Inorganic Chemistry — Chemistry

Periodic Table Organisation

• s-block (Groups 1–2): alkali and alkaline earth metals — fill ns orbitals
• p-block (Groups 13–18): fill np orbitals; includes metalloids, nonmetals, noble gases
• d-block (Groups 3–12): transition metals — fill (n−1)d orbitals
• f-block (Lanthanides, Actinides): fill (n−2)f orbitals; placed separately below
• Period number = number of shells; Group number relates to valence electrons

Periodic Trends

Key anomalies in IE: Be > B (2s vs 2p); N > O (half-filled 2p stable); Mg > Al; P > S — extra stability of half-filled/filled subshells.

Electron affinity anomalies: N has zero/negative EA (half-filled 2p repels extra e⁻); F < Cl (F is too small, e⁻ repulsion).

Chemical Bonding Types

• Formal charge = Valence e⁻ − Non-bonding e⁻ − ½(Bonding e⁻)
• Lattice energy ∝ (charge product)/(ionic radii sum); more negative = more stable ionic compound
• Bond order = (bonding e⁻ − antibonding e⁻) / 2; higher BO → shorter, stronger bond

Rock salt, NaCl — The Cl⁻ ions sit on a face-centred cubic (fcc) lattice, at the 8 corners and 6 face centres of the cell. The Na⁺ ions fill every octahedral void of that lattice: the 12 edge centres and the body centre. Each Na⁺ has 6 Cl⁻ round it at a/2, at the corners of an octahedron (90° apart), and each Cl⁻ has 6 Na⁺ in the same way, one of them in the next cell: the coordination is 6:6. The radius ratio r⁺/r⁻ = 102/181 = 0.56 lies in the octahedral range, 0.414 to 0.732. Na⁺ and Cl⁻ touch along every edge, so \(a = 2(r^+ + r^-)\) = 2(102 + 181) = 566 pm (X-ray: 564 pm); the Cl⁻ do not touch one another, since \(a/\sqrt{2}\) = 400 pm is more than 2r⁻ = 362 pm. A corner is shared by 8 cells, an edge by 4 and a face by 2, so one cell holds Cl⁻: 8 × 1/8 + 6 × 1/2 = 4 and Na⁺: 12 × 1/4 + 1 × 1 = 4, that is Z = 4 formula units of NaCl. Radii are six-coordinate values (Shannon); the ball model shrinks the ions, and the cut-away view is to scale.

VSEPR Theory — Molecular Shapes

Lone pair repulsion > bond pair repulsion → lone pairs compress bond angles (NH₃: 107°, H₂O: 104.5° vs 109.5° tetrahedral).

VSEPR shapes with 5, 6 and 7 electron pairs — Five electron pairs point to the corners of a trigonal bipyramid: three equatorial pairs 120° apart and two axial pairs at 90° to them. An axial pair has 3 other pairs at 90° to it, an equatorial pair only 2, so a lone pair, which repels more than a bond pair, takes an equatorial corner. (The 3D view finds every placement by counting these 90° contacts.) PCl₅ (AX₅) is trigonal bipyramidal, 90° and 120°; its two axial bonds are longer than the three equatorial ones, since each meets 3 bonds at 90° and an equatorial bond only 2. SF₄ (AX₄E) has one equatorial lone pair and is see-saw shaped: the measured F–S–F angles are 101.6° between the equatorial F and 173.1° between the axial F. ClF₃ (AX₃E₂) has two equatorial lone pairs and is T-shaped, F–Cl–F 87.5° (measured). XeF₂ (AX₂E₃) has all three lone pairs equatorial and is linear, 180°. Six pairs point to the corners of an octahedron, 90° apart: SF₆ (AX₆) is octahedral, and BrF₅ (AX₅E) square pyramidal. In XeF₄ (AX₄E₂) the two lone pairs sit opposite each other (trans), never at 90°, so XeF₄ is square planar, 90°. IF₇ (AX₇) has seven pairs and is pentagonal bipyramidal: five equatorial F 72° apart (360°/5) and two axial F at 90° to them. XeF₆ also has seven pairs, one of them a lone pair, and is a distorted octahedron; it is not drawn, because VSEPR does not fix how far it is distorted. BrF₅ is drawn at the ideal 90°, though its real angles differ a little. Bond lengths and lone-pair clouds are not to scale.

