Chemistry Chapter 5: Coordination Compounds

Chapter 5: Coordination Compounds

Key Topics: Werner's Theory, Ligands & Coordination Sphere, Valence Bond Theory (VBT), Crystal Field Theory (CFT), and Isomerism.

1. Fundamental Definitions

Coordination compounds are addition compounds in which a central metal ion is bound to a number of ions or neutral molecules (ligands) via coordinate covalent bonds.

  • Central Metal Atom/Ion: The acceptor of electron pairs (Lewis acid).
  • Ligands: Neutral molecules or anions that donate electron pairs to the metal (Lewis base).
  • Coordination Number: Total number of ligand donor atoms bonded directly to the central metal ion.

2. Werner's Theory of Coordination Compounds

  • Primary Valency: Non-directional, ionizable, corresponds to the oxidation state of the central metal.
  • Secondary Valency: Directional, non-ionizable, corresponds to the coordination number of the metal.

3. Valence Bond Theory (VBT) & Geometry

Coordination Number Hybridization Geometry Example
4 $sp^3$ Tetrahedral $[\text{Ni(CO)}_4], [\text{NiCl}_4]^{2-}$
4 $dsp^2$ Square Planar $[\text{Ni(CN)}_4]^{2-}, [\text{Pt(NH}_3)_4]^{2+}$
6 $sp^3d^2$ (Outer orbital) Octahedral $[\text{CoF}_6]^{3-}, [\text{Fe(H}_2\text{O)}_6]^{3+}$
6 $d^2sp^3$ (Inner orbital) Octahedral $[\text{Co(NH}_3)_6]^{3+}, [\text{Fe(CN)}_6]^{3-}$

4. Magnetic Moment Formula

Spin-Only Magnetic Moment ($\mu_s$): $$\mu_s = \sqrt{n(n+2)} \quad \text{B.M.}$$ Where: $$n = \text{Number of unpaired electrons on the central metal ion}$$ $$\text{B.M.} = \text{Bohr Magneton}$$

5. Crystal Field Theory (CFT) Equations

In an octahedral crystal field, the five degenerate $d$-orbitals split into two sets: lower energy $t_{2g}$ orbitals ($d_{xy}, d_{yz}, d_{xz}$) and higher energy $e_g$ orbitals ($d_{z^2}, d_{x^2-y^2}$).

Crystal Field Splitting Energy ($\Delta_o$) in Octahedral Complex: $$\Delta_o = E(e_g) - E(t_{2g})$$
Crystal Field Stabilization Energy (CFSE) for Octahedral Complexes: $$\text{CFSE} = \left( -0.4 \times n_{t2g} + 0.6 \times n_{eg} \right) \Delta_o + n_P \cdot P$$ Where: $$n_{t2g} = \text{Number of electrons in } t_{2g} \text{ orbitals}$$ $$n_{eg} = \text{Number of electrons in } e_g \text{ orbitals}$$ $$P = \text{Pairing energy}$$
Relationship between Tetrahedral ($\Delta_t$) and Octahedral ($\Delta_o$) Splitting Energy: $$\Delta_t = \frac{4}{9} \Delta_o$$

6. Stability of Coordination Complexes

Overall Stability Constant ($\beta_n$): For the stepwise equilibrium reaction $M + nL \rightleftharpoons ML_n$: $$\beta_n = \frac{[ML_n]}{[M][L]^n} = K_1 \times K_2 \times \dots \times K_n$$
Instability (Dissociation) Constant: $$\text{Instability Constant} = \frac{1}{\beta_n}$$