Chapters

Everything NCERT Class 12 Unit 5 (Coordination Compounds) 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

Every formula and counting rule in the chapter on one screen, for the last pass. Details and examples are in the sections below.

Quantity	Formula	Watch
Oxidation number of M	charge of entity − Σ ligand charges	NO⁺ in brown ring; CO, NH₃, en neutral
Coordination number	number of donor atoms bonded (σ only)	en, ox count 2; EDTA 6
AgCl from a chloride complex	moles AgCl = Cl⁻ outside the bracket	Inside Cl doesn't precipitate
van 't Hoff factor	i = ions per formula unit	[Co(NH₃)₅Cl]Cl₂ → 3
Spin-only moment	μ = √(n(n+2)) BM	n from the d count in that field
Octahedral split	eg +0.6Δo; t₂g −0.4Δo	Barycentre conserved
Tetrahedral split	t₂ +0.4Δt; e −0.6Δt; Δt = (4/9)Δo	Almost always high spin
CFSE, octahedral · Beyond NCERT	(−0.4 n(t₂g) + 0.6 n(eg))Δo (+ pairing P)	Count electrons, not orbitals
CFSE, tetrahedral · Beyond NCERT	(−0.6 n(e) + 0.4 n(t₂))Δt
Absorbed light	Δ = hc/λ (per ion) = Nₐ hc/λ (per mol)	Colour seen = complementary
Stability · Beyond NCERT	β₄ = K₁K₂K₃K₄; dissociation constant = 1/β	log β adds
EAN · Beyond NCERT	Z − oxidation state + 2 × CN	36 for Ni(CO)₄, Fe(CO)₅, Cr(CO)₆

High spin vs low spin (octahedral):

dⁿ	Weak field (Δo < P)	Strong field (Δo > P)
d⁴	t₂g³eg¹, 4 unpaired	t₂g⁴, 2 unpaired
d⁵	t₂g³eg², 5 unpaired	t₂g⁵, 1 unpaired
d⁶	t₂g⁴eg², 4 unpaired	t₂g⁶, 0 unpaired
d⁷	t₂g⁵eg², 3 unpaired	t₂g⁶eg¹, 1 unpaired

d¹–d³ and d⁸–d¹⁰ have one arrangement whatever the ligand.

0 · What JEE Main asks from this chapter

290 questions in JEE Main 2019–2026, the most of any inorganic chapter: about 2 per paper. Grouped by type (counts are approximate):

Type	Share	Typical question
Magnetic moment, VBT hybridisation, inner/outer orbital	~26%	Hybridisation and magnetism of [Mn(CN)₆]⁴⁻ and [Fe(CN)₆]³⁻
CFT: Δ, spectrochemical series, CFSE, colour, t₂g/eg count	~26%	Order of wavelength absorbed by Co(III) ammine complexes
Isomerism: counting, geometrical, optical, fac/mer, structural	~17%	Stereoisomers of [Co(ox)₂Br(NH₃)]²⁻
Werner, AgCl precipitation, conductance, CN, oxidation number, denticity	~14%	CoCl₃·xNH₃ gives 2 AgCl → x
Applications, biological, tests (DMG, Prussian blue, brown ring)	~9%	Compound used for lead poisoning
Metal carbonyls	~4%	Bridging CO and Co–Co bonds in Co₂(CO)₈
Nomenclature	~4%	IUPAC name of K₃[Co(C₂O₄)₃]

Many are "how many of these" counts. List the complexes, write each one's dⁿ and field strength, then count.

1 · Werner's theory

Alfred Werner (Swiss) studied cobalt(III) chloride–ammonia compounds. With excess AgNO₃ in the cold, some chloride precipitates as AgCl and some doesn't:

Compound (colour)	AgCl per mol	Werner's formula (electrolyte)
CoCl₃·6NH₃ (yellow)	3	[Co(NH₃)₆]³⁺ 3Cl⁻ (1 : 3)
CoCl₃·5NH₃ (purple)	2	[CoCl(NH₃)₅]²⁺ 2Cl⁻ (1 : 2)
CoCl₃·4NH₃ (green)	1	[CoCl₂(NH₃)₄]⁺ Cl⁻ (1 : 1)
CoCl₃·4NH₃ (violet)	1	[CoCl₂(NH₃)₄]⁺ Cl⁻ (1 : 1)

Six groups stay bound to Co throughout. The last two have the same formula but different properties: isomers (trans is green, cis violet).