Dipole moment as a vector sum — A polar bond has a bond dipole, drawn as an arrow from δ+ to δ− (towards the more electronegative atom). A molecule’s dipole moment is the vector sum of its bond dipoles, so it depends on the shape. In linear CO₂ the two C=O dipoles point in opposite directions; in trigonal planar BF₃ the three B–F dipoles are 120° apart; in tetrahedral CCl₄ the four C–Cl dipoles point to the corners of a tetrahedron. In each the sum is exactly zero, so these molecules have no dipole moment although their bonds are polar. In bent H₂O (H–O–H 104.5°) the two O–H dipoles add up to a resultant along the bisector, towards O, so water is polar. NH₃ and NF₃ are both pyramidal, with a lone pair on N. In NH₃ the N–H dipoles point towards N, so their resultant points the same way as the lone pair’s moment and the two add: μ = 4.90 × 10⁻³⁰ C m. In NF₃ the N–F dipoles point away from N, so their resultant opposes the lone pair’s moment and μ is only 0.8 × 10⁻³⁰ C m, although F is more electronegative than H (both values from NCERT). Arrow lengths are schematic: only their directions and the zero sums are worked out.

Hybridisation

Hybrid orbitals in 3D — Mixing orbitals gives exactly as many hybrids as orbitals mixed: sp (one s + one p) gives 2 hybrids 180° apart; sp² gives 3 at 120° in a plane; sp³ gives 4 at 109.5°; sp³d gives 5 (trigonal bipyramidal, 90° and 120°); sp³d² gives 6 (octahedral, 90°). Each hybrid has one big lobe pointing along its bond and a small back lobe of opposite sign. Its s character falls from 50% (sp) to 33% (sp²) and 25% (sp³), and its back lobe grows from 7% to 18% to 25% of the main lobe's length. sp leaves two p orbitals and sp² one p orbital unhybridised, at right angles to the hybrids; these form π bonds. In sp³d the three equatorial hybrids (33% s) and the two axial ones (made from p and d only: slimmer, with a small ring round the middle instead of a back lobe) are not equivalent. The 3D view draws each hybrid as a polar plot of its angular part: a lobe's length in each direction shows how likely the electron is to be found that way.

σ and π bonds in 3D — Two carbon 2p orbitals 133 pm apart (the C=C bond length). Meeting end-on, they overlap on the bond axis and make a σ bond (overlap S = 0.32); side by side, they overlap above and below the axis and make a π bond (S = 0.27), whose nodal plane contains the axis. Turn one end 90° about the axis and the overlap falls to exactly zero (it goes as cos θ), so the π bond breaks: this is why a C=C bond does not rotate freely, and cis and trans isomers are different compounds. In C=C the σ bond is made by sp² hybrids (S = 0.75) and the π bond by the leftover 2p orbitals; in C≡C (120 pm) the σ bond is made by sp hybrids (S = 0.81), and two π bonds (S = 0.34 each) lie at right angles. In every case the σ overlap is the larger, which is why a σ bond is stronger than a π bond. Each surface encloses 90% of the probability; colour shows the sign of ψ, not charge.

Molecular Orbital Theory

• MOs formed by LCAO: bonding MO (lower energy, σ or π), antibonding MO (higher energy, σ* or π*)
• Filling order (homonuclear diatomics up to N₂): σ1s, σ*1s, σ2s, σ*2s, π2p (before σ2p), σ2p, π*2p, σ*2p
• For O₂, F₂: σ2p fills before π2p (order reverses after N₂)
• Bond order = (bonding − antibonding)/2; paramagnetism if unpaired electrons in MOs
• O₂: BO = 2, paramagnetic (2 unpaired e⁻ in π*2p) — explains liquid O₂ being attracted to magnets
• N₂: BO = 3, diamagnetic; CO: BO = 3, diamagnetic (isoelectronic with N₂)

