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

First: three ideas the traps assume

Before the trap bank, three things must be seen, not just named — the questions below lean on them constantly.

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

Definition σ-bonds and π-bonds — how a shared electron pair sits between two atoms

When two orbitals overlap head-on, along the straight line joining the nuclei, the shared electron cloud sits directly between the atoms — that is a σ-bond (sigma). It is strong and lets atoms rotate freely. When two leftover p orbitals (the unblended ones on $s p^{2}$ carbons) overlap sideways, above and below the bond line, the cloud sits in two lobes off to the side — that is a π-bond (pi). π-electrons are held more loosely, so in graphite they can delocalise (roam) across the whole sheet. Look at the figure: σ is the on-axis overlap; π is the sideways overlap. "All electrons in σ-bonds" (diamond) → nothing free to roam → insulator; "spare p → π-cloud" (graphite) → mobile charge → conductor.

Intuition Why exactly 12 pentagons close the ball (walk the Euler count)

Take an $s p^{2}$ carbon cage: every carbon is a vertex joined to 3 others, made of $P$ pentagons and $H$ hexagons.

Edges: each vertex sends out 3 edges, so summing over all $V$ vertices counts $3 V$ edge-ends; each edge has 2 ends, so $E = \frac{3 V}{2}$ .
Vertices from faces: each pentagon has 5 corners, each hexagon 6, and 3 faces meet at every vertex, so $V = \frac{5 P + 6 H}{3}$ .
Edges from faces: each edge is shared by 2 faces, so $E = \frac{5 P + 6 H}{2}$ , and faces $F = P + H$ . Put these into Euler's $V - E + F = 2$ (see Euler's formula for polyhedra): $\frac{5 P + 6 H}{3} - \frac{5 P + 6 H}{2} + (P + H) = 2$ Multiply through by 6: $2 (5 P + 6 H) - 3 (5 P + 6 H) + 6 (P + H) = 12$ , i.e. $- (5 P + 6 H) + 6 P + 6 H = 12$ , giving $P = 12$ . The hexagon count $H$ cancelled — so any such cage needs exactly 12 pentagons, whatever its size. For C₆₀, $H = 20$ .

True or false — justify

Graphite conducts electricity equally well in all directions.

False. Free π-electrons move within a layer (in-plane), but crossing the weak van der Waals gap between layers is hard — so graphite conducts well along sheets, poorly perpendicular to them.

Diamond is an insulator because it is chemically pure carbon.

False. Purity has nothing to do with it; conductivity needs mobile charge. All four of diamond's valence electrons are locked in σ-bonds (head-on overlaps, no free lobes), so none are free to carry current.

Graphite is soft because its C–C bonds are weak.

False. The in-plane C–C bonds (≈141.5 pm) are actually stronger and shorter than diamond's (≈154 pm). Softness comes from weak van der Waals forces between layers, which let whole sheets slide — see Van der Waals forces.

C₆₀ and diamond are both giant covalent network solids.

False. Diamond is a giant covalent network, but C₆₀ is a discrete molecule — a finite 60-atom cage held to its neighbours only by weak van der Waals forces in the solid.

All carbon allotropes are three-dimensional structures.

False. Dimensionality varies: diamond is 3-D, graphene is a 2-D sheet, CNTs are 1-D tubes, and C₆₀ is effectively a 0-D molecule. This range is exactly why the Giant covalent vs molecular solids distinction matters.

Melting diamond and subliming graphite both require breaking strong covalent bonds.

True. Both are giant covalent networks, so a phase change means breaking C–C σ-bonds — not merely overcoming van der Waals forces — which is why both need enormous temperatures (~3550 °C).

Graphene and a single graphite layer have different bonding.

False. They are the same thing — graphene is literally one isolated graphite layer: an

s p^{2}

honeycomb sheet. The difference is only that graphene stands alone, without layers stacked above and below.

A carbon nanotube is always metallic.

False. A CNT can be metallic or semiconducting depending on the chirality — the direction the graphene sheet is rolled — because rolling selects which slices of graphene's electron-energy pattern survive, and only some rolling directions leave a slice with zero band gap (metallic).

Since all of graphite, graphene, fullerene and CNT are

s p^{2}

, they must have identical properties.

False. They share hybridisation but differ in arrangement/dimensionality — sheet vs stacked layers vs cage vs tube — and structure, not hybridisation alone, sets the properties.

Diamond is the best thermal conductor even though it does not conduct electricity.

True. Heat here travels as lattice vibrations through the stiff, uniform 3-D covalent network — no free electrons required. Electrical conduction needs mobile charge; thermal conduction here needs efficient vibration transfer, and these are separate mechanisms.

Spot the error

"Carbon forms many allotropes because it has 6 electrons."

The relevant number is 4 valence electrons (plus small size and

s

–

p

orbital closeness), enabling catenation and flexible hybridisation — see Catenation in Group 14. The total electron count (6) is not the reason.

"In diamond every carbon is

s p^{2}

hybridised with bond angle 120°."

Diamond is

s p^{3}

, tetrahedral, with bond angle 109.5°. The

s p^{2}

/120° description belongs to graphite, graphene, fullerene and CNTs.

