Coordination Compounds · Lesson 12 of 12
Chapter Summary and Practice
“Integrate composition, geometry, electron structure and chemical function through connected examples and chapter-wide practice.”
• Analyse a complex from formula through geometry and electron occupation. • Select evidence that distinguishes competing structural descriptions. • Combine nomenclature, isomerism, magnetism and spectroscopy. • Apply coordination principles to analytical and industrial problems.
One chain of reasoning connects the chapter
A coordination formula contains several independent kinds of information. Square brackets identify a chemical entity, ligand formulas establish composition, and charges constrain oxidation state. Donor atoms and denticity determine coordination number. Geometry determines which spatial arrangements are possible. The ligand field and d-electron count then determine orbital occupancy, magnetic behaviour and part of the absorption spectrum. Finally, equilibria and reaction pathways determine how that entity behaves in solution or in a process. Skipping a link can produce a correct-looking answer for the wrong reason.
| Question | Method | Typical mistake to avoid |
|---|---|---|
| What species dissolves? | Separate bracketed entity from counter ions | Treating every ligand as a separate ion |
| What is the metal state? | Metal state + ligand charges = entity charge | Equating entity charge with metal state |
| How many donor sites? | Sum actual denticities | Counting ligand molecules only |
| What shape is present? | Use structural evidence and bonding context | CN 4 automatically means square planar |
| Which isomerism? | Separate connectivity from spatial arrangement | Counting rotations as different molecules |
| How many unpaired electrons? | Fill the geometry-appropriate levels | Using free-ion spin without checking the field |
| Why this colour? | Identify transitions and remaining light | Equating paired electrons with colourlessness |
The compact reference, with conditions
| Relationship | Symbols and units | Conditions |
|---|---|---|
| x + Σnᵢqᵢ = Q | Formal oxidation states and charges | Known ligand identities and charge assignments |
| CN = sum of direct donor attachments | Dimensionless donor count | Actual binding mode stated; π bonding not counted twice |
| μso = √[n(n+2)] BM | n unpaired electrons | Spin-only approximation; orbital effects neglected |
| E(t₂g)=−0.4Δo; E(e_g)=+0.6Δo | Common energy units per particle or mole | Octahedral electrostatic splitting model |
| E_CF=(−0.4N_t+0.6N_e)Δo | N_t,N_e electron counts | Pairing-energy terms separate |
| Δt ≈ 4Δo/9 | Same energy units | Ideal comparable metal, ligand and distance |
| ΔE = hc/λ | J per photon; λ in m | Identified transition; multiply by NA for molar energy |
| n(metal)=n(EDTA) | Moles | Usual 1:1 chelation under suitable titration conditions |
For octahedral d⁴–d⁷, compare splitting with pairing energy before assigning high or low spin. For d¹–d³ the lower t₂g orbitals fill singly. Ordinary octahedral d⁸ has two unpaired electrons; a square-planar d⁸ field can instead favour complete pairing. A tetrahedral diagram reverses the octahedral ordering and usually has a smaller gap. The orbital labels are geometry-specific, not universal boxes that can be copied onto every entity.
Naming connects charge to composition
Within a name, alphabetise ligands before the metal and ignore multiplying prefixes in that order. Use ammine for NH₃, aqua for water, chlorido for coordinated chloride and cyanido for CN⁻. Give an anionic entity a metal name ending in -ate and specify oxidation state in Roman numerals. For the complete salt, name cation before anion and balance their charges in the formula. Donor labels such as nitrito-κN and nitrito-κO specify linkage, whereas cis/trans and fac/mer specify spatial arrangement.
Isomerism at a glance
| Category | Change | Representative consequence |
|---|---|---|
| Geometrical | Relative ligand positions | cis/trans square-planar PtCl₂(NH₃)₂ |
| Optical | Non-superimposable mirror arrangement | Two helicities of [Co(en)₃]³⁺ |
| Linkage | Donor atom of one ligand | M–NO₂ versus M–ONO |
| Coordination | Ligand distribution across metal-containing ions | Exchange of Co/Cr ligand sets |
| Ionisation | Ligand versus counter-ion membership | Different rapid sulfate/halide tests |
| Hydrate | Coordinated versus lattice water | Different numbers of free chlorides |
Count geometrical classes first, then their optical subdivisions. MA₃B₃ in an octahedron has fac and mer forms. M(AA)₂B₂ has cis/trans classes, with an optical cis pair and an achiral trans form. M(AA)A₂B₂ has three geometrical classes and four principal stereoisomers. Tetrahedral MA₂B₂ has no cis/trans pair, while ideal square-planar MABCD has three geometrical isomers and no optical pairs with achiral ligands.
Integrated example: analyse a hydrated chelate salt
Problem
Analyse K[Cr(H₂O)₂(C₂O₄)₂]·3H₂O.
- 1.K⁺ requires a −1 entity. Two oxalates contribute −4 and water contributes zero, so x − 4 = −1 and Cr is +3, d³.
- 2.Two bidentate oxalates provide four O donors and two aqua ligands add two: CN 6. The three waters after the dot are lattice water and add no donors.
- 3.Name potassium diaquabis(oxalato)chromate(III) trihydrate. An octahedral structure is appropriate. The two coordinated waters can be cis or trans, with the cis class forming an optical pair.
- 4.Octahedral d³ is t₂g³, with three unpaired electrons and μso = √15 = 3.87 BM. In the elementary VBT label it is an inner-orbital d²sp³ case, but the CFT occupation gives the clearer magnetic explanation.
Problem
Compare [CoCl(NH₃)₅]Cl₂, Cs[FeCl₄] and K₄[Mn(CN)₆].
