Coordination Compounds

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Coordination Compounds — Key Facts for JEE Advanced

Key Definitions:

• Coordination Complex: Central metal atom/ion surrounded by ligands (neutral, anionic, or cationic)
• Ligand: Lewis base (donates electron pair) attached to metal center
• Coordination Number (CN): Number of donor atoms attached to the central metal ion
• Counter ions: Ions outside the coordination sphere that balance charge
• [Co(NH₃)₆]Cl₃: Coordination sphere = [Co(NH₃)₆]³⁺; counter ion = 3Cl⁻

⚡ JEE Warning: Don’t confuse oxidation state with coordination number. Oxidation state is the charge on metal after removing ligands as neutral/anionic. CN is the number of attachment points. For [Co(NH₃)₆]Cl₃: Co oxidation state = +3, CN = 6, coordination geometry = octahedral.

Nomenclature — Key Rules:

1. Name the cation first, then anion
2. Ligand names: anionic ligands get –o suffix (Cl⁻ = chloro, OH⁻ = hydroxo, CN⁻ = cyano, NO₂⁻ = nitro or nitrito, SCN⁻ = thiocyanato)
3. Neutral and cationic ligands: use their common names (NH₃ = ammine, H₂O = aqua, CO = carbonyl, NO = nitrosyl)
4. Number prefixes: di-, tri-, tetra-, penta-, hexa- for multiple ligands
5. If multiple ligands: name in alphabetical order (ignoring di-, tri-, etc.)
6. Oxidation state of metal in parentheses after name: [Co(NH₃)₆]Cl₃ = hexamminecobalt(III) chloride

Isomerism — Must Know:

• Ionization isomer: Counter ion and ligand exchange positions (e.g., [Co(NH₃)₅(SO₄)]Br vs [Co(NH₃)₅Br]SO₄)
• Hydrate isomerism: Water inside vs outside coordination sphere (e.g., [Cr(H₂O)₆]Cl₃ vs [Cr(H₂O)₅Cl]Cl₂·H₂O)
• Linkage isomerism: Ligand can bind through different atoms (e.g., NO₂⁻: can bind through N (nitro) or O (nitrito))
• Geometrical isomerism: cis vs trans in square planar and octahedral complexes
• Optical isomerism: Non-superimposable mirror images (chiral complexes)

⚡ Exam Tip: [Co(en)₂Cl₂]⁺ has optical isomerism (en = ethylenediamine = H₂N–CH₂–CH₂–NH₂). The cis isomer has a plane of symmetry → achiral. The trans isomer has a center of symmetry → achiral. Wait — actually [Co(en)₃]³⁺ (tris-ethylenediamine) is chiral. [Co(en)₂Cl₂]⁺: trans has a C₂ axis + center of symmetry → achiral. The cis form has a C₂ axis but no plane or center → chiral.

⚡ Exam Tip: For square planar complexes, [Pt(NH₃)₂Cl₂] exists as cis and trans isomers. Cis is clinically used as an anticancer drug (cisplatin). Trans isomer has different pharmacological activity.

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🟡 Standard — Regular Study (2d–2mo)

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Coordination Compounds — Chemistry Study Guide

1. Structure & Bonding:

Valence Bond Theory (VBT):

• Metal uses d-orbitals for bonding
• Strong Field Ligands (NH₃, CN⁻, CO, en): cause pairing of electrons → fewer unpaired electrons → low spin complexes
• Weak Field Ligands (H₂O, F⁻, Cl⁻, Br⁻, I⁻): do not cause pairing → high spin complexes
• Spectrochemical Series (field strength order):

  CO > CN⁻ > NO₂⁻ > phen > NH₃ > H₂O > F⁻ > OH⁻ > Cl⁻ > Br⁻ > I⁻
  Strong ←————————————————————————————→ Weak
  (low spin)                              (high spin)

• For octahedral complexes: eg orbitals are antibonding (higher in energy)
• t₂g orbitals are non-bonding (lower)

