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5.5 Complexometric (EDTA), Redox, and Precipitation (Argentometric) Titrimetry
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3 Chapter 3: Inorganic Chemistry: Coordination Compounds and Transition Metals
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6 Chapter 6: Analytical Chemistry: Electroanalytical Methods and Separations
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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
5.5 Complexometric (EDTA), Redox, and Precipitation (Argentometric) Titrimetry
Key Takeaways Explain This Topic AI
EDTA is a hexadentate chelating ligand forming 1:1 complexes with polyvalent cations; its thermodynamic stability is enhanced by the chelate effect (favorable positive entropy Δ S ∘ \Delta S^\circ Δ S ∘ ).
The conditional formation constant ( K f ′ = α Y 4 − K f K'_f = \alpha_{Y^{4-}} K_f K f ′ = α Y 4 − K f ) governs EDTA titrations at a fixed p H pH p H ; trivalent cations ( F e 3 + , B i 3 + Fe^{3+}, Bi^{3+} F e 3 + , B i 3 + ) can be titrated at p H 1 − 2 pH\ 1-2 p H 1 − 2 , whereas alkaline earths ( C a 2 + , M g 2 + Ca^{2+}, Mg^{2+} C a 2 + , M g 2 + ) require p H 10 − 12 pH\ 10-12 p H 10 − 12 .
Water hardness determination differentiates total hardness ( C a 2 + + M g 2 + Ca^{2+} + Mg^{2+} C a 2 + + M g 2 + at p H 10 pH\ 10 p H 10 with Calmagite/EBT) from calcium hardness (at p H 12 − 13 pH\ 12-13 p H 12 − 13 with Murexide, precipitating M g ( O H ) 2 Mg(OH)_2 M g ( O H ) 2 ); results are reported as mg/L C a C O 3 \text{mg/L } CaCO_3 mg/L C a C O 3 equivalent.
Redox titrimetry relies on half-cell potentials and the Nernst equation: permanganometry ( K M n O 4 KMnO_4 K M n O 4 ) is self-indicating in hot H 2 S O 4 H_2SO_4 H 2 S O 4 , dichromatometry ( K 2 C r 2 O 7 K_2Cr_2O_7 K 2 C r 2 O 7 ) is an air-stable primary standard in H C l HCl H Cl , and iodometry titrates liberated I 3 − I_3^- I 3 − with thiosulfate ( N a 2 S 2 O 3 Na_2S_2O_3 N a 2 S 2 O 3 ).
Starch indicator in iodometric titrations must be introduced immediately before the equivalence point to prevent irreversible iodine entrapment; Karl Fischer titration quantifies water via the modified Bunsen reaction using coulometry for trace levels.
Last updated: October 2026
Complexometric (EDTA) and Oxidation-Reduction (Redox) Titrimetry
Complexometric and oxidation-reduction (redox) titrimetry are foundations of classical wet analysis, and the Analytical TOS lists both among its volumetric methods. Expect equilibrium derivations, coordination chemistry, multi-electron electrochemical stoichiometry, and specialized indicator mechanics.
- 1. Chelation Thermodynamics and EDTA Coordination Chemistry
- Ligand Denticity and the Chelate Effect
Ligand: A Lewis base containing at least one unshared electron pair that binds to a central metal cation (Lewis acid) via coordinate covalent bonding.
Denticity: The number of donor atoms through which a single ligand coordinates to the metal (monodentate, bidentate, tridentate, hexadentate).
The Chelate Effect: Complexes formed by polydentate chelating ligands exhibit extraordinarily higher thermodynamic stability constants ( K f K_f K f ) than analogous complexes formed by equivalent numbers of monodentate ligands. Thermodynamic Origin: Consider the substitution of six monodentate ammonia ligands by one hexadentate ligand ( Y 4 − Y^{4-} Y 4 − ): [ Ni ( NH 3 ) 6 ] 2 + + Y 4 − ⇌ [ Ni Y ] 2 − + 6 NH 3 [\text{Ni}(\text{NH}_3)_6]^{2+} + Y^{4-} \rightleftharpoons [\text{Ni}Y]^{2-} + 6\text{NH}_3 [ Ni ( NH 3 ) 6 ] 2 + + Y 4 − ⇌ [ Ni Y ] 2 − + 6 NH 3 The reaction produces seven independent product particles from two reactant particles. This dramatic increase in system translational disorder yields a large positive standard entropy change ( Δ S ∘ ≫ 0 \Delta S^\circ \gg 0 Δ S ∘ ≫ 0 ). Because Δ G ∘ = Δ H ∘ − T Δ S ∘ \Delta G^\circ = \Delta H^\circ - T\Delta S^\circ Δ G ∘ = Δ H ∘ − T Δ S ∘ , this positive entropy drives Δ G ∘ \Delta G^\circ Δ G ∘ heavily negative, producing high formation constants ( K f K_f K f ).
Ethylenediaminetetraacetic Acid (EDTA)
EDTA (represented as H 4 Y \text{H}_4\text{Y} H 4 Y ) is a hexadentate ligand containing two tertiary amino nitrogen atoms and four carboxylic acid oxygen atoms.
