of data using Q test
• Numerical problems

Classification of analytical techniques

Analytical chemistry deals with finding what is present in a sample (qualitative) and how much is present (quantitative).

• Qualitative analysis: identification of elements, ions, functional groups or compounds (e.g. salt analysis, flame test, spot tests, IR spectrum).
• Quantitative analysis: determination of amount or concentration (e.g. titration of acid, gravimetric estimation of Ba²⁺, colorimetric estimation of Cu²⁺).

Factors affecting choice of analytical method

1. Nature of the information needed (qualitative/quantitative, total or species).
2. Amount of sample available and concentration range of the analyte (major, minor, trace).
3. Required accuracy and precision.
4. Interferences present (matrix).
5. Number of samples, time and speed required.
6. Cost and availability of equipment and trained staff.
7. Whether the method must be non-destructive; safety and environmental issues.

Errors in chemical analysis and types of errors

Error = observed value − true value.

• Systematic (determinate) errors: have a definite cause and direction; can be found and corrected. Types: instrumental (uncalibrated burette, faulty balance), method errors (indicator end point differs from equivalence point, co-precipitation, side reactions), personal errors (colour judgement, parallax), reagent errors (impure chemicals). Reduced by calibration, blank determination, control (standard) samples, independent methods, standard addition.
• Random (indeterminate) errors: small, unpredictable variations in both directions from uncontrollable causes (temperature fluctuation, reading the last digit). They cannot be removed but are treated by statistics; averaging many readings reduces them.
• Absolute error E = x − x_t; relative error = (x − x_t)/x_t × 100% (or in ppt).
• Additive (constant) error: same size whatever the sample size (e.g. a constant indicator blank) — its relative effect falls as sample size increases. Proportional error: size increases in proportion to sample size (e.g. an impurity in the sample, wrongly standardised titrant) — relative error constant.

Normal distribution of indeterminate errors

When a measurement is repeated many times, random errors follow the normal (Gaussian) distribution — a symmetrical bell-shaped curve centred on the mean μ. Small errors are more common than large ones; positive and negative errors are equally likely. About 68.3% of results fall within μ ± 1σ, 95.4% within μ ± 2σ and 99.7% within μ ± 3σ.

Statistical parameters for data evaluation

• Mean x̄ = Σx_i/n.
• Median: middle value when results are arranged in order (average of the two middle values for an even number).
• Average deviation d̄ = Σ|x_i − x̄|/n.
• Standard deviation s = √[Σ(x_i − x̄)²/(n − 1)].
• Relative standard deviation RSD = s/x̄; coefficient of variation CV = (s/x̄) × 100%.

Accuracy and precision

• Accuracy: closeness of a result to the true (accepted) value; expressed as error. Affected by systematic errors.
• Precision: closeness of repeated results to one another; expressed as standard deviation/CV. Affected by random errors.
• Results can be precise but not accurate (all close together but far from true value — systematic error present). Good analysis needs both.

Comparison of data — F-test and t-test; rejection of data — Q-test

• F-test compares the precision of two sets: F = s₁²/s₂² (larger variance on top). If F_calc > F_table, the precisions differ significantly.
• t-test compares a mean with a true value: t = |x̄ − μ|√n / s; or two means x̄₁, x̄₂: t = (|x̄₁ − x̄₂|/s_pooled)√[n₁n₂/(n₁ + n₂)]. If t_calc > t_table (for n − 1 degrees of freedom at the chosen confidence level), the difference is significant (a systematic error is likely).
• Q-test (Dixon) decides whether a suspect (outlying) result may be rejected: Q = |suspect value − nearest value| / range. If Q_calc > Q_crit the value is rejected. Q_crit (90%): n = 3: 0.94, n = 4: 0.76, n = 5: 0.64, n = 6: 0.56, n = 7: 0.51.

Numerical problems

Example 1. Results (% Cl): 10.08, 10.11, 10.09, 10.10, 10.12. Find mean, median, average deviation, s and CV.
Mean = 50.50/5 = 10.10; median = 10.10; deviations 0.02, 0.01, 0.01, 0.00, 0.02 → d̄ = 0.06/5 = 0.012; Σ(dev)² = 0.0010 → s = √(0.0010/4) = 0.0158; CV = 0.0158/10.10 × 100 = 0.16%.