Molecular orbitals in 3D — The six molecular orbitals NCERT draws, each made from two atomic orbitals: in phase (ψ_A + ψ_B) for a bonding MO, out of phase (ψ_A − ψ_B) for an antibonding one. σ1s and σ*1s are drawn for H₂ (74 pm; overlap S = 0.75); σ2p_z, σ*2p_z, π2p_x and π*2p_x for O₂ (121 pm; S = 0.31 end-on and 0.15 side by side). A bonding MO builds up electron density between the nuclei; every antibonding MO has a nodal plane between them. A σ MO is unchanged by turning about the bond axis; a π MO has a nodal plane containing the axis, so π*2p_x has two nodal planes. Each surface encloses 90% of the probability and is drawn to scale; colour shows the sign of ψ, not charge.

Hydrogen Bonding

• Forms between H bonded to highly electronegative atom (F, O, N) and lone pair of another F/O/N
• Intermolecular H-bonding: H₂O, HF, NH₃, carboxylic acids — raises BP and melting point
• Intramolecular H-bonding: o-nitrophenol, salicylaldehyde — lowers BP (no intermolecular association)
• HF has highest BP among hydrogen halides (strong H-bonding); H₂O has anomalously high BP vs H₂S
• Ice is less dense than water (open H-bond network) — maximum density at 4°C

Ice: an open hexagonal network — In ice each O holds 2 H by covalent bonds and accepts 2 hydrogen bonds from H of neighbouring molecules, so it has 4 O neighbours at the corners of a tetrahedron (O–O–O 109.5°), each 276 pm away (NCERT). Every H lies between two O: covalent to one, hydrogen-bonded to the other. The molecules join in puckered rings of 6 O, which stack to leave wide open channels. That open structure is why ice is less dense than water: this ideal geometry gives 0.92 g cm⁻³ (measured, 0.917 g cm⁻³ at 0 °C), against 1.00 g cm⁻³ for liquid water at 4 °C, so ice floats. When ice melts the network partly collapses into the holes. The H shown are one arrangement that keeps two near and two far from every O; in real ice the arrangement varies.

Group 13 — Boron Family (ns²np¹)

• Members: B, Al, Ga, In, Tl. Boron is a metalloid; rest are metals.
• Inert pair effect: Down the group, ns² electrons become less available for bonding due to poor shielding by d/f electrons → Tl prefers +1 over +3, In shows both +1 and +3.
• Boron: BCl₃ — sp², trigonal planar, Lewis acid (vacant p orbital accepts lone pair). BF₃ + NH₃ → BF₃·NH₃ (coordinate bond).
• Aluminium: AlCl₃ forms dimer Al₂Cl₆ in vapour (two Cl bridge-bonds). Amphoteric oxide (Al₂O₃ reacts with both acids and bases).
• Diagonal relationship: B resembles Si (both form covalent hydrides, acidic oxides, complex anions like [BO₃]³⁻ and [SiO₄]⁴⁻).

BF₃ + NH₃ in 3D — In BF₃, boron uses three sp² hybrids for its three B–F bonds (trigonal planar, 120°). That leaves 6 electrons round boron and its remaining 2p orbital, at right angles to the plane, empty. NH₃’s lone pair, in an sp³ hybrid, points straight at that empty orbital: nitrogen gives both electrons of the new N→B bond (a coordinate bond), so NH₃ acts as a Lewis base and BF₃ as a Lewis acid. In BF₃·NH₃ boron has four bonds and 8 electrons round it, so it becomes sp³ and the three B–F bonds fold back to the tetrahedral angle (109.5°). Bond lengths are not to scale.

AlCl₃ and its dimer Al₂Cl₆ in 3D — In AlCl₃ each Al has 3 Cl round it (trigonal planar, 120°) and only 3 bond pairs, 6 electrons: 2 short of an octet, with an empty orbital. Two molecules join when a Cl of each gives a lone pair to the other Al (a coordinate bond). In Al₂Cl₆, 2 Cl bridge the two Al and 4 are terminal; each Al now has 4 Cl and 8 electrons round it, at the centre of a tetrahedron, and the two AlCl₄ tetrahedra share an edge (the 2 bridging Cl). Once formed, the four bridge bonds are alike. The tetrahedra are drawn regular; the real angles differ, so none is shown. Bond lengths are not to scale.

