The d- and f-Block Elements

The d-block lies between the s-block and p-block, spanning groups 3 to 12. It contains four series, each corresponding to the filling of a different set of d orbitals: the 3d series (Sc to Zn, Z = 21-30), the 4d series (Y to Cd, Z = 39-48), the 5d series (La, then Hf to Hg, Z = 57, 72-80), and the largely incomplete 6d series (Ac, then Rf onwards).

The general electronic configuration of d-block atoms is (n-1)d¹⁻¹⁰ns⁰⁻², reflecting the fact that the (n-1)d and ns subshells have very close orbital energies, so electrons occupy both as the series is traversed.

Strictly, a transition element is one whose atom (in the ground state) or one of whose commonly formed ions has an incompletely filled d subshell. By this definition, Zn, Cd and Hg are excluded from the "typical" transition elements: their atoms are (n-1)d¹⁰ns², and in their only common oxidation state (+2) they lose the ns electrons to leave a still-complete (n-1)d¹⁰ ion.

Two configurations break the simple (n-1)d¹⁻⁹ns² pattern: chromium and copper. A half-filled or completely filled d subshell combined with a half-filled s subshell is more stable than the "expected" configuration, because of extra exchange energy when electrons of parallel spin occupy separate orbitals. Hence Cr (Z = 24) is [Ar]3d⁵4s¹ (not 3d⁴4s²), and Cu (Z = 29) is [Ar]3d¹⁰4s¹ (not 3d⁹4s²). The same reasoning extends to Mo, W, Ag, Au and several actinoids.

Worked example - configuration of an ion: Find the ground-state configuration of Fe (Z = 26) and hence of Fe³⁺, and count its unpaired electrons.

1. Fe (Z = 26): [Ar] 3d⁶4s².
2. When a transition metal forms a cation, the ns electrons are always removed before any (n-1)d electrons. Removing both 4s electrons gives Fe²⁺: [Ar]3d⁶.
3. Removing one more electron (from 3d) gives Fe³⁺: [Ar]3d⁵.
4. 3d⁵ is exactly half-filled, so by Hund's rule all five electrons are unpaired: Fe³⁺ has 5 unpaired electrons, which is why it is markedly paramagnetic.

Across any transition series, atomic and ionic radii fall gradually rather than sharply. Increasing nuclear charge pulls the electron cloud inward, but the added electrons enter the inner (n-1)d subshell, which screens the outer ns electrons reasonably well; radii level off towards the middle of a series and creep up slightly near the end where d-d electron repulsion becomes significant. A striking outcome (covered fully in the lanthanoid section) is that corresponding 4d and 5d elements - e.g. Zr and Hf - end up with almost the same radius.

Because unpaired d electrons contribute to metallic bonding in addition to the s electrons, elements near the middle of a series (Cr, Mo, W; Fe) have the greatest number of unpaired electrons and hence the strongest metallic bonding, the highest melting points, and the highest enthalpies of atomisation. Tungsten has the highest melting point of any metal. Elements at the ends of a series (Sc, Zn) have fewer unpaired d electrons and correspondingly lower atomisation enthalpies.

Ionisation enthalpies generally increase across a series but with irregularities, because successive electrons are removed from configurations of differing relative stability. Removing an electron from a stable half-filled (d⁵) or fully filled (d¹⁰) ion is harder than the general trend predicts - this is why the third ionisation enthalpy of manganese (breaking into the stable Mn²⁺, 3d⁵ configuration) is unusually high.

Transition metals show variable oxidation states that typically differ by units of 1 (e.g. Fe²⁺/Fe³⁺, Mn²⁺/Mn³⁺/Mn⁴⁺), unlike main-group elements, whose states usually differ by 2. Both the ns and several (n-1)d electrons lie close enough in energy to take part in bonding. Manganese shows the widest range in the 3d series, from +2 up to +7 (as in MnO₄⁻); the number of accessible states rises from Sc to Mn and falls again towards Zn.

Most transition metal ions are coloured because their partially filled d orbitals allow electrons to be promoted between split d-orbital energy levels by absorbing visible light (a "d-d transition"). Ions with no d electrons (d⁰, e.g. Sc³⁺, Ti⁴⁺) or a completely filled set (d¹⁰, e.g. Zn²⁺, Cu⁺) have no d-d transition available and are colourless.

Because of unpaired d electrons, most transition metal ions are paramagnetic; the number of unpaired electrons can be estimated from the measured magnetic moment.

Worked example: Estimate the spin-only magnetic moment of Mn²⁺.

1. Mn (Z = 25): [Ar]3d⁵4s². Mn²⁺ is formed by removing the two 4s electrons: [Ar]3d⁵.
2. 3d⁵ is exactly half-filled, so all 5 electrons are unpaired: n = 5.
3. μ = √(n(n+2)) BM = √(5 × 7) BM = √35 BM ≈ 5.92 BM, consistent with the strong paramagnetism of Mn²⁺ salts.