Example 2 (t-test). If the true value for Example 1 is 10.14: t = |10.10 − 10.14| × √5 / 0.0158 = 5.66. t_table (4 d.f., 95%) = 2.78. Since 5.66 > 2.78, the difference is significant — a systematic error is present.

Example 3 (Q-test). Normality values: 0.1050, 0.1053, 0.1048, 0.1072. Suspect = 0.1072. Q = (0.1072 − 0.1053)/(0.1072 − 0.1048) = 0.0019/0.0024 = 0.79. Q_crit (n = 4, 90%) = 0.76. Q > Q_crit, so 0.1072 is rejected.

Likely exam questions

1. (Long, 8 marks) What are errors? Explain systematic and random errors. How can systematic errors be minimised?
2. (Long, 8 marks) Explain the F-test, t-test and Q-test. Replicate results are 20.12, 20.15, 20.11, 20.31. Should 20.31 be rejected at 90% confidence (Qcrit = 0.76)?
3. (Short, 4 marks) Distinguish between accuracy and precision.
4. (Short, 4 marks) Define standard deviation and coefficient of variation.
5. (Short, 4 marks) Distinguish between classical and instrumental methods of analysis.

Syllabus topics (RTMNU)

• Criteria for representative sample
• Bulk, gross, incremental and analysis sample
• Sampling statistics
• Techniques of sampling of ambient air, water and soil samples
• Methods of sample size reduction: Coning and quartering, rolling and quartering
• Hazards in sampling
• Sample dissolution methods for elemental analysis: Dry and wet ashing, acid digestion, fusion processes and dissolution of organic samples
• Types of analysis: Macro, semi-micro, micro, sub-micro and ultramicro
• Major, minor and trace constituents of a sample

Criteria for a representative sample

The result of an analysis is only as good as the sample. A representative sample has the same composition as the whole material (the lot or population). Criteria: (1) collected randomly from many points/depths/times; (2) large enough to cover heterogeneity; (3) not contaminated or changed during collection, transport and storage (proper container, preservation, labelling); (4) collected by a planned, documented procedure.

Bulk, gross, incremental and analysis sample

• Bulk (lot): the whole material to be analysed (a wagon of coal, a lake).
• Increment: an individual portion taken from the lot at one point and one time.
• Gross sample: all increments combined; still large and representative.
• Laboratory sample: the gross sample reduced in size and made uniform, sent to the lab.
• Analysis (test) sample: the small, accurately weighed/measured portion actually taken for analysis.

Sampling statistics

The total variance of a result is the sum of sampling variance and analytical variance: s_o² = s_s² + s_a². When the material is heterogeneous, sampling error usually dominates, so improving the analytical method alone does not help. The number of increments needed for a given relative uncertainty is n = t²s_s²/(R x̄)², where R is the allowed relative error; more increments are needed for more heterogeneous material and for better confidence.

Techniques of sampling of ambient air, water and soil

• Ambient air: high-volume samplers pull a known volume of air through a filter (PM₁₀/PM_2.5 particulates); gases are collected by bubbling through absorbing solutions (impingers, e.g. SO₂ in tetrachloromercurate, NO₂ in NaOH), on adsorbent tubes (charcoal) or in evacuated canisters/bags; flow rate and time are recorded; sampler kept 1.5–2 m above ground, away from obstructions.
• Water: grab (spot) samples or composite samples (mixed over time/places); depth samplers for lakes/rivers; tap water after flushing; clean, rinsed bottles (glass for organics, polyethylene for metals); preservation — cooling to 4 °C, acidifying with HNO₃ for metals, separate sterile bottles for bacteria, DO fixed on site.
• Soil: divide field into uniform areas; take cores with an auger from 10–20 spots in a zig-zag pattern at a fixed depth (0–15 cm for agriculture); mix to a composite; air dry, remove stones and roots, grind and sieve (2 mm); store in labelled bags.

Methods of sample size reduction

• Coning and quartering: the crushed gross sample is piled into a cone, flattened into a circular cake, divided into four quarters; two opposite quarters are kept and the other two rejected; the process is repeated till the required size is obtained.
• Rolling and quartering: the sample is placed on a sheet (cloth/paper) and mixed by lifting corners alternately so it rolls over itself; then flattened and quartered as above. Suitable for smaller samples (powders). Mechanical riffle samplers do the same job.

