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Chemistry · Lesson

Redox and complexometric titrations

Count electrons in specified redox nets and ligand amounts in a selected metal–EDTA model. Keep reaction medium, conditional binding and a combined reporting basis explicit.

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By the end, you can

  • Use the acidic permanganate–iron electron balance.
  • Calculate iodine inventory on a specified I₂ basis.
  • Interpret combined Ca/Mg amount on a CaCO₃-equivalent basis.
  • Compare finite binding at equal total inventories using assigned conditional constants.
01

The selected products determine the electron factor

Redox titrimetry uses a specified electron-transfer reaction to connect amounts. Identify the starting states, products and medium before assigning a coefficient. An observable response must also be related to progress of that reaction; a strong color or potential change alone is not proof of a selective, complete net.

For the selected acidic reduction, MnO₄⁻+8H⁺+5e⁻→Mn²⁺+4H₂O. Iron oxidation is Fe²⁺→Fe³⁺+e⁻. Adding five iron steps cancels the electrons and gives MnO₄⁻+8H⁺+5Fe²⁺→Mn²⁺+4H₂O+5Fe³⁺. Both sides have net charge +17 and conserved Mn, Fe, O and H atoms.

Thus one permanganate corresponds to five Fe²⁺ in this net. The Mn(VII)-to-Mn(II) factor must not be transferred to a reaction with different manganese products or medium. An invented equivalence volume 12.40 mL at 0.0200 mol L⁻¹ gives 0.2480 mmol permanganate and 1.240 mmol Fe²⁺, with 1.240 mmol electrons transferred.

02

Specify whether the iodine inventory is written as I₂ or another form

A selected net is I₂+2S₂O₃²⁻→2I⁻+S₄O₆²⁻. Two thiosulfate units correspond to one I₂, with four S and six O atoms conserved and net charge −4 on both sides. I₂ accepts two electrons in the overall formal ledger.

If an iodine-containing solution is described on a triiodide I₃⁻ basis instead, the written net includes an additional iodide in the reactant/product inventory: I₃⁻+2S₂O₃²⁻→3I⁻+S₄O₆²⁻. The transferred two-electron inventory can be preserved while the whole-entity formula and charge differ. Do not silently relabel the entities.

For a separate invented I₂-basis model, 18.60 mL of 0.100 mol L⁻¹ thiosulfate corresponds to 1.860 mmol thiosulfate, 0.9300 mmol I₂ and 0.9300 mmol tetrathionate. The selected net produces 1.860 mmol iodide. No actual iodine speciation or endpoint procedure is supplied.

03

Metal–ligand amount ratios do not count donor contacts

Ethylenediaminetetraacetic acid, EDTA, has protonation states and donor groups that affect metal binding. An electron-pair donor acts as a Lewis base. In the usual specified mononuclear analytical model, one ligand entity binds one metal entity; that 1:1 ratio is not a one-donor-contact statement or a universal assertion about every EDTA structure.

Write the selected fully deprotonated net as M²⁺+Y⁴⁻⇌MY²⁻. On an H₂Y²⁻ input basis, M²⁺+H₂Y²⁻⇌MY²⁻+2H⁺. Both retain one metal per ligand entity, while their proton inventories differ. Metal side reactions, ligand protonation and competing ions affect whether the selected model supports an effective analytical endpoint.

Suppose an invented 50.0 mL sample has only Ca²⁺ and Mg²⁺ as titratable metals under a stipulated effective 1:1 endpoint model. A given equivalence volume 28.0 mL of 0.0100 mol L⁻¹ EDTA gives combined metal amount 0.280 mmol and combined amount concentration 0.00560 mol L⁻¹. That single response does not separately determine Ca and Mg.

With assigned rounded molar mass 100.09 g mol⁻¹, the reporting basis “as CaCO₃” gives 0.560504 g L⁻¹=560.504 mg L⁻¹. It is a metal-amount-equivalent mass basis, not a claim that all those dissolved metals were actual CaCO₃ molecules or solid.

04

Protonation can change the effective binding strength

For an optional deeper original ideal model at fixed conditions, assign dimensionless formation constant K_f=10¹⁰ for M²⁺+Y⁴⁻⇌MY²⁻, standard concentration c°=1 mol L⁻¹ and unit activity coefficients. Let α be the fraction of total uncomplexed ligand present as Y⁴⁻ at the maintained pH. The conditional dimensionless constant is K′=αK_f; its concentration-form coefficient is K′/c° in L mol⁻¹.

Choose invented α values 0.00100 and 10⁻⁷, rather than actual pH values or real-metal constants. They give K′=10⁷ and 10³. With equal total metal and total ligand concentrations C_T=0.00100 mol L⁻¹, and no metal side complexes, bound concentration x satisfies x=(K′/c°)(C_T−x)². Free metal and total uncomplexed ligand each equal C_T−x.

The two bound fractions are approximately 0.990049875 and 0.381966011: 99.0049875% and 38.1966011%. Equal total inventories do not force complete binding. The α values refer to the uncomplexed ligand pool, not all ligand including the complex. A maintained protonation environment and excluded competing species are essential to this toy.

Equal total metal and ligand amounts with different conditional binding
Assigned αConditional K′Free metal / μmol L⁻¹Bound complex / μmol L⁻¹Bound fraction
0.0010010⁷9.950125990.0498750.990049875
10⁻⁷10³618.033989381.9660110.381966011

Original fixed-condition ideal 1:1 model with K_f=10¹⁰, c°=1 mol L⁻¹, unit activity coefficients and equal totals 1.000 mmol L⁻¹. α specifies Y⁴⁻ fraction of uncomplexed ligand at maintained pH. No real pH, metal constant or actual endpoint is assigned; metal side complexes are excluded.

