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

WHY do allotropes exist at all?

WHY carbon especially? Carbon's $2s$ and $2p$ orbitals are close in energy, so it can hybridise as:

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

So hybridisation choice is the master switch.

1. Diamond — the $sp^3$ giant

HOW the properties follow (derive, don't memorise):

All 4 electrons locked in σ-bonds → no free electrons → electrical insulator.
3-D rigid network, strong C–C everywhere → hardest natural substance, very high m.p. (~3550 °C: you must break covalent bonds to melt it).
Strong bonds carry vibrations efficiently → best thermal conductor known.
C–C bond length $\approx 154$ pm, bond angle $=109.5^\circ$ .

2. Graphite — the $sp^2$ layered conductor

HOW properties follow:

Delocalised p-electrons move along sheets → good electrical conductor (in-plane).
Weak inter-layer forces → layers slide → soft, slippery → lubricant, pencil "lead".
C–C in-layer $\approx 141.5$ pm (shorter than diamond because of partial double-bond character), inter-layer spacing $\approx 335$ pm.
Bond angle $120^\circ$ .

3. Fullerenes — molecular cages (e.g. C₆₀)

Structure of C₆₀ — derive the geometry with Euler's formula:

Made of 12 pentagons and 20 hexagons. Each C is at a vertex shared by 3 faces, bonded to 3 others ( $sp^2$ ).
Euler: $V - E + F = 2$ . Each vertex has degree 3 ⇒ $E=\tfrac{3V}{2}$ . $60 - \frac{3(60)}{2} + F = 2 \Rightarrow 60 - 90 + F = 2 \Rightarrow F = 32$ $=12\ \text{pentagons} + 20\ \text{hexagons}\ \checkmark$ Why this step? A football pattern needs exactly 12 pentagons to curve a sheet of hexagons into a closed ball — Euler's formula proves it must.

4. Graphene & 5. Carbon nanotubes (CNTs)

Strongest material tested, excellent conductor (free π-electrons), transparent, flexible.

Very high tensile strength along the axis; can be metallic or semiconducting depending on rolling direction (chirality).

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	$sp^3$	3-D	giant covalent	No	abrasive, jewellery
Graphite	$sp^2$	2-D layers + vdW	giant covalent	Yes (in-plane)	lubricant, electrodes
Fullerene (C₆₀)	$sp^2$	0-D cage	discrete molecule	semicond.	drug delivery, catalysis
Graphene	$sp^2$	2-D single sheet	giant covalent	Yes	electronics, sensors
CNT	$sp^2$	1-D tube	rolled sheet	metallic/semicond.	composites, nano-wires

Forecast-then-Verify drill

Before reading the answer, predict:

Melt diamond vs sublime graphite — both need huge energy. Why? (Forecast) … (Verify: both are giant covalent; you must break C–C bonds, not just overcome vdW — hence very high temperatures.)
Will C₆₀ dissolve in benzene? (Forecast) … (Verify: yes — it's a discrete non-polar molecule, unlike network solids diamond/graphite.)

Recall Feynman: explain to a 12-year-old

Imagine the same LEGO bricks (carbon atoms). If you connect each brick to 4 others in every direction, you get a super-strong solid block — that's diamond, so hard it cuts glass. If instead you build flat sheets stacked like paper, the sheets slide — that's graphite, soft enough to write with a pencil. Roll one sheet into a tube → nanotube; one single sheet → graphene; bend it into a tiny ball → a buckyball. Same bricks, totally different toys — it all depends on the pattern.

Flashcards

What property lets carbon form so many allotropes?

Catenation (strong self-bonding) + ability to hybridise as

sp

sp^2

sp^3

Hybridisation of carbon in diamond and the bond angle?

sp^3

109.5^\circ

, tetrahedral.

Why is diamond an electrical insulator?

All 4 valence electrons are localised in σ-bonds — no free/mobile electrons.

Why is graphite a good conductor?

Each

sp^2

C has one delocalised p-electron forming a mobile π-electron cloud within each layer.

Why is graphite soft/slippery despite strong bonds?

Weak van der Waals forces between layers let them slide; the in-plane covalent bonds are actually strong.

Hybridisation in graphite, graphene, fullerene, CNT?

All

sp^2

How many pentagons and hexagons in C₆₀?

12 pentagons and 20 hexagons (32 faces total).

Use Euler's formula to find faces of C₆₀.

V-E+F=2

with

E=3V/2=90

V=60

⇒

F=32

What is graphene?

A single one-atom-thick layer of graphite (

sp^2

honeycomb 2-D sheet).

What is a carbon nanotube?

A graphene sheet rolled into a cylinder; metallic or semiconducting by chirality.

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

Diamond 154 pm; graphite 141.5 pm (shorter, partial double-bond character).

Why does C₆₀ dissolve in organic solvents but diamond doesn't?

C₆₀ is a discrete molecule; diamond is a giant covalent network solid.

Why does a sheet of hexagons need pentagons to form a ball?

Pentagons introduce positive curvature; exactly 12 are needed to close the cage.

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

Concept Map

Hinglish (regional understanding)

Intuition Hinglish mein samjho

Dekho, carbon ek hi element hai, lekin uske paas 4 valence electrons hote hain aur size chhota hai, isliye wo apne hi atoms ke saath bahut strong bonds banata hai — ise catenation kehte hain. Sabse important baat: carbon alag-alag tarah se hybridise kar sakta hai, aur jaisa arrangement, waisa material. Yahi reason hai ki ek hi carbon se diamond, graphite, fullerene, graphene aur nanotube — sab ban jaate hain. Structure decides properties — ye poore chapter ka soul hai.

Diamond mein har carbon $sp^3$ hota hai, char directions mein bonded, 3-D network — isliye sabse hard, electrical insulator (koi free electron nahi). Graphite mein carbon $sp^2$ hai, flat hexagon sheets banta hai aur har atom ka ek p-electron free ghoomta hai — isliye conductor. Sheets ke beech sirf weak van der Waals force hota hai, isliye wo slide karti hain aur graphite soft/lubricant hota hai. Yaad rakho: graphite soft isliye nahi ki bond weak hai — andar ke bond toh diamond se bhi strong hain, sirf layers slip karti hain.

Fullerene (C₆₀) ek football jaisa cage hai — 12 pentagon + 20 hexagon. Pentagons isliye chahiye kyunki sirf hexagons se flat sheet banti, ball banane ke liye curvature chahiye. Graphene matlab graphite ki sirf ek single layer, aur CNT matlab usi sheet ko tube mein roll kar do. Exam mein hybridisation, bond length, conductivity ka reason, aur C₆₀ ka 12-20 wala fact — ye guaranteed important hain. Bas ek line yaad rakho: same carbon, different pattern, different magic.

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

WHY do allotropes exist at all?

1. Diamond — the $sp^3$ giant

2. Graphite — the $sp^2$ layered conductor

3. Fullerenes — molecular cages (e.g. C₆₀)

4. Graphene & 5. Carbon nanotubes (CNTs)

Master comparison table

Forecast-then-Verify drill

Flashcards

Connections

Concept Map

Hinglish (regional understanding)

Go deeper — visual, from zero

Test yourself — p-Block

Connections