VBT applied to complexes — inner vs outer orbital, hybridization, magnetism

3.4.7 · Chemistry › Coordination Chemistry

VBT yahan hai KYA?

VBT jinhe answer karta hai, wo key questions hain:

Geometry → hybridization type se.
Magnetic moment → unpaired electrons ki sankhya se.
Inner vs outer → kaun se $d$ -orbitals hybridize hue.

Complex banana KAISE hai — recipe

C.N.	Hybridization	Geometry	Kaun sa $d$
2	$s p$	linear	koi nahi
4	$s p^{3}$	tetrahedral	koi nahi → outer
4	$d s p^{2}$	square planar	$(n - 1) d$ → inner
6	$s p^{3} d^{2}$	octahedral	$n d$ → outer
6	$d^{2} s p^{3}$	octahedral	$(n - 1) d$ → inner

Magnetism follow KYUN karta hai? — $μ$ scratch se derive karo

A magnetic moment unpaired electron spins se aata hai. Har electron ka spin quantum number $s = \frac{1}{2}$ hota hai. $n$ unpaired electrons ke liye total spin $S = n \cdot \frac{1}{2} = \frac{n}{2}$ hota hai.

Spin angular momentum ki magnitude (QM mein) $S (S + 1) ℏ$ hoti hai, aur magnetic moment usi ke saath scale karta hai. $S = \frac{n}{2}$ substitute karne par:

$S (S + 1) = \frac{n}{2} (\frac{n}{2} + 1) = \frac{n}{2} \cdot \frac{n + 2}{2} = \frac{n ( n + 2 )}{4}$

Toh $S (S + 1) = \frac{1}{2} n (n + 2)$ , aur $μ$ ko Bohr magnetons mein measure karte hain (gyromagnetic ratio $g \approx 2$ ka factor 2, $\frac{1}{2}$ ko cancel kar deta hai):

$n$	0	1	2	3	4	5
$μ$ (BM)	0	1.73	2.83	3.87	4.90	5.92

Figure — VBT applied to complexes — inner vs outer orbital, hybridization, magnetism

Worked Examples

Forecast-then-Verify drill

Recall Forecast:

$[CoF_{6}]^{3 -}$ — padhne se pehle predict karo Co $^{3 +} = 3 d^{6}$ , $F^{-}$ weak → pairing nahi → $d^{6} =↑↓ ↑ ↑ ↑ ↑$ , $n = 4$ . Outer $s p^{3} d^{2}$ , octahedral, paramagnetic $μ = 4 \cdot 6 = 4.90$ BM. Example 4 se compare karo ( $n = 0$ ): same ion, ligand sab kuch decide karta hai.

Common Mistakes (Steel-man + fix)

Recall Feynman: 12-saal ke bache ko samjhao

Socho metal ek hotel hai jisme empty rooms (orbitals) hain. Ligands guests hain jo gifts (lone pairs) lekar aate hain aur sirf empty rooms mein jaate hain. Hotel ko guests aane se pehle apne rooms ko ek neat shape (square, triangle-pyramid, octahedron) mein arrange karna padta hai — yahi arranging "hybridization" hai. Kuch pushy guests (strong ligands jaise CN⁻) hotel ke apne residents ko rooms share (pair up) karne par majboor karte hain taaki zyada fancy inner rooms khul jaayein — yahi inner complex hai, aur kyunki sab paired hain, hotel "magnetic" nahi hota. Polite guests (weak ligands jaise F⁻) sharing force nahi karte, toh hotel extra outer rooms kholata hai, residents ko un-paired rehne deta hai, aur building magnetic ho jaati hai. Akele (unpaired) residents ginlo, $n (n + 2)$ mein daalo, aur pata chal jaata hai kitna magnetic hai!

Active-Recall Flashcards

VBT ke according metal–ligand bond kya hota hai?

Ek coordinate (dative) covalent bond: ligand lone pair metal ke vacant hybrid orbital mein donate hoti hai.

Spin-only magnetic moment formula kya hai?

μ = n (n + 2)

BM,

n

= unpaired electrons ki sankhya.

Inner-orbital octahedral complex ki hybridization aur geometry kya hoti hai?

d^{2} s p^{3}

, octahedral, inner

(n - 1) d

orbitals use karta hai, low spin.

Outer-orbital octahedral complex ki hybridization kya hoti hai?

s p^{3} d^{2}

, octahedral, outer

n d

orbitals use karta hai, high spin.

4-coordinate mein square planar vs tetrahedral ki hybridization kya hai?

Square planar =

d s p^{2}

(inner

d

); tetrahedral =

s p^{3}

Transition-metal cation banate waqt pehle kaun se electrons hataate hain?

n s

electrons,

(n - 1) d

se pehle.

Fe^{2 +}

aur

Fe^{3 +}

ka d-config kya hai?

3 d^{6}

aur

3 d^{5}

[Fe (CN)_{6}]^{4 -}

ki magnetism kaisi hai?

n = 0

, diamagnetic (

d^{2} s p^{3}

, inner).

[FeF_{6}]^{3 -}

ki magnetism kaisi hai?

n = 5

μ = 5.92

BM, paramagnetic (

s p^{3} d^{2}

, outer).

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

square planar kyun hai lekin

[NiCl_{4}]^{2 -}

tetrahedral kyun hai?

CN⁻ strong hai →

d^{8}

pair hota hai → ek

3 d

free hota hai →

d s p^{2}

square planar; Cl⁻ weak hai → pairing nahi →

s p^{3}

tetrahedral.

VBT ki do major failures kya hain?

Colour (spectra) explain nahi kar sakta aur predict nahi kar sakta ki ligands strong/weak kyun hain; orbital splitting energies ko ignore karta hai.

n = 3

unpaired electrons ke liye

μ

kya hai?

3 \cdot 5 = 15 = 3.87

BM.

Strong-field vs weak-field ka spin par kya effect hota hai?

Strong field → pairing → low spin/inner; weak field → pairing nahi → high spin/outer.

Connections

Crystal Field Theory — colour aur ligand strength explain karta hai jo VBT nahi kar sakta.
Spectrochemical Series — ligands ko strong/weak field mein order karta hai.
Magnetic Properties of Complexes — $μ$ measure karke $n$ back-calculate karna.
Hybridization — yahan use hone wale $s, p, d$ mixing rules.
Coordination Number and Geometry — C.N. ko shape se link karta hai.
Oxidation State Determination — har problem ka pehla step.