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5.3 Gravimetric Analysis and Precipitation Equilibria ($K_{sp}$)
PRC Chemist Licensure Examination Exam
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1 Chapter 1: Exam Overview, Chemistry Law (RA 10657), and Laboratory Safety
1.1 PRC Chemist Licensure Examination: Format, Schedule, Grading, and Passing Standards 1.2 Republic Act 10657 (Chemistry Profession Act) and Professional Ethics 1.3 Chemical Laboratory Safety, GHS Classification, Hazardous Waste Management, and Quality Assurance
2 Chapter 2: Inorganic Chemistry: Atomic Structure, Periodicity, and Chemical Bonding
2.1 Atoms, Ions, Compounds, Inorganic Nomenclature, and Stoichiometry 2.2 Quantum Numbers, Electronic Configurations, and Periodic Trends 2.3 Chemical Bonding Models: Lewis Structures, VSEPR Theory, and Molecular Polarity 2.4 Molecular Orbital Theory and Magnetochemistry of Diatomic Molecules
3 Chapter 3: Inorganic Chemistry: Coordination Compounds and Transition Metals
3.1 Coordination Chemistry: Nomenclature, Formulas, and Isomerism 3.2 Crystal Field Theory, Ligand Field Theory, d-Orbital Splitting, and Reaction Mechanisms 3.3 Electronic Absorption Spectra, Tanabe-Sugano Diagrams, and Magnetic Properties
4 Chapter 4: Inorganic Chemistry: Main Group, Reactivity, Solid State, Nuclear, and Applied Topics
4.1 Systematic Descriptive Chemistry of Main Group Elements (s- and p-Blocks) 4.2 Reactivity of Inorganic Compounds: Acid-Base Concepts, HSAB, and Redox Diagrams 4.3 Solid-State Chemistry: Crystal Systems, Unit Cells, and Band Theory 4.4 Bioinorganic Chemistry: Metalloproteins, Oxygen Carriers, and Metal Ion Toxicity 4.5 Organometallic Chemistry: 18-Electron Rule, Carbonyl Complexes, and Catalysis 4.6 Nuclear Chemistry: Stability, Decay, Transmutation, and Radioanalytical Methods 4.7 Industrial, Environmental, and Atmospheric Inorganic Chemistry and Advanced Materials
5 Chapter 5: Analytical Chemistry: Measurements, Statistics, Classical Wet Analysis, and Chemical Equilibria
5.1 Analytical Measurements: Apparatus, Units, Concentration, Sampling, and Sample Preparation 5.2 Analytical Data Evaluation: Errors, Uncertainty, Statistics, and Calibration 5.3 Gravimetric Analysis and Precipitation Equilibria ($K_{sp}$) 5.4 Neutralization Titrimetry, Polyprotic Systems, Buffers, and Alpha Fractions 5.5 Complexometric (EDTA), Redox, and Precipitation (Argentometric) Titrimetry
6 Chapter 6: Analytical Chemistry: Electroanalytical Methods and Separations
6.1 Potentiometry, Ion-Selective Electrodes, and Voltammetric Techniques 6.2 Analytical Separations: Solvent Extraction, SPE, Ion Exchange, Precipitation, Masking, and Electrodeposition 6.3 Fundamentals of Chromatography: Theoretical Plates, Resolution, and van Deemter Equation 6.4 Gas Chromatography (GC): Columns, Stationary Phases, Detectors, and Applications 6.5 High-Performance Liquid Chromatography (HPLC): Normal vs. Reversed Phase and Method Development
7 Chapter 7: Analytical Chemistry: Spectroscopic, Mass Spectrometric, and Other Instrumental Methods
7.1 Molecular UV-Vis Spectroscopy and Quantitative Beer-Lambert Law 7.2 Infrared (FTIR) and Raman Spectroscopy: Vibrational Modes and Instrumentation 7.3 Atomic Spectroscopy: Atomic Absorption (AAS) and Inductively Coupled Plasma (ICP-OES/MS) 7.4 Mass Spectrometry: Ionization Sources, Mass Analyzers, and Fragmentation Analysis 7.5 Other Instrumental Methods (XRF, Flame Emission, CE, SFC, Thermal Analysis, Electronics) and Method Selection
8 Chapter 8: Physical Chemistry: Gases, Thermodynamics, and Thermochemistry
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9 Chapter 9: Physical Chemistry: Equilibrium, Phase Equilibria, Solutions, and Electrochemistry
