Group 14 (Carbon family) — allotropes of C (diamond, graphite, fullerenes, graphene, CNTs)

3.2.3 · Chemistry › p-Block

Allotropes exist karte hi kyun hain?

Carbon hi kyun especially? Carbon ke $2 s$ aur $2 p$ orbitals energy mein kaafi kareeb hote hain, isliye yeh hybridise kar sakta hai:

$s p^{3}$ → 4 σ-bonds, tetrahedral → diamond
$s p^{2}$ → 3 σ-bonds + 1 delocalised p-electron → graphite, graphene, fullerene, CNT
$s p$ → linear chains → carbyne (rare)

Toh hybridisation ka choice hi master switch hai.

1. Diamond — $s p^{3}$ giant

HOW properties follow karte hain (derive karo, ratto mat):

Saare 4 electrons σ-bonds mein lock hain → koi free electron nahi → electrical insulator.
3-D rigid network, C–C bonds har jagah mazboot → sabse hardest natural substance, bahut zyada high m.p. (~3550 °C: melt karne ke liye covalent bonds todne padte hain).
Mazboot bonds vibrations ko efficiently carry karti hain → jaana hua sabse accha thermal conductor.
C–C bond length $\approx 154$ pm, bond angle $= 109. 5^{\circ}$ .

2. Graphite — $s p^{2}$ layered conductor

HOW properties follow karte hain:

Delocalised p-electrons sheets ke along move karte hain → acha electrical conductor (in-plane).
Weak inter-layer forces → layers slide karti hain → soft, slippery → lubricant, pencil "lead".
In-layer C–C $\approx 141.5$ pm (diamond se chhota kyunki partial double-bond character hai), inter-layer spacing $\approx 335$ pm.
Bond angle $12 0^{\circ}$ .

3. Fullerenes — molecular cages (jaise C₆₀)

C₆₀ ki Structure — geometry Euler's formula se derive karo:

12 pentagons aur 20 hexagons se bana hai. Har C ek vertex par hai jo 3 faces share karta hai, 3 doosre atoms se bonded ( $s p^{2}$ ).
Euler: $V - E + F = 2$ . Har vertex ki degree 3 hai ⇒ $E = \frac{3 V}{2}$ . $60 - \frac{3 ( 60 )}{2} + F = 2 \Rightarrow 60 - 90 + F = 2 \Rightarrow F = 32$ $= 12 pentagons + 20 hexagons ✓$ Yeh step kyun? Ek football pattern ko hexagons ki flat sheet ko closed ball mein curve karne ke liye exactly 12 pentagons chahiye — Euler's formula prove karta hai ki aisa hona hi hai.

4. Graphene & 5. Carbon nanotubes (CNTs)

Tested materials mein sabse strong, excellent conductor (free π-electrons), transparent, flexible.

Axis ke along bahut zyada tensile strength; rolling direction (chirality) ke hisaab se metallic ya semiconducting ho sakti hai.

Figure — Group 14 (Carbon family) — allotropes of C (diamond, graphite, fullerenes, graphene, CNTs)

Master comparison table

Allotrope	Hybridisation	Dimensionality	Bonding network	Conductor?	Key use
Diamond	$s p^{3}$	3-D	giant covalent	Nahi	abrasive, jewellery
Graphite	$s p^{2}$	2-D layers + vdW	giant covalent	Haan (in-plane)	lubricant, electrodes
Fullerene (C₆₀)	$s p^{2}$	0-D cage	discrete molecule	semicond.	drug delivery, catalysis
Graphene	$s p^{2}$	2-D single sheet	giant covalent	Haan	electronics, sensors
CNT	$s p^{2}$	1-D tube	rolled sheet	metallic/semicond.	composites, nano-wires

Forecast-then-Verify drill

Answer padhne se pehle predict karo:

Diamond ko melt karo vs graphite ko sublime karo — dono mein bahut zyada energy lagti hai. Kyun? (Forecast) … (Verify: dono giant covalent hain; C–C bonds todne padte hain, sirf vdW overcome nahi karna — isliye bahut high temperatures.)
Kya C₆₀ benzene mein dissolve hoga? (Forecast) … (Verify: haan — yeh ek discrete non-polar molecule hai, unlike network solids diamond/graphite.)

Recall Feynman: ek 12-saal ke bachche ko samjhao

Socho same LEGO bricks (carbon atoms) hain. Agar har brick ko 4 doosron se har direction mein connect karo, toh ek super-strong solid block milta hai — woh hai diamond, itna hard ki glass kaat de. Agar instead flat sheets banao jo paper ki tarah stack hon, toh sheets slide karti hain — woh hai graphite, itna soft ki pencil se likha ja sake. Ek sheet ko tube mein roll karo → nanotube; ek single sheet → graphene; ise ek chhoti si ball mein mod do → buckyball. Same bricks, bilkul alag toys — sab kuch pattern par depend karta hai.

Flashcards

Carbon itne saare allotropes kaise banata hai?

Catenation (mazboot self-bonding) +

s p

s p^{2}

s p^{3}

mein hybridise karne ki ability.

Diamond mein carbon ki hybridisation aur bond angle kya hai?

s p^{3}

109. 5^{\circ}

, tetrahedral.

Diamond electrical insulator kyun hai?

Saare 4 valence electrons σ-bonds mein localised hain — koi free/mobile electron nahi.

Graphite acha conductor kyun hai?

Har

s p^{2}

C ka ek delocalised p-electron hota hai jo har layer ke andar mobile π-electron cloud banata hai.

Graphite strong bonds ke bawajood soft/slippery kyun hai?

Layers ke beech weak van der Waals forces unhe slide karne deti hain; in-plane covalent bonds actually strong hote hain.

Graphite, graphene, fullerene, CNT mein hybridisation kya hai?

Sab

s p^{2}

C₆₀ mein kitne pentagons aur hexagons hain?

12 pentagons aur 20 hexagons (32 faces total).

C₆₀ ke faces Euler's formula se nikalo.

V - E + F = 2

ke saath

E = 3 V /2 = 90

V = 60

⇒

F = 32

Graphene kya hai?

Graphite ki ek single one-atom-thick layer (

s p^{2}

honeycomb 2-D sheet).

Carbon nanotube kya hota hai?

Ek graphene sheet jo cylinder mein roll ki gayi ho; chirality se metallic ya semiconducting.

C–C bond length: diamond vs graphite (in-plane)?

Diamond 154 pm; graphite 141.5 pm (chhota, partial double-bond character ki wajah se).

C₆₀ organic solvents mein dissolve ho jaata hai lekin diamond kyun nahi?

C₆₀ ek discrete molecule hai; diamond ek giant covalent network solid hai.

Hexagons ki sheet ko ball banane ke liye pentagons kyun chahiye?

Pentagons positive curvature introduce karte hain; exactly 12 cage ko close karne ke liye chahiye.

Connections

Catenation in Group 14
Hybridisation sp sp2 sp3
Van der Waals forces
Giant covalent vs molecular solids
Conductivity and delocalised electrons
Euler's formula for polyhedra
Silicon and its differences from carbon