Hazards in sampling

Toxic gases and fumes (H₂S, CO in sewers/mines), oxygen-deficient confined spaces, corrosive or flammable materials, radioactive or biological hazards (pathogens in sewage), falling into tanks/rivers, moving machinery, high-temperature streams. Precautions: protective equipment (gloves, goggles, masks), gas detectors, working in pairs, safe sampling devices, proper labelling and training.

Sample dissolution methods for elemental analysis

• Dry ashing: organic sample heated in a crucible in a muffle furnace (450–550 °C) to burn off organic matter; ash dissolved in dilute acid. Simple, many samples at once, but volatile elements (Hg, As, Pb, Se) may be lost.
• Wet ashing (wet digestion): heating with oxidising acids — HNO₃, HNO₃ + H₂SO₄, HNO₃ + HClO₄, H₂O₂. Faster, fewer losses, but needs care (perchloric acid is explosive with organics).
• Acid digestion: metals and alloys dissolved in HCl, HNO₃, aqua regia (3HCl : 1HNO₃, for Au, Pt); silicates in HF; often in closed microwave digestion vessels (faster, no loss of volatiles).
• Fusion: insoluble materials (silicates, refractory oxides, ores) are fused with a flux — Na₂CO₃, NaOH, Na₂O₂ (basic fluxes) or KHSO₄, K₂S₂O₇ (acidic fluxes), lithium metaborate — in Pt or Ni crucibles; the melt is dissolved in water/acid.
• Dissolution of organic samples: in suitable organic solvents (ethanol, chloroform, hexane, DMSO) for molecular analysis; for elements, combustion methods (oxygen flask, Schöniger) or Kjeldahl digestion (N).

Types of analysis by sample size; major, minor and trace constituents

By amount of analyte in the sample: major constituent 1–100%; minor 0.01–1%; trace < 0.01% (100 ppm or below); ultratrace < 1 ppm (ppb level).

Likely exam questions

1. (Long, 8 marks) What is a representative sample? Describe the techniques of sampling of air, water and soil.
2. (Long, 8 marks) Describe the methods of sample dissolution for elemental analysis: dry ashing, wet ashing, acid digestion and fusion.
3. (Short, 4 marks) Explain coning and quartering.
4. (Short, 4 marks) Distinguish between gross sample and analysis sample.
5. (Short, 4 marks) Classify analysis on the basis of sample size.

Syllabus topics (RTMNU)

• General principle
• Criteria for reactions used in titrimetric analysis
• Primary standards and secondary standards
• Concepts of equivalent weight and molecular weight, normality, molarity and various methods of expressing concentrations
• Internal and external indicators
• Theories of indicators in acid-base, precipitation, redox and complexometric titrations
• Calculations involving preparation of standard solutions
• Stoichiometric calculations in various types of titrations

General principle of volumetric (titrimetric) analysis

A solution of accurately known concentration (standard solution, titrant) is added from a burette to a measured volume of the solution being analysed until the reaction is just complete (equivalence point), detected by an indicator or instrument (end point). From the volume used and the stoichiometry, the amount of analyte is calculated: N₁V₁ = N₂V₂ (or M₁V₁/n₁ = M₂V₂/n₂).

Criteria for reactions used in titrimetric analysis

1. The reaction must be stoichiometric — a definite, known equation, no side reactions.
2. It must be rapid (or made fast by catalyst/heating).
3. It must be practically complete at the equivalence point (large equilibrium constant).
4. A suitable method (indicator/instrument) must be available to detect the end point.
5. No interference from other substances present (or they can be masked).

Primary and secondary standards

• Primary standard: a substance of high purity whose solution can be made by direct weighing. Requirements: very pure (≥ 99.9%), stable in air (not hygroscopic, not oxidised, no CO₂ absorption), easy to dry, high equivalent weight (less weighing error), soluble, reacts stoichiometrically. Examples: anhydrous Na₂CO₃, oxalic acid dihydrate, potassium hydrogen phthalate (KHP), K₂Cr₂O₇, Mohr's salt (FeSO₄(NH₄)₂SO₄·6H₂O), NaCl, AgNO₃, EDTA disodium salt (dried), ZnSO₄ metal (Zn).
• Secondary standard: a substance whose solution must be standardised against a primary standard because it is not pure or stable enough. Examples: NaOH (absorbs CO₂, hygroscopic), HCl, H₂SO₄, KMnO₄ (contains MnO₂), Na₂S₂O₃, I₂.