"C₆₀ is built from 12 hexagons and 20 pentagons."

The counts are swapped: C₆₀ has 12 pentagons and 20 hexagons (32 faces). Mnemonic order "12–5, 20–6" fixes it.

"Euler's formula gives

V - E + F = 0

for the buckyball."

The correct relation for a closed polyhedron is

V - E + F = 2

. Here

E = \frac{3 V}{2}

because every carbon (vertex) sends out 3 edges and each edge is counted at both its ends, so

E = 3 V /2 = 90

; then

F = 32

— see Euler's formula for polyhedra.

"Graphite's layers are held together by covalent bonds, which is why it's a solid."

The layers are held by weak van der Waals forces, not covalent bonds. Covalent bonding is only within each layer; the weak inter-layer force is what allows sliding.

"You can dissolve diamond in benzene because both are made of carbon."

Diamond is a giant covalent network — no discrete molecules to separate — so it does not dissolve. Only molecular C₆₀ dissolves in non-polar solvents like benzene.

"A flat hexagon sheet naturally curls into a ball if you make it big enough."

Pure hexagons stay flat (zero curvature); you need pentagons to introduce positive curvature. Working Euler through (see the derivation box above) shows exactly 12 pentagons are needed to close the sheet, whatever its size.

Why questions

Why does graphite conduct but diamond does not, given both are pure carbon?

Graphite's

s p^{2}

carbons each leave one unblended p orbital → a delocalised π-cloud of mobile electrons; diamond's

s p^{3}

carbons lock all four electrons in σ-bonds. Conduction needs mobile charge, which only graphite has.

Why is the in-plane C–C bond in graphite shorter than in diamond?

The delocalised π-electrons give each in-plane bond partial double-bond character (extra sideways overlap), tightening it to ≈141.5 pm versus diamond's pure single σ-bonds at ≈154 pm.

Why does making pentagons let a hexagon sheet close into C₆₀?

Hexagons tile flat (angles sum to 360° around a vertex); replacing some with pentagons removes angle and forces curvature. Feeding

V - E + F = 2

through the vertex/edge/face counts (box above) forces exactly 12 pentagons to seal the ball.

Why does a CNT have very high tensile strength along its axis?

Along the axis you are pulling directly against continuous strong

s p^{2}

C–C σ-bonds of the rolled honeycomb, so there is no weak link to break first.

Why can a CNT be metallic for one rolling direction and semiconducting for another?

Rolling the graphene sheet forces its electrons onto only certain allowed "slices" of graphene's energy pattern (a zone-folding effect). Some roll-up directions include the special slice where graphene's filled and empty energy levels touch → no band gap → metallic; others miss it, leaving a gap → semiconducting.

Why can carbon form far more allotropes than silicon?

Carbon's small size and effective

2 p

–

2 p

sideways overlap give strong C–C σ-bonds and stable π-bonds, enabling

s p^{2}

s p

networks; silicon's larger size makes Si–Si and π-bonding weaker — see Silicon and its differences from carbon.

Why does hybridisation act as the "master switch" for carbon's structures?

The choice of

s p

s p^{2}

s p^{3}

(see Hybridisation sp sp2 sp3) sets how many σ-bonds and what geometry each carbon adopts, which fixes whether you get a 3-D network, flat sheets, or linear chains — and geometry drives every property.

Why is graphite used as a lubricant but diamond as an abrasive?

Graphite's sliding layers make it slippery; diamond's rigid 3-D network with no weak planes makes it the hardest natural substance, ideal for cutting/grinding.

Edge cases

What holds a solid sample of C₆₀ together, given the molecule itself is covalently bonded?

The cage is covalent internally, but neighbouring C₆₀ molecules attract only through weak van der Waals forces — so solid C₆₀ is a soft, low-melting molecular solid, unlike network diamond.

If you keep peeling graphite one layer at a time, what is the limiting single layer?

A single peeled layer is graphene — the 2-D limiting case of graphite, where inter-layer van der Waals forces have been entirely removed.

Does breaking a diamond require breaking covalent bonds, unlike separating graphite layers?

Yes. Cleaving diamond means snapping strong 3-D C–C σ-bonds everywhere; separating graphite layers only overcomes weak van der Waals attraction — hence the huge hardness difference.

Is carbyne (

s p

carbon) consistent with the "hybridisation decides structure" rule?

Yes —

s p

carbon makes 2 σ-bonds in a straight line, giving linear chains (a 1-D degenerate case), exactly as the rule predicts for the least-branched hybridisation.

Can a substance conduct heat well yet not conduct electricity?

Yes — diamond does exactly this. Heat rides lattice vibrations through the stiff network, while the absence of free electrons blocks electric current, showing the two conduction mechanisms are independent.

What happens to graphite's conductivity if you measure straight through the stack of layers?

It drops sharply, because electrons must cross the weak, wide van der Waals gaps between layers rather than travelling freely within a sheet — anisotropic conduction.

Recall One-line self-test before you close

Cover everything: name the odd one out and why — diamond, graphite, graphene, C₆₀. Odd one out ::: C₆₀ — the only discrete molecular allotrope here; the other three are giant covalent/extended structures.

Connections

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