Universal 1 : 1 1:1 1 : 1 Stoichiometry: Regardless of the charge of the metal cation ( M 2 + , M 3 + , M 4 + M^{2+}, M^{3+}, M^{4+} M 2 + , M 3 + , M 4 + ), EDTA wraps around the central ion in an octahedral coordination sphere, always forming a rigid 1 : 1 1:1 1 : 1 metal-chelate complex: M n + + Y 4 − ⇌ [ MY ] n − 4 \text{M}^{n+} + \text{Y}^{4-} \rightleftharpoons [\text{MY}]^{n-4} M n + + Y 4 − ⇌ [ MY ] n − 4 K f = [ MY n − 4 ] [ M n + ] [ Y 4 − ] K_f = \frac{[\text{MY}^{n-4}]}{[\text{M}^{n+}][\text{Y}^{4-}]} K f = [ M n + ] [ Y 4 − ] [ MY n − 4 ]
Acid-Base Equilibria of EDTA and α Y 4 − \alpha_{\text{Y}^{4-}} α Y 4 −
EDTA is a hexaprotic acid system ( [ H 6 Y ] 2 + [\text{H}_6\text{Y}]^{2+} [ H 6 Y ] 2 + through Y 4 − \text{Y}^{4-} Y 4 − ). The stepwise acid dissociation constants at 25 ∘ C 25^\circ\text{C} 2 5 ∘ C are: p K 1 = 0.0 , p K 2 = 1.5 , p K 3 = 2.0 , p K 4 = 2.66 , p K 5 = 6.16 , p K 6 = 10.24 pK_1 = 0.0, \quad pK_2 = 1.5, \quad pK_3 = 2.0, \quad pK_4 = 2.66, \quad pK_5 = 6.16, \quad pK_6 = 10.24 p K 1 = 0.0 , p K 2 = 1.5 , p K 3 = 2.0 , p K 4 = 2.66 , p K 5 = 6.16 , p K 6 = 10.24 The active complexing species is the fully deprotonated tetravalent anion Y 4 − \text{Y}^{4-} Y 4 − . The fraction of EDTA existing as Y 4 − \text{Y}^{4-} Y 4 − ( α Y 4 − \alpha_{\text{Y}^{4-}} α Y 4 − ) is strongly p H pH p H -dependent: α Y 4 − = [ Y 4 − ] C EDTA = K 1 K 2 K 3 K 4 K 5 K 6 [ H + ] 6 + K 1 [ H + ] 5 + ⋯ + K 1 K 2 K 3 K 4 K 5 K 6 \alpha_{\text{Y}^{4-}} = \frac{[\text{Y}^{4-}]}{C_{\text{EDTA}}} = \frac{K_1 K_2 K_3 K_4 K_5 K_6}{[\text{H}^+]^6 + K_1[\text{H}^+]^5 + \dots + K_1 K_2 K_3 K_4 K_5 K_6} α Y 4 − = C EDTA [ Y 4 − ] = [ H + ] 6 + K 1 [ H + ] 5 + ⋯ + K 1 K 2 K 3 K 4 K 5 K 6 K 1 K 2 K 3 K 4 K 5 K 6
p H pH p H α Y 4 − \alpha_{\text{Y}^{4-}} α Y 4 − Predominant Species Metal Titration Applicability
2.0 2.0 2.0 3.7 × 10 − 14 3.7 \times 10^{-14} 3.7 × 1 0 − 14 H 4 Y / H 3 Y − \text{H}_4\text{Y} / \text{H}_3\text{Y}^- H 4 Y / H 3 Y − Only high-affinity cations ( Fe 3 + , Bi 3 + , Th 4 + \text{Fe}^{3+}, \text{Bi}^{3+}, \text{Th}^{4+} Fe 3 + , Bi 3 + , Th 4 + )
4.0 4.0 4.0 3.6 × 10 − 9 3.6 \times 10^{-9} 3.6 × 1 0 − 9 H 2 Y 2 − \text{H}_2\text{Y}^{2-} H 2 Y 2 − Transition metals ( Cu 2 + , Pb 2 + , Zn 2 + \text{Cu}^{2+}, \text{Pb}^{2+}, \text{Zn}^{2+} Cu 2 + , Pb 2 + , Zn 2 + )
6.0 6.0 6.0 2.2 × 10 − 5 2.2 \times 10^{-5} 2.2 × 1 0 − 5 HY 3 − \text{HY}^{3-} HY 3 − Moderately stable chelates ( Cd 2 + , Ni 2 + \text{Cd}^{2+}, \text{Ni}^{2+} Cd 2 + , Ni 2 + )
8.0 8.0 8.0 5.4 × 10 − 3 5.4 \times 10^{-3} 5.4 × 1 0 − 3 HY 3 − \text{HY}^{3-} HY 3 − Mg 2 + , Ca 2 + \text{Mg}^{2+}, \text{Ca}^{2+} Mg 2 + , Ca 2 + (marginal)
10.0 10.0 10.0 0.35 0.35 0.35 Y 4 − \text{Y}^{4-} Y 4 − Alkaline earth metals ( Ca 2 + , Mg 2 + , Sr 2 + , Ba 2 + \text{Ca}^{2+}, \text{Mg}^{2+}, \text{Sr}^{2+}, \text{Ba}^{2+} Ca 2 + , Mg 2 + , Sr 2 + , Ba 2 + )
12.0 12.0 12.0 0.98 0.98 0.98 Y 4 − \text{Y}^{4-} Y 4 − Complete deprotonation; selective Ca 2 + \text{Ca}^{2+} Ca 2 + titration
- 2. Conditional Formation Constants, Auxiliary Reagents, and Titration Techniques
- The Conditional Formation Constant ( K f ′ K'_f K f ′ )