9.1 Chemical Equilibrium: Equilibrium Constants, Le Chatelier's Principle, and the van 't Hoff Equation 9.2 Phase Rule, Phase Diagrams of One- and Two-Component Systems, and Clausius-Clapeyron Equation 9.3 Solutions: Raoult's and Henry's Laws, Colligative Properties, and Electrolytes 9.4 Electrochemistry: Galvanic Cells, Standard Potentials, and the Nernst Equation 9.5 Electrolyte Conductance, Ionic Mobility, Transport Numbers, and Concentration Cells
10 Chapter 10: Physical Chemistry: Kinetics, Surface Chemistry, and Quantum Mechanics
10.1 Reaction Rates, Rate Laws, and Integrated Rate Equations 10.2 Temperature Dependence of Rates: Arrhenius Equation, Collision Theory, and Transition State Theory 10.3 Reaction Mechanisms: Steady-State Approximation, Chain Reactions, and Catalysis 10.4 Surface Chemistry, Adsorption Isotherms, Colloids, and Macromolecular Solutions 10.5 Postulates of Quantum Mechanics, Operators, Particle in a Box, and Harmonic Oscillator 10.6 Atomic Spectra, the Hydrogen Atom, Many-Electron Atoms, and Term Symbols
11 Chapter 11: Organic Chemistry: Structure, Stereochemistry, and Hydrocarbons
11.1 Systematic IUPAC Nomenclature and Conformational Analysis of Alkanes and Cycloalkanes 11.2 Stereochemistry: Chirality, Enantiomers, Diastereomers, (R)/(S) Configuration, and Optical Activity 11.3 Alkenes and Alkynes: Addition Reactions, Markovnikov Rule, and Stereospecificity 11.4 Aromaticity: Hückel's Rule, Electrophilic Aromatic Substitution, and Directing Effects
12 Chapter 12: Organic Chemistry: Functional Groups, Mechanisms, Synthesis, and Structure Elucidation
12.1 Nucleophilic Aliphatic Substitution ($S_N1$, $S_N2$) and Elimination ($E_1$, $E_2$) Mechanisms 12.2 Alcohols, Phenols, Ethers, and Epoxides: Structure, Synthesis, and Reactivity 12.3 Carbonyl Compounds I: Aldehydes and Ketones, Nucleophilic Addition, and Oxidation/Reduction 12.4 Carbonyl Compounds II: Carboxylic Acids and Derivatives, Enolate Chemistry, and Condensations 12.5 Amines: Basicity, Synthesis, Reactions, and Arenediazonium Chemistry 12.6 Structure Elucidation: NMR Spectroscopy, Combined Spectral Problems, and Qualitative Organic Tests 12.7 Organic Synthesis Strategy, Protecting Groups, Rearrangements, and Pericyclic Reactions
13 Chapter 13: Biochemistry: Cells, Biomolecules, Enzymes, and Membranes
13.1 Cells, Organelles, Water, and Biological Acid-Base Buffers 13.2 Amino Acids, Peptides, and Hierarchical Protein Structure 13.3 Protein Purification and Biochemical Analysis of Proteins, Carbohydrates, and Lipids 13.4 Enzyme Nomenclature and Classification, Cofactors, Coenzymes, and Vitamin Precursors 13.5 Enzyme Kinetics: Michaelis-Menten Model, Lineweaver-Burk Analysis, and Enzyme Inhibition 13.6 Carbohydrates, Lipids, Biological Membranes, and Membrane Transport
14 Chapter 14: Biochemistry: Metabolism, Bioenergetics, Photosynthesis, and Molecular Genetics
14.1 Carbohydrate Catabolism and Anabolism: Glycolysis, Gluconeogenesis, Glycogen, and Pentose Phosphate Pathway 14.2 Citric Acid Cycle, Mitochondrial Electron Transport, Oxidative Phosphorylation, and $\beta$-Oxidation 14.3 Photosynthesis: Light Reactions, Photophosphorylation, and the Calvin Cycle 14.4 Lipolysis and Lipid Biosynthesis: Fatty Acids, Triacylglycerols, and Cholesterol 14.5 Nitrogen Metabolism: Nitrogen Fixation, Amino Acid Metabolism, and the Urea Cycle 14.6 Nucleic Acids, DNA Replication, Transcription, Translation, and Recombinant DNA Techniques 14.7 Regulation of Gene Expression, Mutation and Mutagens, DNA Repair, Carcinogenesis, and cDNA Cloning
5.3 Gravimetric Analysis and Precipitation Equilibria ($K_{sp}$)
Key Takeaways Explain This Topic AI
Gravimetric analysis is an absolute primary analytical method relying solely on mass measurements and stoichiometric Gravimetric Factors ( G F = a ⋅ F W ( analyte ) b ⋅ F W ( precipitate ) GF = \frac{a \cdot FW(\text{analyte})}{b \cdot FW(\text{precipitate})} GF = b ⋅ F W ( precipitate ) a ⋅ F W ( analyte ) ).