Group 14 — Carbon Family (ns²np²)

• Carbon allotropes: Diamond (sp³, 3D network, hardest natural substance), Graphite (sp², layered, conductor due to delocalised π electrons), Fullerene C₆₀ (sp², soccer-ball, 20 hexagons + 12 pentagons).
• CO vs CO₂: CO is a ligand (strong field via C lone pair), toxic (binds Hb). CO₂ is linear (sp), acidic oxide.
• Silicon: SiO₂ is giant covalent solid (each Si tetrahedral, high mp). Silicones are polymers (Si–O backbone).
• Inert pair: Pb prefers +2 (PbO, PbCl₂) over +4; Sn shows both +2 and +4 (SnCl₂ reducing agent, SnCl₄ Lewis acid).
• C–C multiple bonding readily; Si cannot (d-orbital back bonding instead).

Silicates: SiO₄ tetrahedra sharing corners — Each Si sits at the centre of a tetrahedron of 4 O, with O–Si–O 109.5°. A corner O shared by two tetrahedra counts half to each Si. With no corner shared the unit is SiO₄⁴⁻, charge (+4) + 4 × (−2) = −4; two tetrahedra sharing one corner give Si₂O₇⁶⁻, charge 2 × (+4) + 7 × (−2) = −6. When all four corners are shared, every O is shared by 2 Si, so there are 4 × 1/2 = 2 O per Si: SiO₂, a three-dimensional network. In silicones two corners of each tetrahedron carry CH₃ groups instead of O, so only two are shared and the tetrahedra form chains with the repeat unit (CH₃)₂SiO. Si–O–Si is drawn straight; in quartz it is bent, about 144°.

Group 15 — Nitrogen Family (ns²np³)

• N₂ is very stable (triple bond, BE = 945 kJ/mol). P₄ (white phosphorus) — tetrahedral, strained 60° angles, highly reactive.
• Hydrides: NH₃ > PH₃ > AsH₃ > SbH₃ — basicity decreases down (less lone pair availability); NH₃ has H-bonding, highest bp.
• Oxides of nitrogen: N₂O (laughing gas), NO (radical), NO₂ (brown, acidic), N₂O₄ (dimer of NO₂), N₂O₅ (anhydride of HNO₃).
• Oxoacids of P: H₃PO₃ (phosphorous acid) — diprotic (one H on P is non-ionisable); H₃PO₄ (phosphoric) — triprotic.
• Nitric acid: Dilute HNO₃ + metal → NO; Concentrated HNO₃ + metal → NO₂. Passivation: Fe, Cr, Al with conc. HNO₃.

White phosphorus, P₄, in 3D — Four P atoms sit at the corners of a tetrahedron and every pair is bonded: 6 P–P bonds, 3 on each P. Each of the 4 faces is an equilateral triangle, so all 12 P–P–P angles are 60°. Bonds bent to only 60° are strained, which is why white phosphorus is so reactive. Each P has 5 valence electrons: 3 bonds and 1 lone pair, so the molecule has 4 lone pairs, each pointing out from the centre. Bond lengths are not to scale.

Oxoacids of phosphorus in 3D — In each acid P is tetrahedral, with 4 groups round it, one of them a P=O. Only an H bonded to O can leave as H⁺, so the basicity is the number of P–OH bonds; an H bonded directly to P does not ionise. H₃PO₄ (orthophosphoric acid) has 3 P–OH: tribasic, with P +5 from 3(+1) + x + 4(−2) = 0. In H₃PO₃ (phosphorous acid) one P–OH is replaced by a P–H: 2 P–OH, dibasic, P +3. In H₃PO₂ (hypophosphorous acid) two are: 1 P–OH and 2 P–H, monobasic, P +1. A P–H bond makes the acid a reducing agent. H₄P₂O₇ (pyrophosphoric acid) is two acids joined through one O, 2H₃PO₄ → H₄P₂O₇ + H₂O: one P–O–P bridge and 4 P–OH, tetrabasic, P +5. The tetrahedra are drawn ideal and bond lengths are not to scale.