⚡ Example: [Co(NH₃)₆]³⁺ vs [CoF₆]³⁻

• [Co(NH₃)₆]³⁺: Co³⁺ = d⁶; NH₃ is strong field → all electrons paired in t₂g → low spin (t₂g⁶eg⁰) → diamagnetic
• [CoF₆]³⁻: Co³⁺ = d⁶; F⁻ is weak field → 4 unpaired (t₂g⁴eg²) → paramagnetic with 4 unpaired electrons

⚡ Example: [Fe(CN)₆]⁴⁻ vs [Fe(H₂O)₆]²⁺

• [Fe(CN)₆]⁴⁻: Fe²⁺ = d⁶; CN⁻ strong field → low spin t₂g⁶ → diamagnetic
• [Fe(H₂O)₆]²⁺: Fe²⁺ = d⁶; H₂O weak field → high spin t₂g⁴eg² → 4 unpaired electrons

Crystal Field Theory (CFT) — Octahedral:

• Δ₀ (crystal field splitting) = energy difference between t₂g and eg sets
• P (pairing energy) = energy cost to pair electrons in same orbital
• If Δ₀ > P → low spin (electrons pair in t₂g before occupying eg)
• If Δ₀ < P → high spin (electrons occupy eg before pairing)
• Δ₀ is larger for: higher oxidation state metals, down a group (3d < 4d < 5d), strong field ligands

Magnetic Moment:

• μ = √(n(n+2)) BM where n = number of unpaired electrons
• n = 0 → μ = 0 (diamagnetic)
• n = 1 → μ = √3 ≈ 1.73 BM
• n = 2 → μ = √8 ≈ 2.83 BM
• n = 3 → μ = √15 ≈ 3.87 BM (for octahedral high-spin d⁴ or low-spin d⁷)
• n = 4 → μ = √24 ≈ 4.90 BM (high-spin d⁶, e.g., [Fe(H₂O)₆]²⁺)
• n = 5 → μ = √35 ≈ 5.92 BM (high-spin d⁵)

⚡ JEE计算题: A complex has magnetic moment of 3.87 BM. What is the number of unpaired electrons? n=3 gives μ=√15=3.87 BM. This could be: high-spin d⁴ or low-spin d⁷ in octahedral geometry.

Coordination Numbers and Geometries:

CN	Geometry	Examples
2	Linear	[Ag(NH₃)₂]⁺, [Cu(CN)₂]⁻
4	Tetrahedral	[Zn(CN)₄]²⁻, [NiCl₄]²⁻
4	Square planar	[Ni(CN)₄]²⁻, [PtCl₄]²⁻ (dsp²), [PdCl₄]²⁻
6	Octahedral	[Co(NH₃)₆]³⁺, [Fe(CN)₆]⁴⁻, [Cr(H₂O)₆]³⁺
12	Cuboctahedral	Very rare, e.g., [Ce(NO₃)₆]²⁻ (12-coordinate Ce)

⚡ Square planar complexes are mainly d⁸ (Ni²⁺, Pd²⁺, Pt²⁺, Au³⁺). The large crystal field splitting in square planar (Δsp) makes it favorable. [Ni(CN)₄]²⁻ is square planar (dsp²), diamagnetic. [NiCl₄]²⁻ is tetrahedral, paramagnetic (2 unpaired).

2. Preparation Methods:

Double Salt Method:

• When two salts are crystallized together in fixed proportions
• Example: Mohr’s salt = (NH₄)₂[Fe(SO₄)₂]·6H₂O = ammonium iron(II) sulfate hexahydrate
• Example: Potash alum = K[Al(SO₄)₂]·12H₂O
• These dissociate into ions in solution: both metal ions behave independently

Complex Formation:

• Metal salt + ligand → coordination complex
• [Cu(H₂O)₆]²⁺ (pale blue) + 4NH₃ → [Cu(NH₃)₄(H₂O)₂]²⁺ (deep blue)
• Transition is dramatic: this is the classic test for Cu²⁺