Precipitate morphology is governed by Relative Supersaturation ( R S S = Q − S S RSS = \frac{Q - S}{S} RSS = S Q − S ); maintaining low R S S RSS RSS by slow precipitant addition, dilute solutions, heating, and digestion favors crystalline over colloidal particles.
Coprecipitation encompasses surface adsorption, occlusion, and inclusion; post-precipitation is a distinct time-dependent surface deposition of an unrelated sparingly soluble phase that increases with digestion time.
Peptization (redispersion of coagulated colloids) is prevented by washing precipitates with volatile electrolytes (e.g., H N O 3 , N H 4 N O 3 HNO_3, NH_4NO_3 H N O 3 , N H 4 N O 3 ) rather than pure deionized water.
Precipitation equilibria are governed by K s p K_{sp} K s p ; common ions depress solubility, whereas increasing ionic strength increases solubility via the diverse ion (salt) effect through activity coefficient depression.
Last updated: October 2026
Gravimetric Analysis and Precipitation Equilibria ( K s p K_{sp} K s p )
Gravimetric analysis encompasses quantitative analytical procedures based on measuring the mass of a pure, stoichiometric chemical substance derived from an analyte. Because mass can be measured with an analytical balance to within ± 0.1 mg \pm 0.1\text{ mg} ± 0.1 mg or better without instrument calibration curves, gravimetry is an absolute primary analytical method. On the PRC Chemist Licensure Examination, gravimetric questions focus on stoichiometric factor calculations, precipitation kinetics, purification mechanisms, and chemical equilibria governing solubility.
1. Principles of Gravimetric Analysis and Gravimetric Factors
In precipitation gravimetry, the analyte in solution is converted into an insoluble precipitate of known or convertible chemical composition, filtered, washed, dried or ignited, and weighed.
Essential Requirements for Successful Gravimetric Precipitates
High Insolubility: The precipitate must be sufficiently insoluble that unprecipitated analyte mass remains below the limit of analytical balance detection (typically < 0.1 mg < 0.1\text{ mg} < 0.1 mg loss, or recovery > 99.99 % > 99.99\% > 99.99% ).
High Purity: The precipitate must be free from coprecipitated matrix impurities and easily purified by washing.
Filterability: Particles must be sufficiently large to be completely retained by standard filter paper (e.g., Whatman No. 42 ashless paper) or sintered-glass/porcelain filtering crucibles without clogging.
Definite Stoichiometric Composition: The weighed form must possess a known, stable chemical formula that is non-hygroscopic and chemically unreactive with atmospheric gases ( H 2 O , C O 2 , O 2 H_2O, CO_2, O_2 H 2 O , C O 2 , O 2 ).
The Gravimetric Factor ( G F GF GF )
The Gravimetric Factor ( G F GF GF ) is the stoichiometric mass ratio that converts the mass of a weighed precipitate into the equivalent mass of the target analyte: G F = a ⋅ F W ( analyte ) b ⋅ F W ( precipitate ) GF = \frac{a \cdot FW(\text{analyte})}{b \cdot FW(\text{precipitate})} GF = b ⋅ F W ( precipitate ) a ⋅ F W ( analyte ) where a a a and b b b are integers chosen to balance the number of moles of the common element (or chemical equivalent) in the numerator and denominator.
