Chapters

Everything NCERT Class 12 Unit 4 (The d- and f-Block Elements) says that can be asked, plus what JEE Main adds beyond the book (marked Beyond NCERT). The short note stays for the last week; this is for a proper revision pass.

Formula sheet

The few formulas and the rules that do a formula's job, on one screen. Details and examples are in the sections below.

Quantity	Rule	Watch
Outer configuration	(n−1)d¹⁻¹⁰ ns¹⁻²	Cr 3d⁵4s¹, Cu 3d¹⁰4s¹; Pd 4d¹⁰5s⁰
Ions	remove ns first, then (n−1)d	Fe²⁺ = 3d⁶, not 3d⁴4s²
Spin-only moment	μ = √(n(n+2)) BM	n = unpaired electrons
Highest oxidation state	ns + (n−1)d electrons, up to Mn	Then it drops: Fe(III), Co(III), Ni(II)
Oxidation states	differ by 1 (d-block)	p-block: by 2
Colour	dⁿ with n = 1–9 coloured	d⁰, d¹⁰ colourless (except charge transfer)
Lanthanoid ion	Ln³⁺ = [Xe]4fⁿ, n = 1 → 14	Ce³⁺ 4f¹ … Lu³⁺ 4f¹⁴
Stable f counts	f⁰, f⁷, f¹⁴	Ce⁴⁺, Eu²⁺, Gd³⁺, Tb⁴⁺, Yb²⁺, Lu³⁺
Dichromate in acid	Cr₂O₇²⁻ + 14H⁺ + 6e⁻ → 2Cr³⁺ + 7H₂O	6 e⁻ per dichromate; E° 1.33 V
Permanganate, acid	MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O	5 e⁻; E° 1.52 V
Permanganate, neutral/alkaline	MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻	3 e⁻
Permanganate → manganate	MnO₄⁻ + e⁻ → MnO₄²⁻	1 e⁻; E° 0.56 V
Chromate ⇌ dichromate	2CrO₄²⁻ + 2H⁺ ⇌ Cr₂O₇²⁻ + H₂O	Cr stays +6

Spin-only moments to know by heart:

Unpaired n	μ (BM)
0	0
1	1.73
2	2.83
3	3.87
4	4.90
5	5.92
6	6.93
7	7.94

0 · What JEE Main asks from this chapter

208 questions in JEE Main 2019–2026, 1 to 2 per paper, nearly all one-step recall. Grouped by type (counts are approximate):

Type	Share	Typical question
Configurations, unpaired electrons, spin-only moment	~24%	Sum of moments of the basic and amphoteric chromium oxides
KMnO₄ and K₂Cr₂O₇: preparation, reactions, structure, chromyl chloride	~24%	MnO₄²⁻ disproportionates in acid → which two products
Trends: atomisation, ionisation, E°, radii, density, oxidation-state stability	~22%	Highest third ionisation enthalpy among Cr, Mn, V, Fe
Lanthanoids and actinoids	~19%	Which lanthanoid ion is a strong reducing agent
Colour, catalysts, interstitial compounds, alloys, oxides, uses	~11%	Wacker process catalyst

Most are MCQs or "how many of these" numericals. Make a short table of the ions in the question before you answer.

1 · Position and configuration

• d-block: groups 3–12, the middle of the periodic table; the (n−1)d orbitals fill. f-block: the separate panel at the bottom; 4f and 5f fill. Common names: transition and inner transition metals.
• Four transition series:

Series	Elements
3d	Sc to Zn
4d	Y to Cd
5d	La, Hf to Hg
6d	Ac, Rf to Cn

• Inner transition: 4f (Ce to Lu) = lanthanoids; 5f (Th to Lr) = actinoids.
• IUPAC definition: a transition metal has an incomplete d subshell in the atom or in one of its ions. Zn, Cd, Hg (and Cn) are (n−1)d¹⁰ns² in the atom and in their common ions, so they are not transition metals, though studied with them as the ends of the series.
• Sc (3d¹) is a transition element; Zn (3d¹⁰ in atom and ion) is not (NCERT 4.1). Ag is 4d¹⁰ in the atom, but Ag²⁺ is 4d⁹, so it counts (intext 4.1). Same logic for Cu (Cu²⁺ is 3d⁹).
• The name came from their chemistry being "transitional" between s- and p-block.

3d configurations (atom):

Element (Z)	Configuration
Sc (21)	3d¹4s²
Ti (22)	3d²4s²
V (23)	3d³4s²
Cr (24)	3d⁵4s¹
Mn (25)	3d⁵4s²
Fe (26)	3d⁶4s²
Co (27)	3d⁷4s²
Ni (28)	3d⁸4s²
Cu (29)	3d¹⁰4s¹
Zn (30)	3d¹⁰4s²

Cr and Cu break the pattern because half-filled and filled sets are extra stable and the 3d–4s gap is small.

4d and 5d exceptions worth knowing: Nb 4d⁴5s¹, Mo 4d⁵5s¹, Ru 4d⁷5s¹, Rh 4d⁸5s¹, Pd 4d¹⁰5s⁰, Ag 4d¹⁰5s¹; W 5d⁴6s², Pt 5d⁹6s¹, Au 5d¹⁰6s¹. (2025: Nb has 4 and Ru 7 electrons in 4d → 11. 2022: Pt is [Xe]4f¹⁴5d⁹6s¹.)