Postulates (1898):

1. Metals show two kinds of linkage (valence): primary and secondary.
2. Primary valences are normally ionisable, satisfied by negative ions. (= oxidation state.)
3. Secondary valences are non-ionisable, satisfied by neutral molecules or negative ions. The secondary valence equals the coordination number and is fixed for a metal.
4. Groups bound by secondary linkages have characteristic spatial arrangements (now coordination polyhedra) for each coordination number: octahedral, tetrahedral and square planar are the commonest.

• [Co(NH₃)₆]³⁺, [CoCl(NH₃)₅]²⁺, [CoCl₂(NH₃)₄]⁺ are octahedral; [Ni(CO)₄] tetrahedral; [PtCl₄]²⁻ square planar.
• Binary CrCl₃, CoCl₂, PdCl₂ have primary valences 3, 2, 2. [Co(NH₃)₅Cl]Cl₂: primary 3, secondary 6 (2023).

Example (NCERT 5.1) · Moles of AgCl per mole with excess AgNO₃: PdCl₂·4NH₃ 2 → secondary 4; NiCl₂·6H₂O 2 → 6; PtCl₄·2HCl 0 → 6; CoCl₃·4NH₃ 1 → 6; PtCl₂·2NH₃ 0 → 4.

Example (2020) · AgNO₃ (0.125 M) to precipitate the chloride in 0.3 g [Co(NH₃)₆]Cl₃ (267.46): 1.12 × 10⁻³ mol × 3 = 3.37 × 10⁻³ mol Cl⁻ → 27 mL.

Example (2020, colligative) · 0.10 m CrCl₃·xNH₃ raises the b.p. twice as much as 0.05 m CaCl₂ (i = 3): i × 0.10 = 2 × 3 × 0.05 → i = 3 → [Cr(NH₃)₅Cl]Cl₂, x = 5.

Double salt vs complex: both form from two or more stable compounds in a fixed ratio. A double salt dissociates completely into simple ions in water: carnallite KCl·MgCl₂·6H₂O, Mohr's salt FeSO₄·(NH₄)₂SO₄·6H₂O, potash alum KAl(SO₄)₂·12H₂O. A complex ion stays intact: [Fe(CN)₆]⁴⁻ from K₄[Fe(CN)₆] gives no Fe²⁺ or CN⁻.

2 · Definitions

• Coordination entity: a central metal atom or ion bonded to a fixed number of ions or molecules. [CoCl₃(NH₃)₃], [Ni(CO)₄], [PtCl₂(NH₃)₂], [Fe(CN)₆]⁴⁻, [Co(NH₃)₆]³⁺.
• Central atom/ion: the one the groups are bound to in a definite geometry; a Lewis acid. In [NiCl₂(H₂O)₄], [CoCl(NH₃)₅]²⁺, [Fe(CN)₆]³⁻: Ni²⁺, Co³⁺, Fe³⁺.
• Ligands: the ions or molecules bound to it: Cl⁻, H₂O, NH₃, H₂NCH₂CH₂NH₂, N(CH₂CH₂NH₂)₃, even proteins.
  • Unidentate: one donor atom (Cl⁻, H₂O, NH₃).
  • Didentate: two (ethane-1,2-diamine en, oxalate ox, C₂O₄²⁻).
  • Polydentate: several (N(CH₂CH₂NH₂)₃). EDTA⁴⁻ is hexadentate: 2 N and 4 O.
  • Chelate: a di- or polydentate ligand binding one metal through two or more donor atoms at once. Chelate complexes are more stable than similar unidentate complexes ([Co(en)₃]²⁺ > [Co(en)₂(NH₃)₂]²⁺ > … > [Co(NH₃)₆]²⁺; 2021). The number of donor groups used is the denticity.
  • Ambidentate: two different donor atoms, either of which can bind: NO₂⁻ (through N, nitrito-N; or O, nitrito-O) and SCN⁻ (through S or N). Also CN⁻ · Beyond NCERT (2024: NO₂⁻, SCN⁻, CN⁻ → 3). Oxalate and EDTA are not ambidentate.
• Coordination number (CN): the number of ligand donor atoms directly bonded; only σ bonds count, not π. [PtCl₆]²⁻ 6; [Ni(NH₃)₄]²⁺ 4; [Fe(C₂O₄)₃]³⁻ and [Co(en)₃]³⁺ 6. K₄[Th(C₂O₄)₄(H₂O)₂]: 4 × 2 + 2 = 10 (2019).
• Coordination sphere: the central atom and its ligands, in square brackets. The ionisable groups outside are counter ions: in K₄[Fe(CN)₆], [Fe(CN)₆]⁴⁻ and K⁺.
• Coordination polyhedron: the spatial arrangement of the donor atoms: octahedral ([Co(NH₃)₆]³⁺), square planar ([PtCl₄]²⁻), tetrahedral ([Ni(CO)₄]), also trigonal bipyramidal and square pyramidal.
• Oxidation number of the central atom: the charge it would carry if all ligands were removed with their shared electron pairs. Written as a Roman numeral: [Cu(CN)₄]³⁻ is Cu(I).
• Homoleptic: one kind of donor group ([Co(NH₃)₆]³⁺, [Ni(CN)₄]²⁻). Heteroleptic: more than one ([Co(NH₃)₄Cl₂]⁺).