Because the concentration of free Y 4 − \text{Y}^{4-} Y 4 − is reduced by protonation at lower p H pH p H , the thermodynamic equilibrium is governed by the conditional formation constant ( K f ′ K'_f K f ′ ): K f ′ = α Y 4 − ⋅ K f = [ MY n − 4 ] [ M n + ] C EDTA K'_f = \alpha_{\text{Y}^{4-}} \cdot K_f = \frac{[\text{MY}^{n-4}]}{[\text{M}^{n+}] C_{\text{EDTA}}} K f ′ = α Y 4 − ⋅ K f = [ M n + ] C EDTA [ MY n − 4 ]
Titration Criterion: For a distinct, quantitative titration endpoint (sharp inflection of Δ p M ≥ 2 \Delta p\text{M} \ge 2 Δ p M ≥ 2 units at equivalence), the conditional constant must satisfy: K f ′ ≥ 10 8 ( or C M ⋅ K f ′ ≥ 10 6 ) K'_f \ge 10^8 \quad (\text{or } C_{\text{M}} \cdot K'_f \ge 10^6) K f ′ ≥ 1 0 8 ( or C M ⋅ K f ′ ≥ 1 0 6 )
Minimum p H pH p H : This allows selective titration of metal ions. Transition metals with high K f K_f K f (e.g., Fe 3 + \text{Fe}^{3+} Fe 3 + , log K f = 25.1 \log K_f = 25.1 lo g K f = 25.1 ) can be titrated at p H 1 − 2 pH\ 1 - 2 p H 1 − 2 without interference from Ca 2 + \text{Ca}^{2+} Ca 2 + ( log K f = 10.7 \log K_f = 10.7 lo g K f = 10.7 ), which requires p H ≥ 8 pH \ge 8 p H ≥ 8 to reach K f ′ ≥ 10 8 K'_f \ge 10^8 K f ′ ≥ 1 0 8 .
Auxiliary Complexing Agents
Many metal cations (e.g., Zn 2 + , Cu 2 + , Ni 2 + \text{Zn}^{2+}, \text{Cu}^{2+}, \text{Ni}^{2+} Zn 2 + , Cu 2 + , Ni 2 + ) precipitate as insoluble metal hydroxides at the alkaline p H pH p H ( 10 10 10 ) needed for high α Y 4 − \alpha_{\text{Y}^{4-}} α Y 4 − .
To prevent precipitation, an auxiliary complexing agent (such as ammonia or tartrate) is added.
The auxiliary ligand binds the metal weakly, maintaining it in solution as an ammine complex ( [ Zn ( NH 3 ) 4 ] 2 + [\text{Zn}(\text{NH}_3)_4]^{2+} [ Zn ( NH 3 ) 4 ] 2 + ). During titration, EDTA displaces the auxiliary ligand because K f ( EDTA ) ≫ β n ( auxiliary ) K_f(\text{EDTA}) \gg \beta_n(\text{auxiliary}) K f ( EDTA ) ≫ β n ( auxiliary ) .
EDTA Titration Methodologies
Direct Titration: The buffered analyte solution is titrated directly with standard EDTA using a metallochromic indicator.
Back-Titration: A measured excess of standard EDTA is added to the sample. The unreacted EDTA is back-titrated with a standard secondary metal solution (e.g., standard Zn 2 + \text{Zn}^{2+} Zn 2 + or Mg 2 + \text{Mg}^{2+} Mg 2 + ). Indications: Used when the analyte reacts sluggishly with EDTA (e.g., Cr 3 + \text{Cr}^{3+} Cr 3 + ), precipitates at the required p H pH p H in the absence of EDTA, or irreversibly blocks the indicator.
Displacement Titration: The analyte displaces an unmeasured excess of a weaker metal-EDTA chelate (typically MgY 2 − \text{MgY}^{2-} MgY 2 − ): M n + + MgY 2 − ⇌ MY n − 4 + Mg 2 + \text{M}^{n+} + \text{MgY}^{2-} \rightleftharpoons \text{MY}^{n-4} + \text{Mg}^{2+} M n + + MgY 2 − ⇌ MY n − 4 + Mg 2 + The liberated Mg 2 + \text{Mg}^{2+} Mg 2 + is then titrated directly with standard EDTA. Useful when no suitable indicator exists for M n + \text{M}^{n+} M n + .
Indirect Titration: Used to determine anions that form insoluble precipitates with metal cations (e.g., sulfate precipitated with excess Ba 2 + \text{Ba}^{2+} Ba 2 + ; unreacted Ba 2 + \text{Ba}^{2+} Ba 2 + is titrated with EDTA).