Group 16 — Chalcogens (ns²np⁴)

• Oxygen: Allotropes O₂ and O₃ (ozone — angular, sp², bent). O₃ is a better oxidising agent than O₂.
• Sulphur allotropes: Rhombic S₈ (stable <96°C), Monoclinic S₈ (stable 96–119°C), Plastic sulphur (supercooled). All contain puckered S₈ rings.
• Acidic character: H₂O < H₂S < H₂Se < H₂Te — increases down (weaker H–X bond, more stable conjugate base anion).
• SO₂: V-shape, reducing agent, acidic oxide; forms H₂SO₃ with water. SO₃ (Lewis acid) + H₂O → H₂SO₄.
• Oleum: H₂SO₄ + SO₃ → H₂S₂O₇ (pyrosulphuric acid); Contact process for H₂SO₄ uses V₂O₅ catalyst.

Ozone, O₃, in 3D: resonance — The central O has 2 bonds and 1 lone pair, 3 electron pairs, so O₃ is bent. One resonance structure has O=O on one side and O–O on the other (bond orders 2 and 1; formal charges 0, +1, −1, where formal charge = 6 − lone-pair electrons − bonds); the other has them the other way round. Neither is the real molecule: in the resonance hybrid each O–O bond has order (2 + 1)/2 = 1.5, so the two bonds are the same length. O–O–O is 117° (NCERT), under the 120° of 3 electron pairs. Bond lengths are not to scale.

S₈: the crown ring in 3D — Rhombic and monoclinic sulphur are both made of S₈ rings: 8 S atoms and 8 S–S bonds, each S with 2 bonds and 2 lone pairs. A flat ring would open every S–S–S angle to 135°, a regular octagon's angle, far wider than the 109.5° that 4 electron pairs round each S allow. The real S–S–S angle is about 108° (measured 107.8°), so the ring puckers into a crown: 4 S above the ring's mean plane and 4 below. Bond lengths are not to scale.

Group 17 — Halogens (ns²np⁵)

• F₂ anomaly: Weakest X–X bond (small size → lone pair repulsion). Only −1 oxidation state (no d orbitals to expand valence).
• Interhalogen compounds: XX′ type (ICl, IBr), XX′₃ (ICl₃), XX′₅ (BrF₅ — square pyramidal), XX′₇ (IF₇ — pentagonal bipyramidal).
• Bleaching powder: Ca(OCl)Cl — formed by Cl₂ + slaked lime.
• Oxoacids: HOCl < HOClO < HOClO₂ < HOClO₃ — acid strength increases with more O atoms (more electronegative, weakens O–H bond).

Group 18 — Noble Gases

• All ns²np⁶ configuration (He: 1s²). High ionisation energy, chemically inert.
• Xenon compounds: XeF₂ (linear, sp³d), XeF₄ (square planar, sp³d²), XeF₆ (distorted octahedral, sp³d³), XeO₃ (pyramidal), XeOF₄ (square pyramidal).
• Kr also forms KrF₂. Rn is radioactive (½-life 3.8 days).
• He: lightest noble gas, used in airships (non-flammable), cryogenics (bp 4.2 K). Ar: most abundant noble gas in atmosphere (0.93%).

Xenon compounds and interhalogens in 3D — Count the electron pairs round the central atom; a Xe=O double bond counts as one. XeF₂: 2 bond pairs + 3 lone pairs = 5, with the lone pairs equatorial, so the molecule is linear (180°). XeF₄: 4 + 2 = 6, with the lone pairs opposite each other, so it is square planar (90°). XeF₆: 6 + 1 = 7, a distorted octahedron; the 3D view does not draw it, because VSEPR does not fix how far it is distorted. XeO₃: 3 + 1 = 4, a trigonal pyramid like NH₃. XeOF₄: 5 + 1 = 6, square pyramidal, with the O at the apex, 180° from the lone pair. Among the interhalogens (Group 17), BrF₅ (5 + 1 = 6) is square pyramidal and IF₇ (7 + 0 = 7) pentagonal bipyramidal, 72° round the ring and 90° to the axial F. XeO₃, XeOF₄ and BrF₅ are drawn at the ideal angles; their real angles differ a little. Bond lengths and lone-pair clouds are not to scale.

