d- and f-Block Elements · Lesson 12 of 12
Chapter Summary and Practice
“Integrate electron structure, chemical environment, material properties and balanced redox calculations.”
• Connect electronic configurations with properties while accounting for ligand, lattice and solvent effects. • Choose and balance the appropriate dichromate or permanganate reaction. • Interpret magnetic, optical and electrochemical evidence together. • Compare d-, 4f- and 5f-series chemistry and solve integrated chapter problems.
A connected reasoning method
The chapter can be organised around one question: what complete change is being compared? A configuration describes an atom or formal metal centre; an ionisation enthalpy describes a gaseous removal; a colour describes a species in a particular environment; a reduction potential describes a written electron-transfer process. Confusing these levels creates many apparent contradictions. d¹⁰ Cu⁺ can disproportionate in water, d⁰ permanganate can be purple, and a metal with a negative reduction potential can react slowly behind a protective film. Each is explained when the omitted environment or pathway is restored.
| Evidence or task | First calculation | Additional information needed |
|---|---|---|
| Ion configuration | Identify Z, charge and electron total | Orbital reordering or the supported ground assignment |
| Oxidation state | Sum ligand and ion charges | Speciation, covalency and competing products |
| Magnetic moment | Find d/f count and unpaired occupancy | Geometry, splitting, pairing and orbital contributions |
| Visible colour | Consider available electronic transitions | Ligands, selection restrictions, charge transfer and hydrolysis |
| Reaction tendency | Combine reduction potentials consistently | Concentration, pH and kinetic barriers |
| Material property | Identify the actual lattice or compound | Bonding, phase structure, composition and conditions |
Reference equations with conditions of use
| Relationship | Meaning and limits |
|---|---|
| d count=group number−positive oxidation state | Formal bookkeeping for common d-metal centres; check ion identity |
| μso=√[n(n+2)] BM | Spin-only approximation; n is unpaired count |
| E°cell=E°cathode−E°anode | Use two reduction potentials; do not multiply potentials by coefficients |
| ΔG°=−nFE°cell | Standard Gibbs energy per balanced reaction; n is transferred electron count |
| ΔE=hc/λ | Energy of an absorbed photon, not the visible transmitted colour |
| Amount=cV | Use compatible concentration and volume units |
| n(reductant)/n(oxidant)=e accepted/e donated | Apply to the actual balanced product pathway |
These equations use n for two different quantities in different contexts: unpaired electrons in magnetism and transferred electrons in electrochemistry. Define the symbol anew in each calculation. BM is a unit of magnetic moment, V of potential, J mol⁻¹ of molar energy and mol L⁻¹ of concentration. A numerical coincidence between values in different units is not a physical relationship.
d-series trends and heavier-metal comparisons
The 3d series has useful recurring patterns: broadly strong metallic bonding, small and irregular radius changes, multiple accessible states and common high-spin aqua ions. The 4d and 5d members can differ in their exact s/d atomic occupations, stronger metal–metal bonding and more persistent high oxidation states. Their ligand-field splittings are often larger, so a first-row spin assignment should not be transferred automatically to a heavier homologue. The 5d radii closely resemble 4d radii because of preceding 4f contraction; they are not uniformly larger by a shell-sized step.
Ionisation enthalpies also reflect stronger attraction, different orbital sizes and relativistic effects, so there is no sound rule that every heavier homologue is simply easier to ionise. Atomic configurations such as Pd 4d¹⁰5s⁰ and Pt 5d⁹6s¹ show why the exact distribution must be checked. The conventional 5d sequence has La 5d¹6s², Hf 5d²6s², Ta 5d³6s², W 5d⁴6s², Re 5d⁵6s², Os 5d⁶6s², Ir 5d⁷6s², Pt 5d⁹6s¹, Au 5d¹⁰6s¹ and Hg 5d¹⁰6s² beyond the appropriate core; La precedes filling of 4f while Hf onward includes filled 4f.
For the conventional superheavy d sequence, Ac has 6d¹7s² and Rf–Ds are commonly represented in simple tables by 6d²–⁸7s²; Rg is represented as 6d¹⁰7s¹ and Cn as 6d¹⁰7s². These are heavy-atom assignments with differing degrees of theoretical dependence. For Mt, Z=109, a conventional configuration is [Rn]5f¹⁴6d⁷7s²; the sum beyond [Rn] is 14+7+2=23, matching 109−86. Do not infer that a schematic table establishes experimentally precise chemical behaviour for every superheavy element.
Reaction maps are maps of conditions as well as formulas
| Starting material | Necessary change | Result |
|---|---|---|
| FeCr₂O₄ | Oxidative alkaline roasting | Yellow CrO₄²⁻ |
| CrO₄²⁻ | Acidification / condensation equilibrium | Orange Cr₂O₇²⁻ |
| Cr₂O₇²⁻ | Base addition | CrO₄²⁻ without changing Cr(VI) |
| Cr₂O₇²⁻ | Six-electron reduction in acid | Two Cr³⁺ |
| MnO₂ | Oxidative alkaline fusion | Green MnO₄²⁻ |
| MnO₄²⁻ | One-electron anodic oxidation | Purple MnO₄⁻ |
| MnO₄²⁻ | Disproportionation on reduced alkalinity | MnO₄⁻ plus MnO₂ |
| MnO₄⁻ | Reduction in an appropriate medium | Mn²⁺, MnO₂ or MnO₄²⁻ |
Problem
What Fe²⁺ amount can react with 0.00100 mol dichromate versus 0.00100 mol permanganate in sufficient acid?
- 1.Dichromate accepts six electrons per ion and Fe²⁺ gives one: amount=6×0.00100=0.00600 mol Fe²⁺.