Metallochromic Indicators and Water Hardness
Eriochrome Black T (EBT): Free indicator is blue at p H 10 pH\ 10 p H 10 ( HIn 2 − \text{HIn}^{2-} HIn 2 − ). When bound to metal ions ( Mg 2 + , Ca 2 + \text{Mg}^{2+}, \text{Ca}^{2+} Mg 2 + , Ca 2 + ), it forms a wine-red chelate ( M-In − \text{M-In}^- M-In − ). At the endpoint, EDTA displaces the metal, restoring the free blue indicator: M-In − ( wine-red ) + HY 3 − → [ MY ] 2 − + HIn 2 − ( pure blue ) + H + \text{M-In}^- (\text{wine-red}) + \text{HY}^{3-} \rightarrow [\text{MY}]^{2-} + \text{HIn}^{2-} (\text{pure blue}) + \text{H}^+ M-In − ( wine-red ) + HY 3 − → [ MY ] 2 − + HIn 2 − ( pure blue ) + H +
Indicator Blocking: Trace amounts of heavy metals ( Cu 2 + , Ni 2 + , Fe 3 + , Co 2 + \text{Cu}^{2+}, \text{Ni}^{2+}, \text{Fe}^{3+}, \text{Co}^{2+} Cu 2 + , Ni 2 + , Fe 3 + , Co 2 + ) bind EBT far more strongly than EDTA ( K M-In > K MY K_{\text{M-In}} > K_{\text{MY}} K M-In > K MY ). The indicator cannot release the metal and remains permanently wine-red. This is prevented by adding masking agents (e.g., CN − \text{CN}^- CN − or triethanolamine).
Determination of Water Hardness
Water hardness is the total concentration of polyvalent alkaline earth cations, primarily Ca 2 + \text{Ca}^{2+} Ca 2 + and Mg 2 + \text{Mg}^{2+} Mg 2 + :
Total Hardness ( Ca 2 + + Mg 2 + \text{Ca}^{2+} + \text{Mg}^{2+} Ca 2 + + Mg 2 + ): Titrated at p H 10 pH\ 10 p H 10 using an ammonia buffer ( NH 3 / NH 4 Cl \text{NH}_3/\text{NH}_4\text{Cl} NH 3 / NH 4 Cl ) and Calmagite or EBT indicator.
Calcium Hardness: Titrated at p H 12 − 13 pH\ 12 - 13 p H 12 − 13 by adding 8 M NaOH 8\text{ M } \text{NaOH} 8 M NaOH . Mg 2 + \text{Mg}^{2+} Mg 2 + precipitates quantitatively as gelatinous Mg(OH) 2 \text{Mg(OH)}_2 Mg(OH) 2 ( K s p = 7.1 × 10 − 12 K_{sp} = 7.1 \times 10^{-12} K s p = 7.1 × 1 0 − 12 ) and does not react with EDTA. Calcium is titrated using Murexide or Hydroxy Naphthol Blue.
Magnesium Hardness: Obtained by difference: Magnesium Hardness = Total Hardness − Calcium Hardness \text{Magnesium Hardness} = \text{Total Hardness} - \text{Calcium Hardness} Magnesium Hardness = Total Hardness − Calcium Hardness
Reporting Units: Expressed as mg/L \text{mg/L} mg/L or ppm CaCO 3 \text{ppm } \text{CaCO}_3 ppm CaCO 3 equivalent ( F W = 100.09 g/mol FW = 100.09\text{ g/mol} F W = 100.09 g/mol ): Hardness (ppm CaCO 3 ) = V EDTA ( L ) × M EDTA ( mol/L ) × 100.09 g/mol × 1000 mg/g V sample ( L ) \text{Hardness (ppm } \text{CaCO}_3) = \frac{V_{\text{EDTA}} (\text{L}) \times M_{\text{EDTA}} (\text{mol/L}) \times 100.09\text{ g/mol} \times 1000\text{ mg/g}}{V_{\text{sample}} (\text{L})} Hardness (ppm CaCO 3 ) = V sample ( L ) V EDTA ( L ) × M EDTA ( mol/L ) × 100.09 g/mol × 1000 mg/g
3. Principles of Oxidation-Reduction (Redox) Titrimetry
Redox titrations involve electron transfer between an analyte and a titrant.
