Inorganic ChemistryTop Priority (3-4 Qs in JEE)

Coordination Compounds Formulas

Werner theory, crystal field splitting (CFT), spectrochemical series, magnetic moments, and isomerism.

9 Formulas•772+ Questions in Bank

Core Formulas & Mathematical Identities

Crystal Field Splitting (Octahedral & Tetrahedral)

\Delta_t = \frac{4}{9}\Delta_o, \quad \text{CFSE}_{\text{oct}} = (-0.4 n_{t_{2g}} + 0.6 n_{e_g})\Delta_o + m P

Splitting of degenerate d-orbitals into t_2g and e_g sets.

Examiner Tip: If Δ_o > P (strong field), electrons pair up in t_2g (low spin).

Spin-Only Magnetic Moment

\mu = \sqrt{n(n + 2)} \text{ BM} \quad (n = \text{number of unpaired electrons})

Bohr Magneton (BM) value indicating paramagnetism.

Examiner Tip: n = 1 -> 1.73 BM, n = 2 -> 2.83 BM, n = 3 -> 3.87 BM, n = 4 -> 4.90 BM, n = 5 -> 5.92 BM.

Spectrochemical Series of Ligands

\text{I}^- < \text{Br}^- < \text{Cl}^- < \text{F}^- < \text{OH}^- < \text{C}_2\text{O}_4^{2-} < \text{H}_2\text{O} < \text{NCS}^- < \text{EDTA}^{4-} < \text{NH}_3 < \text{en} < \text{CN}^- < \text{CO}

Empirical ordering of ligands by their crystal field splitting power Δ.

Examiner Tip: Carbonyl (CO) and cyanide (CN⁻) are the strongest field ligands.

Effective Atomic Number (EAN Rule)

\text{EAN} = Z - (\text{Oxidation State}) + 2 \times (\text{Coordination Number})

Sidgwick's stability rule: complex is exceptionally stable when EAN equals the atomic number of the next noble gas.

Examiner Tip: Metals in low or zero oxidation states (metal carbonyls) obey the 18-electron rule.

Synergic Bonding in Metal Carbonyls

M \xleftarrow{\sigma} \text{CO} \quad + \quad M(d) \xrightarrow{\pi} \text{CO}(\pi^*), \quad \text{Bond Length } (\text{C-O}) \propto \frac{1}{\nu_{\text{CO}}} \propto \text{Negative charge on } M

Dual bonding: ligand-to-metal σ donation and metal d-to-CO π* back-donation strengthens M-C bond while weakening C-O bond.

Examiner Tip: Decreasing order of C-O bond strength (and stretching frequency): [Mn(CO)₆]⁺ > [Cr(CO)₆] > [V(CO)₆]⁻.

Square Planar Crystal Field Splitting (d⁸ Ions)

\Delta_{sp} \approx 1.3 \Delta_o, \quad \text{Energy Order: } d_{x^2-y^2} \gg d_{xy} > d_{z^2} > d_{xz} \approx d_{yz}

Extreme tetragonal elongation removes axial ligands, placing d_{x²-y²} at highest energy. Characteristic of Pt(II), Pd(II), and [Ni(CN)₄]²⁻.

Examiner Tip: All 4d and 5d metals form square planar low-spin diamagnetic complexes with coordination number 4 regardless of ligand strength.

Octahedral & Square Planar Isomerism Summary

[Ma_2b_2] \to \text{cis/trans (2)}, \quad [Mabcd] \to 3\,\text{GI}, \quad [Ma_3b_3] \to \text{fac/mer (2)}, \quad [M(AA)_2b_2] \to \text{cis (chiral) } + \text{ trans (achiral)}

Geometrical (GI) and Optical (OI) isomer counts. Square planar complexes cannot show optical activity due to molecular plane.

Examiner Tip: Tris-bidentate complex [M(AA)₃] (like [Co(en)₃]³⁺) has NO plane of symmetry and exists as an enantiomeric pair (d and l).

CFSE Values for Octahedral d^n Configurations

\text{CFSE (oct, high spin): } d^1\!=\!-0.4, d^2\!=\!-0.8, d^3\!=\!-1.2, d^4\!=\!-0.6, d^5\!=\!0, d^6\!=\!-0.4, d^7\!=\!-0.8, d^8\!=\!-1.2, d^9\!=\!-0.6, d^{10}\!=\!0 \;(\times\Delta_o)

Crystal Field Stabilisation Energy in units of Δ_o for high-spin octahedral complexes (no extra pairing energy P). Low-spin complexes have greater CFSE (more electrons in t_2g): e.g. d⁶ low-spin = -2.4Δ_o + P.

Examiner Tip: d³ and d⁸ have maximum CFSE in high-spin octahedral field (-1.2Δ_o) → most stable complexes (Cr³⁺ and Ni²⁺ form very stable octahedral complexes). d⁰, d⁵ (HS), d¹⁰ have zero CFSE.

Stability Constant (K_f) & Lability of Complexes

K_f = \frac{[\text{ML}_n]}{[\text{M}][\text{L}]^n}, \quad \log K_f \propto \text{Stability}, \quad \beta_n = K_{f1} \times K_{f2} \times \cdots \times K_{fn} \; (\text{overall stability})

Formation constant K_f (also called stability constant) measures thermodynamic stability of a complex. β_n is the cumulative/overall stability constant for stepwise addition of n ligands.

Examiner Tip: EDTA forms highly stable 1:1 chelate complexes (log K_f ~ 18 for Ca²⁺). Chelate effect: polydentate ligands are more stable than monodentate equivalents due to entropy gain. Lability ≠ thermodynamic stability (e.g., [Co(NH₃)₆]³⁺ is thermodynamically stable but kinetically inert).

Top Examiner Traps & Pitfalls

Frequently tested misconceptions in Coordination Compounds

•Strong field ligands (CN⁻, CO, en) cause electron pairing (low spin); weak field ligands (halides) do not pair electrons (high spin).
•Tetrahedral field splitting Δ_t is ALWAYS less than pairing energy (Δ_t = 4/9 Δ_o), hence tetrahedral complexes are always high spin.

Previous Chapter

Chemical Bonding & VSEPR

7 Formulas•Inorganic Chemistry

Next Chapter

d- & f-Block Elements

Inorganic Chemistry•8 Formulas