3. Important Complexes:

Cisplatin: [Pt(NH₃)₂Cl₂] — square planar, anticancer drug (binds to DNA guanine bases)

Chlorophyll: Mg²⁺ complex with porphyrin ring (photosynthesis pigment); central Mg is coordinated to 4 N atoms of the porphyrin + one water

Hemoglobin: Fe²⁺ in porphyrin + histidine + H₂O (or O₂ when oxygenated); deoxyhemoglobin has H₂O; oxyhemoglobin has O₂ coordinated

Wilkinson’s Catalyst: [Rh(PPh₃)₃Cl] — Rh(I), square planar, used in hydrogenation catalysis

Zeise’s Salt: [Pt(C₂H₄)Cl₃]⁻ — first metal-olefin complex discovered

Tetramminecopper(II): [Cu(NH₃)₄(H₂O)₂]²⁺ — deep blue-violet complex; formation of this from [Cu(H₂O)₄]²⁺ is a qualitative test for Cu²⁺

4. Thermodynamic and Kinetic Stability:

Thermodynamic Stability (Kf):

• Overall formation constant βₙ for: M + nL ⇌ [MLₙ]
• Large β means thermodynamically stable complex
• Stepwise formation constants: K₁, K₂, K₃…
• βₙ = K₁ × K₂ × K₃ × … × Kₙ

⚡ JEE Tip: For [Ag(NH₃)₂]⁺: Kf = K₁ × K₂. The stepwise constants are different. K₁ (for first NH₃) is always larger than K₂ (second) because electrostatic: positively charged metal + positively charged [M(NH₃)]ⁿ⁺ → less favorable to add another.

Kinetic Stability (Labile vs Inert):

• Labile complexes: Fast ligand substitution (kinetics fast) — usually high spin d⁵, d⁶ high spin
• Inert complexes: Slow ligand substitution — usually low spin d⁴, d⁵, d⁶ (especially Cr³⁺, Co³⁺, low spin Fe²⁺, Ni²⁺ in certain geometries)
• Inert but not thermodynamically stable: [Co(NH₃)₆]³⁺ is kinetically inert (very slow substitution) but thermodynamically unstable in acidic solution

⚡ Classic inert complexes: [Co(NH₃)₆]³⁺ (low spin d⁶, kinetically inert, doesn’t exchange NH₃ readily), [Cr(H₂O)₆]³⁺ (low spin d³, kinetically inert), [Fe(CN)₆]⁴⁻ (low spin d⁶).

⚡ Labile complexes: [Cu(H₂O)₆]²⁺, [Zn(H₂O)₆]²⁺ (d¹⁰ systems — no CFSE, no kinetic advantage), [Ni(H₂O)₆]²⁺.

5. Valence Bond Theory — Hybridization Examples:

[Fe(CN)₆]⁴⁻ (Hexacyanoferrate(II)):

• Fe²⁺ = d⁶
• CN⁻ is strong field → all electrons pair → low spin
• Configuration: t₂g⁶ eg⁰ (all paired)
• Hybridization: d²sp³ (inner orbital, octahedral)
• Magnetic: diamagnetic (μ = 0 BM)
• Note: Sometimes represented as d²sp³ but with t₂g orbitals used (completely filled t₂g are non-bonding)

[Fe(H₂O)₆]²⁺:

• Fe²⁺ = d⁶
• H₂O is weak field → high spin
• Configuration: t₂g⁴ eg² (four unpaired)
• Hybridization: sp³d² (outer orbital, octahedral)
• Magnetic: 4 unpaired → μ = √24 = 4.90 BM

[Ni(CN)₄]²⁻:

• Ni²⁺ = d⁸
• Square planar (strong field CN⁻)
• dsp² hybridization (inner orbital)
• Diamagnetic (all electrons paired)
• In VBT: one d orbital from dₓ₂₋ᵧ₂ is used for dsp²

[NiCl₄]²⁻:

• Ni²⁺ = d⁸
• Tetrahedral geometry
• sp³ hybridization (no d-orbital involvement)
• Paramagnetic: 2 unpaired electrons (μ ≈ 2.83 BM)
• In tetrahedral crystal field: t₂ orbitals are higher than e, but the geometry is tetrahedral so pairing energy vs Δt favors no pairing

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Coordination Compounds — Comprehensive Chemistry Notes

1. Detailed Crystal Field Theory:

Octahedral Complexes — d-Orbital Splitting:

         eg (dz², dxy)
        /        \
      /          \
    /            \
t₂g (dxy, dyz, dxz)
Energy:       +0.6Δ₀   (eg)
              -0.4Δ₀   (t₂g)

Crystal Field Stabilization Energy (CFSE):

CFSE = (# t₂g electrons × –0.4Δ₀) + (# eg electrons × +0.6Δ₀) + pairing correction

Examples:

• d⁶ low spin (t₂g⁶): CFSE = 6(–0.4)Δ₀ = –2.4Δ₀ (very stable, inert)
• d⁶ high spin (t₂g⁴eg²): CFSE = 4(–0.4)Δ₀ + 2(+0.6)Δ₀ = –1.6Δ₀ + 1.2Δ₀ = –0.4Δ₀
• d⁵ high spin (t₂g³eg²): CFSE = 3(–0.4)Δ₀ + 2(+0.6)Δ₀ = –1.2Δ₀ + 1.2Δ₀ = 0 (no stabilization)
• d⁴ high spin (t₂g²eg²): CFSE = 2(–0.4)Δ₀ + 2(+0.6)Δ₀ = –0.8Δ₀ + 1.2Δ₀ = +0.4Δ₀

⚡ CFSE = 0 for d⁰, d⁵ high spin, d¹⁰. These have no crystal field stabilization. This explains why d¹⁰ complexes like [Zn(H₂O)₆]²⁺ are labile — no CFSE advantage to any particular geometry.

Factors Affecting Δ₀ (Crystal Field Splitting):

1. Oxidation state of metal: Higher oxidation state → larger Δ₀ (stronger M–L interaction). Fe³⁺ complexes have larger Δ₀ than Fe²⁺ complexes.

   • Example: [Co(NH₃)₆]³⁺ (Co³⁺, d⁶) is low spin; [Co(NH₃)₆]²⁺ (Co²⁺, d⁷) is high spin

2. Period of metal: Down a group, Δ₀ increases (4d > 3d, 5d > 4d)

   • [Rh(NH₃)₆]³⁺ has larger Δ₀ than [Co(NH₃)₆]³⁺ (5d vs 3d metals)

3. Nature of ligand: The Spectrochemical Series defines ligand field strength

   • Strong field (CO, CN⁻, NO₂⁻, phen) → large Δ → low spin
   • Weak field (I⁻, Br⁻, Cl⁻, F⁻, H₂O) → small Δ → high spin

4. Nature of donor atom: Down a group in periodic table: C ≈ N >> S > Cl > Br > I (for halides and chalcogenides as donors)

Jahn-Teller Distortion:

• Any nonlinear molecule in a degenerate electronic state will undergo distortion to remove degeneracy
• Important for: d⁹ (Cu²⁺), high spin d⁴ (Mn³⁺, Cr²⁺)
• Example: [Cu(H₂O)₆]²⁺ is Jahn-Teller distorted → elongated octahedron (two axial bonds longer than four equatorial bonds)
• This is why Cu²⁺ complexes are often square planar or distorted octahedral, not regular octahedral

⚡ JEE计算题: Calculate CFSE for [Co(NH₃)₆]³⁺ (Co³⁺ = d⁶, strong field, low spin):

• Configuration: t₂g⁶eg⁰
• CFSE = 6(–0.4)Δ₀ + 0 = –2.4Δ₀
• No pairing energy needed beyond what the strong field provides
• This large negative CFSE explains why Co³⁺ complexes are so stable and inert.