Electrochemical Potentials and the Nernst Equation
For a reversible reduction half-reaction: Ox + n e − ⇌ Red \text{Ox} + n e^- \rightleftharpoons \text{Red} Ox + n e − ⇌ Red : E = E ∘ − 0.05916 n log ( [ Red ] [ Ox ] ) at 25 ∘ C E = E^\circ - \frac{0.05916}{n} \log\left(\frac{[\text{Red}]}{[\text{Ox}]}\right) \quad \text{at } 25^\circ\text{C} E = E ∘ − n 0.05916 lo g ( [ Ox ] [ Red ] ) at 2 5 ∘ C
Redox Titration Curves and Equivalence Potential ( E e q E_{eq} E e q )
Consider the titration of Fe 2 + \text{Fe}^{2+} Fe 2 + with Ce 4 + \text{Ce}^{4+} Ce 4 + : Fe 2 + + Ce 4 + ⇌ Fe 3 + + Ce 3 + \text{Fe}^{2+} + \text{Ce}^{4+} \rightleftharpoons \text{Fe}^{3+} + \text{Ce}^{3+} Fe 2 + + Ce 4 + ⇌ Fe 3 + + Ce 3 +
Before Equivalence: The cell potential is governed by the unreacted analyte couple ( Fe 3 + / Fe 2 + \text{Fe}^{3+}/\text{Fe}^{2+} Fe 3 + / Fe 2 + ): E = E Fe 3 + / Fe 2 + ∘ − 0.05916 log ( [ Fe 2 + ] [ Fe 3 + ] ) E = E^\circ_{\text{Fe}^{3+}/\text{Fe}^{2+}} - 0.05916 \log\left(\frac{[\text{Fe}^{2+}]}{[\text{Fe}^{3+}]}\right) E = E Fe 3 + / Fe 2 + ∘ − 0.05916 lo g ( [ Fe 3 + ] [ Fe 2 + ] )
At Equivalence: Both redox couples reach dynamic electrochemical equilibrium. For symmetrical reactions where stoichiometry is 1 : 1 1:1 1 : 1 and no p H pH p H -dependent protons are involved: E e q = n 1 E 1 ∘ + n 2 E 2 ∘ n 1 + n 2 = ( 1 ) ( 0.771 V ) + ( 1 ) ( 1.44 V ) 1 + 1 = 1.11 V E_{eq} = \frac{n_1 E^\circ_1 + n_2 E^\circ_2}{n_1 + n_2} = \frac{(1)(0.771\text{ V}) + (1)(1.44\text{ V})}{1 + 1} = 1.11\text{ V} E e q = n 1 + n 2 n 1 E 1 ∘ + n 2 E 2 ∘ = 1 + 1 ( 1 ) ( 0.771 V ) + ( 1 ) ( 1.44 V ) = 1.11 V
After Equivalence: Potential is governed by excess titrant couple ( Ce 4 + / Ce 3 + \text{Ce}^{4+}/\text{Ce}^{3+} Ce 4 + / Ce 3 + ): E = E Ce 4 + / Ce 3 + ∘ − 0.05916 log ( [ Ce 3 + ] [ Ce 4 + ] ) E = E^\circ_{\text{Ce}^{4+}/\text{Ce}^{3+}} - 0.05916 \log\left(\frac{[\text{Ce}^{3+}]}{[\text{Ce}^{4+}]}\right) E = E Ce 4 + / Ce 3 + ∘ − 0.05916 lo g ( [ Ce 4 + ] [ Ce 3 + ] )
Redox Indicators
Redox indicators change color upon oxidation or reduction: In o x + n e − ⇌ In r e d \text{In}_{ox} + n e^- \rightleftharpoons \text{In}_{red} In o x + n e − ⇌ In re d .
Transition potential interval: E = E I n ∘ ± 0.05916 n V E = E^\circ_{In} \pm \frac{0.05916}{n}\text{ V} E = E I n ∘ ± n 0.05916 V .
Ferroin: Tris(1,10-phenanthroline)iron(II) complex ( [ Fe ( p h e n ) 3 ] 2 + [\text{Fe}(phen)_3]^{2+} [ Fe ( p h e n ) 3 ] 2 + ). Changes from intense red (reduced form) to pale blue (oxidized form [ Fe ( p h e n ) 3 ] 3 + [\text{Fe}(phen)_3]^{3+} [ Fe ( p h e n ) 3 ] 3 + ) at E ∘ = + 1.06 V E^\circ = +1.06\text{ V} E ∘ = + 1.06 V .
Diphenylamine Sulfonic Acid: Changes from colorless to red-violet at E ∘ = + 0.85 V E^\circ = +0.85\text{ V} E ∘ = + 0.85 V . Phosphoric acid ( H 3 PO 4 \text{H}_3\text{PO}_4 H 3 PO 4 ) is added during iron titrations to complex yellow Fe 3 + \text{Fe}^{3+} Fe 3 + into colorless [ Fe ( HPO 4 ) ] + [\text{Fe}(\text{HPO}_4)]^+ [ Fe ( HPO 4 ) ] + , lowering the formal potential of iron and sharpening the indicator transition.
- 4. Reagent Systems: Permanganometry, Dichromatometry, and Iodometry
- 1. Permanganometry ( KMnO 4 \text{KMnO}_4 KMnO 4 )
Potassium permanganate is a powerful oxidizing agent: MnO 4 − + 8 H + + 5 e − ⇌ Mn 2 + + 4 H 2 O ( E ∘ = + 1.51 V ) \text{MnO}_4^- + 8\text{H}^+ + 5e^- \rightleftharpoons \text{Mn}^{2+} + 4\text{H}_2\text{O} \quad (E^\circ = +1.51\text{ V}) MnO 4 − + 8 H + + 5 e − ⇌ Mn 2 + + 4 H 2 O ( E ∘ = + 1.51 V )
Self-Indicating: The intense purple MnO 4 − \text{MnO}_4^- MnO 4 − color serves as its own indicator. A slight excess of 0.02 mL 0.02\text{ mL} 0.02 mL ( 0.01 M 0.01\text{ M} 0.01 M ) imparts a readable faint pink hue lasting > 30 seconds > 30\text{ seconds} > 30 seconds .