3 · Nomenclature (IUPAC)

Writing formulas:

1. Central atom first.
2. Ligands in alphabetical order, regardless of charge (2004 IUPAC draft). Abbreviated ligands go by the abbreviation's first letter.
3. The whole entity in square brackets; polyatomic ligands and abbreviations in parentheses.
4. No space between the ligands and the metal.
5. Charge of a lone entity as a right superscript, number before sign: [Co(CN)₆]³⁻, [Cr(H₂O)₆]³⁺.
6. Cation charge balances anion charge.

Naming (additive nomenclature):

1. Cation first, whether the complex is the cation or the anion.
2. Ligands in alphabetical order before the metal (the reverse of the formula order, which puts the metal first). Multiplying prefixes are ignored when alphabetising.
3. Anionic ligands end in –o (2004 draft: –ido; chloro becomes chlorido). Neutral and cationic ligands keep their names, except aqua (H₂O), ammine (NH₃), carbonyl (CO), nitrosyl (NO).
4. Prefixes di, tri, tetra count simple ligands; bis, tris, tetrakis count ligands whose names already contain a number, with the ligand in parentheses: [NiCl₂(PPh₃)₂] is dichloridobis(triphenylphosphine)nickel(II).
5. Oxidation state as a Roman numeral in parentheses.
6. In a complex cation or neutral molecule the metal keeps its name (cobalt, platinum). In a complex anion the metal ends in –ate (cobaltate), with Latin roots for some: ferrate (Fe), argentate (Ag), cuprate (Cu), aurate (Au), plumbate (Pb), stannate (Sn).

Ligand	Name
Cl⁻, Br⁻, F⁻	chlorido, bromido, fluorido
CN⁻	cyanido
OH⁻	hydroxido
C₂O₄²⁻	oxalato
CO₃²⁻	carbonato
NO₂⁻ (N) / ONO⁻ (O)	nitrito-N / nitrito-O
SCN⁻ (S) / NCS⁻ (N)	thiocyanato-S / thiocyanato-N
H₂O, NH₃	aqua, ammine
CO, NO	carbonyl, nitrosyl
en, py, PPh₃	ethane-1,2-diamine, pyridine, triphenylphosphine
CH₃NH₂	methanamine

Example (NCERT) · [Cr(NH₃)₃(H₂O)₃]Cl₃: triamminetriaquachromium(III) chloride. [Co(en)₃]₂(SO₄)₃: tris(ethane-1,2-diamine)cobalt(III) sulphate. [Ag(NH₃)₂][Ag(CN)₂]: diamminesilver(I) dicyanidoargentate(I).

Example (NCERT 5.2, 5.3) · Tetraammineaquachloridocobalt(III) chloride = [Co(NH₃)₄(H₂O)Cl]Cl₂. Potassium tetrahydroxidozincate(II) = K₂[Zn(OH)₄]. Potassium trioxalatoaluminate(III) = K₃[Al(C₂O₄)₃]. Tetracarbonylnickel(0) = [Ni(CO)₄]. [Pt(NH₃)₂Cl(NO₂)] = diamminechloridonitrito-N-platinum(II). [Co(NH₃)₅(CO₃)]Cl = pentaamminecarbonatocobalt(III) chloride.

Example (2020, 2023, 2024) · [Pt(NH₃)₂Cl(NH₂CH₃)]Cl = diamminechlorido(methanamine)platinum(II) chloride. K₃[Co(C₂O₄)₃] = potassium trioxalatocobaltate(III). [PtBr₂(PMe₃)₂] = dibromidobis(trimethylphosphine)platinum(II). K₂MnO₄ = potassium tetraoxidomanganate(VI).