Mass of Analyte = Mass of Weighed Precipitate × G F \text{Mass of Analyte} = \text{Mass of Weighed Precipitate} \times GF Mass of Analyte = Mass of Weighed Precipitate × GF % Analyte = Mass of Precipitate × G F Mass of Sample × 100 % \%\text{ Analyte} = \frac{\text{Mass of Precipitate} \times GF}{\text{Mass of Sample}} \times 100\% % Analyte = Mass of Sample Mass of Precipitate × GF × 100%
Standard Gravimetric Factors in Analytical Chemistry
Analyte Sought Weighed Precipitate Form Stoichiometric Ratio Gravimetric Factor ( G F GF GF ) Formula
Fe \text{Fe} Fe Fe 2 O 3 \text{Fe}_2\text{O}_3 Fe 2 O 3 2 Fe ≡ 1 Fe 2 O 3 2\text{ Fe} \equiv 1\text{ Fe}_2\text{O}_3 2 Fe ≡ 1 Fe 2 O 3 2 ⋅ F W ( Fe ) F W ( Fe 2 O 3 ) \frac{2 \cdot FW(\text{Fe})}{FW(\text{Fe}_2\text{O}_3)} F W ( Fe 2 O 3 ) 2 ⋅ F W ( Fe )
Fe 3 O 4 \text{Fe}_3\text{O}_4 Fe 3 O 4 Fe 2 O 3 \text{Fe}_2\text{O}_3 Fe 2 O 3 2 Fe 3 O 4 ≡ 3 Fe 2 O 3 2\text{ Fe}_3\text{O}_4 \equiv 3\text{ Fe}_2\text{O}_3 2 Fe 3 O 4 ≡ 3 Fe 2 O 3 2 ⋅ F W ( Fe 3 O 4 ) 3 ⋅ F W ( Fe 2 O 3 ) \frac{2 \cdot FW(\text{Fe}_3\text{O}_4)}{3 \cdot FW(\text{Fe}_2\text{O}_3)} 3 ⋅ F W ( Fe 2 O 3 ) 2 ⋅ F W ( Fe 3 O 4 )
P \text{P} P Mg 2 P 2 O 7 \text{Mg}_2\text{P}_2\text{O}_7 Mg 2 P 2 O 7 2 P ≡ 1 Mg 2 P 2 O 7 2\text{ P} \equiv 1\text{ Mg}_2\text{P}_2\text{O}_7 2 P ≡ 1 Mg 2 P 2 O 7 2 ⋅ F W ( P ) F W ( Mg 2 P 2 O 7 ) \frac{2 \cdot FW(\text{P})}{FW(\text{Mg}_2\text{P}_2\text{O}_7)} F W ( Mg 2 P 2 O 7 ) 2 ⋅ F W ( P )
P 2 O 5 \text{P}_2\text{O}_5 P 2 O 5 Mg 2 P 2 O 7 \text{Mg}_2\text{P}_2\text{O}_7 Mg 2 P 2 O 7 1 P 2 O 5 ≡ 1 Mg 2 P 2 O 7 1\text{ P}_2\text{O}_5 \equiv 1\text{ Mg}_2\text{P}_2\text{O}_7 1 P 2 O 5 ≡ 1 Mg 2 P 2 O 7 F W ( P 2 O 5 ) F W ( Mg 2 P 2 O 7 ) \frac{FW(\text{P}_2\text{O}_5)}{FW(\text{Mg}_2\text{P}_2\text{O}_7)} F W ( Mg 2 P 2 O 7 ) F W ( P 2 O 5 )
SO 4 2 − \text{SO}_4^{2-} SO 4 2 − BaSO 4 \text{BaSO}_4 BaSO 4 1 SO 4 2 − ≡ 1 BaSO 4 1\text{ SO}_4^{2-} \equiv 1\text{ BaSO}_4 1 SO 4 2 − ≡ 1 BaSO 4 F W ( SO 4 2 − ) F W ( BaSO 4 ) \frac{FW(\text{SO}_4^{2-})}{FW(\text{BaSO}_4)} F W ( BaSO 4 ) F W ( SO 4 2 − )
Cl − \text{Cl}^- Cl − AgCl \text{AgCl} AgCl 1 Cl − ≡ 1 AgCl 1\text{ Cl}^- \equiv 1\text{ AgCl} 1 Cl − ≡ 1 AgCl F W ( Cl ) F W ( AgCl ) \frac{FW(\text{Cl})}{FW(\text{AgCl})} F W ( AgCl ) F W ( Cl )
Ni \text{Ni} Ni Ni ( C 4 H 7 N 2 O 2 ) 2 \text{Ni}(\text{C}_4\text{H}_7\text{N}_2\text{O}_2)_2 Ni ( C 4 H 7 N 2 O 2 ) 2 (Ni-DMG) 1 Ni ≡ 1 Ni-DMG 1\text{ Ni} \equiv 1\text{ Ni-DMG} 1 Ni ≡ 1 Ni-DMG F W ( Ni ) F W ( Ni-DMG ) \frac{FW(\text{Ni})}{FW(\text{Ni-DMG})} F W ( Ni-DMG ) F W ( Ni )
Worked Example: Gravimetric Iron Determination
A 0.5432 g 0.5432\text{ g} 0.5432 g sample of iron ore is dissolved in hydrochloric acid, oxidized with nitric acid to convert all iron to Fe 3 + \text{Fe}^{3+} Fe 3 + , and precipitated as hydrous ferric oxide ( Fe(OH) 3 ⋅ x H 2 O \text{Fe(OH)}_3 \cdot x\text{H}_2\text{O} Fe(OH) 3 ⋅ x H 2 O ). After filtration and washing, the precipitate is ignited at 900 ∘ C 900^\circ\text{C} 90 0 ∘ C to constant mass, yielding 0.2456 g 0.2456\text{ g} 0.2456 g of pure anhydrous ferric oxide ( Fe 2 O 3 \text{Fe}_2\text{O}_3 Fe 2 O 3 , F W = 159.69 g/mol FW = 159.69\text{ g/mol} F W = 159.69 g/mol ).
