Chemca Formula Sheet - Coordination Compounds

CHEMCA

EXAM MASTER FORMULA SHEET

Coordination Compounds

Strategic Summary for JEE Main, Advanced & NEET

1. Werner's Theory & EAN

Primary Valency

• Corresponds to the Oxidation State of the central metal.
• Always satisfied by negative ions.
• Ionizable & Non-directional. (Denoted by dotted lines).

Secondary Valency

• Corresponds to the Coordination Number (C.N.).
• Satisfied by ligands (neutral molecules or negative ions).
• Non-ionizable & Directional (Dictates Geometry). (Denoted by solid lines).

Effective Atomic Number (EAN) Rule:

Proposed by Sidgwick. Total number of electrons possessed by the central metal ion plus the electrons donated by the ligands.

\[ \text{EAN} = Z - \text{O.S.} + 2 \times (\text{C.N.}) \]

If EAN equals the atomic number of the next noble gas (e.g., 36, 54, 86), the complex follows the EAN rule and is generally highly stable (especially true for Metal Carbonyls).

2. Isomerism in Complexes

Structural Isomerism

• Ionization: Exchange of ions inside and outside the coordination sphere. Give different ions in solution. E.g., $\ce{[Co(NH3)5Br]SO4}$ and $\ce{[Co(NH3)5SO4]Br}$.
• Linkage: Occurs in complexes containing ambidentate ligands (like $\ce{SCN^-/NCS^-}$, $\ce{NO2^-/ONO^-}$).
• Hydrate/Solvate: Difference in the number of water molecules inside/outside the sphere as ligands vs water of crystallization.
• Coordination: Exchange of ligands between cationic and anionic coordination spheres in a complex salt.

Stereoisomerism

Geometrical (Cis-Trans):
• Sq. Planar ($C.N.=4$): $MA_2B_2$ shows Cis-Trans. ($MA_4, MA_3B$ do not).
• Octahedral ($C.N.=6$): $MA_4B_2$ shows Cis-Trans. $MA_3B_3$ shows Facial (fac) and Meridional (mer) isomers.
Optical Isomerism:
Shown by non-superimposable mirror images (enantiomers) lacking a plane of symmetry.
• Very common in Octahedral complexes with bidentate chelating ligands (e.g., $\ce{[Co(en)3]^{3+}}$ or Cis-$\ce{[Co(en)2Cl2]+}$).
• Trans isomers are usually optically inactive due to symmetry.

3. Valence Bond Theory (VBT) Master Table

Explains geometry and magnetic properties based on hybridization of vacant metal orbitals.

C.N.	Hybridization	Geometry	Classic Example	Magnetic Nature
4	$sp^3$	Tetrahedral	$\ce{[Ni(CO)4]}$ ($d^{10}$)	Diamagnetic
4	$dsp^2$	Square Planar	$\ce{[Ni(CN)4]^{2-}}$ ($d^8$, SFL)	Diamagnetic
4	$sp^3$	Tetrahedral	$\ce{[NiCl4]^{2-}}$ ($d^8$, WFL)	Paramagnetic ($n=2$)
6	$sp^3d^2$	Octahedral (Outer Orbital / High Spin)	$\ce{[CoF6]^{3-}}$ ($d^6$, WFL)	Paramagnetic ($n=4$)
6	$d^2sp^3$	Octahedral (Inner Orbital / Low Spin)	$\ce{[Co(NH3)6]^{3+}}$ ($d^6$, SFL)	Diamagnetic ($n=0$)

4. Crystal Field Theory (CFT)

Treats metal-ligand interaction as purely electrostatic. Ligands cause splitting of degenerate d-orbitals.

Octahedral Splitting ($\Delta_o$):

Splitting pattern: $t_{2g}$ (Lower energy, $-0.4\Delta_o$), $e_g$ (Higher energy, $+0.6\Delta_o$)

\[ \text{CFSE} = [-0.4 n_{t_{2g}} + 0.6 n_{e_g}]\Delta_o + mP \]

$P$ = Pairing Energy, $m$ = No. of paired electron sets.

Tetrahedral Splitting ($\Delta_t$):

Splitting pattern: $e$ (Lower energy), $t_2$ (Higher energy). Splitting is smaller.

\[ \Delta_t = \frac{4}{9} \Delta_o \]

Because $\Delta_t < P$, tetrahedral complexes are almost always High Spin.

Spectrochemical Series:

Arrangement of ligands in increasing order of Crystal Field Splitting Energy ($\Delta_o$).

\[ \ce{I- < Br- < SCN- < Cl- < S^2- < F- < OH- < C2O4^2- < H2O < NCS- < EDTA^4- < NH3 < en < CN- < CO} \]

Weak Field Ligands (WFL):
Halides, $\ce{H2O}$. Cause small splitting ($\Delta_o < P$). Electrons fill higher orbitals before pairing. Forms High Spin complexes.

Strong Field Ligands (SFL):
$\ce{CN^-, CO, NH3}$. Cause large splitting ($\Delta_o > P$). Electrons pair up in lower orbitals. Forms Low Spin complexes.

5. Stability & Synergic Bonding

Stepwise Stability Constant

\[ M + 4L \rightleftharpoons ML_4 \] \[ \beta_4 = K_1 \cdot K_2 \cdot K_3 \cdot K_4 \]

Higher overall stability constant ($\beta$) indicates a more thermodynamically stable complex.
Chelate Effect: Complexes containing multidentate chelating ligands (like $en$, $EDTA$) are significantly more stable than those with monodentate ligands due to a positive entropy change ($\Delta S > 0$).

Synergic Bonding (Metal Carbonyls)

The $\ce{M-C}$ bond possesses both $\sigma$ and $\pi$ character.
1. $\sigma$-bond: Formed by donation of lone pair from Carbonyl carbon into vacant metal orbital.
2. $\pi$-backbond: Formed by donation of electrons from a filled metal d-orbital into the vacant antibonding $\pi^*$ orbital of $\ce{CO}$.

Consequences of Synergic Effect:

• Strengthens the $\ce{M-C}$ bond (bond order increases).
• Weakens the $\ce{C-O}$ bond (bond order decreases, bond length increases, stretching frequency decreases).

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Exam Master Review Sheet - Coordination Compounds