• d orbitals reach further to the atom's edge than s and p, so they feel the surroundings most. Ions of the same dⁿ (n = 1–9) have similar magnetic and electronic properties.
• Partly filled d orbitals give the family traits: variable oxidation states, coloured ions, complexes, catalysis, paramagnetism.
• Horizontal similarities are stronger than in the main groups, though group similarities exist too.

2 · Physical properties of the transition metals

• Typical metals: high tensile strength, ductile, malleable, good conductors, lustrous. All but Zn, Cd, Hg and Mn have one or more typical metallic structures at room temperature.
• Except Zn, Cd and Hg: very hard, low volatility, high melting and boiling points, because (n−1)d electrons join the ns electrons in metallic bonding.
• Melting points rise to a maximum near d⁵ in each row, except for the anomalous Mn and Tc, then fall. (2025: Mn < Fe, Tc < Ru, Re < Os.) W has the highest melting point of all.
• Enthalpy of atomisation is high, peaking mid-series: one unpaired electron per d orbital favours strong interatomic bonding; more valence electrons, stronger bonds.

• Zn's is lowest (126 kJ mol⁻¹): no unpaired d electrons for metallic bonding (intext 4.2). Mn dips (d⁵ electrons held back).
• 4d and 5d metals have higher atomisation enthalpies than 3d, so heavy transition metals show far more metal–metal bonding.
• High atomisation enthalpy (high boiling point) makes a metal noble in its reactions.

Atomic and ionic radii.

• Ions of the same charge shrink slowly across a series: each new electron enters a d orbital, which shields poorly, so effective nuclear charge rises. Atomic radii do the same, but the change is small.
• 4d radii are larger than 3d, but 5d ≈ 4d, because of the lanthanoid contraction (§8): 4f fills before 5d and its poor shielding cancels the expected increase. Zr 160 pm, Hf 159 pm; so Zr/Hf, Nb/Ta, Mo/W are near twins in size and chemistry (2019: Mo and W have similar radii; 2020: Ag is closest to Au).
• Density rises across the 3d row (smaller radius, larger mass): Ti 4.1 → Cu 8.9 g cm⁻³.

3 · Ionisation enthalpy

• IE rises across each series as nuclear charge rises, but much less steeply than across a main-group period; successive IEs don't climb as steeply either.
• First IE is irregular but chemically unimportant: removing a 4s electron shifts the 3d–4s energies. Electrons go into 3d, which shields 4s from the rising nuclear charge, so radii fall slowly and IE₁ rises only slightly.
• Ions M²⁺ and higher have no 4s electrons: dⁿ.
• Exchange energy: stabilisation from pairs of parallel spins in degenerate orbitals (Hund's rule). Losing it costs energy, so a half-filled d⁵ resists ionisation; d⁶ has no exchange energy to lose.
  • IE₂ is unusually high for Cr and Cu: Cr⁺ is d⁵, Cu⁺ is d¹⁰.
  • IE₂ of Zn is low: removing the second 4s electron leaves stable d¹⁰.
  • IE₂ of Mn < Cr: Mn⁺ is 3d⁵4s¹, it loses the 4s electron; Cr⁺ is d⁵ (2026).
  • IE₃ is high for Mn (d⁵ → d⁴) and Zn (d¹⁰ → d⁹); Fe's IE₃ is lower than Mn's because Fe²⁺ (d⁶) → Fe³⁺ (d⁵) gains stability. Highest IE₃ among Cr, Mn, V, Fe: Mn (2024).
• IE₃ is high for Cu, Ni and Zn, which is why oxidation states above +2 are hard for them.
• Forming M²⁺ needs atomisation + IE₁ + IE₂; IE₂ dominates.
• 3d metals have higher IE₁ than group 2 metals: the 3d electrons shield poorly (2023).

3d data (NCERT Table 4.2, kJ mol⁻¹):

Metal	IE₁ / IE₂ / IE₃	E°(M²⁺/M), V
Sc	631 / 1235 / 2393	—
Ti	656 / 1309 / 2657	−1.63
V	650 / 1414 / 2833	−1.18
Cr	653 / 1592 / 2990	−0.90
Mn	717 / 1509 / 3260	−1.18
Fe	762 / 1561 / 2962	−0.44
Co	758 / 1644 / 3243	−0.28
Ni	736 / 1752 / 3402	−0.25
Cu	745 / 1958 / 3556	+0.34
Zn	906 / 1734 / 3837	−0.76

4 · Oxidation states

Metal	Oxidation states (common in bold)
Sc	+3
Ti	+2, +3, +4
V	+2, +3, +4, +5
Cr	+2, +3, +4, +5, +6
Mn	+2, +3, +4, +5, +6, +7
Fe	+2, +3, +4, +6
Co	+2, +3, +4
Ni	+2, +3, +4
Cu	+1, +2
Zn	+2