- 1.The cobalt entity is +2, but cobalt is +3, d⁶. The established ammine-rich octahedral environment is low spin, n = 0; name pentaamminechloridocobalt(III) chloride.
- 2.Cs⁺ requires [FeCl₄]⁻. x − 4 = −1 gives Fe(III), d⁵. Its tetrahedral weak-field arrangement has five unpaired electrons, μso ≈ 5.92 BM; name caesium tetrachloridoferrate(III).
- 3.Four K⁺ require [Mn(CN)₆]⁴⁻. Mn is +2, d⁵, but cyanido gives low-spin octahedral t₂g⁵ with one unpaired electron, μso ≈ 1.73 BM; name potassium hexacyanidomanganate(II).
- 4.The salts illustrate why neither entity charge nor metal d count alone determines magnetism.
Bonding models explain different levels of detail
Werner’s theory organises constitution and geometry from experimental evidence. Elementary VBT gives directional bonding labels and accommodates known pairing patterns. CFT relates geometry to d-level splitting, spin and simple colour arguments. Carbonyl σ donation and π back-donation reveal covalent interactions that go beyond the point-charge model. These models are complementary tools with limits, not interchangeable proofs of every property.
Carbonyl back-donation strengthens metal–carbon interaction while weakening internal C–O bonding. In applications, ligand binding can lower free-metal activity, create soluble extraction species, stabilise a volatile purification intermediate or tune an active site. Chelation may favour a complex at equilibrium, but inertness and rate require separate evidence. Precipitation depends on competing equilibria and cannot be inferred from a statement that a complex “never dissociates”.
Use observations at the strength they support
An AgCl yield constrains immediately free chloride under defined conditions. A measured magnetic moment constrains unpaired-electron count within a model. An absorption band constrains an electronic transition. A colour or phase change indicates changed chemical species but does not uniquely identify a solid formula. Good chemical reasoning combines these observations and states assumptions where the data are insufficient. This is how composition, structure and function can be connected without replacing explanation with memorised labels.
Quick Quiz
Quiz
What is the oxidation state and CN of Cr in K[Cr(H₂O)₂(C₂O₄)₂]·3H₂O?
The entity is −1, two oxalates total −4, and six donors exclude lattice water.
Which octahedral d⁵ entity is expected to have the smaller spin-only moment?
Low-spin cyanido d⁵ has one unpaired electron, while the weak-field examples have five.
What distinguishes linkage from geometrical isomerism?
NO₂/ONO changes connectivity; cis/trans retains donor connectivity.
Which process uses a soluble silver thiosulfate complex?
Thiosulfate dissolves residual AgBr by stabilising [Ag(S₂O₃)₂]³⁻.
Which evidence is insufficient by itself to determine an exact precipitate formula?
Colour is not a unique compositional fingerprint.
Practice Problems
- A compound with composition CoCl₃·4NH₃ gives one mol rapid AgCl per mole. Analyse its structure and possible isomers.
- Give the full analysis of K₃[Co(C₂O₄)₃], cis-[CrCl₂(en)₂]Cl, (NH₄)₂[CoF₄] and [Mn(H₂O)₆]SO₄.
- Name and analyse [CrCl₃(py)₃] and explain why stereochemistry must be specified separately.
- Compare μso for K[Cr(H₂O)₂(C₂O₄)₂]·3H₂O, [CoCl(NH₃)₅]Cl₂, [CrCl₃(py)₃], Cs[FeCl₄] and K₄[Mn(CN)₆].
- Construct all principal stereoisomers of [CoCl₂(en)₂]⁺, [CoCl(NH₃)(en)₂]²⁺ and [Co(NH₃)₂Cl₂(en)]⁺.
- Calculate ΔE for a 600 nm band and compare it with a 400 nm band.
- For octahedral d⁶ compare Δo = 16 000 cm⁻¹ and 26 000 cm⁻¹ when P = 20 000 cm⁻¹.
- Distinguish [CoCl(NH₃)₅]SO₄ from [Co(NH₃)₅(SO₄)]Cl and describe a hydrate-isomer comparison.
- Write and explain the two electron-density transfers in an M–CO unit.
- A 20.0 mL water sample consumes 8.00 mL of 0.0150 M EDTA. Calculate total titratable divalent-metal concentration.
- Verify 2[Au(CN)₂]⁻ + Zn → 2Au + [Zn(CN)₄]²⁻ and explain its role.
- Explain the limits of a simple-ion copper test after adding excess NH₃ or CN⁻.
- Relate coordination chemistry to four distinct applications without simply naming them.
- Correct four claims: CN equals ligand count; low spin means diamagnetic; tetrahedral means cis/trans; all coloured complexes require unpaired d electrons.
- Explain what additional evidence you would seek for a green copper-fluoride precipitate and an alleged ten-isomer pentaammine salt.
1. One external chloride leaves [CoCl₂(NH₃)₄]Cl. 2. Co is +3; four N plus two Cl donors give CN 6, octahedral. 3. The chlorido pair may be cis or trans; conductivity and this AgCl count do not choose between them. 4. Both ideal classes with achiral monodentate ligands are achiral.
Key Takeaways
• Start from bracket membership, ligand charges and actual donor atoms. • Geometry is required before counting isomers or filling orbitals. • A metal oxidation state does not uniquely fix magnetism or colour. • Use the spin-only moment and photon-energy formulas with their assumptions. • CFT and VBT are limited models of real bonding. • CO donation/back-donation adds covalent reasoning beyond point charges. • Coordination equilibria connect structure with analysis, extraction and biology. • State what evidence supports and what remains unspecified.
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Coordination Chemistry in Use
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