d-Block: Electronic Configuration

• General configuration: [noble gas] (n−1)d¹⁻¹⁰ ns⁰⁻². First row: Sc (3d¹4s²) to Zn (3d¹⁰4s²).
• Exceptions: Cr: [Ar] 3d⁵4s¹ (half-filled d, more stable). Cu: [Ar] 3d¹⁰4s¹ (fully filled d). Similar for Mo, W, Ag, Au.
• When forming ions: ns electrons are lost first (ns is higher in energy for the cation), then nd. Fe²⁺: [Ar] 3d⁶; Fe³⁺: [Ar] 3d⁵.
• Zn, Cd, Hg (Group 12) are sometimes excluded as transition metals because they have completely filled d¹⁰ in all oxidation states.

Characteristic Properties of Transition Metals

Interstitial compounds: small atoms in the voids — An fcc metal has N = 8 × 1/8 + 6 × 1/2 = 4 atoms per cell. Its octahedral voids, at the body centre and the 12 edge centres, number 12 × 1/4 + 1 × 1 = 4 = N, one per atom; each is surrounded by 6 atoms and holds a sphere of radius up to 0.414 r, where r is the metal atom's radius. Its tetrahedral voids, all 8 inside the cell, number 2N; each is surrounded by 4 atoms and holds up to 0.225 r. In an interstitial compound small atoms such as H, C and N sit in these voids (C in an octahedral void of iron, for example), so every lattice site keeps its metal atom: nothing is substituted. Filling every octahedral void gives MX (TiC); filling every tetrahedral void would give MX₂. These compounds are hard, high-melting and still conduct, and are often non-stoichiometric (TiH₁.₇, VH₀.₅₆). By contrast, in a substitutional alloy such as brass a Zn atom takes a Cu site.

Colour and d–d Transitions

• When ligands surround a metal, they split d orbitals into groups of different energy (crystal field splitting).
• Electrons absorb photons to jump to higher d level. The frequency absorbed determines the colour seen (complementary).
• Sc³⁺, Ti⁴⁺, Cu⁺, Zn²⁺ are colourless — either no d electrons or fully filled d¹⁰ (no d–d transition possible).
• MnO₄⁻ is intensely purple due to charge-transfer (not d–d) — LMCT (ligand to metal charge transfer).

Important Oxoanions of Transition Metals

Cr₂O₇²⁻ + H₂O ⇌ 2CrO₄²⁻ + 2H⁺: Dichromate (orange, acidic) ⇌ Chromate (yellow, basic) — pH-dependent equilibrium.

KMnO₄ in acidic medium: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O (Mn: +7 → +2). In basic medium: MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻ (Mn: +7 → +4).

Chromate, dichromate and permanganate in 3D — CrO₄²⁻ is tetrahedral, every O–Cr–O 109.5°, with Cr +6 from x + 4(−2) = −2. In acid two chromate ions join, 2CrO₄²⁻ + 2H⁺ → Cr₂O₇²⁻ + H₂O, and a base reverses it. Cr₂O₇²⁻ is two CrO₄ tetrahedra sharing one corner O: 6 terminal and 2 bridging Cr–O bonds, Cr–O–Cr 126° (NCERT), and Cr still +6, from 2x + 7(−2) = −2. MnO₄⁻ is tetrahedral too, with Mn +7 from x + 4(−2) = −1. Cr (group 6) at +6 and Mn (group 7) at +7 have no d electrons left (d⁰), so their strong colours cannot come from d–d transitions: they come from charge transfer from O to the metal. The tetrahedra are drawn regular and bond lengths are not to scale.

f-Block: Lanthanides and Actinides

• Lanthanides (Ce–Lu): Fill 4f orbitals. Common oxidation state +3 (due to extra stability of [Xe] core). Ce also shows +4; Eu and Yb show +2.
• Lanthanide contraction: As 4f electrons are added, nuclear charge increases but 4f electrons are poor shielders → Z_eff increases → ionic radius contracts steadily from La³⁺ to Lu³⁺.
• Consequences of lanthanide contraction:
  — 4d and 5d elements have nearly identical radii (e.g., Zr ≈ Hf, Nb ≈ Ta) → similar properties, hard to separate.
  — Basicity of Ln(OH)₃ decreases from La(OH)₃ to Lu(OH)₃ (smaller ion, more charge density, less hydroxide).
• Actinides (Th–Lr): Fill 5f orbitals. Show much wider range of oxidation states (+2 to +6 or +7) because 5f, 6d, and 7s energies are close. Many are radioactive.
• Actinide contraction is slightly larger than lanthanide contraction (5f electrons even poorer shielders).