• Most states mid-series; Mn shows every state from +2 to +7. Fewer at the ends: Sc and Ti have too few electrons to lose; Cu and Zn have too many d electrons (fewer free orbitals to share).
• Sc(II) is virtually unknown; Sc shows only +3 (no variable states; NCERT 4.3). Ti(IV) is more stable than Ti(III) or Ti(II). Zn is only +2 (no d electrons used).
• Up to Mn, the highest stable state = s + d electrons: Ti(IV)O₂, V(V)O₂⁺, Cr(VI)O₄²⁻, Mn(VII)O₄⁻. Then stability of high states falls abruptly: Fe(II, III), Co(II, III), Ni(II), Cu(I, II), Zn(II).
• d-block states differ by one; p-block states by two.
• Down a d-block group, higher states get more stable (the reverse of the p-block's inert pair effect): Mo(VI) and W(VI) are more stable than Cr(VI). So acidic dichromate is a strong oxidant, while MoO₃ and WO₃ are not.
• Low (even zero) states appear with π-acceptor ligands: Ni(CO)₄ and Fe(CO)₅ have the metal at 0.
• RuO₄ and OsO₄ have Ru and Os at +8 (2023) · Beyond NCERT.

Disproportionation: one oxidation state turns into a higher and a lower one. Mn(VI) in acid: 3MnO₄²⁻ + 4H⁺ → 2MnO₄⁻ + MnO₂ + 2H₂O (NCERT 4.9). Cu(I) in water: 2Cu⁺ → Cu²⁺ + Cu.

5 · Electrode potentials and stability

E°(M²⁺/M) (table above):

• Cu alone is positive (+0.34 V): its high atomisation enthalpy plus IE₁ + IE₂ isn't repaid by its hydration enthalpy. So Cu can't liberate H₂ from acids; only oxidising acids (HNO₃, hot concentrated H₂SO₄) react, and they are reduced.
• The general drift to less negative E° across the row follows the rising IE₁ + IE₂.
• Mn, Ni and Zn are more negative than the trend: Mn²⁺ is d⁵ and Zn²⁺ is d¹⁰ (stable), and Ni²⁺ has the most negative hydration enthalpy.
• The irregular values come from irregular IE₁ + IE₂ and the low sublimation enthalpies of Mn and V (NCERT 4.6).
• Except Cu, the 3d metals are oxidised by 1 M H⁺, though Ti and V are passive to dilute non-oxidising acids at room temperature.

E°(M³⁺/M²⁺), V: Ti −0.37, V −0.26, Cr −0.41, Mn +1.57, Fe +0.77, Co +1.97.

• Mn³⁺ and Co³⁺ are the strongest oxidising agents in water (2022).
• Ti²⁺, V²⁺ and Cr²⁺ are strong reducing agents and liberate H₂ from dilute acid: 2Cr²⁺ + 2H⁺ → 2Cr³⁺ + H₂ (2024: all three).
• Mn³⁺/Mn²⁺ is much more positive than Cr³⁺/Cr²⁺ or Fe³⁺/Fe²⁺ because Mn's IE₃ (d⁵ → d⁴) is very large; so Mn(III) matters little (NCERT 4.7).
• Fe³⁺/Fe²⁺ is comparatively low: Fe³⁺ is d⁵, extra stable. V's is low: V²⁺ has a half-filled t₂g set. Sc³⁺ has a noble gas configuration.
• Cr²⁺ reducing, Mn³⁺ oxidising, both d⁴ (NCERT 4.4): Cr²⁺ → Cr³⁺ gives d³ (half-filled t₂g); Mn³⁺ → Mn²⁺ gives d⁵.
• Cr²⁺ is a stronger reducing agent than Fe²⁺ (E° −0.41 vs +0.77).
• Mn²⁺ compounds resist oxidation to +3 more than Fe²⁺: Mn²⁺ is already d⁵.
• Cu²⁺(aq) is more stable than Cu⁺(aq): Cu²⁺'s much more negative hydration enthalpy more than repays Cu's IE₂.

Highest states in halides and oxides (NCERT Tables 4.5, 4.6):

• Fluorides: TiX₄, VF₅, CrF₆ are the highest. Mn(VII) has no simple halide, only MnO₃F; the highest manganese fluoride is MnF₄. Beyond Mn the only trihalides are FeX₃ (X = F, Cl, Br) and CoF₃. F stabilises high states by high lattice energy (CoF₃) or strong bonds (VF₅, CrF₆).
• V(V) appears only in VF₅; the other halides hydrolyse to oxohalides VOX₃. Low-state fluorides are unstable: VX₂ exists for Cl, Br, I; likewise CuX.
• All Cu(II) halides exist except CuI₂: 2Cu²⁺ + 4I⁻ → Cu₂I₂(s) + I₂. (Only iodide does this; 2023.) FeX₂ exists for X = F, Cl, Br, I; FeX₃ only for F, Cl, Br (2021).
• Oxides: the highest oxidation number equals the group number from Sc₂O₃ to Mn₂O₇. Nothing above Fe₂O₃ for iron, though ferrate(VI), FeO₄²⁻, forms in alkali and soon decomposes to Fe₂O₃ and O₂.
• Oxygen stabilises high states better than fluorine because it forms multiple bonds: highest Mn fluoride MnF₄, highest oxide Mn₂O₇. Oxocations stabilise V(V) as VO₂⁺, V(IV) as VO²⁺, Ti(IV) as TiO²⁺.
• In covalent Mn₂O₇, each Mn is tetrahedral and there is one Mn–O–Mn bridge (so 6 Mn=O bonds; 2022). Tetrahedral [MO₄]ⁿ⁻ ions are known for V(V), Cr(VI), Mn(V), Mn(VI), Mn(VII).
• Mixed oxides: Mn₃O₄, Fe₃O₄, Co₃O₄ (2026: count 3).
• Oxidising power rises VO₂⁺ < Cr₂O₇²⁻ < MnO₄⁻: the lower species they become are increasingly stable (NCERT 4.5).

