Coordination Compounds and the d- and f-Block — NEET Chemistry

Transition metals are the chemistry of partly filled $d$ orbitals — and that single fact explains their colour, magnetism, variable valency and their genius for forming complexes. Coordination chemistry is the crown of the inorganic syllabus and one of NEET's most reliable 3–4 mark blocks: nomenclature, isomerism, hybridisation, crystal-field splitting and magnetic moments come up every year. This chapter first fixes the d- and f-block trends, then builds coordination compounds from Werner's insight through both bonding theories, working every configuration, colour and magnetic-moment calculation the exam demands.

Part A — The d- and f-Block Elements

1. Transition elements and their characteristic properties

Transition (d-block) elements have a partly filled $d$ sub-shell in the element or a common ion; general configuration $(n-1)d^{1-10}n{s}^{1-2}$. Their shared properties all stem from those $d$ electrons:

• Variable oxidation states — because $(n-1)d$ and $ns$ electrons are close in energy, several can be lost. Mn shows the widest range (+2 to +7). The +2 state is common early; higher states appear in oxides/fluorides.
• Coloured ions — $d$–$d$ electronic transitions absorb visible light; the complementary colour is seen. Ions with $d^0$ (Sc³⁺, Ti⁴⁺) or $d^{10}$ (Zn²⁺, Cu⁺) are colourless (no $d$–$d$ transition possible).
• Paramagnetism — from unpaired $d$ electrons; the more unpaired, the stronger.
• Catalytic activity — variable oxidation states and surface adsorption (Fe in Haber, V₂O₅ in Contact, Ni in hydrogenation).
• Complex formation — small, highly charged ions with available $d$ orbitals bind ligands readily.
• Alloy formation — similar atomic sizes let them substitute in a lattice (brass, steel).

Magnetic moment (spin-only) from $n$ unpaired electrons:

$\mu =\sqrt{n(n+2)}\text{BM (Bohr magnetons)}$

Worked example 1.1. Magnetic moment of Fe³⁺ ($3d^5$)? Fe³⁺ = $[Ar]3d^5$ → 5 unpaired electrons. $\mu =\sqrt{5(5+2)}=\sqrt{35}=5.92$ BM.

Worked example 1.2. Why is Zn²⁺ colourless but Cu²⁺ blue? Zn²⁺ is $3d^{10}$ (fully filled) — no $d$–$d$ transition possible → colourless. Cu²⁺ is $3d^9$ (one gap) → absorbs red light in a $d$–$d$ transition, appearing blue.

2. Trends across the transition series

• Atomic/ionic radii decrease across a series then stay nearly constant (poor $d$-shielding balances rising nuclear charge).
• Ionisation enthalpies rise gradually across.
• Melting points are high (strong metallic + covalent bonding via $d$ electrons), peaking mid-series.
• $E^{\ominus }$ values: most are reducing; anomalies (Cu is the only one with a positive $M^{2+}/M$ potential — it does not liberate H₂ from acids).

3. The lanthanoid contraction and its consequences

Across the lanthanoids (Ce → Lu, filling $4f$), the size decreases steadily — the lanthanoid contraction — because $4f$ electrons shield the nucleus poorly. Consequences NEET tests:

• The second and third transition series have almost identical sizes (e.g. Zr ≈ Hf, Nb ≈ Ta), so those pairs are hard to separate.
• Basicity of lanthanoid hydroxides decreases across.
• Lanthanoids show a common +3 oxidation state; the actinoids show more variability and are radioactive.

Worked example 3.1. Why are zirconium and hafnium so difficult to separate chemically? The lanthanoid contraction makes Hf almost the same size as the lighter Zr, so their ions have nearly identical radii and charge — hence near-identical chemistry, making separation very hard.

4. Two important compounds: KMnO₄ and K₂Cr₂O₇

Potassium permanganate (KMnO₄): Mn in +7, deep purple, a powerful oxidising agent (especially in acidic medium):

$Mn{O}_4^{-}+8H^{+}+5e^{-}\to M{n}^{2+}+4H_{2}O(E^{\ominus }=+1.51\text{ V})$

Here Mn goes +7 → +2 (5-electron change). In neutral/basic medium it goes to MnO₂ (+4).

Potassium dichromate (K₂Cr₂O₇): Cr in +6, orange, an oxidiser in acid:

$C{r}_2{O}_7^{2-}+14H^{+}+6e^{-}\to 2C{r}^{3+}+7H_{2}O$

The dichromate ($C{r}_2{O}_7^{2-}$, orange) ⇌ chromate ($Cr{O}_4^{2-}$, yellow) equilibrium is pH-dependent (acid → orange, base → yellow).

Worked example 4.1. What is the oxidation-state change of Mn when acidic KMnO₄ acts as an oxidiser? Mn goes from +7 (in MnO₄⁻) to +2 (Mn²⁺) — a 5-electron reduction, which is why the permanganate ion accepts 5 electrons per formula unit.