NCERT slip: Example 5.3(e) names Hg[Co(SCN)₄] "mercury(I) tetrathiocyanato-S-cobaltate(III)". The charges say Hg²⁺ and [Co(SCN)₄]²⁻: mercury(II) tetrathiocyanato-S-cobaltate(II).

4 · Isomerism

Same formula, different arrangement of atoms, so different physical or chemical properties.

Kind	Type	Arises from
Stereoisomerism (same bonds, different spatial arrangement)	Geometrical	ligand positions (cis/trans, fac/mer)
	Optical	non-superimposable mirror images
Structural isomerism (different bonds)	Linkage	ambidentate ligand
	Coordination	ligands swapped between cation and anion
	Ionisation	counter ion swaps with a ligand
	Solvate (hydrate)	solvent inside vs outside the sphere

4.1 Geometrical isomerism (heteroleptic complexes, CN 4 and 6):

• Square planar [MX₂L₂]: cis (X adjacent) and trans (X opposite). [Pt(NH₃)₂Cl₂].
• Square planar [MABXL]: three isomers, two cis and one trans.
• Tetrahedral: no geometrical isomers: every position is adjacent to every other (NCERT 5.4).
• Octahedral [MX₂L₄]: cis and trans ([Co(NH₃)₄Cl₂]⁺). The Cl–Co–Cl angle is 90° in cis, 180° in trans (2020).
• Octahedral [MX₂(L–L)₂]: cis and trans ([CoCl₂(en)₂]).
• Octahedral [Ma₃b₃]: fac (the three a on one face) and mer (on a meridian). [Co(NH₃)₃(NO₂)₃]. In fac every Cl–Co–Cl angle is 90° (2023); in mer they are 90° and 180°.

4.2 Optical isomerism. Mirror images that cannot be superimposed are enantiomers; such molecules are chiral. d (dextro) rotates plane-polarised light right, l (laevo) left, in a polarimeter. Common in octahedral complexes with didentate ligands.

• [Co(en)₃]³⁺: d and l.
• [PtCl₂(en)₂]²⁺: only the cis isomer is optically active; trans has a mirror plane.
• cis-[CrCl₂(ox)₂]³⁻ is chiral; trans is not (NCERT 5.5).

Counting stereoisomers · Beyond NCERT (the count questions):

Type	Geometrical	Total stereoisomers
Square planar MA₂B₂	2	2 (no optical: planar)
Square planar MABCD	3	3
Tetrahedral MA₂B₂, MABCD	0	1; 2 for MABCD (optical)
Octahedral MA₄B₂	2	2
Octahedral MA₃B₃	2 (fac, mer)	2
Octahedral M(AA)₃	0	2 (d, l)
Octahedral M(AA)₂B₂	2	3 (cis d, cis l, trans)
Octahedral M(AA)₂BC	2	3
Octahedral MA₂B₂C₂	5	6 (one pair)

Example (2019) · Square planar [MCl(F)(NO₂)(SCN)]: 3 geometrical × 2 (NO₂⁻ via N or O) × 2 (SCN⁻ via S or N) = 12.

Example (2021, 2023, 2025) · [Co(ox)₂Br(NH₃)]²⁻ and [Cr(ox)₂ClBr]³⁻: 3 stereoisomers each. [CrCl₃(py)₃]: 2; [CrCl₂(ox)₂]³⁻: 3. Triamminetrinitrocobalt(III) has 2 geometrical; trioxalatochromate(III) has 0 (it has 2 optical).

4.3 Linkage isomerism: an ambidentate ligand binds through either atom. M–NCS vs M–SCN. Jørgensen found [Co(NH₃)₅(NO₂)]Cl₂ as a red form (nitrito-O, –ONO) and a yellow form (nitrito-N, –NO₂).

4.4 Coordination isomerism: ligands swap between the cationic and anionic entities of different metals: [Co(NH₃)₆][Cr(CN)₆] and [Cr(NH₃)₆][Co(CN)₆].

4.5 Ionisation isomerism: the counter ion can itself be a ligand and swap with one: [Co(NH₃)₅(SO₄)]Br (gives AgBr, not BaSO₄) and [Co(NH₃)₅Br]SO₄ (gives BaSO₄, not AgBr).