Calculate the percentage of elemental Fe \text{Fe} Fe ( F W = 55.845 g/mol FW = 55.845\text{ g/mol} F W = 55.845 g/mol ): G F Fe = 2 × 55.845 159.69 = 111.69 159.69 = 0.69942 GF_{\text{Fe}} = \frac{2 \times 55.845}{159.69} = \frac{111.69}{159.69} = 0.69942 G F Fe = 159.69 2 × 55.845 = 159.69 111.69 = 0.69942 Mass of Fe = 0.2456 g × 0.69942 = 0.17178 g \text{Mass of Fe} = 0.2456\text{ g} \times 0.69942 = 0.17178\text{ g} Mass of Fe = 0.2456 g × 0.69942 = 0.17178 g % Fe = 0.17178 g 0.5432 g × 100 % = 31.62 % \%\text{Fe} = \frac{0.17178\text{ g}}{0.5432\text{ g}} \times 100\% = 31.62\% % Fe = 0.5432 g 0.17178 g × 100% = 31.62%
Calculate the percentage expressed as Magnetite ( Fe 3 O 4 \text{Fe}_3\text{O}_4 Fe 3 O 4 , F W = 231.53 g/mol FW = 231.53\text{ g/mol} F W = 231.53 g/mol ): G F Fe 3 O 4 = 2 × 231.53 3 × 159.69 = 463.06 479.07 = 0.96658 GF_{\text{Fe}_3\text{O}_4} = \frac{2 \times 231.53}{3 \times 159.69} = \frac{463.06}{479.07} = 0.96658 G F Fe 3 O 4 = 3 × 159.69 2 × 231.53 = 479.07 463.06 = 0.96658 Mass of Fe 3 O 4 = 0.2456 g × 0.96658 = 0.23739 g \text{Mass of } \text{Fe}_3\text{O}_4 = 0.2456\text{ g} \times 0.96658 = 0.23739\text{ g} Mass of Fe 3 O 4 = 0.2456 g × 0.96658 = 0.23739 g % Fe 3 O 4 = 0.23739 g 0.5432 g × 100 % = 43.70 % \%\text{Fe}_3\text{O}_4 = \frac{0.23739\text{ g}}{0.5432\text{ g}} \times 100\% = 43.70\% % Fe 3 O 4 = 0.5432 g 0.23739 g × 100% = 43.70%
2. Mechanisms of Precipitate Formation: Nucleation vs. Particle Growth
The physical characteristics (crystal size, surface area, filterability) of a precipitate are governed by the kinetics of particle formation.
Von Weimarn's Ratio and Relative Supersaturation ( R S S RSS RSS )
P.P. von Weimarn discovered that the initial particle size of a precipitate is inversely proportional to the Relative Supersaturation ( R S S RSS RSS ) of the solution during precipitation: R S S = Q − S S RSS = \frac{Q - S}{S} RSS = S Q − S where:
Q Q Q = instantaneous solute concentration when reagents are mixed.
S S S = equilibrium molar solubility of the precipitate under experimental conditions.
( Q − S ) (Q - S) ( Q − S ) = excess supersaturation driving precipitation.
Two Competing Precipitation Mechanisms
Nucleation: A process where a small number of ions or molecules (typically 4–20 units) spontaneously coalesce to create stable solid micro-clusters (nuclei).
Rate of nucleation: R n u c l e a t i o n = k 1 ( Q − S S ) n R_{nucleation} = k_1 \left(\frac{Q - S}{S}\right)^n R n u c l e a t i o n = k 1 ( S Q − S ) n (where n > 1 n > 1 n > 1 ).
Dominates when R S S RSS RSS is extremely large → \rightarrow → produces trillions of tiny nuclei, resulting in colloidal suspensions ( 1 nm − 1 μ m 1\text{ nm} - 1\ \mu\text{m} 1 nm − 1 μ m ), which pass through filters and are difficult to wash.
Particle Growth: Deposition of dissolved solute ions onto pre-existing nuclei or seed crystals.
Rate of particle growth: R g r o w t h = k 2 ( Q − S ) R_{growth} = k_2 (Q - S) R g ro wt h = k 2 ( Q − S ) .
Dominates when R S S RSS RSS is low → \rightarrow → existing nuclei grow into large, dense, easily filterable crystalline precipitates ( > 10 μ m > 10\ \mu\text{m} > 10 μ m ).
Practical Experimental Conditions for Obtaining Crystalline Precipitates
To maximize crystal size and purity, analysts deliberately maintain R S S RSS RSS as small as possible:
Minimize Q Q Q : Add precipitating reagent slowly dropwise with vigorous mechanical stirring, and use dilute solutions.