2. Electronic Spectra (d-d Transitions):

Color in Complexes:

• Complexes are colored because d-d transitions absorb visible light
• The color we see is the complementary color of what is absorbed
• [Ti(H₂O)₆]³⁺: d¹, absorbs green-yellow → appears violet
• [Cu(H₂O)₆]²⁺: d⁹, absorbs red-orange → appears blue
• [Fe(H₂O)₆]²⁺: d⁶ high spin, very pale green (weak absorption)

⚡ d-d transition selection rules:

• Laporte (orbital) forbidden: d-d transitions are Laporte-forbidden → low intensity (ε ~ 10-100 L mol⁻¹ cm⁻¹)
• Spin forbidden: ΔS = 0 required; transitions between different spin states are very weak
• σ → σ⁺ transitions in UV region; d → d in visible/near-UV
• Coordination lowers symmetry → relaxes Laporte rule somewhat → we see the colors

Tanabe-Sugano Diagrams:

• Used to analyze d-d spectra of octahedral complexes
• Energy (E/Δ₀) on y-axis vs electron configuration on x-axis
• Two types of diagrams: high spin and low spin
• From spectrum: identify v₁, v₂, v₃ bands → calculate Δ₀ and B (Racah parameter)

3. Isomerism — Detailed:

Geometrical Isomerism in Octahedral Complexes:

With 6 identical ligands (e.g., [Co(NH₃)₆]): No geometrical isomerism.

With two types of ligands (e.g., [Co(NH₃)₄Cl₂]):

• [Co(NH₃)₄Cl₂]Cl has:
  • Fac isomer: All three identical ligands on one face (fac = facial) — gives facial arrangement
  • Mer isomer: All three identical ligands spread across meridional positions — one position has 2 like ligands
• In fac-[Co(NH₃)₃Cl₃]: three NH₃ occupy one triangular face
• In mer-[Co(NH₃)₃Cl₃]: three NH₃ are at positions 1, 2, 4 (around the meridian)

With bidentate ligands (e.g., [Co(en)₂Cl₂]):

• cis-[Co(en)₂Cl₂]⁺: two Cl are adjacent; the two en rings are in the same plane or perpendicular — chiral or achiral depending on arrangement
• Actually: [Co(en)₂Cl₂]⁺ has optical isomers for the cis form (it has a plane of symmetry only in certain arrangements)
• trans-[Co(en)₂Cl₂]⁺: the two Cl are opposite; this form has a center of symmetry → achiral

⚡ Determining chirality in [Co(en)₃]³⁺:

• Three bidentate en ligands arranged octahedrally
• The complex exists as a pair of enantiomers (Λ and Δ)
• These are non-superimposable mirror images
• This is THE classic optical isomerism example in coordination chemistry

Square Planar Geometrical Isomerism:

• [Pt(NH₃)₂Cl₂]: exists as cis (Cl atoms adjacent) and trans (Cl atoms opposite)
• Only cisplatin has anticancer activity; trans has no therapeutic value
• cis → Cl atoms 90° apart; trans → 180° apart
• cis is polar (net dipole moment ≠ 0); trans has dipole moment = 0 (symmetric)

Ionization Isomerism:

[Co(NH₃)₅SO₄]Br (red-violet) vs [Co(NH₃)₅Br]SO₄ (green)
In first: SO₄²⁻ is ligand (bound to Co through O)
In second: Br is ligand (bound to Co)
These give different colors and different Ag⁺ precipitation tests
(First: Br⁻ is free counterion → AgBr precipitate with AgNO₃
 Second: SO₄²⁻ is counterion → BaSO₄ precipitate with BaCl₂)

Linkage Isomerism (Ambidentate Ligands):

• NO₂⁻: can bind through N (nitro) or O (nitrito)
• SCN⁻: can bind through S (thiocyanato) or N (isothiocyanato)
• CN⁻: can bind through C (cyano) or N (isocyano) — less common
• Example: [Co(NO₂)₆]³⁻ (all nitro, through N) vs [Co(ONO)₆]³⁻ (all nitrito, through O)

Stereoisomerism vs Structural Isomerism:

• Stereoisomers: same connectivity, different spatial arrangement
• Structural isomers: different connectivity
• Types we covered: ionization (structural), hydrate (structural), linkage (structural), geometrical (stereochemical), optical (stereochemical)

4. Ligand Field Theory (LFT) — Beyond CFT:

MOT for Coordination Complexes:

• In octahedral: metal d orbitals interact with ligand orbitals
• t₂g orbitals: overlap with ligand orbitals less (they point between ligands)
• eg orbitals: overlap more directly with ligand donor orbitals → more antibonding
• Bonding molecular orbitals (lower energy): formed from metal d + ligand orbitals
• Antibonding MOs (t₂g* and eg*): metal d character dominates

π-Bonding:

• Backbonding: metal dπ → ligand π* orbitals (CO, CN⁻, NO, phen)
• This strengthens M–L bond and reduces bond order of the ligand
• In metal carbonyls: C–O bond order is slightly less than 3 (in free CO, bond order is 3)
• π-acceptor ligands (backbonding ligands): CO, CN⁻, NO, aromatic ligands
• π-donor ligands: X⁻ (halides), OH⁻, H₂O (to lesser extent)

⚡ Spectrochemical Series can be explained by π-interactions:

• Weak field (I⁻, Br⁻, Cl⁻): π-donors → they donate electron density to metal through π — reduces Δ₀
• Strong field (CO, CN⁻): π-acceptors → they accept electron density from metal through π-backbonding — increases Δ₀
• This explains why CO, CN⁻ are such strong field ligands

4. Synthesis and Applications:

Complexometric Titration:

EDTA (ethylenediaminetetraacetic acid): Y⁴⁻ + M²⁺ → [M–EDTA]²⁻
EDTA is hexadentate: coordinates through 2 N atoms + 4 O atoms
Used to determine water hardness (Ca²⁺, Mg²⁺)
Indicator: Eriochrome Black T (changes from wine red to blue at endpoint)

⚡ JEE analytically tests: The metal-EDTA complex has higher formation constant (Kf) with smaller, more highly charged metal ions. Ca²⁺ (Kf ~10¹⁰) vs Mg²⁺ (Kf ~10⁸).

Biological Coordination Chemistry:

Hemoglobin:

• Fe²⁺ in porphyrin (Fe is in +2 oxidation state)
• Binds O₂ reversibly at the 6th coordination position
• O₂ binding is cooperative: binding of first O₂ makes second easier (the Fe moves into the plane of the porphyrin, causing a conformational change)
• CO is toxic because it binds to Fe²⁺ 25,000× more strongly than O₂ (via π-backbonding)
• The porphyrin ring is a tetraaza macrocycle (four N donors in square planar arrangement around Fe)

Chlorophyll:

• Mg²⁺ at center of porphyrin-like ring (chlorin, which is a reduced porphyrin)
• The Mg²⁺ is coordinated to 4 N atoms of the chlorin ring + one water (axial)
• The visible light absorption by chlorophyll drives photosynthesis
• Substitution of Mg²⁺ by Cu²⁺ gives a green dye (copper phthalocyanine, commercial pigment)

Cyanocobalamin (Vitamin B₁₂):

• Co³⁺ in a corrin ring (corrin is a macrocycle similar to porphyrin)
• Contains Co–C bond (organometallic)
• Essential for blood formation; deficiency causes pernicious anemia

Siderophores:

• Bacterial iron transport agents
• Catechol and hydroxamate groups bind Fe³⁺ very strongly
• Enterobactin: one of the strongest Fe³⁺ chelators known (Kf ~10⁵²)

5. Important Calculations:

Determining Oxidation State:

[Co(NH₃)₅Cl]SO₄:
- NH₃ is neutral (0)
- Cl as ligand: usually Cl⁻ (–1) unless bridging
- SO₄ is counterion (–2)
- Charge on [Co(NH₃)₅Cl]: +2 (to balance SO₄²⁻)
- Co + 0 + (–1) = +2 → Co = +3
Answer: cobalt(III)