4.6 Solvate isomerism (hydrate isomerism when water): the solvent is bonded to the metal or sits free in the lattice. [Cr(H₂O)₆]Cl₃ (violet) and [Cr(H₂O)₅Cl]Cl₂·H₂O (grey-green). Further: [Cr(H₂O)₄Cl₂]Cl·2H₂O (dark green) · Beyond NCERT.

5 · Valence bond theory

Werner could not explain why only some elements form complexes, why the bonds are directional, or why complexes have characteristic magnetic and optical properties. Theories since: VBT, CFT, ligand field theory, MO theory.

VBT: under the ligands' influence, the metal uses its (n−1)d, ns, np or ns, np, nd orbitals to make equivalent hybrids of definite geometry; each hybrid accepts an electron pair from a ligand.

CN	Hybridisation	Shape
4	sp³	tetrahedral
4	dsp²	square planar
5	sp³d	trigonal bipyramidal
6	sp³d²	octahedral (outer orbital)
6	d²sp³	octahedral (inner orbital)

The worked cases:

Complex	Metal ion; hybridisation, shape	Magnetism
[Co(NH₃)₆]³⁺	Co³⁺ d⁶ (paired); d²sp³, octahedral	diamagnetic; inner orbital, low spin, spin paired
[CoF₆]³⁻	Co³⁺ d⁶; sp³d² (uses 4d), octahedral	4 unpaired; outer orbital, high spin, spin free
[NiCl₄]²⁻	Ni²⁺ d⁸; sp³, tetrahedral	2 unpaired, paramagnetic
[Ni(CO)₄]	Ni(0), 3d¹⁰ (4s² moved in); sp³, tetrahedral	diamagnetic
[Ni(CN)₄]²⁻	Ni²⁺ d⁸ (paired); dsp², square planar	diamagnetic

Hybrid orbitals don't really exist; hybridisation is a mathematical device.

Magnetic data and VBT. Magnetic susceptibility measurements give the number of unpaired electrons, and so the structure.

• d¹ (Ti³⁺), d² (V³⁺), d³ (Cr³⁺): two 3d orbitals are free for d²sp³, so complex and free ion have the same magnetism.
• d⁴ (Cr²⁺, Mn³⁺), d⁵ (Mn²⁺, Fe³⁺), d⁶ (Fe²⁺, Co³⁺): two free 3d orbitals appear only by pairing, which leaves 2, 1 and 0 unpaired. d⁶ agrees with maximum pairing in many cases; d⁴ and d⁵ have complications.

Complex	Hybridisation	Unpaired
[Mn(CN)₆]³⁻	d²sp³ (inner)	2
[Fe(CN)₆]³⁻	d²sp³ (inner)	1
[Co(C₂O₄)₃]³⁻	d²sp³ (inner)	0
[MnCl₆]³⁻	sp³d² (outer)	4
[FeF₆]³⁻	sp³d² (outer)	5
[CoF₆]³⁻	sp³d² (outer)	4

Example (NCERT 5.7) · [MnBr₄]²⁻ has μ = 5.9 BM: 5 unpaired, so Mn²⁺ is d⁵ with nothing paired → sp³, tetrahedral (dsp² would need pairing).

Example (2021) · [Mn(CN)₆]⁴⁻ (Mn²⁺ d⁵, strong field, 1 unpaired) and [Fe(CN)₆]³⁻ (Fe³⁺ d⁵, 1 unpaired): both d²sp³, paramagnetic.

Example (2023) · [Ni(NH₃)₆]²⁺ is outer orbital (sp³d²) even with NH₃: Ni²⁺ is d⁸, so two 3d orbitals can't be emptied. [Co(NH₃)₆]³⁺ is inner orbital (NCERT intext 5.8).

Limitations of VBT: (i) many assumptions; (ii) no quantitative magnetic data; (iii) no explanation of colour; (iv) no quantitative thermodynamic or kinetic stability; (v) no exact prediction of tetrahedral vs square planar for CN 4; (vi) no distinction between weak and strong ligands.

6 · Crystal field theory

CFT is electrostatic: the metal–ligand bond is treated as purely ionic. Anionic ligands are point charges; neutral ones are point dipoles. The five d orbitals of a free ion are degenerate; a spherical field keeps them so, but ligands in a definite geometry lift the degeneracy: crystal field splitting.

Octahedral field. Ligands approach along the axes. d(x²−y²) and d(z²) point at them and are raised: the eg set. dxy, dyz, dxz point between the axes and are lowered: the t₂g set. The gap is Δo: eg goes up by 0.6Δo, t₂g down by 0.4Δo. (The orbitals that "face the ligands" in an octahedral complex are eg; 2019.)