Maximize S S S : Carry out precipitation in hot solutions (elevated temperature increases S S S ), and adjust p H pH p H to maintain moderate solubility during initial mixing.
Digestion (Ostwald Ripening): Allow the precipitate to stand in contact with the hot mother liquor for 1–2 hours. According to the Kelvin equation, small particles have higher surface curvature, higher chemical potential, and greater solubility than large particles. Small particles dissolve, and their solute recrystallizes onto the surfaces of larger crystals, increasing average grain size and expelling trapped impurities.
Homogeneous Precipitation: Precipitating agent is generated in situ throughout the entire solution via a slow chemical reaction, maintaining Q Q Q barely above S S S at all times:
Generating Hydroxide ( O H − OH^- O H − ): Urea hydrolysis at 90 − 100 ∘ C 90-100^\circ\text{C} 90 − 10 0 ∘ C : ( NH 2 ) 2 CO + 3 H 2 O → Δ 2 NH 4 + + CO 2 + 2 OH − (\text{NH}_2)_2\text{CO} + 3\text{H}_2\text{O} \xrightarrow{\Delta} 2\text{NH}_4^+ + \text{CO}_2 + 2\text{OH}^- ( NH 2 ) 2 CO + 3 H 2 O Δ 2 NH 4 + + CO 2 + 2 OH − This slowly raises p H pH p H uniformly, yielding dense, crystalline basic salts (e.g., for Al 3 + , Fe 3 + \text{Al}^{3+}, \text{Fe}^{3+} Al 3 + , Fe 3 + ) rather than gelatinous hydroxides.
Generating Sulfate ( SO 4 2 − \text{SO}_4^{2-} SO 4 2 − ): Hydrolysis of dimethyl sulfate or sulfamic acid.
Generating Oxalate ( C 2 O 4 2 − \text{C}_2\text{O}_4^{2-} C 2 O 4 2 − ): Hydrolysis of dimethyl oxalate.
3. Coprecipitation Phenomena and Purification
Coprecipitation is the phenomenon where normally soluble chemical species precipitate alongside the analyte precipitate from solution.
Four Primary Mechanisms of Coprecipitation
Mechanism Physical Description Occurrence Remediation
Surface Adsorption Normally soluble foreign counter-ions are electrostatically held in the counter-ion layer on the surface of primary precipitate particles. Major issue in colloidal precipitates with large specific surface areas (e.g., AgCl \text{AgCl} AgCl ). Washing with volatile electrolyte; digestion (reduces surface area); reprecipitation.
Occlusion Pockets of mother liquor containing dissolved foreign ions are mechanically trapped within cavities of rapidly growing crystal aggregates. Crystalline precipitates experiencing rapid, non-uniform growth. Slow precipitation; prolonged digestion (allows crystal recrystallization).
Inclusion (Isomorphous Replacement) A foreign ion with identical charge and similar ionic radius ( < 15 % < 15\% < 15% difference) substitutes directly into host lattice sites (solid solution). Systems with crystallographic similarity (e.g., Pb 2 + \text{Pb}^{2+} Pb 2 + in BaSO 4 \text{BaSO}_4 BaSO 4 ; Br − \text{Br}^- Br − in AgCl \text{AgCl} AgCl ). Chemical pre-separation of the interfering ion; reprecipitation.
Post-Precipitation Deposition of a second, sparingly soluble substance on the surface of the primary precipitate after primary precipitation has concluded. Time-dependent; occurs when a secondary compound forms a metastable supersaturated solution (e.g., MgC 2 O 4 \text{MgC}_2\text{O}_4 MgC 2 O 4 onto CaC 2 O 4 \text{CaC}_2\text{O}_4 CaC 2 O 4 ). Opposite of digestion! Precipitate must be filtered rapidly (within 30–60 min) before post-precipitation starts.
Peptization and Washing
Peptization: The process where a coagulated colloidal precipitate reverts back to a dispersed colloidal sol when washed with pure deionized water.
Mechanism: Washing with pure water dilutes the electrolyte concentration in the electrical double layer. The repulsive counter-ion barrier expands, overcoming attractive van der Waals forces and disintegrating the aggregates into unfilterable particles.
Prevention: Always wash colloidal precipitates with an aqueous solution of a volatile electrolyte (e.g., dilute HNO 3 \text{HNO}_3 HNO 3 for AgCl \text{AgCl} AgCl ; NH 4 NO 3 \text{NH}_4\text{NO}_3 NH 4 NO 3 for Fe(OH) 3 \text{Fe(OH)}_3 Fe(OH) 3 ). The electrolyte preserves ionic strength to prevent peptization, and volatilizes completely during crucible drying or ignition ( > 100 ∘ C > 100^\circ\text{C} > 10 0 ∘ C ), leaving no non-volatile residue.