6 · Magnetic properties, colour, complexes, catalysis

Magnetism. Diamagnetic substances are repelled by a field; paramagnetic ones are attracted; ferromagnetic ones very strongly (an extreme form of paramagnetism). Paramagnetism comes from unpaired electrons (spin and orbital moments). For the 3d series the orbital part is quenched, so the spin-only formula works:

Ion	Configuration	Unpaired · μ calc · μ obs (BM)
Sc³⁺	3d⁰	0 · 0 · 0
Ti³⁺	3d¹	1 · 1.73 · 1.75
Ti²⁺	3d²	2 · 2.84 · 2.76
V²⁺	3d³	3 · 3.87 · 3.86
Cr²⁺	3d⁴	4 · 4.90 · 4.80
Mn²⁺	3d⁵	5 · 5.92 · 5.96
Fe²⁺	3d⁶	4 · 4.90 · 5.3–5.5
Co²⁺	3d⁷	3 · 3.87 · 4.4–5.2
Ni²⁺	3d⁸	2 · 2.84 · 2.9–3.4
Cu²⁺	3d⁹	1 · 1.73 · 1.8–2.2
Zn²⁺	3d¹⁰	0 · 0 · 0

Example (NCERT 4.8) · Divalent ion of Z = 25: Mn²⁺, d⁵, μ = √35 = 5.92 BM.

Example (2024) · Sum of moments of the basic and the amphoteric oxide among CrO, Cr₂O₃, CrO₃: CrO (Cr²⁺, d⁴) 4.90 + Cr₂O₃ (Cr³⁺, d³) 3.87 = 8.77 BM.

Example (2021) · Atomic Fe (3d⁶4s²): 4 unpaired → 4.90 BM. Np (Z = 93, [Rn]5f⁴6d¹7s²): 18 f electrons counting the 4f¹⁴.

For these questions, the ion often isn't named: identify it first ("the oxidant among Co³⁺, Ti²⁺, V²⁺, Cr²⁺" is Co³⁺, d⁶ free ion, 4.90 BM).

Coloured ions. An electron jumps from a lower to a higher d orbital (d–d transition), absorbing visible light; we see the complementary colour. The frequency depends on the ligand; in water the ligand is H₂O.

dⁿ	Ion: colour
d⁰	Sc³⁺, Ti⁴⁺: colourless
d¹	Ti³⁺: purple; V⁴⁺: blue
d²	V³⁺: green
d³	V²⁺: violet; Cr³⁺: violet
d⁴	Mn³⁺: violet; Cr²⁺: blue
d⁵	Mn²⁺: pink; Fe³⁺: yellow
d⁶	Fe²⁺: green; Co³⁺: blue
d⁷	Co²⁺: pink
d⁸	Ni²⁺: green
d⁹	Cu²⁺: blue
d¹⁰	Zn²⁺: colourless

• 2025: the same colour (violet) for V²⁺, Cr³⁺, Mn³⁺. 2021: the colours in 5Fe²⁺ + MnO₄⁻ + 8H⁺ → … are green Fe²⁺ to yellow Fe³⁺.
• Colourless: d⁰ (Sc³⁺, Ti⁴⁺) and d¹⁰ (Zn²⁺, Cu⁺, Cd²⁺, Hg²⁺). Cu(I) compounds are generally colourless (CuCl dissolves colourless; CuCl₂ gives colour).
• Charge transfer · Beyond NCERT: MnO₄⁻ (Mn⁷⁺, d⁰) and Cr₂O₇²⁻ (Cr⁶⁺, d⁰) are intensely coloured by ligand-to-metal charge transfer, not d–d (2024).
• The red of ruby is Cr³⁺ (in Al₂O₃), not Co³⁺ (2021) · Beyond NCERT.

Complexes. Transition metals form many: small ions, high charge, d orbitals available for bonding. [Fe(CN)₆]³⁻, [Fe(CN)₆]⁴⁻, [Cu(NH₃)₄]²⁺, [PtCl₄]²⁻. Details in Coordination Compounds.

Catalysts. Two reasons: multiple oxidation states and complex formation.

• On a solid surface, reactants bond to surface atoms (3d metals use 3d and 4s electrons): local concentration rises and the reactants' bonds weaken, lowering Ea (2026: "3d only" was false).
• Changing oxidation state: Fe(III) catalyses 2I⁻ + S₂O₈²⁻ → I₂ + 2SO₄²⁻ by 2Fe³⁺ + 2I⁻ → 2Fe²⁺ + I₂, then 2Fe²⁺ + S₂O₈²⁻ → 2Fe³⁺ + 2SO₄²⁻. Fe³⁺ oxidises iodide; Fe²⁺ reduces persulphate (2024).