Spectrochemical series (experimental, from absorption spectra), weak to strong field:

Filling the levels. d¹–d³ go singly into t₂g (Hund). For d⁴ the fourth electron either pairs in t₂g or goes up to eg, depending on Δo against the pairing energy P:

• Δo < P: t₂g³eg¹. Weak field ligands, high spin complexes.
• Δo > P: t₂g⁴eg⁰. Strong field ligands, low spin complexes.
• d⁴ to d⁷ entities are more stable in strong fields than in weak.

What makes Δ large · Beyond NCERT (asked every year):

• Ligand: further right in the series.
• Metal charge: M³⁺ > M²⁺ for the same metal and ligand.
• Row: 4d and 5d metals have Δ 30–50% larger than 3d, and are almost always low spin ([Os(H₂O)₆]³⁺ > [Mo(H₂O)₆]³⁺ > 3d; 2022).
• Geometry: Δo > Δt.

Tetrahedral field. The splitting is inverted (e below, t₂ above) and smaller: Δt = (4/9)Δo for the same metal, ligands and distances. Too small to force pairing, so low-spin tetrahedral complexes are rarely seen. No "g" subscript: a tetrahedron has no centre of symmetry (octahedral and square planar do).

Square planar · Beyond NCERT: removing both axial ligands lowers every orbital with a z component; d(x²−y²) stays highest, alone (2019). That is why d⁸ ions with strong ligands (Ni²⁺ with CN⁻; Pd²⁺, Pt²⁺ always) go square planar and diamagnetic.

CFSE · Beyond NCERT

Example (2019) · [Fe(H₂O)₆]Cl₂: Fe²⁺ d⁶, weak field, t₂g⁴eg²: 4(−0.4) + 2(0.6) = −0.4Δo. K₂[NiCl₄]: tetrahedral d⁸, e⁴t₂⁴: 4(−0.6) + 4(0.4) = −0.8Δt.

Example (2022) · [Fe(CN)₆]³⁻, inner orbital, t₂g⁵: 5 × (−0.4) = −2.0Δo (ignoring pairing). Δo = 0 only for d⁰, d¹⁰ and high-spin d⁵ (2025: [Mn(SCN)₆]⁴⁻, 5.92 BM).

Colour. White light passes through; the complex absorbs part of it; the colour we see is the complementary colour (absorb green, look red). CFT puts it down to d–d transitions.

Entity	λ absorbed (nm)	Absorbed → seen
[CoCl(NH₃)₅]²⁺	535	yellow → violet
[Co(NH₃)₅(H₂O)]³⁺	500	blue-green → red
[Co(NH₃)₆]³⁺	475	blue → yellow-orange
[Co(CN)₆]³⁻	310	ultraviolet → pale yellow
[Cu(H₂O)₄]²⁺	600	red → blue
[Ti(H₂O)₆]³⁺	498	blue-green → violet

Stronger ligand → larger Δ → shorter λ absorbed: Cl⁻ < H₂O < NH₃ < CN⁻ above (2019, 2024, 2025).

• [Ti(H₂O)₆]³⁺ is violet: Ti³⁺ is d¹; blue-green light lifts the electron t₂g¹eg⁰ → t₂g⁰eg¹.
• No ligand, no splitting, no colour: heated [Ti(H₂O)₆]Cl₃ loses water and turns colourless; anhydrous CuSO₄ is white, CuSO₄·5H₂O blue.
• Ligand changes colour: adding en to [Ni(H₂O)₆]²⁺ (green) in ratios 1:1, 2:1, 3:1 gives [Ni(H₂O)₄(en)]²⁺ pale blue, [Ni(H₂O)₂(en)₂]²⁺ blue/purple, [Ni(en)₃]²⁺ violet (2025).
• Gemstones: ruby is Al₂O₃ with 0.5–1% Cr³⁺ (d³) in octahedral sites. In emerald Cr³⁺ sits in beryl (Be₃Al₂Si₆O₁₈); its absorption bands shift to longer wavelength (yellow-red and blue), so emerald transmits green.

Example (2021) · [Ti(H₂O)₆]³⁺ absorbs at 498 nm: Δo = hc/λ = (6.626 × 10⁻³⁴ × 3 × 10⁸)/(498 × 10⁻⁹) = 4.0 × 10⁻¹⁹ J per ion, × Nₐ = 240 kJ mol⁻¹. CFSE (d¹) = −0.4 × 240 = −96 kJ mol⁻¹.