Thermal Decomposition and Volatilization Gravimetry
Precipitates are dried or ignited to remove solvent and convert the precipitate into a stoichiometric weighing form:
Calcium Oxalate Ignition Stages: CaC 2 O 4 ⋅ H 2 O ( s ) → 100 − 250 ∘ C CaC 2 O 4 ( s ) + H 2 O ( g ) \text{CaC}_2\text{O}_4 \cdot \text{H}_2\text{O}_{(s)} \xrightarrow{100-250^\circ\text{C}} \text{CaC}_2\text{O}_{4(s)} + \text{H}_2\text{O}_{(g)} CaC 2 O 4 ⋅ H 2 O ( s ) 100 − 25 0 ∘ C CaC 2 O 4 ( s ) + H 2 O ( g ) CaC 2 O 4 ( s ) → 400 − 500 ∘ C CaCO 3 ( s ) + CO ( g ) \text{CaC}_2\text{O}_{4(s)} \xrightarrow{400-500^\circ\text{C}} \text{CaCO}_{3(s)} + \text{CO}_{(g)} CaC 2 O 4 ( s ) 400 − 50 0 ∘ C CaCO 3 ( s ) + CO ( g ) CaCO 3 ( s ) → 700 − 900 ∘ C CaO ( s ) + CO 2 ( g ) \text{CaCO}_{3(s)} \xrightarrow{700-900^\circ\text{C}} \text{CaO}_{(s)} + \text{CO}_{2(g)} CaCO 3 ( s ) 700 − 90 0 ∘ C CaO ( s ) + CO 2 ( g )
Combustion Volatilization Analysis (Pregl-Liebig Method): Carbon and hydrogen in organic samples are combusted in pure O 2 \text{O}_2 O 2 . Formed H 2 O \text{H}_2\text{O} H 2 O is absorbed in anhydrous magnesium perchlorate (Anhydrone), and CO 2 \text{CO}_2 CO 2 is absorbed in sodium hydroxide on silicate (Ascarite). The mass increase of each absorption tube yields %H and %C.
4. Precipitation Equilibria: K s p K_{sp} K s p , Ionic Strength, and Chemical Effects
Precipitation reactions in aqueous solution are governed by chemical equilibrium.
Solubility Product ( K s p K_{sp} K s p ) and Molar Solubility ( S S S )
For a general sparingly soluble salt M a X b \text{M}_a\text{X}_b M a X b : M a X b ( s ) ⇌ a M ( a q ) m + + b X ( a q ) n − \text{M}_a\text{X}_{b(s)} \rightleftharpoons a\ \text{M}^{m+}_{(aq)} + b\ \text{X}^{n-}_{(aq)} M a X b ( s ) ⇌ a M ( a q ) m + + b X ( a q ) n − K s p = [ M m + ] a [ X n − ] b = ( a S ) a ( b S ) b = a a b b S a + b K_{sp} = [\text{M}^{m+}]^a [\text{X}^{n-}]^b = (aS)^a (bS)^b = a^a b^b S^{a+b} K s p = [ M m + ] a [ X n − ] b = ( a S ) a ( b S ) b = a a b b S a + b S = K s p a a b b a + b S = \sqrt[a+b]{\frac{K_{sp}}{a^a b^b}} S = a + b a a b b K s p
1 : 1 1:1 1 : 1 Salt ( AgCl , BaSO 4 \text{AgCl}, \text{BaSO}_4 AgCl , BaSO 4 ): K s p = S 2 ⟹ S = K s p K_{sp} = S^2 \implies S = \sqrt{K_{sp}} K s p = S 2 ⟹ S = K s p
1 : 2 1:2 1 : 2 Salt ( PbCl 2 , CaF 2 \text{PbCl}_2, \text{CaF}_2 PbCl 2 , CaF 2 ): K s p = 4 S 3 ⟹ S = K s p 4 3 K_{sp} = 4S^3 \implies S = \sqrt[3]{\frac{K_{sp}}{4}} K s p = 4 S 3 ⟹ S = 3 4 K s p
1 : 3 1:3 1 : 3 Salt ( BiI 3 , Fe(OH) 3 \text{BiI}_3, \text{Fe(OH)}_3 BiI 3 , Fe(OH) 3 ): K s p = 27 S 4 ⟹ S = K s p 27 4 K_{sp} = 27S^4 \implies S = \sqrt[4]{\frac{K_{sp}}{27}} K s p = 27 S 4 ⟹ S = 4 27 K s p
2 : 3 2:3 2 : 3 Salt ( Ca 3 ( PO 4 ) 2 \text{Ca}_3(\text{PO}_4)_2 Ca 3 ( PO 4 ) 2 ): K s p = 108 S 5 ⟹ S = K s p 108 5 K_{sp} = 108S^5 \implies S = \sqrt[5]{\frac{K_{sp}}{108}} K s p = 108 S 5 ⟹ S = 5 108 K s p
Common Ion Effect vs. Diverse Ion (Salt) Effect