Process	Catalyst
Contact process (SO₂ → SO₃, H₂SO₄)	V₂O₅
Haber process (NH₃)	finely divided Fe
Hydrogenation of oils and fats	Ni
Ziegler catalyst (polythene)	TiCl₄ + Al(CH₃)₃
Wacker process (ethyne/ethene → ethanal)	PdCl₂ (not PtCl₂; 2024)
Polymerising alkynes, benzene	Ni complexes

Interstitial compounds: small atoms (H, C, N) trapped in the metal lattice. TiC, Mn₄N, Fe₃H, VH₀.₅₆, TiH₁.₇: usually non-stoichiometric, neither ionic nor covalent. Properties: (i) melting points higher than the pure metal, (ii) very hard (some borides near diamond), (iii) keep metallic conductivity, (iv) chemically inert. (2019 and 2026: "chemically reactive" or "soft and ionic" are the false options.)

Alloys: blends of metals; homogeneous solid solutions form when metallic radii are within about 15%. Transition metals alloy readily; the alloys are hard and high-melting. Steels and stainless steel use Cr, V, W, Mo, Mn. With non-transition metals: brass (Cu–Zn), bronze (Cu–Sn).

7 · Important compounds

Oxides. Made by heating the metal with oxygen. All except Sc form ionic MO.

• As the oxidation number rises, ionic character falls and acidic character rises. Mn₂O₇ is a covalent green oil (2024); CrO₃ and V₂O₅ have low melting points.
• Mn₂O₇ gives HMnO₄; CrO₃ gives H₂CrO₄ and H₂Cr₂O₇.
• V₂O₅ is amphoteric, mainly acidic: with alkali it gives VO₄³⁻ (V +5), with acid VO₂⁺. Basicity: V₂O₃ > V₂O₄ > V₂O₅ (2023). V₂O₄ dissolves in acid to VO²⁺ salts.
• CrO is basic; Cr₂O₃ is amphoteric; CrO₃ acidic.

Potassium dichromate, K₂Cr₂O₇ (used in leather industry, and as an oxidant for azo compounds).

1. Fuse chromite ore with Na₂CO₃ (or K₂CO₃) in air: 4FeCr₂O₄ + 8Na₂CO₃ + 7O₂ → 8Na₂CrO₄ + 2Fe₂O₃ + 8CO₂. Yellow chromate dissolves; Fe₂O₃ (160 g mol⁻¹) is the water-insoluble product (2025).
2. Filter, acidify with H₂SO₄: 2Na₂CrO₄ + 2H⁺ → Na₂Cr₂O₇ + 2Na⁺ + H₂O; orange Na₂Cr₂O₇·2H₂O crystallises.
3. Na₂Cr₂O₇ is more soluble, so add KCl: Na₂Cr₂O₇ + 2KCl → K₂Cr₂O₇ + 2NaCl; orange K₂Cr₂O₇ crystallises.

Chromate ⇌ dichromate by pH; Cr is +6 in both (difference 0; 2022):

Acid → orange dichromate; base → yellow chromate.

Chromate is tetrahedral (4 Cr–O); dichromate is two tetrahedra sharing a corner, Cr–O–Cr 126°, non-linear and symmetrical (2021), with 6 terminal O and 8 Cr–O bonds. 4 + 8 = 12 Cr–O bonds in the two ions together (2020).

• Both dichromates are strong oxidants. Na₂Cr₂O₇ (more soluble) is used in organic chemistry; K₂Cr₂O₇ is a primary standard in volumetric analysis (not the sodium salt; 2023, 2026).
• Acidic dichromate (+6 → +3) oxidises:

Reductant	Half-reaction
iodide	6I⁻ → 3I₂ + 6e⁻
tin(II)	3Sn²⁺ → 3Sn⁴⁺ + 6e⁻
H₂S	3H₂S → 6H⁺ + 3S + 6e⁻
iron(II)	6Fe²⁺ → 6Fe³⁺ + 6e⁻

Full equation by adding: Cr₂O₇²⁻ + 14H⁺ + 6Fe²⁺ → 2Cr³⁺ + 6Fe³⁺ + 7H₂O. Orange turns green (Cr³⁺); a paper soaked in acidified K₂Cr₂O₇ turns green with SO₂ (2026).

Chromyl chloride test · Beyond NCERT (the test for Cl⁻, asked almost every year):

• Chloride + K₂Cr₂O₇ + concentrated H₂SO₄ → CrO₂Cl₂, orange-red vapour (Cr +6).
• CrO₂Cl₂ + 4NaOH → Na₂CrO₄ (yellow) + 2NaCl + 2H₂O.
• Acidify, add amyl alcohol and H₂O₂ → CrO₅, blue in the organic layer. Cr is +6: one Cr=O and two peroxide groups ("butterfly").

Potassium permanganate, KMnO₄.