Limitations of CFT: ligands as point charges imply anionic ligands should split most, yet they sit at the weak end of the spectrochemical series. It ignores the covalent character of the bond. Ligand field theory and MO theory fix these. (2023: CFT cannot explain the order of the spectrochemical series.)

Jahn–Teller · Beyond NCERT: octahedral Cu(II) (d⁹, uneven eg) is distorted, axial bonds lengthened.

7 · Metal carbonyls

Homoleptic carbonyls (CO only) form with most transition metals; simple, well defined structures:

Carbonyl	Structure
[Ni(CO)₄], tetracarbonylnickel(0)	tetrahedral
[Fe(CO)₅], pentacarbonyliron(0)	trigonal bipyramidal
[Cr(CO)₆], hexacarbonylchromium(0)	octahedral
[Mn₂(CO)₁₀], decacarbonyldimanganese(0)	two square-pyramidal Mn(CO)₅ joined by a Mn–Mn bond; no bridging CO
[Co₂(CO)₈], octacarbonyldicobalt(0)	a Co–Co bond bridged by two CO; 6 terminal CO

Each Mn in Mn₂(CO)₁₀ is octahedral counting the Mn–Mn bond (2024). Co₂(CO)₈: 1 Co–Co bond + 6 terminal CO = 7 (2022).

Synergic bonding: the M–C bond has both σ and π character.

• σ: CO's carbon lone pair donates into a vacant metal orbital.
• π (back-bonding): a filled metal d orbital donates into CO's vacant antibonding π* orbital.
• Each strengthens the other: the synergic effect strengthens the M–CO bond (and weakens C–O).
• So π-acceptor ligands stabilise low (even zero) oxidation states: Ni(CO)₄, Fe(CO)₅ (2022). Bonding in Ni(CO)₄ is properly explained only by MO theory (2020).

EAN rule · Beyond NCERT: stable carbonyls reach the next noble gas count. Ni(CO)₄: 28 + 8 = 36; Fe(CO)₅: 26 + 10 = 36; Cr(CO)₆: 24 + 12 = 36. Mn(CO)₅ would be 35, so it dimerises.

8 · Importance and applications

Analysis:

• Colour reactions with chelating ligands detect and estimate metals: EDTA, DMG (dimethylglyoxime), α-nitroso-β-naphthol, cupron.
• Hardness of water by titration with Na₂EDTA: Ca²⁺ and Mg²⁺ form stable complexes; their different stability constants allow selective estimation.

Metallurgy:

• Gold (and silver) extraction: Au + CN⁻ + O₂ + H₂O → [Au(CN)₂]⁻; then zinc displaces gold.
• Purification: impure Ni → [Ni(CO)₄] → decomposed to pure Ni (Mond process).

Biology:

Compound	Metal
Chlorophyll	Mg
Haemoglobin	Fe
Vitamin B₁₂ (cyanocobalamin, anti-pernicious anaemia factor)	Co
Carboxypeptidase A, carbonic anhydrase	Zn · Beyond NCERT (NCERT names the enzymes only)

Industry and medicine:

• Wilkinson's catalyst [(Ph₃P)₃RhCl]: hydrogenation of alkenes.
• Electroplating with Ag and Au from [Ag(CN)₂]⁻ and [Au(CN)₂]⁻ is smoother and more even than from simple ions.
• Photography: hypo dissolves undecomposed AgBr as [Ag(S₂O₃)₂]³⁻.
• Chelate therapy: excess Cu and Fe removed by D-penicillamine and desferrioxime B; EDTA for lead poisoning; cis-platin, cis-[PtCl₂(NH₃)₂], inhibits tumours (trans does not).