- 2.Permanganate reduced to Mn²⁺ accepts five: amount=0.00500 mol Fe²⁺.
- 3.The result compares electron capacity per mole for specified pathways, not which oxidant has the larger potential or faster reaction. Stronger potential and larger stoichiometric capacity are different ideas.
Problem
A group-7 complex has formal oxidation state +2. Could a moment near 1.8 BM and one near 5.9 BM both be reasonable?
- 1.The centre is d⁵. In an octahedral strong field a low-spin t₂g⁵ arrangement has one unpaired electron and a spin-only value near 1.73 BM.
- 2.A high-spin arrangement has five unpaired electrons and a value near 5.92 BM. A weak-field tetrahedral Mn(II) complex commonly follows this case.
- 3.The same formal d count can therefore yield very different moments. Include ligand and geometry information before counting unpaired electrons.
Compare 4f and 5f without overgeneralising
Lanthanoid chemistry is dominated by similar trivalent ions with comparatively buried 4f electrons. Their gradual same-charge contraction produces small chemical differences within the series and pronounced size effects after it. Early actinoids use their less buried 5f electrons more readily in bonding, producing varied states and speciation; later members more closely resemble the trivalent lanthanoids. All actinoids are radioactive, whereas the lanthanoid series includes many stable-isotope elements and radioactive promethium. Orbital effects matter in both series’ magnetism.
Special occupations f⁰,f⁷ and f¹⁴ help explain selected +2/+4 states. They do not imply that every other state is impossible or that a favourable occupation overrules hydration, lattice formation and ligand bonding. The useful endpoint is a method: identify the species, count electrons correctly, specify the medium, balance the proposed change and then evaluate what the evidence actually establishes.
Common errors to repair before solving
| Tempting shortcut | Repair |
|---|---|
| All d-block elements are transition elements | Test incomplete d occupation in atom or accessible cation |
| All d⁵ ions have the same chemistry | Specify element, charge, ligand and comparison reaction |
| Colourless means diamagnetic | Colour and unpaired occupancy probe different processes |
| Every coloured metal compound uses d–d absorption | Consider charge transfer and ligand absorption |
| A positive E° guarantees instant reaction | Assess kinetics and passivation separately |
| All permanganate reactions use five electrons | Identify Mn reduction product first |
| A source answer must be right | Check atom, charge, electron and numerical balance |
| A radius or half-life is one universal elemental number | State radius convention or isotope and conditions |
Quick Quiz
Quiz
Which observation is consistent with a formally d⁰ metal?
Explanation: A d⁰ count rules out ordinary occupied-d excitation but not charge transfer.
Which acidic reagent amount oxidises 0.00600 mol Fe²⁺?
Explanation: Each dichromate accepts six electrons, matching six Fe²⁺.
What explains 4d/5d radius similarity?
Explanation: Poor 4f shielding offsets much of the expected radius increase.
What additional information is essential for a d⁶ magnetic prediction?
Explanation: d⁶ can be high- or low-spin depending on its environment.
Which statement best connects f-series chemistry?
Explanation: The relative accessibility of f electrons helps explain the contrast.
Practice Problems
- Classify Sc,Zn,Cu and Ag using configurations.
- Write the configurations of Cr³⁺, Pm³⁺, Cu⁺, Ce⁴⁺, Co²⁺, Lu²⁺, Mn²⁺ and Th⁴⁺.
- Compare hypothetical d³s²,d⁵s²,d⁸s² and d⁴s² valence patterns in oxidation-state prediction.
- Use −0.4, +0.8 and +1.5 V for Cr³⁺/Cr²⁺, Fe³⁺/Fe²⁺ and Mn³⁺/Mn²⁺ to compare reduction tendency.
- Derive acidic dichromate reactions with iodide and H₂S.
- Derive acidic permanganate reactions with Fe²⁺, SO₂ and oxalic acid.
- A 20.00 mL Fe²⁺ sample needs 16.00 mL of 0.02500 M permanganate in acid. Find its concentration.
- Balance and distinguish manganate disproportionation and Mn(VII)/Mn(II) comproportionation.
- Count unpaired electrons for hydrated Ti²⁺, V²⁺, Cr³⁺, Mn²⁺, Fe²⁺, Fe³⁺, Co²⁺, Ni²⁺ and Cu²⁺.
- Interpret 2.2,5.3 and 5.9 BM for [Mn(CN)₆]⁴⁻,[Fe(H₂O)₆]²⁺ and [MnCl₄]²⁻.
- Explain why high-state oxides and low-state oxides differ in acidity.
- Connect lanthanoid contraction to both separation and Zr/Hf similarity.
- Compare lanthanoid and actinoid electronic structure, states and chemical reactivity.
- Write configurations for Z=61,91,101,109 and identify the last actinoid.
- Explain why neither d¹ instability nor d³ stability is universal.
- Compare alloys, interstitial compounds and complexes with one example each.
Sc qualifies through its d¹ atom; Zn is d-block but its ordinary atom/ions retain d¹⁰; Cu qualifies through d⁹ Cu²⁺; Ag qualifies through accessible d⁹ Ag²⁺ despite d¹⁰ Ag and Ag⁺. Classification applies to the element, not only one selected ion.
Key Takeaways
• Identify the actual atom, ion, complex or solid before applying a configuration rule. • Use total energy and chemical environment to interpret oxidation-state stability. • Magnetic, optical and electrochemical observations provide different kinds of evidence. • Balance atoms, charge and electrons independently in every redox reaction. • Permanganate stoichiometry depends on its final manganese state and the medium. • Lanthanoid contraction explains both subtle within-series differences and later d-metal similarities. • Early actinoid bonding is more variable because several valence levels are accessible. • A sound explanation states both its assumptions and the limits of its evidence.