Werner's Theory

• Primary valence (ionisable): Satisfied by negative ions; equals oxidation state of metal.
• Secondary valence (non-ionisable): Satisfied by ligands; equals coordination number (CN).
• Secondary valences are directed in space → determines geometry of the complex.
• Example: [Co(NH₃)₆]Cl₃ — Co has OS +3 (primary valence = 3), CN = 6 (secondary valence = 6), 3 Cl⁻ are counter-ions.

Coordination geometries in 3D — In [Co(NH₃)₆]Cl₃ the six NH₃ ligands sit inside the coordination sphere at the corners of an octahedron, 90° apart: coordination number 6, Werner’s secondary valence, which points in fixed directions and so fixes the shape. The 3 Cl⁻ ions sit outside the sphere. They are ionisable, so one mole of the complex gives 3 mol AgCl with AgNO₃, and they balance cobalt’s oxidation state, +3 (the primary valence; Co³⁺ is d⁶). In [CoCl(NH₃)₅]Cl₂ one Cl⁻ has moved inside: it counts towards both valences and is no longer ionisable, so only 2 AgCl precipitate. Coordination number 4 has two shapes: [Ni(CN)₄]²⁻ (Ni²⁺, d⁸) is square planar, ligands 90° apart, while [Ni(CO)₄] (nickel in oxidation state 0, d¹⁰) is tetrahedral, 109.5°; folding the square turns one into the other. Bond lengths are not to scale.

Key Terminology

Chelate rings in 3D — A chelating ligand bonds through two or more donor atoms and closes a ring with the metal. en (ethane-1,2-diamine) is bidentate: its 2 N take two cis sites, 90° apart, and with the metal and the two CH₂ carbons make a 5-membered ring, M–N–C–C–N. ox²⁻ (oxalate) is bidentate through 2 O and also makes a 5-membered ring, M–O–C–C–O. EDTA⁴⁻ is hexadentate: its 2 N and 4 O fill all six octahedral sites, wrapping round the metal and closing 5 rings, each 5-membered. The rings are counted from the bonds (rings = bonds − atoms + 1). Bond lengths are not to scale, the rings are drawn flat and H atoms are not shown.

IUPAC Nomenclature Rules

• Name the cation first, then the anion (as in ionic nomenclature).
• Within the complex ion: ligands are named alphabetically before the metal.
• Anionic ligands end in -o: Cl⁻ = chlorido, CN⁻ = cyanido, OH⁻ = hydroxido, NO₂⁻ = nitrito, O²⁻ = oxido.
• Neutral ligands retain their names (with exceptions): NH₃ = ammine, H₂O = aqua, CO = carbonyl, NO = nitrosyl.
• Multiplying prefixes: di, tri, tetra, penta, hexa (for simple); bis, tris, tetrakis (for ligands containing a number).
• Metal oxidation state given in Roman numerals in parentheses after metal name.
• If complex is an anion, metal name gets suffix -ate (e.g., ferrate, cuprate, platinate).

Types of Isomerism in Coordination Compounds

Geometric isomers in 3D — Two Cl can be placed on the six sites of octahedral [CoCl₂(NH₃)₄]⁺ (type MA₄B₂) in 15 ways, but turning the ion shows that most are the same. Grouping the placements that one of the octahedron’s 24 rotations maps onto each other leaves 2 isomers: cis, Cl–Co–Cl 90° (12 placements), and trans, 180° (3 placements). In the figure a 120° turn about the centres of two opposite faces lays one cis placement exactly on another. No turn makes cis into trans, because a turn keeps every angle. For MA₃B₃, [Co(NH₃)₃(NO₂)₃], the 20 placements make 2 isomers: fac, with the three NO₂ on one face of the octahedron, all 90° apart (8 placements, one per face), and mer, with the three on a meridian, 90°, 90° and 180° apart (12 placements). None of these is chiral. The same count gives 5 geometric isomers for MA₂B₂C₂, one of them chiral, so 6 stereoisomers in all. Bond lengths are not to scale.

