Notes on the d- and f-block Elements: Key Concepts, Trends, and Classic Reactions

The d-Block and f-Block Elements: Overview

• The d-block comprises groups 3–12 in the periodic table; the f-block sits below, comprising the 4f and 5f orbitals progressively filling as you move across the lanthanoids and actinoids.
• Names: transition metals refer to the d-block; inner transition metals refer to the f-block. IUPAC definition of transition metals: metals that have an incomplete d subshell either in the neutral atom or in their ions.
• Exclusions: Zn, Cd, and Hg (group 12) have a fully filled d10 configuration in ground state and common oxidation states, hence they are not regarded as transition metals, though their chemistry is studied with transition metals since they lie at the ends of 3d, 4d, and 5d series.
• Four main series of transition elements (by principal quantum number of the outer d shell):
  • 3d series: Sc to Zn
  • 4d series: Y to Cd
  • 5d series: La and Hf to Hg
  • 6d series: Ac and elements from Rf to Cn
• Two inner transition series: 4f (Ce to Lu) and 5f (Th to Lr) → known as lanthanoids and actinoids respectively.
• Historical note: transition metals were named because their properties appeared transitional between s- and p-block elements; IUPAC now defines them by incomplete d subshells.
• Practical note: common properties of transition elements include: multiple oxidation states, colored ions, complex formation, catalytic activity, and paramagnetism; these arise from partly filled d (and sometimes f) orbitals.
• Unit objectives (from the text):
  • Locate d- and f-block elements in the periodic table;
  • Know electronic configurations of transition and inner-transition elements;
  • Understand relative stability of oxidation states in terms of electrode potentials;
  • Describe preparation, properties, structures, and uses of compounds (e.g., K2Cr2O7 and KMnO4);
  • Understand general characteristics and horizontal/group trends;
  • Compare lanthanoids and actinoids on electronic configurations, oxidation states, and chemistry.

Position and Electronic Configurations of the d-Block (Overview)

• The d-block occupies the large central part of the periodic table, flanked by s- and p-blocks. The d orbitals of the penultimate energy level receive electrons to give rise to four series: 3d, 4d, 5d, and 6d.
• General outer-electron configuration (ground state) for many transition elements: $(n-1)d^{1-10} \, ns^{1-2}$
  • Exception for Pd: $4d^{10} \, 5s^{0}$.
• The inner (n–1)d orbitals may have 1–10 electrons; the outermost ns may have 1–2 electrons.
• Notable anomalies and stabilizations:
  • Cr in 3d series: Cr typically adopts 3d^5 4s^1 rather than 3d^4 4s^2 because the energy gap between 3d and 4s is small; half-filled stability (d^5) provides extra stability.
  • Cu in 3d series: Cu adopts 3d^{10} 4s^1 instead of 3d^9 4s^2 for similar stabilization reasons.
• 3d to 6d series show progressive filling of (n–1)d with varying ns occupancy; the presence of partly filled d or f orbitals leads to distinctive chemistry (multiple oxidation states, colored ions, complex formation, catalysis).

Ground-State Outer Configurations: 3d, 4d, 5d Series (Representative Data)

• 1st (3d) series: Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn. Outer configurations (4s and 3d in Table 4.1) show typical progression with occasional exceptions (Cr, Cu).
• 2nd (4d) series: Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd.
• 3rd (5d) series: La, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg.
• 4th (6d) series: Ac, Rf, Db, Sg, Bh, Hs, Mt, Ds, Rg, Cn.
• Note on radii and contractions: as one moves across a series, ionic radii in the dn configurations typically decrease; the lanthanoid contraction (4f electrons) causes 4f shielding to be less effective, leading to similar radii for successive elements in the 2nd and 3rd d-series (e.g., Zr and Hf have very similar radii).

Variation in Atomic and Ionic Sizes: Lanthanoid Contraction

• The lanthanoid contraction arises because 4f electrons shield less effectively than 4f or 3d electrons, so increasing nuclear charge along the lanthanoid series reduces the size of all subsequent atoms and ions.
• Result: Second and third transition series exhibit very similar radii (e.g., Zr ≈ Hf, ~160 pm), facilitating occurrence together in nature and complicating separation.
• Consequences: contraction affects chemistry of successive periods, including bond lengths, densities, and catalytic properties.
• Data snapshot: atomic radii of first 3d elements show a smooth decrease along the series; lanthanoid contraction offsets the expected size increase when comparing 4d and 5d series relative to 3d.
• Densities tend to increase across the 3d to 4d to 5d progression (e.g., Ti to Cu shows marked density increase).

Enthalpies and Sizes: Enthalpy of Atomisation and Ionic Radii Trends

• Enthalpy of atomisation (ΔaHo) trends: transition metals have high ΔaHo; it tends to peak near the middle of each series due to the stability of unpaired d electrons (one unpaired electron per d orbital is particularly favorable for strong interatomic bonding).
• General consequence: higher ΔaHo correlates with stronger interatomic bonding and higher standard electrode potentials for certain oxidation states.
• Ion sizes: for a given series, ions of the same charge show a progressive decrease in radius with increasing atomic number due to less shielding and greater effective nuclear charge; the lanthanoid contraction makes similar radii across the 2nd and 3rd series.