Determining Coordination Number from Crystal Structure:

• In [Co(en)₃]³⁺: en is bidentate, 3 en ligands → CN = 6
• In [Co(NH₃)₆]³⁺: 6 monodentate NH₃ ligands → CN = 6
• In [Cu(EDTA)]²⁻: EDTA is hexadentate (6 donor atoms) → CN = 6

Magnetic Moment Calculation:

[Fe(H₂O)₆]²⁺: Fe²⁺ = d⁶, weak field (H₂O) → high spin
High spin d⁶: t₂g⁴ eg² → 4 unpaired electrons
μ = √(4×5) = √20 = 4.47 BM (spin-only formula, slightly modified by orbital contribution)
Spin-only formula: μ_so = √(n(n+2)) BM
For 4 unpaired: μ = √(4×6) = √24 = 4.90 BM (this is what we use in JEE)
Actually: n(n+2) for n=4: 4×6 = 24, √24 = 4.90 BM

⚡ JEE常常考: “The spin-only magnetic moment of [CoF₆]³⁻ is 4.90 BM. What does this tell you?” Since Co³⁺ is d⁶ and F⁻ is weak field, we have high spin d⁶ (t₂g⁴eg², 4 unpaired). Co³⁺ is usually low spin in complexes (strong field) but F⁻ being weak field causes high spin. So [CoF₆]³⁻ = high spin d⁶, 4 unpaired electrons, μ = 4.90 BM.

6. Stability Constants and Their Use:

Stepwise vs Overall Constants:

M + L ⇌ ML: K₁
ML + L ⇌ ML₂: K₂
ML₂ + L ⇌ ML₃: K₃
Overall β₃ = K₁ × K₂ × K₃

Irving-Williams Series (stability order for divalent metal ions with same ligand):

Ba²⁺ < Ca²⁺ < Mg²⁺ < Mn²⁺ < Fe²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺ < Zn²⁺

⚡ This is for high spin complexes with similar ligands. The stability generally correlates with ionic radius and CFSE. Cu²⁺ is an outlier (Jahn-Teller distortion affects it).

⚡ Chelate Effect: Complexes with polydentate ligands (chelating ligands) are more stable than those with comparable monodentate ligands. Example: [Ni(en)₃]²⁺ is much more stable than [Ni(NH₃)₆]²⁺. This is because:

1. Enthalpy: multiple donor atoms from same ligand → better bonding
2. Entropy: one chelating ligand replaces multiple monodentate ligands → more particles in solution → greater entropy gain

7. Industrial and Environmental Applications:

• Nickel plating: [Ni(CN)₄]²⁻ complex dissociates to give Ni²⁺ for plating
• Photography: [Ag(S₂O₃)₂]³⁻ (thiosulfate complex) dissolves AgBr in fixing
• Qualitative analysis: Group separation using complex formation:
  • Group IV (Zn²⁺): forms [Zn(NH₃)₆]²⁺ — doesn’t precipitate with H₂S in ammoniacal medium
  • Group III (Fe³⁺, Al³⁺): do not form stable ammine complexes
• Metal extraction: Cyanide leaching of gold: 4Au + 8CN⁻ + O₂ + 2H₂O → 4[Au(CN)₂]⁻ + 4OH⁻
• Water treatment: EDTA sequesters Ca²⁺ and Mg²⁺ (water softening)
• Cisplatin: Pt-based anticancer drug (DNA crosslinking)
• Carboplatin, Oxaliplatin: Second and third generation Pt drugs with fewer side effects
• ** Gadolinium DTPA:** MRI contrast agent (Gd³⁺ chelate)
• ** Prussian Blue:** Fe₄[Fe(CN)₆]₃ — deep blue pigment; used to treat cesium-137 and thallium poisoning

⚡ Environmental: EDTA in waterways can mobilize heavy metals (lead, cadmium) by forming soluble complexes, making them bioavailable. This is why NTA (nitrilotriacetic acid) was developed as a phosphate substitute in detergents — it biodegrades better than EDTA.

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