Transition metals are also widely used as catalysts (variable oxidation states let them form reactive intermediates), readily form interstitial compounds (small atoms such as H, C or N occupy gaps in the metal lattice, giving hard, high-melting, conducting solids), and form alloys easily with one another because their atomic sizes are similar.

Potassium dichromate (K₂Cr₂O₇) is manufactured from chromite ore (FeCr₂O₄) in three stages. First, the ore is fused with sodium carbonate in free access of air, converting the chromium into water-soluble sodium chromate while iron is oxidised to insoluble Fe₂O₃: 4FeCr₂O₄ + 8Na₂CO₃ + 7O₂ → 8Na₂CrO₄ + 2Fe₂O₃ + 8CO₂.

The filtered yellow sodium chromate solution is acidified, converting chromate (CrO₄²⁻) into the more stable orange dichromate (Cr₂O₇²⁻): 2Na₂CrO₄ + 2H⁺ → Na₂Cr₂O₇ + 2Na⁺ + H₂O. Finally, treating the sodium dichromate solution with potassium chloride precipitates the less soluble potassium dichromate on cooling: Na₂Cr₂O₇ + 2KCl → K₂Cr₂O₇ + 2NaCl. The dichromate ion consists of two CrO₄ tetrahedra (Cr in +6) sharing one corner oxygen.

Chromate and dichromate interconvert reversibly with pH: 2CrO₄²⁻ + 2H⁺ ⇌ Cr₂O₇²⁻ + H₂O. Acid shifts the equilibrium towards orange dichromate; base shifts it back towards yellow chromate.

In acidic solution, dichromate is a powerful oxidant, reduced to green Cr³⁺: Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O (E° = +1.33 V). It oxidises iodide to iodine and Fe²⁺ to Fe³⁺, and is used in volumetric analysis.

Potassium permanganate (KMnO₄) is manufactured from pyrolusite (MnO₂). Fusing MnO₂ with KOH in the presence of an oxidant (air or KNO₃) gives the green manganate ion: 2MnO₂ + 4KOH + O₂ → 2K₂MnO₄ + 2H₂O. The manganate is then oxidised (commercially by electrolytic oxidation at the anode) to deep purple permanganate, MnO₄⁻ (Mn in +7, tetrahedral).

KMnO₄ is an even stronger oxidant than dichromate in acid, reduced all the way to Mn²⁺: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O (E° = +1.51 V). In neutral/faintly alkaline solution the product is brown MnO₂ (Mn reduced only to +4), and in strongly alkaline solution the product is green manganate, MnO₄²⁻ (Mn reduced only to +6) - the depth of reduction, and hence oxidising strength, depends on pH.

Worked example - redox titration: What volume of 0.02 M KMnO₄ is required to completely oxidise the Fe²⁺ in 25.0 mL of 0.1 M FeSO₄ solution in acidic medium?

1. Balanced equation: MnO₄⁻ + 5Fe²⁺ + 8H⁺ → Mn²⁺ + 5Fe³⁺ + 4H₂O, so 1 mol MnO₄⁻ reacts with 5 mol Fe²⁺.
2. Moles of Fe²⁺ = 0.1 mol L⁻¹ × 0.0250 L = 2.5 × 10⁻³ mol.
3. Moles of MnO₄⁻ needed = (2.5 × 10⁻³)/5 = 5.0 × 10⁻⁴ mol.
4. Volume of 0.02 M KMnO₄ = (5.0 × 10⁻⁴ mol)/(0.02 mol L⁻¹) = 0.025 L = 25.0 mL.

The lanthanoids are the 14 elements from cerium (Ce, Z = 58) to lutetium (Lu, Z = 71) that follow lanthanum (La, Z = 57), corresponding to progressive filling of the 4f orbitals. Their general configuration is [Xe]4f¹⁻¹⁴5d⁰⁻¹6s² (La itself, often studied alongside them, is [Xe]4f⁰5d¹6s²).

Because 4f orbitals lie deep inside the atom, shielded by the filled 5s and 5p subshells, they take almost no part in bonding. All lanthanoids are therefore chemically similar, and +3 is overwhelmingly the characteristic oxidation state. A few elements also show +2 or +4 when this produces a specially stable f⁰, f⁷ (half-filled) or f¹⁴ (fully filled) configuration.

Worked example - anomalous oxidation states:

1. Ce (Z = 58): [Xe]4f¹5d¹6s². Losing all four outer electrons gives Ce⁴⁺: [Xe]4f⁰ - an empty f subshell, isoelectronic with the preceding noble gas Xe. This extra stability makes Ce⁴⁺ compounds useful oxidising agents, unusual for a lanthanoid.
2. Eu (Z = 63): [Xe]4f⁷6s². Losing only the two 6s electrons gives Eu²⁺: [Xe]4f⁷ - an exactly half-filled f subshell with maximum exchange stabilisation, so Eu commonly appears as Eu²⁺ alongside the "normal" Eu³⁺.

The defining structural feature of the series is the lanthanoid contraction: atomic and ionic radii decrease steadily from La to Lu. Each additional 4f electron shields the rising nuclear charge poorly, because 4f orbitals are diffuse with a complex radial shape, so the effective nuclear charge felt by outer electrons rises steadily, pulling the electron cloud inward.