Primary Standard: Sodium oxalate ( Na 2 C 2 O 4 \text{Na}_2\text{C}_2\text{O}_4 Na 2 C 2 O 4 ): 5 C 2 O 4 2 − + 2 MnO 4 − + 16 H + → 10 CO 2 + 2 Mn 2 + + 8 H 2 O 5\text{C}_2\text{O}_4^{2-} + 2\text{MnO}_4^- + 16\text{H}^+ \rightarrow 10\text{CO}_2 + 2\text{Mn}^{2+} + 8\text{H}_2\text{O} 5 C 2 O 4 2 − + 2 MnO 4 − + 16 H + → 10 CO 2 + 2 Mn 2 + + 8 H 2 O Operational Requirements: Titration must be carried out in hot solution ( 60 − 70 ∘ C 60 - 70^\circ\text{C} 60 − 7 0 ∘ C ) because the uncatalyzed initial reaction is slow. The reaction is autocatalytic , as generated Mn 2 + \text{Mn}^{2+} Mn 2 + accelerates subsequent kinetics.
Acid Medium Trap: Only sulfuric acid ( H 2 SO 4 \text{H}_2\text{SO}_4 H 2 SO 4 ) can be used! Hydrochloric acid ( HCl \text{HCl} HCl ) cannot be used because MnO 4 − \text{MnO}_4^- MnO 4 − oxidizes Cl − \text{Cl}^- Cl − into toxic chlorine gas ( Cl 2 \text{Cl}_2 Cl 2 ), causing a positive error. If HCl \text{HCl} HCl must be present, Zimmermann-Reinhardt reagent (containing MnSO 4 , H 2 SO 4 , H 3 PO 4 \text{MnSO}_4, \text{H}_2\text{SO}_4, \text{H}_3\text{PO}_4 MnSO 4 , H 2 SO 4 , H 3 PO 4 ) must be added.
Stability: KMnO 4 \text{KMnO}_4 KMnO 4 solutions slowly decompose in the presence of light, heat, and traces of organic matter to form MnO 2 \text{MnO}_2 MnO 2 precipitate. Solutions must be boiled, filtered through sintered glass (never filter paper, which reduces permanganate), and stored in amber bottles.
2. Dichromatometry ( K 2 Cr 2 O 7 \text{K}_2\text{Cr}_2\text{O}_7 K 2 Cr 2 O 7 )
Potassium dichromate is reduced to chromic ions: Cr 2 O 7 2 − + 14 H + + 6 e − ⇌ 2 Cr 3 + + 7 H 2 O ( E ∘ = + 1.33 V ) \text{Cr}_2\text{O}_7^{2-} + 14\text{H}^+ + 6e^- \rightleftharpoons 2\text{Cr}^{3+} + 7\text{H}_2\text{O} \quad (E^\circ = +1.33\text{ V}) Cr 2 O 7 2 − + 14 H + + 6 e − ⇌ 2 Cr 3 + + 7 H 2 O ( E ∘ = + 1.33 V )
Key Advantages over Permanganate: Available in ultra-pure primary standard grade (can be weighed directly without standardization); stable indefinitely in aqueous solution; does not oxidize Cl − \text{Cl}^- Cl − in moderate acid ( < 1 M HCl < 1\text{ M } \text{HCl} < 1 M HCl ).
Indicator: Requires an external redox indicator (sodium diphenylamine sulfonate) with phosphoric acid.
3. Iodimetry vs. Iodometry
Feature Direct Iodimetry Indirect Iodometry
Role of Iodine Standard I 3 − \text{I}_3^- I 3 − is the titrant (oxidizing agent). Iodine ( I 3 − \text{I}_3^- I 3 − ) is liberated by analyte, then titrated.
Analyte Type Strong reducing agents ( As 2 O 3 \text{As}_2\text{O}_3 As 2 O 3 , Vitamin C, SO 3 2 − \text{SO}_3^{2-} SO 3 2 − ). Oxidizing agents ( Cu 2 + , IO 3 − , OCl − , Cr 2 O 7 2 − , H 2 O 2 \text{Cu}^{2+}, \text{IO}_3^-, \text{OCl}^-, \text{Cr}_2\text{O}_7^{2-}, \text{H}_2\text{O}_2 Cu 2 + , IO 3 − , OCl − , Cr 2 O 7 2 − , H 2 O 2 ).
Titrant Standard I 2 / KI \text{I}_2 / \text{KI} I 2 / KI solution. Standard Sodium Thiosulfate ( Na 2 S 2 O 3 \text{Na}_2\text{S}_2\text{O}_3 Na 2 S 2 O 3 ).
