Why O₂ is paramagnetic (MOT prediction) — Hinglish notes

2.3.14 · Chemistry › Chemical Bonding

HUM actually KYA explain kar rahe hain?

YE KYUN ZAROORI HAI: Lewis/VBT, O₂ ko double bond aur saare electrons paired ke saath draw karta hai → diamagnetic predict karta hai → GALAT. MOT sahi se paramagnetism predict karta hai. Ye MOT ki VBT par textbook "jeet" hai, isliye ye guaranteed exam favourite hai.

MOT O₂ ko scratch se KAISE banata hai

Step 1 — Electrons count karo. Har O atom mein 8 electrons hain, toh O₂ mein kul $8 + 8 = 16$ electrons hain. Ye step kyun? MOT molecular orbitals fill karta hai bilkul waise hi jaise Aufbau principle atomic orbitals fill karta hai — pehle humein total electron count chahiye.

Step 2 — MO energy order jaano. O₂ aur F₂ ke liye (yaani aisi molecules jisme kul electrons $> 14$ hain, jahan $s$ – $p$ mixing weak hoti hai), order ye hai:

$σ_{1 s} < σ_{1 s}^{*} < σ_{2 s} < σ_{2 s}^{*} < σ_{2 p_{z}} < (π_{2 p_{x}} = π_{2 p_{y}}) < (π_{2 p_{x}}^{*} = π_{2 p_{y}}^{*}) < σ_{2 p_{z}}^{*}$

Ye order kyun? O₂/F₂ ke liye $σ_{2 p_{z}}$ do π-bonding orbitals ke niche rehta hai. (Compare karo: B₂, C₂, N₂ ke liye jisme $\leq 14$ electrons hain, strong $s$ – $p$ mixing $σ_{2 p_{z}}$ ko π's ke upar push karti hai — ye ek common trap hai.)

Step 3 — 16 electrons ko Aufbau + Hund's rule se fill karo.

MO	electrons	running total
$σ_{1 s}$	2	2
$σ_{1 s}^{*}$	2	4
$σ_{2 s}$	2	6
$σ_{2 s}^{*}$	2	8
$σ_{2 p_{z}}$	2	10
$π_{2 p_{x}}, π_{2 p_{y}}$	4	14
$π_{2 p_{x}}^{}, π_{2 p_{y}}^{}$	2	16
$σ_{2 p_{z}}^{*}$	0	16

Step 4 — Aakhri do electrons ka crucial moment. Aakhri 2 electrons degenerate (equal energy wale) pair $π_{2 p_{x}}^{*}$ aur $π_{2 p_{y}}^{*}$ mein jaate hain. Hund's rule ke anusar, ye pairing se pehle alag-alag orbitals mein parallel spins ke saath baithe hain. Ye step kyun? Hund's rule (total spin maximize karo) force karta hai ki ek electron har ek π* orbital mein jaaye → 2 unpaired electrons → paramagnetic. Yahi pura answer hai.

Figure — Why O₂ is paramagnetic (MOT prediction)

Bond Order derive karna (aur ye kyun 2 rehta hai)

O₂ ke liye derivation (table se count karo):

Bonding electrons $N_{b}$ : $σ_{1 s} (2) + σ_{2 s} (2) + σ_{2 p_{z}} (2) + π (4) = 10$
Antibonding electrons $N_{a}$ : $σ_{1 s}^{*} (2) + σ_{2 s}^{*} (2) + π^{*} (2) = 6$

$B.O. = \frac{10 - 6}{2} = 2$

Ye kyun matter karta hai: MOT double bond (B.O. = 2) deta hai bilkul Lewis ki tarah — toh ye bond strength se contradict nahi karta — AUR ye additionally wo 2 unpaired electrons bhi reveal karta hai jo Lewis miss kar gaya. Dono ka best.

Worked Examples

Common Mistakes (Steel-manned)

Recall Feynman: ek 12-saal ke bachche ko explain karo

Socho 16 bachche buses ki ek set mein chadh rahe hain (molecular orbitals), pehle aage ki seats fill kar rahe hain. Bilkul end mein, do bachche bache hain aur bilkul same "coolness" wali do khali double-seat buses hain. Bachche kisi ke saath squeeze karne se zyada alag baithna prefer karte hain, toh har ek apni bus leta hai. Ye do "loners" akele spinning electrons hain — aur ek spinning lone electron ek tiny magnet ki tarah kaam karta hai. Isliye oxygen magnet se chipakta hai, chahe simple dot-picture kehe ki nahi chipakna chahiye!

Flashcards

O₂ paramagnetic kyun hai?

Isme 2 unpaired electrons hain, ek each degenerate π₂p orbital mein (Hund's rule). O₂ mein kul kitne electrons hain aur kitne unpaired hain? ::: 16 kul; 2 unpaired. O₂ ke aakhri 2 electrons kaunse MOs mein hain? ::: Degenerate pair π₂pₓ aur π₂p_y mein (ek-ek electron). O₂ ka bond order (dikhao)? ::: (N_b − N_a)/2 = (10 − 6)/2 = 2. O₂ ka spin-only magnetic moment? ::: √(n(n+2)) = √8 ≈ 2.83 BM for n = 2. O₂ ki magnetism ke liye Lewis structure kyun fail hoti hai? ::: Ye saare electrons pair kar deta hai aur degenerate π orbitals mein single occupancy nahi dikha sakta.

O₂/F₂ ke liye σ2p_z, π orbitals ke relative kahaan hai?

π bonding orbitals ke niche (weak s–p mixing).

Kya O₂²⁻ (peroxide) para- ya diamagnetic hai aur uska bond order kya hai?

Diamagnetic (n=0); bond order 1.

Kya O₂⁻ (superoxide) magnetic hai; bond order?

Paramagnetic (n=1, μ≈1.73 BM); bond order 1.5.

Paramagnetism decide karta hai — bond order ya unpaired electrons?

Sirf unpaired electrons ki sankhya.

Connections

Molecular Orbital Theory — parent framework
Bond Order — yahan derive kiya, stability aur length se link
Hund's Rule — wo rule jo unpaired electrons create karta hai
Aufbau Principle — MOs ka filling order
Paramagnetism and Diamagnetism — magnetic classification
Valence Bond Theory limitations — VBT yahan kyun fail hoti hai
N2 vs O2 MO diagram — s–p mixing order change
Superoxide and Peroxide ions — O₂⁻, O₂²⁻ comparisons