1. Fuse MnO₂ (pyrolusite) with KOH and an oxidant (air or KNO₃): 2MnO₂ + 4KOH + O₂ → 2K₂MnO₄ + 2H₂O. Dark green manganate, Mn +6.
2. Manganate disproportionates in neutral or acidic solution: 3MnO₄²⁻ + 4H⁺ → 2MnO₄⁻ + MnO₂ + 2H₂O.
3. Commercially: alkaline oxidative fusion, then electrolytic oxidation of manganate in alkaline solution → permanganate.
4. In the lab: Mn²⁺ oxidised by peroxodisulphate: 2Mn²⁺ + 5S₂O₈²⁻ + 8H₂O → 2MnO₄⁻ + 10SO₄²⁻ + 16H⁺.

• Dark purple (almost black) crystals, isostructural with KClO₄; not very soluble (6.4 g per 100 g water at 293 K).
• On heating at 513 K: 2KMnO₄ → K₂MnO₄ + MnO₂ + O₂ (2024; the K₂MnO₄ is green and paramagnetic).
• Intense colour and diamagnetism with weak temperature-dependent paramagnetism (explained by MO theory).
• Manganate and permanganate are both tetrahedral; π bonds form by p(O)–d(Mn) overlap. Manganate (d¹) is green and paramagnetic; permanganate (d⁰) is purple and diamagnetic.

Which product, by medium:

Medium	Mn goes to	Electrons per MnO₄⁻
Acidic	Mn²⁺ (+7 → +2)	5
Neutral or faintly alkaline	MnO₂ (+7 → +4)	3
Strongly alkaline · Beyond NCERT	MnO₄²⁻ (+7 → +6)	1

E° MnO₄⁻/MnO₄²⁻ 0.56 V; MnO₄⁻/MnO₂ 1.69 V; MnO₄⁻/Mn²⁺ 1.52 V, so [H⁺] decides the outcome. By E°, permanganate should oxidise water at [H⁺] = 1, but the reaction is very slow unless Mn²⁺ is present or it is heated.

In acid (Mn²⁺):

• 10I⁻ + 2MnO₄⁻ + 16H⁺ → 2Mn²⁺ + 8H₂O + 5I₂
• 5Fe²⁺ + MnO₄⁻ + 8H⁺ → Mn²⁺ + 4H₂O + 5Fe³⁺ (green → yellow)
• 5C₂O₄²⁻ + 2MnO₄⁻ + 16H⁺ → 2Mn²⁺ + 8H₂O + 10CO₂, at 333 K
• 5S²⁻ + 2MnO₄⁻ + 16H⁺ → 2Mn²⁺ + 8H₂O + 5S
• 5SO₃²⁻ + 2MnO₄⁻ + 6H⁺ → 2Mn²⁺ + 3H₂O + 5SO₄²⁻
• 5NO₂⁻ + 2MnO₄⁻ + 6H⁺ → 2Mn²⁺ + 5NO₃⁻ + 3H₂O
• With H₂O₂ · Beyond NCERT: Mn²⁺, H₂O and O₂ (2022). In basic medium H₂O₂ gives MnO₂, Mn +4.

In neutral or faintly alkaline solution (MnO₂):

• Iodide to iodate: 2MnO₄⁻ + H₂O + I⁻ → 2MnO₂ + 2OH⁻ + IO₃⁻ (acid gives I₂ instead; 2023).
• Thiosulphate almost quantitatively to sulphate: 8MnO₄⁻ + 3S₂O₃²⁻ + H₂O → 8MnO₂ + 6SO₄²⁻ + 2OH⁻ (S +6; Mn changes by 3).
• Mn²⁺ to MnO₂, catalysed by ZnSO₄ or ZnO: 2MnO₄⁻ + 3Mn²⁺ + 2H₂O → 5MnO₂ + 4H⁺.

Permanganate titrations in HCl are unsatisfactory: HCl is oxidised to Cl₂. Use H₂SO₄.

Uses: analytical chemistry; a favourite oxidant in organic synthesis; bleaching wool, cotton, silk and textile fibres; decolourising oils.

Both oxidise in acid · Beyond NCERT (2025): I⁻ → I₂, S²⁻ → S, Fe²⁺ → Fe³⁺. Only alkaline KMnO₄ gives IO₃⁻ or SO₄²⁻ from thiosulphate.

8 · The lanthanoids

The 14 elements after La (Ce to Lu); La is discussed with them (symbol Ln). They resemble one another more than any transition row does, and have essentially one stable oxidation state, +3.

Configurations: 6s² common, with variable 4f occupancy; every Ln³⁺ is [Xe]4fⁿ, n = 1 to 14.

Element (Z)	Atom	Ln³⁺
La (57)	5d¹6s²	4f⁰
Ce (58)	4f¹5d¹6s²	4f¹ (Ce⁴⁺ 4f⁰)
Pr (59)	4f³6s²	4f²
Nd (60)	4f⁴6s²	4f³ (Nd²⁺ 4f⁴)
Pm (61)	4f⁵6s²	4f⁴
Sm (62)	4f⁶6s²	4f⁵ (Sm²⁺ 4f⁶)
Eu (63)	4f⁷6s²	4f⁶ (Eu²⁺ 4f⁷)
Gd (64)	4f⁷5d¹6s²	4f⁷
Tb (65)	4f⁹6s²	4f⁸ (Tb⁴⁺ 4f⁷)
Dy (66)	4f¹⁰6s²	4f⁹
Ho (67)	4f¹¹6s²	4f¹⁰
Er (68)	4f¹²6s²	4f¹¹
Tm (69)	4f¹³6s²	4f¹² (Tm²⁺ 4f¹³)
Yb (70)	4f¹⁴6s²	4f¹³ (Yb²⁺ 4f¹⁴)
Lu (71)	4f¹⁴5d¹6s²	4f¹⁴

Gd keeps 4f⁷ and puts the extra electron in 5d; Lu has a full 4f¹⁴ and a 5d¹.