Core Reaction H 3 AsO 3 + I 3 − + H 2 O → H 3 AsO 4 + 3 I − + 2 H + \text{H}_3\text{AsO}_3 + \text{I}_3^- + \text{H}_2\text{O} \rightarrow \text{H}_3\text{AsO}_4 + 3\text{I}^- + 2\text{H}^+ H 3 AsO 3 + I 3 − + H 2 O → H 3 AsO 4 + 3 I − + 2 H + I 3 − + 2 S 2 O 3 2 − → 3 I − + S 4 O 6 2 − \text{I}_3^- + 2\text{S}_2\text{O}_3^{2-} \rightarrow 3\text{I}^- + \text{S}_4\text{O}_6^{2-} I 3 − + 2 S 2 O 3 2 − → 3 I − + S 4 O 6 2 − (tetrathionate)
Starch Indicator Mechanics: Starch consists of amylose and amylopectin. Amylose forms an intense dark-blue helical inclusion complex with triiodide ( I 3 − \text{I}_3^- I 3 − ).
Common Trap (Starch Timing): In iodometric titrations, starch must NOT be added at the beginning of the titration! At high iodine concentrations, iodine binds tightly within the amylose helical core, releasing slowly and causing a sluggish, delayed endpoint. Starch must be added only when the dark brown solution has faded to a pale straw-yellow (indicating that nearly all iodine has been reduced). Titration then continues until the intense blue color turns permanently colorless.
5. Karl Fischer Titration for Quantitative Water Determination
Karl Fischer titrimetry is the worldwide reference method for quantifying trace moisture in chemical, pharmaceutical, and food matrices.
Fundamental Reaction Mechanism
Based on the Bunsen reaction in non-aqueous solvent: H 2 O + I 2 + SO 2 + 3 RN + CH 3 OH → 2 RNH + I − + RNH + [ CH 3 OSO 3 − ] \text{H}_2\text{O} + \text{I}_2 + \text{SO}_2 + 3\text{RN} + \text{CH}_3\text{OH} \rightarrow 2\text{RNH}^+\text{I}^- + \text{RNH}^+[\text{CH}_3\text{OSO}_3^-] H 2 O + I 2 + SO 2 + 3 RN + CH 3 OH → 2 RNH + I − + RNH + [ CH 3 OSO 3 − ] where RN \text{RN} RN is an organic base (historically pyridine; modern reagents use non-toxic imidazole ). Methanol ( CH 3 OH \text{CH}_3\text{OH} CH 3 OH ) is essential: it reacts with the sulfur dioxide intermediate to form an alkylsulfite ester salt, preventing secondary water-consuming reactions.
Volumetric vs. Coulometric Karl Fischer
Volumetric KF: Automated buret delivers standardized Karl Fischer reagent containing known concentration of I 2 \text{I}_2 I 2 . Suitable for samples containing 0.1 % − 100 % 0.1\% - 100\% 0.1% − 100% water ( 1 mg − 100 mg H 2 O 1\text{ mg} - 100\text{ mg } \text{H}_2\text{O} 1 mg − 100 mg H 2 O ).
Coulometric KF: Reagent contains iodide ( I − \text{I}^- I − ). Iodine is generated in situ electrochemically at a platinum generator anode: 2 I − → I 2 + 2 e − 2\text{I}^- \rightarrow \text{I}_2 + 2e^- 2 I − → I 2 + 2 e − Water is calculated directly from total electric charge ( Q Q Q ) via Faraday's Law: Q = I × t Q = I \times t Q = I × t Moles H 2 O = Moles I 2 = Q n F = Q 2 × 96485 C/mol \text{Moles } \text{H}_2\text{O} = \text{Moles } \text{I}_2 = \frac{Q}{n F} = \frac{Q}{2 \times 96485\text{ C/mol}} Moles H 2 O = Moles I 2 = n F Q = 2 × 96485 C/mol Q Mass of H 2 O = Q × 18.015 g/mol 2 × 96485 C/mol \text{Mass of } \text{H}_2\text{O} = \frac{Q \times 18.015\text{ g/mol}}{2 \times 96485\text{ C/mol}} Mass of H 2 O = 2 × 96485 C/mol Q × 18.015 g/mol Sensitivity: Coulometry determines trace moisture from 1 ppm 1\text{ ppm} 1 ppm to 1 % 1\% 1% (down to 10 μ g H 2 O 10\ \mu\text{g } \text{H}_2\text{O} 10 μ g H 2 O ) with high precision.