Ionisation Enthalpies and Orbital Stability (First Three Ions)

• Ionisation enthalpies increase along each series from left to right due to increasing nuclear charge.
• Variation in ΔiH1°, ΔiH2°, ΔiH3° in the 3d series is not monotonic because removing electrons occurs first from ns, then from (n–1)d; as d-electrons are added, shielding is uneven, and the energy differences between 4s and 3d are small.
• Notable irregularities: Mn^2+ and Cr^+ display stability patterns tied to half-filled and other stable d configurations (e.g., d^5 stability for Mn^2+; d^4 to d^3 for Cr^2+).
• Reported data (examples from Table 4.2):
  • Sc: ΔiH1° ≈ 631 kJ/mol; ΔiH2° ≈ 1235 kJ/mol; ΔiH3° ≈ 2393 kJ/mol.
  • Ti: ΔiH1° ≈ 656 kJ/mol; ΔiH2° ≈ 1309 kJ/mol; ΔiH3° ≈ 2657 kJ/mol.
  • Cr: ΔiH1° ≈ 653 kJ/mol; ΔiH2° ≈ 1592 kJ/mol; ΔiH3° ≈ 2833 kJ/mol.
  • Mn: ΔiH1° ≈ 717 kJ/mol; ΔiH2° ≈ 1509 kJ/mol; ΔiH3° ≈ 3260 kJ/mol.
  • Fe: ΔiH1° ≈ 762 kJ/mol; ΔiH2° ≈ 1561 kJ/mol; ΔiH3° ≈ 2962 kJ/mol.
  • Co: ΔiH1° ≈ 758 kJ/mol; ΔiH2° ≈ 1644 kJ/mol; ΔiH3° ≈ 3243 kJ/mol.
  • Ni: ΔiH1° ≈ 736 kJ/mol; ΔiH2° ≈ 1752 kJ/mol; ΔiH3° ≈ 3402 kJ/mol.
  • Cu: ΔiH1° ≈ 745 kJ/mol; ΔiH2° ≈ 1958 kJ/mol; ΔiH3° ≈ 3556 kJ/mol.
  • Zn: ΔiH1° ≈ 906 kJ/mol; ΔiH2° ≈ 1734 kJ/mol; ΔiH3° ≈ 3837 kJ/mol.
• Consequences: the second ionisation enthalpy often shows a pronounced rise due to removal of an electron from a more stable configuration; Mn^2+ and Zn^2+ show notable deviations explained by half-filled (d^5) and filled (d^10) configurations, respectively.
• Additional note: the third ionisation enthalpies in many 3d elements are very high, reflecting the difficulty of removing electrons from d orbitals.

Common Oxidation States of the First-Row Transition Elements

• The first-row transition metals display a wide range of oxidation states, typically varying by units of one. Common states (majority highlighted) include:
  • Sc: +2, +3 (predominant +3 in many compounds; Sc^3+ is noble-gas-like)
  • Ti: +2, +3, +4
  • V: +2, +3, +4, +5
  • Cr: +2, +3, +4, +6 (Cr(VI) in chromates; dichromate CrO4^2− and Cr2O7^2− are common higher-oxidation-state species)
  • Mn: +2, +3, +4, +6, +7 (Mn shows the greatest variety; Mn^2+ and Mn^7+ in MnO4^−, MnO4^−)
  • Fe: +2, +3
  • Co: +2, +3
  • Ni: +2, (occasionally +3 in some complexes)
  • Cu: +1, +2 (Cu^2+ is common; Cu^+ is common but often unstable in water as disproportionation occurs)
  • Zn: +2 (no d-electrons in Zn^2+; no higher common oxidation states)
• The prevalence of oxidation states near the middle of the series (e.g., Mn, Fe, Co) is tied to incomplete filling of d orbitals and the stability of certain d^n configurations (e.g., d^5, d^4, d^9, etc.).
• The variability of oxidation states is a hallmark of transition elements, contrasting with main-group elements where oxidation state changes are typically by one unit.
• An interesting anomaly: in groups 4–10, heavier members may stabilize higher oxidation states more than expected (e.g., Cr(VI) in CrO4^2− is strong oxidant; Mo(VI)/W(VI) often more stable than Cr(VI) in certain oxides).

The M2+/M and M3+/M2+ Redox Potentials: Trends and Implications

• Table 4.4 summarizes thermochemical data for transformation of solid M to M^{2+} in solution and standard electrode potentials E°(M^{2+}/M) and E°(M^{3+}/M^{2+}). Representative values (first-row metals Ti–Zn):
  • E°(M^{2+}/M): Ti ≈ -1.63 V, V ≈ -1.18 V, Cr ≈ -0.90 V, Mn ≈ -1.18 V, Fe ≈ -0.44 V, Co ≈ -0.28 V, Ni ≈ -0.25 V, Cu ≈ +0.34 V, Zn ≈ -0.76 V.
  • E°(M^{3+}/M^{2+}) shows more irregular trends due to changes in d-electron configurations and high third ionisation enthalpies for some elements (e.g., Mn^3+/Mn^2+ is relatively strong oxidant). The data help explain why Mn, Ni, Zn have unusually negative M^{2+/M} and why Mn^{3+} is often a strong oxidant in aqueous solution.
• Key implications:
  • Irregular E° values can be traced to the irregular variation of ionisation enthalpies (ΔiH1°, ΔiH2°, ΔiH3°) and to hydration/volatility factors.
  • The highest oxidation state tendency correlates with the ability to stabilize high oxidation numbers in oxides and fluorides, as well as with ligand stabilisation and lattice energy considerations.
• Notable example: Copper has a positive E° for Cu^{2+}/Cu because of its high lattice/hydration energy balance; this makes Cu less likely to liberate H2 from acids.
• The Mn^{2+} (d^5) configuration is particularly stable and influences redox behavior toward Mn^{3+} and Mn^{7+} in aqueous chemistry.

Magnetic Properties of the d-Block Elements

• Magnetic behaviour is largely governed by unpaired electrons (paramagnetism) and, in some cases, ferromagnetism in certain compounds. Diamagnetism occurs in species with all electrons paired; paramagnetism arises from unpaired electrons.
• For the first-row transition metals, orbital angular momentum is largely quenched; the magnetic moment is well described by the spin-only formula:
  $$ \