Common Ion Effect: Adding a soluble salt that shares an ion with the precipitate shifts the equilibrium to the left (Le Chatelier's principle), significantly reducing molar solubility ( S S S ). For example, the solubility of BaSO 4 \text{BaSO}_4 BaSO 4 ( K s p = 1.1 × 10 − 10 K_{sp} = 1.1 \times 10^{-10} K s p = 1.1 × 1 0 − 10 ) in pure water is 1.05 × 10 − 5 M 1.05 \times 10^{-5}\text{ M} 1.05 × 1 0 − 5 M . In 0.010 M Na 2 SO 4 0.010\text{ M } \text{Na}_2\text{SO}_4 0.010 M Na 2 SO 4 , the solubility drops to S = 1.1 × 10 − 10 0.010 = 1.1 × 10 − 8 M S = \frac{1.1 \times 10^{-10}}{0.010} = 1.1 \times 10^{-8}\text{ M} S = 0.010 1.1 × 1 0 − 10 = 1.1 × 1 0 − 8 M (a 1,000-fold decrease).
Ionic Strength ( μ \mu μ ) and Diverse Ion (Salt) Effect: Adding an "inert" non-common electrolyte (e.g., KNO 3 \text{KNO}_3 KNO 3 ) increases the ionic strength of the solution: μ = 1 2 ∑ i = 1 n c i z i 2 \mu = \frac{1}{2} \sum_{i=1}^n c_i z_i^2 μ = 2 1 ∑ i = 1 n c i z i 2 According to the Debye-Hückel limiting law, increased ionic strength compresses the ionic atmosphere around ions, lowering their activity coefficients ( γ i < 1 \gamma_i < 1 γ i < 1 ): log γ i = − 0.51 z i 2 μ \log \gamma_i = -0.51 z_i^2 \sqrt{\mu} lo g γ i = − 0.51 z i 2 μ Because the thermodynamic equilibrium constant is fixed ( K s p ∘ = [ M m + ] [ X n − ] γ M γ X K_{sp}^\circ = [\text{M}^{m+}][\text{X}^{n-}]\gamma_M \gamma_X K s p ∘ = [ M m + ] [ X n − ] γ M γ X ), a decrease in γ \gamma γ forces the molar concentrations [ M m + ] [\text{M}^{m+}] [ M m + ] and [ X n − ] [\text{X}^{n-}] [ X n − ] to rise. Therefore, inert salts increase precipitate solubility .
Effect of p H pH p H and Complexation on Solubility
p H pH p H Effect: Salts containing basic anions (e.g., carbonates, oxalates, sulfides, fluorides) dissolve in acidic media because protons bind the anion, shifting the dissolution equilibrium to the right: CaCO 3 ( s ) + H + ⇌ Ca 2 + + HCO 3 − \text{CaCO}_{3(s)} + \text{H}^+ \rightleftharpoons \text{Ca}^{2+} + \text{HCO}_3^- CaCO 3 ( s ) + H + ⇌ Ca 2 + + HCO 3 −
Complexation Effect: Precipitates dissolve in the presence of ligands that form stable coordination complexes with the cation. For example, AgCl \text{AgCl} AgCl dissolves in aqueous ammonia: AgCl ( s ) + 2 NH 3 ⇌ [ Ag ( NH 3 ) 2 ] + + Cl − ( K = K s p ⋅ β 2 ) \text{AgCl}_{(s)} + 2\text{NH}_3 \rightleftharpoons [\text{Ag}(\text{NH}_3)_2]^+ + \text{Cl}^- \quad (K = K_{sp} \cdot \beta_2) AgCl ( s ) + 2 NH 3 ⇌ [ Ag ( NH 3 ) 2 ] + + Cl − ( K = K s p ⋅ β 2 )
Fractional Precipitation
When a titrant can precipitate multiple ions present in the same solution, the less soluble compound (the one requiring the lowest titrant concentration to exceed its K s p K_{sp} K s p ) precipitates first.
Quantitative separation of ion A A A from ion B B B is achievable if > 99.9 % > 99.9\% > 99.9% of A A A precipitates before B B B begins to precipitate.