6. Precipitation Titrimetry: Argentometric Methods
Precipitation titrations use a reaction that forms a sparingly soluble product. Silver nitrate is by far the most common titrant, so these methods are called argentometric . They determine halides ( C l − Cl^- C l − , B r − Br^- B r − , I − I^- I − ), thiocyanate, and cyanide. The TOS lists precipitation titrations alongside acid-base, complexometric, and redox titrations, so know the three classic endpoint methods:
Method Titration Mode Indicator and Endpoint Signal Required Conditions Typical Use
Mohr Direct titration of C l − Cl^- C l − or B r − Br^- B r − with A g + Ag^+ A g + Chromate ( C r O 4 2 − CrO_4^{2-} C r O 4 2 − ); first excess A g + Ag^+ A g + forms red-brown A g 2 C r O 4 Ag_2CrO_4 A g 2 C r O 4 Neutral to mildly basic, about pH 6.5 to 10; acid converts chromate to dichromate, while base precipitates A g O H AgOH A g O H / A g 2 O Ag_2O A g 2 O Chloride in water samples
Volhard Back-titration: add excess standard A g + Ag^+ A g + , then titrate the leftover A g + Ag^+ A g + with S C N − SCN^- SC N − Iron(III) alum; first excess S C N − SCN^- SC N − forms red F e S C N 2 + FeSCN^{2+} F e SC N 2 + Strongly acidic ( H N O 3 HNO_3 H N O 3 ), which also prevents interference from carbonate and oxalate Halides in acidic solution
Fajans Direct titration with A g + Ag^+ A g + Adsorption indicator such as dichlorofluorescein; the dye adsorbs on the positively charged precipitate after the equivalence point and turns pink pH suited to the dye (dichlorofluorescein works from about pH 4); keep the precipitate colloidal and protect it from light Chloride, bromide, iodide
Why the Mohr Indicator Works
At the equivalence point of a chloride titration, [ A g + ] = K s p ( A g C l ) = 1.82 × 10 − 10 = 1.35 × 10 − 5 M [Ag^+] = \sqrt{K_{sp}(AgCl)} = \sqrt{1.82 \times 10^{-10}} = 1.35 \times 10^{-5}\text{ M} [ A g + ] = K s p ( A g Cl ) = 1.82 × 1 0 − 10 = 1.35 × 1 0 − 5 M . Red A g 2 C r O 4 Ag_2CrO_4 A g 2 C r O 4 ( K s p = 1.2 × 10 − 12 K_{sp} = 1.2 \times 10^{-12} K s p = 1.2 × 1 0 − 12 ) begins to precipitate when [ A g + ] 2 [ C r O 4 2 − ] = K s p [Ag^+]^2[CrO_4^{2-}] = K_{sp} [ A g + ] 2 [ C r O 4 2 − ] = K s p , so the chromate concentration that would signal the exact equivalence point is:
[ C r O 4 2 − ] = 1.2 × 10 − 12 1.82 × 10 − 10 = 6.6 × 10 − 3 M [CrO_4^{2-}] = \frac{1.2 \times 10^{-12}}{1.82 \times 10^{-10}} = 6.6 \times 10^{-3}\text{ M} [ C r O 4 2 − ] = 1.82 × 1 0 − 10 1.2 × 1 0 − 12 = 6.6 × 1 0 − 3 M
The intense yellow of that much chromate masks the red, so analysts use about 2.5 × 10 − 3 M 2.5 \times 10^{-3}\text{ M} 2.5 × 1 0 − 3 M and subtract an indicator blank run on a chloride-free suspension of C a C O 3 CaCO_3 C a C O 3 .
Volhard Determination of Chloride
A g C l AgCl A g Cl ( K s p = 1.82 × 10 − 10 K_{sp} = 1.82 \times 10^{-10} K s p = 1.82 × 1 0 − 10 ) is more soluble than A g S C N AgSCN A g SCN ( K s p ≈ 1.1 × 10 − 12 K_{sp} \approx 1.1 \times 10^{-12} K s p ≈ 1.1 × 1 0 − 12 ). Near the endpoint, thiocyanate would slowly convert A g C l AgCl A g Cl to A g S C N AgSCN A g SCN and give a fading endpoint and a low chloride result. The fix is to filter off the AgCl or coat it with nitrobenzene before back-titrating. Bromide and iodide do not need this step because A g B r AgBr A g B r and A g I AgI A g I are less soluble than A g S C N AgSCN A g SCN .
Worked Example: Mohr Titration
A 25.00 mL 25.00\text{ mL} 25.00 mL water sample needs 21.45 mL 21.45\text{ mL} 21.45 mL of 0.1000 M A g N O 3 0.1000\text{ M } AgNO_3 0.1000 M A g N O 3 , and the indicator blank is 0.15 mL 0.15\text{ mL} 0.15 mL .
Corrected volume: 21.45 − 0.15 = 21.30 mL 21.45 - 0.15 = 21.30\text{ mL} 21.45 − 0.15 = 21.30 mL
Moles of C l − Cl^- C l − : 0.02130 L × 0.1000 M = 2.130 × 10 − 3 mol 0.02130\text{ L} \times 0.1000\text{ M} = 2.130 \times 10^{-3}\text{ mol} 0.02130 L × 0.1000 M = 2.130 × 1 0 − 3 mol
Chloride concentration: 2.130 × 10 − 3 mol × 35.45 g/mol 0.02500 L = 3.020 g/L = 3020 mg/L \frac{2.130 \times 10^{-3}\text{ mol} \times 35.45\text{ g/mol}}{0.02500\text{ L}} = 3.020\text{ g/L} = 3020\text{ mg/L} 0.02500 L 2.130 × 1 0 − 3 mol × 35.45 g/mol = 3.020 g/L = 3020 mg/L
Combining Methods
Real samples often need more than one technique. For example, total hardness by EDTA, chloride by Mohr titration, and sulfate by B a S O 4 BaSO_4 B a S O 4 gravimetry together characterize a groundwater. Cross-checking a titrimetric result against an instrumental one, such as chloride by ion chromatography, is a standard way to confirm accuracy.