Equivalent weight, molecular weight and ways of expressing concentration

• Equivalent weight = molar mass / n-factor (n = basicity of acid, acidity of base, electrons gained/lost in redox, total charge for salts). Ex: H₂SO₄ 98/2 = 49; Na₂CO₃ 106/2 = 53; oxalic acid dihydrate 126/2 = 63; KMnO₄ in acid 158/5 = 31.6; K₂Cr₂O₇ 294.2/6 = 49.03.
• Molarity (M) = moles of solute per litre of solution. Normality (N) = gram-equivalents per litre; N = M × n-factor.
• Molality (m) = moles per kg of solvent; mole fraction; % w/w, % w/v, % v/v; ppm (mg L^–1 for dilute aqueous solutions) and ppb; formality (formula weights per litre); titre (mg of analyte equivalent to 1 mL of titrant).

Internal and external indicators

• Internal indicator: added to the titration flask; changes colour at the end point — phenolphthalein, methyl orange (acid–base), diphenylamine (redox), Eriochrome Black T (complexometric), K₂CrO₄ (Mohr's method). KMnO₄ acts as its own (self) indicator.
• External indicator: used outside the flask: a drop of the titration mixture is brought into contact with the indicator on a spot plate. Example: potassium ferricyanide for Fe²⁺ in K₂Cr₂O₇ titration (blue colour while Fe²⁺ remains; end point when no blue appears).

Theories of indicators

• Acid–base — Ostwald's theory: an indicator is a weak acid (HIn) or weak base whose ionised and un-ionised forms have different colours: HIn ⇌ H⁺ + In^–. pH = pK_In + log([In^–]/[HIn]); colour change is seen over pH = pK_In ± 1. Phenolphthalein (8.2–10) for weak acid–strong base; methyl orange (3.1–4.4) for strong acid–weak base. Quinonoid theory: the two forms are benzenoid and quinonoid structures of different colour (e.g. phenolphthalein's colourless lactone vs pink quinonoid dianion).
• Precipitation: Mohr's method — K₂CrO₄ gives red Ag₂CrO₄ after all Cl^– is precipitated as AgCl (fractional precipitation, based on solubility products); Volhard's method — Fe³⁺ gives red [Fe(SCN)]²⁺ with excess SCN^–; Fajans method — adsorption indicators (fluorescein, eosin) are adsorbed on the charged precipitate surface after the equivalence point, changing colour.
• Redox: the indicator itself is oxidised/reduced with a colour change at a definite potential: E = E°_In ± 0.059/n. Diphenylamine (colourless → violet, E° ≈ 0.76 V), ferroin (red → pale blue, E° ≈ 1.06 V); H₃PO₄ is added in the dichromate titration to lower the Fe³⁺/Fe²⁺ potential.
• Complexometric (metallochromic): the indicator forms a coloured complex with the metal ion that is less stable than the metal–EDTA complex. At the end point EDTA takes the metal from the indicator and the free indicator colour appears: Mg–EBT (wine red) + EDTA → Mg–EDTA + EBT (blue) at pH 10. Others: murexide (Ca, Ni), xylenol orange.

Calculations — preparation of standard solutions

Mass required (g) = N × Eq. wt × V(L) or = M × Molar mass × V(L).

Example 1. Prepare 250 mL of 0.1 N oxalic acid (H₂C₂O₄·2H₂O, eq. wt 63.04): mass = 0.1 × 63.04 × 0.250 = 1.576 g.

Example 2. Prepare 250 mL of 0.05 M Na₂CO₃ (M = 106.0): mass = 0.05 × 106.0 × 0.250 = 1.325 g.

Example 3 (dilution). Volume of 10 N H₂SO₄ to make 500 mL of 0.1 N: V₁ = 0.1 × 500/10 = 5 mL.

Stoichiometric calculations in various titrations

Acid–base: 25.0 mL of 0.05 M Na₂CO₃ is titrated with 0.1 M HCl to methyl orange (Na₂CO₃ + 2HCl → 2NaCl + H₂O + CO₂). Moles Na₂CO₃ = 0.05 × 0.025 = 1.25 × 10^–3; moles HCl = 2.5 × 10^–3; volume = 2.5 × 10^–3/0.1 = 25.0 mL.

Redox: 20.0 mL of Fe²⁺ solution needs 18.0 mL of 0.02 M KMnO₄ (MnO₄^– + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O). Moles MnO₄^– = 3.6 × 10^–4; moles Fe²⁺ = 1.8 × 10^–3; [Fe²⁺] = 1.8 × 10^–3/0.020 = 0.090 M (= 5.03 g L^–1 Fe).