This contraction has consequences beyond the lanthanoids themselves: it almost exactly cancels the size increase normally expected on descending a group, so the 4d and 5d transition elements of a given group end up nearly identical in radius (e.g. Zr ≈ Hf, Nb ≈ Ta), making such pairs difficult to separate and chemically very alike. Within the lanthanoids, the steadily shrinking, increasingly charge-dense Ln³⁺ ions become progressively less basic, so the base strength of Ln(OH)₃ falls steadily from La(OH)₃ to Lu(OH)₃.

Most Ln³⁺ ions are coloured, from f-f transitions among partly filled 4f orbitals; ions with f⁰, f⁷ or f¹⁴ configurations (La³⁺, Gd³⁺, Lu³⁺) are essentially colourless. Practically, lanthanoids are used as mischmetal (a lanthanoid-iron alloy used in lighter flints), as catalysts in petroleum cracking, and in glass and ceramic formulations.

The actinoids are the 14 elements from thorium (Th, Z = 90) to lawrencium (Lr, Z = 103) that follow actinium (Ac, Z = 89), corresponding to filling of the 5f orbitals. Their general configuration is [Rn]5f¹⁻¹⁴6d⁰⁻¹7s², but with more frequent irregularities than the lanthanoids because 5f, 6d and 7s orbitals lie unusually close together in energy.

Worked example - configuration irregularities:

1. Th (Z = 90): no 5f electron at all in the ground state - [Rn]6d²7s² (analogous to the La anomaly among lanthanoids).
2. U (Z = 92): [Rn]5f³6d¹7s² - both 5f and 6d orbitals are occupied.
3. Because 5f, 6d and 7s electrons are all comparably easy to remove or share, uranium can adopt oxidation states from +3 up to +6 (the +6 state occurs as the uranyl ion, UO₂²⁺), unlike lanthanoids, which are almost always +3.

Every actinoid is radioactive; only thorium and uranium occur in nature in appreciable quantity, while the rest are obtained in trace amounts or synthesised artificially. This radioactivity, together with the very short half-lives of the heaviest members, makes some of their chemical properties difficult to study experimentally.

Actinoids show a much wider range of oxidation states than lanthanoids, especially among earlier members: +3 is common throughout, but +4 (Th, U, Pu), +5 and +6 (U, Np, Pu, as oxo-cations like UO₂²⁺) and even +7 (Np, Pu under strongly oxidising conditions) are known. This reflects the closely spaced 5f/6d/7s orbital energies, allowing more electrons to be involved in bonding than the deeply buried, largely non-bonding 4f electrons of lanthanoids.

Like lanthanoids, actinoids show a steady contraction in atomic and ionic radii across the series (the "actinoid contraction"), caused by poor shielding of the increasing nuclear charge by 5f electrons. Because 5f orbitals are even more diffuse and penetrate less effectively than 4f orbitals, the actinoid contraction per element is somewhat larger than the lanthanoid contraction. Actinoid ions are also frequently coloured, from 5f-5f (and sometimes 5f-6d) transitions, and actinoids show a greater tendency to form complexes than lanthanoids, since their 5f, 6d and 7s orbitals are all energetically accessible for bonding.

Lanthanoids and actinoids are both "f-block" families and share several resemblances: both show a steady contraction in radius across the series, both are dominated (though to different extents) by the +3 oxidation state, and within each family the elements are chemically very similar to one another. The differences are equally important for understanding their chemistry.

• All actinoids are radioactive; only a few lanthanoids (like promethium) are radioactive, the rest are stable.
• Actinoids show a much wider spread of oxidation states (+3 to +7 for some elements) because 5f, 6d and 7s orbital energies are close together; lanthanoids are overwhelmingly +3, with only occasional +2/+4 exceptions.
• The actinoid contraction (per element) is greater than the lanthanoid contraction, since 5f orbitals shield the nuclear charge even less effectively than 4f orbitals.
• Actinoids have a distinctly greater tendency to form coordination complexes than lanthanoids, because more of their orbitals are available for bonding.

Both the d-block and f-block families underpin many practical applications. Transition metals and their compounds are used extensively as catalysts - iron in the Haber process for ammonia, vanadium(V) oxide in the Contact process for sulfuric acid, and finely divided nickel or platinum/palladium for hydrogenation reactions. Their ability to form alloys readily (owing to similar atomic sizes) gives us steel and stainless steel (Fe with C, Cr, Ni). Transition-metal compounds are also valued for their colour and redox behaviour - titanium dioxide as a white pigment, and manganese dioxide as the oxidant in ordinary dry-cell batteries.

f-block elements have their own distinctive applications: mischmetal (a lanthanoid alloy) in lighter flints, mixed lanthanoid oxides as catalysts and in glass-polishing/decolourising formulations, and - most significantly for actinoids - thorium, uranium and plutonium as nuclear fuels, exploiting the very properties (variable oxidation states, large diffuse f orbitals, radioactivity) that define this family.