Part B — Coordination Compounds

5. Werner's theory and basic terms

Alfred Werner explained complexes with two kinds of valency:

• Primary (ionisable) valency = the oxidation state, satisfied by anions.
• Secondary (non-ionisable) valency = the coordination number, satisfied by ligands, giving a fixed geometry.

Key definitions:

• Central metal atom/ion — the Lewis acid accepting electron pairs.
• Ligand — the Lewis base donating a lone pair. By denticity: monodentate (Cl⁻, NH₃, H₂O), bidentate (ethylenediamine en, oxalate), polydentate (EDTA, hexadentate). Ambidentate ligands can bind through either of two atoms (NO₂⁻ vs ONO⁻; SCN⁻ vs NCS⁻).
• Chelate — a ring formed by a polydentate ligand; chelates are extra stable (the chelate effect).
• Coordination number — number of ligand donor atoms bonded to the metal (commonly 4 or 6).
• Coordination sphere — the metal + ligands in [ ]; the counter-ion sits outside.

Worked example 5.1. In $[Co(N{H}_3{)}_6]C{l}_3$, identify the oxidation state, coordination number and what ionises. The three Cl⁻ are outside the sphere (primary valency 3 → Co is +3); the six NH₃ are ligands (coordination number 6). Only the three chloride ions ionise in solution.

6. IUPAC nomenclature

Rules to name a complex:

1. Cation named first, then anion (as in any salt).
2. Within the sphere: ligands alphabetically, then the metal.
3. Ligand prefixes di/tri/tetra (or bis/tris for complex ligand names).
4. Anionic ligands end in -o (chloro, cyano, hydroxo, sulphato); neutral ligands keep their name except aqua (H₂O), ammine (NH₃), carbonyl (CO), nitrosyl (NO).
5. Metal oxidation state in Roman numerals in parentheses.
6. In an anionic complex the metal takes the suffix -ate (ferrate, cuprate, argentate).

Worked example 6.1. Name $K_4[Fe(CN{)}_6]$. Anionic complex → metal is "ferrate". Six cyano ligands, Fe is +2. Potassium hexacyanoferrate(II).

Worked example 6.2. Formula of tetraamminecopper(II) sulphate? Cu²⁺ with 4 NH₃ → $[Cu(N{H}_3{)}_4{]}^{2+}$, balanced by sulphate: $[Cu(N{H}_3{)}_4]S{O}_4$.

7. Isomerism in coordination compounds

Structural isomerism (different bonds):

• Ionisation — different ions in solution: $[Co(N{H}_3{)}_{5}Br]S{O}_4$ vs $[Co(N{H}_3{)}_{5}S{O}_4]Br$.
• Linkage — ambidentate ligand binds through different atoms: $[Co(N{H}_3{)}_5(N{O}_2){]}^{2+}$ (nitro, N-bound) vs $(ONO)$ (nitrito, O-bound).
• Coordination — ligand exchange between cation and anion complexes.
• Hydrate/solvate — water inside vs outside the sphere: $[Cr(H_{2}O{)}_6]C{l}_3$ (violet) vs $[Cr(H_{2}O{)}_{5}Cl]C{l}_2\cdot H_{2}O$ (green).

Stereoisomerism (same bonds, different arrangement):

• Geometrical (cis–trans) — in square planar $M{A}_2{B}_2$ and octahedral $M{A}_4{B}_2$ complexes. (Tetrahedral complexes show no cis–trans.)
• Optical — non-superimposable mirror images, common in octahedral chelate complexes like $[Co(en{)}_3{]}^{3+}$.

Worked example 7.1. Does the tetrahedral complex $[Zn(N{H}_3{)}_{2}C{l}_2]$ show cis–trans isomerism? No. In a tetrahedron all four positions are adjacent (equivalent), so there is no cis/trans distinction. Geometrical isomerism needs a square-planar or octahedral geometry.

8. Valence bond theory of complexes

VBT describes bonding by hybridisation of the metal's empty orbitals to accept ligand lone pairs:

• Inner-orbital (low-spin) complexes use inner $(n-1)d$ orbitals → strong-field ligands force pairing → fewer unpaired electrons.
• Outer-orbital (high-spin) complexes use outer $nd$ orbitals → weak-field ligands → maximum unpaired electrons.

VBT predicts magnetic behaviour but not colour or the spectrochemical order — that needs crystal-field theory.

Worked example 8.1. Hybridisation and magnetism of $[Fe(CN{)}_6{]}^{4-}$? Fe²⁺ = $3d^6$. CN⁻ is a strong-field ligand → pairs all six $d$ electrons into three orbitals, freeing two inner $d$ orbitals → $d^{2}s{p}^3$ (inner-orbital, octahedral), 0 unpaired electrons → diamagnetic (low spin).

9. Crystal field theory (CFT)

CFT treats the metal–ligand interaction as electrostatic. The approaching ligands split the five degenerate $d$ orbitals by energy.