Tests JEE asks · Beyond NCERT

Test	Complex	Note
Ni²⁺ with DMG + NH₄OH	[Ni(dmgH)₂]	red, square planar, diamagnetic; two 5-membered chelate rings held by O–H···O bonds; 14 H; insoluble
Prussian blue	Fe₄[Fe(CN)₆]₃	Fe³⁺ + excess ferrocyanide
Brown ring (nitrate)	[Fe(H₂O)₅(NO)]²⁺	Fe +1, NO⁺
Sulphide with nitroprusside	[Fe(CN)₅(NOS)]⁴⁻	violet
Co²⁺ in water, then conc. HCl	[Co(H₂O)₆]²⁺ pink → [CoCl₄]²⁻ blue	octahedral → tetrahedral
CuSO₄·5H₂O	[Cu(H₂O)₄]SO₄·H₂O	4 H₂O coordinated, 1 hydrogen-bonded
AgCl in aqueous NH₃	[Ag(NH₃)₂]Cl	dissolves

Example (2021) · Overall formation constant of [Cu(NH₃)₄]²⁺ = 2.1 × 10¹³. Overall dissociation constant = 1/β = 4.8 × 10⁻¹⁴.

9 · Traps

Trap	What goes wrong	Do this
Oxidation state first	Counting d electrons of the atom	Find M's charge, then dⁿ of the ion
CN with chelates	Counting ligands, not donor atoms	en, ox = 2 each; EDTA = 6
Which Cl precipitates	Counting all Cl	Only Cl outside the bracket gives AgCl
High or low spin	Assuming NH₃ always pairs	Co³⁺ + NH₃ low spin; Ni²⁺ (d⁸) stays outer orbital; Co²⁺ + H₂O high spin
4d/5d metals	Treating them as high spin	Large Δ: low spin, Pt(II), Pd(II) square planar
Tetrahedral spin	Writing low-spin tetrahedral	Δt = 4/9 Δo; high spin
Δ and λ	Bigger Δ, longer wavelength	Bigger Δ, shorter λ, higher energy
Colour seen	Reporting the absorbed colour	Seen = complementary
Optical activity	Calling trans-[M(AA)₂X₂] chiral	Only cis is chiral
Tetrahedral isomers	Counting cis/trans	None geometrical
Alphabetical order	Putting "di" or "tri" into the order	Alphabetise on the ligand name
Anion names	Iron in an anion as "ironate"	ferrate, cuprate, argentate, aurate
Bridging CO	Saying Mn₂(CO)₁₀ has bridges	Mn₂(CO)₁₀ none; Co₂(CO)₈ two
Carbonyl magnetism	Calling Ni(CO)₄ paramagnetic	Ni(0): 4s² paired into 3d, d¹⁰, diamagnetic
Ni(II) four-coordinate	One rule for all	Cl⁻: tetrahedral, paramagnetic; CN⁻: square planar, diamagnetic

10 · Numbers worth knowing

Complex	Unpaired · μ (BM)
[Co(NH₃)₆]³⁺, [Co(CN)₆]³⁻, [Fe(CN)₆]⁴⁻	0 · 0
[Fe(CN)₆]³⁻	1 · 1.73
[Mn(CN)₆]³⁻, [NiCl₄]²⁻, [Ni(NH₃)₆]²⁺	2 · 2.83
[Cr(H₂O)₆]³⁺, [Cr(NH₃)₆]³⁺, [Co(H₂O)₆]²⁺	3 · 3.87
[CoF₆]³⁻, [MnCl₆]³⁻, [Fe(H₂O)₆]²⁺, [Cr(H₂O)₆]²⁺	4 · 4.90
[FeF₆]³⁻, [Mn(H₂O)₆]²⁺, [MnBr₄]²⁻	5 · 5.92
[Ni(CO)₄], [Ni(CN)₄]²⁻, [Cu(CN)₄]³⁻	0 · 0
[Cu(NH₃)₄]²⁺, [Cu(H₂O)₆]²⁺	1 · 1.73

• Δt = 4/9 Δo; eg +0.6Δo, t₂g −0.4Δo; e −0.6Δt, t₂ +0.4Δt.
• hc = 1.99 × 10⁻²⁵ J m; Nₐhc = 0.1196 J m mol⁻¹, so Δ (kJ mol⁻¹) ≈ 119 600/λ(nm).
• EDTA: 6 donor atoms (2 N, 4 O). Ruby: 0.5–1% Cr³⁺.

11 · For the boards only

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

• Alfred Werner (1866–1919), born in Mülhouse, Alsace; studied at Karlsruhe and Zurich; doctoral thesis 1890 on isomerism in nitrogen compounds; full professor in Zurich at 29 (1895); developed coordination theory in 1890–93; first to find optical activity in coordination compounds; first Swiss chemist to win the Nobel Prize (1913).
• Coordination compounds are the backbone of modern inorganic and bio-inorganic chemistry and the chemical industry; they are used in metallurgy, catalysis, analysis, electroplating, textile dyeing and medicine.