Optical isomers in 3D — [Co(en)₃]³⁺ and its mirror image cannot be superimposed. Each en bridges two cis sites, 90° apart, and the three chelates twist like the blades of a propeller: right-handed in Δ, left-handed in its mirror image Λ (IUPAC names the twist by how any two chelates, seen as skew lines, wind round each other). Of all 24 turns, the best lays only 1 of the 3 en of Λ on an en of Δ, so the ion is chiral: Δ and Λ are enantiomers, and optically active. The 8 ways to place three en make just these 2 isomers, 4 each. cis-[CoCl₂(en)₂]⁺ (often written [Co(en)₂Cl₂]⁺) is chiral too: the best turn lays both Cl of its mirror image on Cl, but 0 of the 2 en on an en. trans-[CoCl₂(en)₂]⁺, with its Cl 180° apart, is achiral: a 90° turn about the Cl–Co–Cl axis lays its mirror image exactly on it. So [CoCl₂(en)₂]⁺ has 3 stereoisomers: trans, and a cis pair of enantiomers (Δ and Λ). Bond lengths are not to scale and H atoms are not shown.

Crystal Field Theory (CFT)

• Ligands are treated as point negative charges; they repel metal d electrons, splitting the degenerate d orbitals.
• Octahedral field: Splits d orbitals into t₂g (dxy, dyz, dxz — lower energy, 3 orbitals) and eg (dx²−y², dz² — higher energy, 2 orbitals). Splitting energy = Δo. t₂g = −0.4Δo; eg = +0.6Δo.
• Tetrahedral field: e (dx²−y², dz²) lower, t₂ (dxy, dyz, dxz) higher. Δt = 4/9 Δo (smaller because only 4 ligands).
• Strong vs weak field ligands:
  Spectrochemical series (increasing Δo):
  I⁻ < Br⁻ < Cl⁻ < F⁻ < OH⁻ < H₂O < SCN⁻ < NH₃ < en < CN⁻ < CO
• Low spin (strong field): Large Δo > pairing energy → electrons pair in t₂g first → fewer unpaired e⁻.
• High spin (weak field): Small Δo < pairing energy → electrons obey Hund's rule → more unpaired e⁻.
• CFSE (Crystal Field Stabilisation Energy) = contribution of t₂g electrons (each −0.4Δo) + eg electrons (each +0.6Δo).

Occurrence of Metals — Ores

Concentration of Ores

Extraction of Metals

Thermodynamic basis — Ellingham diagram: plots ΔG° vs T for metal oxide formation. A metal can reduce another metal's oxide if its ΔG° line lies below the other at that temperature. Carbon and CO are powerful reducing agents at high temperatures.

Blast Furnace — Iron Extraction

Charge: haematite (Fe₂O₃) + coke (C) + limestone (CaCO₃). Temperature zones (bottom to top): tuyere zone (~1500°C), fusion zone, reduction zone, absorption zone.

• CaCO₃ → CaO + CO₂ (flux formation)
• C + O₂ → CO₂; CO₂ + C → 2CO (reducing agent)
• Fe₂O₃ + 3CO → 2Fe + 3CO₂ (main reduction)
• CaO + SiO₂ → CaSiO₃ (slag — removes gangue)
• Pig iron (~4% C) tapped from bottom; slag floats above

Hall-Héroult Process — Aluminium

Al₂O₃ dissolved in molten cryolite (Na₃AlF₆) at ~950°C; electrolysed in carbon-lined cell.

• Cathode: Al³⁺ + 3e⁻ → Al (liquid, sinks to bottom)
• Anode (carbon): 2O²⁻ → O₂ + 4e⁻; O₂ burns anode → CO₂
• Anodes must be replaced periodically (consumed)
• Cryolite lowers melting point and increases conductivity

Refining of Metals

Important Alloys