Lanthanoid contraction: atomic and ionic radii fall overall from La to Lu. Regular for M³⁺ (La³⁺ 106 pm → Yb³⁺ 86 pm), less regular for atoms (Eu 199 pm is unusually large). Cause: the imperfect shielding of one 4f electron by another, even weaker than d by d, so each added proton pulls the whole 4f shell in.

• Consequence: 5d radii ≈ 4d radii. Zr (160 pm) and Hf (159 pm) occur together in nature and are hard to separate.
• Bk³⁺ < Np³⁺ is actinoid contraction, not lanthanoid (2021).
• The basicity of Ln(OH)₃ falls from La to Lu as the ions shrink · Beyond NCERT.

Oxidation states: +3 (La(III) and Ln(III)) dominates; +2 and +4 occasionally, from the stability of empty, half-filled and filled f.

Ion	Why it forms	Behaviour
Ce⁴⁺	noble gas (4f⁰)	strong oxidant, E° +1.74 V; would oxidise water but slowly, so a good analytical reagent
Pr, Nd, Tb, Dy (+4)	—	only in oxides MO₂ (Yb forms no MO₂; 2021)
Tb⁴⁺	4f⁷	oxidant
Eu²⁺	loses only the 6s², leaving 4f⁷	strong reductant → +3 (aqueous EuSO₄; 2021)
Yb²⁺	4f¹⁴	reductant; diamagnetic
Sm²⁺	—	like Eu, +2 and +3

Eu²⁺ is the most stable divalent lanthanoid (2022) yet still a reductant.

General characteristics:

• Silvery white, soft metals that tarnish in air; hardness rises with Z (Sm is steel-hard). Melting points 1000–1200 K, but Sm 1623 K. Good conductors. Density and other properties change smoothly, except at Eu and Yb (sometimes Sm and Tm).
• Colour: many Ln³⁺ are coloured in solid and solution, from f electrons; the absorption bands are narrow (f–f transitions). La³⁺ and Lu³⁺ are colourless (2024: 2 colourless among Eu³⁺, Lu³⁺, Nd³⁺, La³⁺, Sm³⁺).
• Magnetism: all paramagnetic except f⁰ (La³⁺, Ce⁴⁺) and f¹⁴ (Yb²⁺, Lu³⁺). Gd³⁺ (4f⁷): 7 unpaired, 7.94 BM.
• Ionisation: IE₁ ~600, IE₂ ~1200 kJ mol⁻¹, like calcium. IE₃ is abnormally low for La, Gd and Lu (giving f⁰, f⁷, f¹⁴) and high for Eu and Yb (2023).
• Reactivity: early members are like calcium; later ones more like aluminium. E°(Ln³⁺/Ln) −2.2 to −2.4 V (Eu −2.0 V).

Reactions of the metals:

Reagent	Product
H₂ (gentle heat)	hydrides
C (2773 K)	carbides Ln₃C, Ln₂C₃, LnC₂
dilute acids	H₂
water	Ln(OH)₃ + H₂
halogens	LnX₃
O₂ (burn)	Ln₂O₃
N₂ (heat)	LnN
S (heat)	Ln₂S₃

Oxides M₂O₃ and hydroxides M(OH)₃; the hydroxides are definite compounds (not hydrated oxides) and basic, like alkaline earth hydroxides.

Uses: alloy steels for plates and pipes. Mischmetall = a lanthanoid metal ~95% + iron ~5% + traces of S, C, Ca, Al; in Mg-based alloys for bullets, shells and lighter flints. Mixed oxides catalyse petroleum cracking; some Ln oxides are phosphors in TV screens.

9 · The actinoids

Th to Lr (with Ac). All radioactive; early members have long half-lives, the last ones very short (Lr 3 minutes), and late members are made only in nanogram amounts. Hence hard to study.