Precipitation: 25.0 mL NaCl needs 20.0 mL of 0.1 M AgNO₃: [NaCl] = 0.1 × 20/25 = 0.08 M (4.68 g L^–1).

Complexometric: 50 mL of hard water needs 8.0 mL of 0.01 M EDTA (1:1). Moles Ca²⁺ = 8.0 × 10^–5 = mass as CaCO₃ 8.0 × 10^–3 g in 50 mL → total hardness = 160 ppm as CaCO₃.

Likely exam questions

1. (Long, 8 marks) What are primary and secondary standards? Give the requirements of a primary standard with examples. Explain the various ways of expressing concentration.
2. (Long, 8 marks) Explain the theory of indicators used in acid–base, redox and complexometric titrations.
3. (Short, 4 marks) Calculate the mass of K₂Cr₂O₇ (eq. wt 49.03) needed to prepare 250 mL of 0.1 N solution.
4. (Short, 4 marks) Distinguish between internal and external indicators.
5. (Short, 4 marks) Write the criteria for a reaction to be used in titrimetric analysis.

Syllabus topics (RTMNU)

• General principles and conditions of precipitation
• Concepts of solubility, solubility product and precipitation equilibria
• Numerical problems based on solubility and solubility product
• Purity of precipitate: Co-precipitation and post-precipitation
• Supersaturation and peptization
• Criteria of selection of wash liquids
• Steps involved in gravimetric analysis of barium as barium sulphate

General principles and conditions of precipitation

Gravimetric analysis determines the amount of a constituent by converting it into a pure, stable compound of known composition that is weighed. In precipitation gravimetry the analyte is precipitated, filtered, washed, dried/ignited and weighed.

Requirements of a good precipitate: very low solubility (quantitative precipitation); easily filtered and washed (large crystals); pure; of known, constant composition after drying/ignition; high molar mass (smaller weighing error).

Conditions of precipitation (to get large, pure crystals — Von Weimarn):

1. Precipitate from dilute solutions.
2. Add the precipitant slowly with constant stirring.
3. Precipitate from hot solution (solubility slightly higher, less supersaturation).
4. Precipitate in slightly acidic medium where suitable (e.g. BaSO₄ in dilute HCl).
5. Digest the precipitate (keep it hot in the mother liquor) — small crystals dissolve and large ones grow (Ostwald ripening), and impurities are released.
6. Use slight excess of precipitant (common-ion effect) but not large excess (complex formation, adsorption).

Relative supersaturation = (Q − S)/S, where Q = concentration at any moment and S = equilibrium solubility. High relative supersaturation → many nuclei → colloidal/fine particles; low → fewer nuclei that grow into large crystals.

Solubility, solubility product and precipitation equilibria

• Solubility (S): maximum amount that dissolves in a given volume at a temperature (mol L^–1 or g L^–1).
• Solubility product (K_sp): for a saturated solution of a sparingly soluble salt A_xB_y ⇌ xA^y+ + yB^x–: K_sp = [A^y+]^x[B^x–]^y; for AB, K_sp = S²; for AB₂ or A₂B, K_sp = 4S³.
• Precipitation condition: ionic product Q > K_sp → precipitate forms; Q = K_sp → saturated; Q < K_sp → no precipitate.
• Common-ion effect: adding an ion common to the precipitate decreases its solubility — used to make precipitation complete and in washing.
• Solubility increases with temperature (usually), with diverse ions (salt effect), with acids (for salts of weak acids like CaC₂O₄) and with complex formation (AgCl in NH₃ or excess Cl^–).

Numerical problems on solubility and solubility product

Example 1. K_sp of BaSO₄ = 1.1 × 10^–10. Find solubility. S = √(1.1 × 10^–10) = 1.05 × 10^–5 mol L^–1 = 1.05 × 10^–5 × 233.4 = 2.45 × 10^–3 g L^–1.

Example 2. K_sp of Ag₂CrO₄ = 1.1 × 10^–12. K_sp = 4S³ → S = (1.1 × 10^–12/4)^1/3 = 6.5 × 10^–5 mol L^–1.

