Coordination number and geometry — 2 (linear), 4 (tetrahedral - square planar), 6 (octahedral)

3.4.4 · Chemistry › Coordination Chemistry

Geometry CN par KYU depend karti hai?

Figure — Coordination number and geometry — 2 (linear), 4 (tetrahedral - square planar), 6 (octahedral)

CN = 2 → Linear (180°)

KYU: Sirf do electron domains ke saath, maximum separation yahi hai ki unhe opposite poles par rakhein.

Yeh kaun karta hai? Zyaadatar Group 11/12 ke $d^{10}$ ions jo extra ligands nahi chahte:

$[Ag(NH_{3})_{2}]^{+}$ (Tollens' reagent)
$[CuCl_{2}]^{-}$
$[Au(CN)_{2}]^{-}$

CN = 4 → Tetrahedral YA Square Planar

Yeh sabse interesting CN hai kyunki do geometries compete karti hain.

Tetrahedral ( $109.5°$ )

KYU choose hota hai: Pure VSEPR optimum (4 points ka maximum spread), tab favoured hota hai jab:

metal $d^{0}$ , $d^{5}$ , ya $d^{10}$ ho (square planar ke liye koi special CFSE advantage nahi),
ligands bulky hon (tetrahedron mein zyaada jagah milti hai),
ligands weak field hon.

Examples: $[NiCl_{4}]^{2 -}$ , $[CoCl_{4}]^{2 -}$ , $[MnO_{4}]^{-}$ , $[Zn(NH_{3})_{4}]^{2 +}$ .

Square Planar ( $90°$ )

KYU choose hota hai: $d^{8}$ ions ke saath strong-field ligands ke liye favoured.

Examples: $[Ni(CN)_{4}]^{2 -}$ (CN⁻ strong), $[PtCl_{4}]^{2 -}$ , $[Pd(NH_{3})_{4}]^{2 +}$ , almost sabhi $Pt(II)$ aur $Pd(II)$ .

CN = 6 → Octahedral ( $90°$ , sabse common)

KYU sabse common: Chhe ek achha compromise hai — bonding/charge satisfy karne ke liye kaafi ligands, jabki $90°$ separation repulsion manageable rakhta hai. Zyaadatar transition metal complexes ( $Co^{3 +}$ , $Fe^{3 +}$ , $Cr^{3 +}$ …) octahedral hote hain.

Examples: $[Co(NH_{3})_{6}]^{3 +}$ , $[Fe(CN_{6})]^{3 -}$ , $[Cr(H_{2} O)_{6}]^{3 +}$ , $[Co(en)_{3}]^{3 +}$ (CN = 6 teen bidentate ligands se).

Quick decision table

CN	Geometry	Kab	Example
2	Linear	$d^{10}$ (Ag⁺, Au⁺, Cu⁺)	$[Ag(NH_{3})_{2}]^{+}$
4	Tetrahedral	$d^{0}, d^{5}, d^{10}$ , weak field, bulky	$[NiCl_{4}]^{2 -}$
4	Square planar	$d^{8}$ + strong field	$[Ni(CN)_{4}]^{2 -}$
6	Octahedral	zyaadatar ions	$[Co(NH_{3})_{6}]^{3 +}$

Worked examples

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho beech mein ek magnet ball hai aur kuch sticky balls hain jo use pakadna chahti hain. Coordination number bas yeh hai ki kitni sticky balls ne pakad liya. Kyunki sticky balls ek dusre ko dhakkelti hain, woh spread ho jaati hain: 2 balls opposite sides par baith jaati hain (ek seedhi line), 4 balls ek chhoti pyramid-ish shape banati hain (tetrahedron) ya kabhi kabhi flat square, aur 6 balls ek perfect "double pyramid" banati hain (octahedron). Ek twist yeh hai: kuch ball-grabbers ke do haath hote hain (clip ki tarah), isliye unhe do grabs maanat hain!

Flashcards

Coordination number kya hai?

Central metal se coordinate bonds ke zariye directly jude donor atoms ki sankhya (donor atoms count karo, ligand molecules nahi).

CN = 2 ke liye geometry?

Linear, bond angle 180°, typically

d^{10}

ions jaise Ag⁺, Au⁺, Cu⁺ mein.

CN = 4 ke liye do possible geometries?

Tetrahedral (109.5°) aur square planar (90°).

CN = 4 square planar kab hota hai tetrahedral ki jagah?

d^{8}

ions ke liye strong-field ligands ke saath (jaise

[Ni(CN)_{4}]^{2 -}

, Pt(II), Pd(II)).

CN = 6 ke liye geometry?

Octahedral, 90° angles; transition complexes ke liye sabse common geometry.

[Co(en)_{3}]^{3 +}

ka CN?

6, kyunki en bidentate hai aur 3 hain (3×2).

[NiCl_{4}]^{2 -}

tetrahedral kyun hai lekin

[Ni(CN)_{4}]^{2 -}

square planar kyun?

Cl⁻ weak field hai (tetrahedral, paramagnetic); CN⁻ strong field hai jo

d^{8}

pairing ko square planar mein force karta hai (diamagnetic).

CN ko denticity se link karne wala formula?

CN = \sum_{i} n_{i} d_{i}

(ligands ki sankhya × har ligand ke donor atoms).

4 monodentate ligands ke liye pure VSEPR se ligand repulsion minimise karne wali geometry?

Tetrahedral (109.5°), maximum-spread arrangement.

d^{10}

ions linear (CN 2) kyun prefer karte hain?

Filled d-shell ko extra crystal-field stabilisation nahi milta, isliye woh sirf do ligands ko door-door pakad ke repulsion minimise karte hain.

Connections

Crystal Field Theory — $d^{8}$ ke liye square-planar vs tetrahedral explain karta hai
VSEPR Theory — linear/tetrahedral/octahedral shapes ki origin
Chelation and Denticity — kyun CN ≠ ligands ki sankhya
Magnetic properties of complexes — diamagnetic square planar vs paramagnetic tetrahedral
Isomerism in coordination compounds — geometry cis/trans aur optical isomers decide karti hai