• Configuration: 7s² with variable 5f and 6d. Th is 6d²7s² (no 5f); from Pa the 5f fills, complete at Lr (103). Irregularities from f⁰, f⁷, f¹⁴: Am [Rn]5f⁷7s², Cm [Rn]5f⁷6d¹7s² (both 7 unpaired; 2026). U [Rn]5f³6d¹7s²; Pu 5f⁶7s²; Es 5f¹¹7s² (2024).
• 5f orbitals have the same angular shape as 4f but are less buried, so 5f electrons take part in bonding far more (2023).
• Actinoid contraction: M³⁺ shrinks across the series, and more from one element to the next than in the lanthanoids: 5f shields even more poorly (intext 4.10).
• Oxidation states: a wider range, because 5f, 6d and 7s are close in energy. +3 is general. Early members go higher: maximum +4 (Th), +5 (Pa), +6 (U), +7 (Np, and Pu), then falling. Np and Pu show the most states (2019). Like lanthanoids, more +3 than +4 compounds; +3 and +4 ions hydrolyse.
• All silvery, with varied structures (metallic radii far more irregular than in lanthanoids).
• Highly reactive, especially finely divided: boiling water gives oxide + hydride; they combine with most non-metals at moderate temperatures. HCl attacks all; HNO₃ barely (protective oxide layer); alkalis have no action.
• Magnetic behaviour more complex than lanthanoids; susceptibility roughly parallels unpaired 5f electrons but is lower than for lanthanoids.
• Early actinoid IEs are lower than early lanthanoids': 5f penetrates less and is better shielded, so outer electrons are freer to bond.
• Lanthanoid-like behaviour shows only in the second half of the series. The lanthanoid contraction matters more, since elements after the actinoids are little known.

	Lanthanoids	Actinoids
Orbitals filled	4f	5f
Oxidation states	mainly +3; few +2, +4	+3 to +7; wider range
Radioactivity	only Pm	all
Contraction per element	smaller	larger
f electrons in bonding	buried, little	far more
Complexes, ionisation	fewer complexes; higher early IEs	more complexes; lower early IEs

10 · Applications

• Iron and steel: reduce iron oxides, remove impurities, add C and alloying metals (Cr, Mn, Ni).
• TiO for pigments; MnO₂ in dry cells; Zn and Ni/Cd in batteries (2024: battery metals Mn, Ni, Cd).
• Group 11 are coinage metals: UK "copper" coins are copper-coated steel, "silver" coins Cu/Ni.
• Catalysts: as listed in §6. AgBr is light-sensitive (photography).

11 · Traps

Trap	What goes wrong	Do this
Ion configurations	Removing 3d before 4s	Fe²⁺ = 3d⁶; Cr³⁺ = 3d³; Cu⁺ = 3d¹⁰
Transition element test	Calling Zn, Cd, Hg transition	Need a partly filled d in atom or ion; Cu and Ag qualify
Fe²⁺ vs Fe³⁺	Giving both 5.92 BM	Fe²⁺ d⁶: 4 unpaired, 4.90; Fe³⁺ d⁵: 5.92
Colour of MnO₄⁻, Cr₂O₇²⁻	Calling it d–d	d⁰: charge transfer
KMnO₄ medium	Writing Mn²⁺ in neutral solution	Acid Mn²⁺ (5e⁻); neutral/alkaline MnO₂ (3e⁻)
Iodide with KMnO₄	I₂ in every medium	Acid I₂; neutral/alkaline IO₃⁻
Group trend of states	Applying the inert pair effect	d-block: heavier = higher states more stable (W(VI) > Cr(VI))
Cr in chromate vs dichromate	Expecting a change	+6 in both; only the pH changes
Highest Mn compounds	Assuming MnF₇	Oxide Mn₂O₇ (+7), fluoride MnF₄ (+4)
Ce⁴⁺ and Eu²⁺	Swapping roles	Ce⁴⁺ oxidant (→ +3), Eu²⁺ reductant (→ +3)
Lanthanoid contraction	Using it for actinoid sizes	Actinoid contraction; and it's larger
Interstitial compounds	Calling them reactive or ionic	Hard, high-melting, conducting, inert
Primary standard	Choosing Na₂Cr₂O₇	K₂Cr₂O₇ (Na salt is hygroscopic and more soluble)
HCl in titrations	Acidifying KMnO₄ with HCl	Use H₂SO₄; HCl is oxidised to Cl₂

12 · Numbers worth knowing

• ΔaH° (kJ mol⁻¹): V 515 highest of 3d, Zn 126 lowest, Mn 281.
• Highest IE₂: Cu (1958), Cr (1592) high; highest IE₃ of Sc–Fe: Mn (3260).
• E°(M²⁺/M): Cu +0.34 (only positive); Zn −0.76; Mn −1.18; Ti −1.63.
• E°(M³⁺/M²⁺): Co +1.97, Mn +1.57, Fe +0.77, Cr −0.41.
• E°: Cr₂O₇²⁻/Cr³⁺ 1.33; MnO₄⁻/Mn²⁺ 1.52; Ce⁴⁺/Ce³⁺ 1.74 V.
• Radii: Zr 160, Hf 159 pm. Cr–O–Cr 126°. KMnO₄ decomposes at 513 K; oxalate titration at 333 K.
• Molar masses: K₂Cr₂O₇ 294, KMnO₄ 158, Fe₂O₃ 160, FeCr₂O₄ 224.
• Mischmetall ~95% lanthanoid, ~5% Fe. Alloys form within ~15% radius difference.

13 · For the boards only

JEE Main doesn't ask this, but the CBSE paper can.

• Fe, Cu, Ag and Au shaped human civilisation; Th, Pa and U are now sources of nuclear energy.
• Ag, Au and Pt are precious metals; Fe, Cu and Ti are industrially important.
• The lattice structures of the transition metals (bcc, hcp, ccp) in NCERT's table.
• The NCERT figures of melting points, atomisation enthalpies and radii across the three series.