05

A correct factor is only one part of a quantitative method

Redox and complexometric inventories can be powerful when the selected chemistry and observation are supported. The actual medium, endpoint, reference, competing constituents and time-dependent behavior determine the scope of the amount inference.

Report a combined quantity as combined unless independent evidence separates its components. Likewise, a formal balanced net and a strong assigned formation constant do not establish complete selectivity or the absence of finite free species in every sample.

Worked examples

Cancel the electrons before relating amounts

Use the selected acidic permanganate–Fe²⁺ net and invented 12.40 mL at 0.0200 mol L⁻¹.

  1. Permanganate amount is 0.2480 mmol.
  2. Five Fe²⁺ per MnO₄⁻ give 1.240 mmol iron.
  3. The exchanged electron amount is 1.240 mmol.

The five-electron factor belongs to the specified Mn²⁺ product net.

Use the I₂-basis coefficient

Use invented 18.60 mL of 0.100 mol L⁻¹ thiosulfate.

  1. Thiosulfate amount is 1.860 mmol.
  2. I₂ amount is half: 0.9300 mmol.
  3. Tetrathionate amount is 0.9300 mmol.
  4. Selected product iodide amount is 1.860 mmol.

A conserved I₂-basis inventory; changing to I₃⁻ changes the written iodide ledger.

Keep combined metal and reporting basis distinct

Use the stipulated Ca/Mg-only 1:1 endpoint model.

  1. Combined metal concentration is 0.00560 mol L⁻¹.
  2. Multiply by assigned 100.09 g mol⁻¹ to give 0.560504 g L⁻¹.
  3. Convert to 560.504 mg L⁻¹ as CaCO₃.
  4. Separate Ca and Mg remain undetermined.

An explicit equivalent basis, without claiming actual CaCO₃ chemical form.

Use finite binding rather than forcing full conversion

Use equal totals 1.000 mmol L⁻¹ and the two assigned conditional constants.

  1. K′=10⁷ gives x≈0.990049875 mmol L⁻¹.
  2. K′=10³ gives x≈0.381966011 mmol L⁻¹.
  3. Free metal equals total minus x in each separate toy.

Different finite bound fractions despite the same total metal-to-ligand ratio.

Try it yourself

  1. Keep the selected acidic net but use 10.00 mL of 0.0200 mol L⁻¹ permanganate. Find the inferred Fe²⁺ amount.

    Show the answer and reasoning

    1.000 mmol.

    Permanganate amount is 0.2000 mmol and the specified factor is five.

  2. A new combined Ca/Mg amount concentration is 0.00200 mol L⁻¹. Use the assigned CaCO₃ molar mass to report the equivalent mass concentration.

    Show the answer and reasoning

    200.18 mg L⁻¹ as CaCO₃.

    0.00200×100.09=0.20018 g L⁻¹; the basis does not identify the actual species.

  3. Does α in the selected conditional model include ligand already bound in MY²⁻?

    Show the answer and reasoning

    No.

    It is the Y⁴⁻ fraction of the total uncomplexed ligand pool at maintained conditions.

  4. Does a 1:1 metal-to-ligand entity ratio mean the ligand provides one donor contact?

    Show the answer and reasoning

    No.

    Entity stoichiometry and the number of attached donor atoms are different counts.

What to carry forward

  • Electron factors require specified products and medium.
  • Name the iodine entity used for the amount basis.
  • Keep ligand-entity ratios distinct from donor counts.
  • Conditional constants refer to defined free pools and conditions.
  • A combined equivalent basis does not identify individual forms.

References

Teaching resources and reference material supporting this lesson’s explanations and examples.

  1. NCERT Class XII Chemistry Laboratory Manual Unit 6: Titrimetric Analysis (Redox Reactions)National Council of Educational Research and Training,India; section individual author unspecifiedSource · PDFncert.nic.inRead source
  2. David T.Harvey, DePauw University,USA2 sources
    1. Analytical Chemistry 2.1: 9.4 Redox TitrationsDavid T.Harvey, DePauw University,USASourcechem.libretexts.orgRead source
    2. Analytical Chemistry Volume I: 9.3 Complexation TitrationsDavid T.Harvey, DePauw University,USASourcechem.libretexts.orgRead source
  3. IUPAC Gold Book Joint Subcommittee; original source identified in entry3 sources
    1. IUPAC Gold Book: Lewis baseIUPAC Gold Book Joint Subcommittee; original source identified in entrySourcegoldbook.iupac.orgRead source
    2. IUPAC Gold Book: equivalent entityIUPAC Gold Book Joint Subcommittee; original source identified in entrySourcegoldbook.iupac.orgRead source
    3. IUPAC Gold Book: equivalence-pointIUPAC Gold Book Joint Subcommittee; original source identified in entrySourcegoldbook.iupac.orgRead source
  4. NIST Chemistry WebBook SRD69: Ethylenediaminetetraacetic acidNational Institute of Standards and Technology,USA; SRD69 compilersSourcewebbook.nist.govRead source
  5. Fitness for Purpose of Analytical Methods, third editionHelen Cantwell (editor); Eurachem Method Validation Working GroupSource · PDFeurachem.orgRead source