Example 3 (common ion). Solubility of BaSO₄ in 0.01 M Na₂SO₄: S = K_sp/[SO₄^2–] = 1.1 × 10^–10/0.01 = 1.1 × 10^–8 mol L^–1 — about 1000 times less than in pure water.

Example 4 (will a precipitate form?). Equal volumes of 2 × 10^–4 M BaCl₂ and 2 × 10^–4 M Na₂SO₄ are mixed. After mixing each is 1 × 10^–4 M; Q = (1 × 10^–4)² = 1 × 10^–8 > 1.1 × 10^–10 → BaSO₄ precipitates.

Purity of precipitate — co-precipitation and post-precipitation

• Co-precipitation: soluble impurities are carried down with the precipitate while it forms. Types: (a) surface adsorption — ions adsorbed on the large surface of colloidal/curdy precipitates (AgCl, hydroxides); (b) occlusion — impurities trapped inside growing crystals; (c) mixed-crystal (isomorphous) formation — e.g. BaSO₄ with PbSO₄ or KMnO₄. Reduced by slow precipitation from dilute hot solution, digestion, washing, re-precipitation.
• Post-precipitation: an impurity precipitates on the surface after the main precipitate has formed, when it is left standing in the mother liquor — e.g. MgC₂O₄ on CaC₂O₄, ZnS on CuS/HgS. It increases with time; avoided by filtering soon (no long digestion).

Supersaturation and peptization

• Supersaturation: a solution holding more solute than its equilibrium solubility; it is unstable and leads to nucleation. High supersaturation gives many tiny particles (colloids) which are hard to filter; low supersaturation gives large crystals.
• Peptization: the reverse of coagulation — a coagulated colloidal precipitate goes back into colloidal solution when washed with pure water, because the electrolyte that kept it coagulated is washed away; the particles pass through the filter and results come low. Prevented by washing with a dilute electrolyte solution (e.g. dilute HNO₃ for AgCl, NH₄NO₃ for hydroxides).

Criteria for selection of wash liquids

1. Should dissolve and remove impurities but not the precipitate (often contains a common ion to lower solubility).
2. Should prevent peptization (contain a volatile electrolyte).
3. Should be volatile or easily removed on drying/ignition (NH₄NO₃, dilute HNO₃, NH₄OH).
4. Should not react with the precipitate or form insoluble products; should prevent hydrolysis.
5. Hot wash liquid is used when the precipitate's solubility does not increase much with temperature (faster filtration).

Washing with several small portions is more efficient than one large portion.

Steps in gravimetric estimation of barium as barium sulphate

1. Sample solution: dissolve a weighed amount of barium salt (e.g. BaCl₂·2H₂O) in water; add a little dilute HCl (prevents precipitation of BaCO₃, BaHPO₄, and gives larger crystals).
2. Precipitation: heat to boiling and add hot dilute H₂SO₄ dropwise with stirring, in slight excess: Ba²⁺ + SO₄^2– → BaSO₄↓ (white).
3. Digestion: keep on a water bath for about an hour; test the supernatant for complete precipitation with a drop of H₂SO₄.
4. Filtration: through ashless filter paper (Whatman No. 42) or a sintered/Gooch crucible.
5. Washing: with hot water until free from chloride (test filtrate with AgNO₃).
6. Drying and ignition: dry, char the paper slowly, ignite in a weighed silica/porcelain crucible at about 800–900 °C (avoid reduction of BaSO₄ to BaS by carbon — burn paper with free air access).
7. Weighing: cool in a desiccator, weigh; repeat ignition to constant weight.
8. Calculation: mass of Ba = mass of BaSO₄ × (137.33/233.39) — gravimetric factor 0.5884.

Example. 0.5000 g of a sample gave 0.4668 g BaSO₄. Ba = 0.4668 × 0.5884 = 0.2747 g → % Ba = 0.2747/0.5000 × 100 = 54.93%.

Likely exam questions

1. (Long, 8 marks) Explain the conditions of precipitation in gravimetric analysis. Describe the steps in the gravimetric estimation of barium as barium sulphate.
2. (Long, 8 marks) What are co-precipitation and post-precipitation? How can the purity of a precipitate be improved?
3. (Short, 4 marks) Ksp of AgCl is 1.8 × 10⁻¹⁰. Calculate its solubility in mol L⁻¹ and g L⁻¹.
4. (Short, 4 marks) What is peptization? How is it prevented?
5. (Short, 4 marks) Give the criteria for selection of a wash liquid.