Octahedral field: the $d$ orbitals split into a lower $t_{2g}$ (three: $d_{xy},d_{yz},d_{zx}$) and a higher $e_g$ (two: $d_{x^2-y^2},d_{z^2}$), separated by the crystal-field splitting energy ${\Delta }_o$.

Tetrahedral field: the splitting is inverted ($e$ below $t_2$) and smaller, ${\Delta }_t=\frac{4}{9}{\Delta }_o$ — so tetrahedral complexes are almost always high spin.

Strong vs weak field — high vs low spin (octahedral $d^4$–$d^7$):

• Strong-field ligand (large ${\Delta }_o$ > pairing energy) → electrons pair in $t_{2g}$ first → low spin, fewer unpaired electrons.
• Weak-field ligand (small ${\Delta }_o$) → electrons spread out (Hund) → high spin, more unpaired electrons.

Spectrochemical series (ligand field strength, increasing):

$I^{-}<B{r}^{-}<C{l}^{-}<F^{-}<O{H}^{-}<H_{2}O<N{H}_3<en<N{O}_2^{-}<C{N}^{-}<CO$

The colour of a complex comes from a $t_{2g}\to e_g$ transition absorbing light of energy ${\Delta }_o$; the colour seen is the complement of the absorbed wavelength. Larger ${\Delta }_o$ (stronger ligand) → absorbs higher-energy (shorter-wavelength) light.

Crystal-field stabilisation energy (CFSE): each $t_{2g}$ electron is stabilised by $-0.4{\Delta }_o$ and each $e_g$ raised by $+0.6{\Delta }_o$.

Worked example 9.1. Compare the number of unpaired electrons in $[Fe(H_{2}O{)}_6{]}^{3+}$ and $[Fe(CN{)}_6{]}^{3-}$ (both Fe³⁺, $d^5$). H₂O is weak field → high spin → $t_{2g}^3{e}_g^2$ → 5 unpaired. CN⁻ is strong field → low spin → $t_{2g}^5{e}_g^0$ → 1 unpaired. Same metal ion, opposite magnetism — CFT's key insight.

Worked example 9.2. Why is $[Ni(H_{2}O{)}_6{]}^{2+}$ green while $[Ni(CN{)}_4{]}^{2-}$ is colourless-to-pale? The weak-field aqua complex has a small ${\Delta }_o$ absorbing in the red, so it looks green (complementary). The strong-field CN⁻ pushes the transition out of the visible range in the square-planar cyanide complex, so little visible light is absorbed.

10. Common traps NEET sets here

• Colour needs partly filled $d$ — $d^0$ and $d^{10}$ ions are colourless.
• Magnetic moment $\mu =\sqrt{n(n+2)}$ — count unpaired electrons after the ligand decides high/low spin.
• Strong field = low spin = fewer unpaired; weak field = high spin = more unpaired.
• Coordination number ≠ oxidation state — count donor atoms, not charge.
• Only the coordination sphere's counter-ions ionise — ligands inside [ ] don't.
• Tetrahedral complexes show no cis–trans and are almost always high spin (${\Delta }_t$ small).
• Spectrochemical order: CN⁻/CO strong, halides weak — memorise the sequence.
• Nomenclature: ligands alphabetical, anionic complex metal ends in -ate, oxidation state in Roman numerals.

11. Memory aids

• "Partly filled $d$ = colour + magnetism" — the source of every transition-metal property.
• "$\sqrt{n(n+2)}$ Bohr magnetons" — spin-only magnetic moment.
• "Strong field, low spin, few singles" — CN⁻/CO pair electrons; weak field does the opposite.
• "I < Br < Cl < F < OH < H₂O < NH₃ < en < NO₂ < CN < CO" — the spectrochemical series.
• "Absorb one colour, see its complement" — the origin of complex colour.
• "-ate for anionic complexes" — ferrate, cuprate, argentate.
• "Lanthanoid contraction makes Zr = Hf" — the size consequence.

12. Exam protocol

1. For a d-block property, trace it to partly filled $d$: variable states, colour ($d$–$d$), paramagnetism, catalysis.
2. Magnetic moment: find the ion's $d^n$, decide high/low spin from the ligand, then $\mu =\sqrt{n(n+2)}$.
3. Complexes: separate the coordination sphere from counter-ions; oxidation state from charge balance; coordination number = donor atoms.
4. Name by IUPAC rules (alphabetical ligands, -ate for anionic complex, Roman-numeral state).
5. Classify isomerism (ionisation, linkage, hydrate; geometrical, optical).
6. VBT: hybridisation ($s{p}^3$, $ds{p}^2$, $d^{2}s{p}^3$/$s{p}^3{d}^2$) and inner vs outer orbital for magnetism.
7. CFT: split $t_{2g}/e_g$, use the spectrochemical series for high/low spin, unpaired count and colour (${\Delta }_o$).