Allotropy — Carbon, Sulphur and Phosphorus Compared
Diamond and graphite are both pure carbon. One is the hardest natural material known and does not conduct electricity; the other is soft enough to write with and conducts well. Nothing about the atoms differs — only how they are joined. That single idea is allotropy, and it is the cleanest demonstration in the whole syllabus that structure decides properties. This page compares the three elements the syllabus asks about most — carbon, sulphur and phosphorus — with the structural reason for every property difference, and the arithmetic the numerical questions expect.
Definition, and the words it is confused with
| Term | Applies to | What differs | Example |
|---|---|---|---|
| Allotropy | Elements | Bonding or arrangement of identical atoms | Diamond and graphite |
| Isotopy | Atoms of one element | Number of neutrons in the nucleus | ¹²C and ¹⁴C |
| Polymorphism | Compounds | Crystal form of the same compound | CaCO₃ as calcite and aragonite |
| Isomerism | Compounds | Arrangement of atoms in a molecule | Ethanol and dimethyl ether |
Allotropes have identical chemical composition and identical atoms — so ¹²C versus ¹⁴C is not allotropy, and calcite versus aragonite is not allotropy either. Getting these four apart is worth an easy mark and is asked directly.
Carbon — the same atom, four different materials
| Diamond | Graphite | Fullerene (C₆₀) | |
|---|---|---|---|
| Hybridisation | sp³ | sp² | sp² (slightly pyramidalised) |
| Bonds per carbon | 4 | 3, plus a delocalised π system | 3 |
| Structure | Three-dimensional tetrahedral network | Flat hexagonal layers stacked with weak forces between them | Discrete cage molecules: 20 hexagons and 12 pentagons |
| C–C distance | about 154 pm | about 142 pm within a layer; about 335 pm between layers | two different lengths in the cage |
| Density | about 3.51 g cm⁻³ | about 2.26 g cm⁻³ | lower than graphite |
| Electrical conduction | No — all four valence electrons localised | Yes, along the layers — one delocalised electron per atom | Poor as a pure solid |
| Hardness | Extremely hard | Soft, slippery | Soft molecular solid |
| Uses | Cutting, drilling, abrasives, jewellery | Pencil leads, electrodes, dry lubricant, moderator | Research materials, chemistry of nanomaterials |
Read every row as a consequence of the first two. Diamond's four covalent bonds per atom lock the whole crystal into one giant molecule, so it is hard and non-conducting and melts extremely high. Graphite uses only three bonds, leaving one electron per carbon in a delocalised π cloud that carries current along a layer; the layers themselves are held to each other by weak forces, so they slide, which is why graphite marks paper and lubricates machinery. Graphene is a single graphite layer, and carbon nanotubes are that layer rolled into a cylinder. Charcoal, coke and lamp black are usually described as amorphous or microcrystalline forms related to graphite rather than as separate crystalline allotropes.
Worked example 1 — molar mass of buckminsterfullerene
C₆₀ contains 60 carbon atoms, atomic mass 12.011.
M(C₆₀) = 60 × 12.011 = 720.66 g/mol
Cross-check: 60 × 12 = 720, plus 60 × 0.011 = 0.66, giving 720.66 ✓
The cage has 20 hexagonal and 12 pentagonal faces — the pattern of a football. The 12 pentagons are what force the sheet to curve; a surface made only of hexagons stays flat, which is exactly what graphene is.
Worked example 2 — why the density difference is not a small detail
Molar volume = molar mass ÷ density. Using 12.011 g/mol for carbon:
Diamond: 12.011 ÷ 3.51 = 3.42 cm³ mol⁻¹
Graphite: 12.011 ÷ 2.26 = 5.31 cm³ mol⁻¹
Ratio = 5.31 ÷ 3.42 = 1.55
One mole of graphite occupies about 55% more space than one mole of diamond, even though both contain exactly 6.022 × 10²³ carbon atoms. The extra volume is the empty gap between the layers — roughly 335 pm, against 154 pm for an actual bond. This is also why turning graphite into diamond industrially requires enormous pressure: you are compressing that gap out.
Sulphur — two crystalline forms of the same S₈ ring
Both common crystalline allotropes of sulphur are built from the same puckered, crown-shaped S₈ ring. They differ only in how those rings stack.
| Rhombic (α) sulphur | Monoclinic (β) sulphur | Plastic sulphur | |
|---|---|---|---|
| Crystal shape | Octahedral | Needle-shaped (prismatic) | Amorphous, rubbery |
| Stable | Below 95.3 °C | Between 95.3 °C and its melting point | Not stable — reverts to rhombic on standing |
| Density (typical tabulated) | about 2.06 g cm⁻³ | about 1.98 g cm⁻³ | — |
| Melting point (typical tabulated) | about 385.8 K (112.8 °C) | about 393 K (119 °C) | — |
| Unit present | S₈ rings | S₈ rings | Long zig-zag chains of S atoms |
| Prepared by | Evaporating a solution of sulphur in CS₂ | Melting sulphur and cooling slowly until crystals form | Pouring boiling sulphur into cold water |
The temperature 95.3 °C is called the transition temperature: at exactly this point the two forms are in equilibrium and can be interconverted in both directions. A change that is reversible at a definite temperature like this is called enantiotropy. Note the sequence when sulphur is heated further — the S₈ rings open and join into long chains, the liquid becomes darker and, unusually, more viscous before thinning again at higher temperature. Almost every other liquid becomes steadily thinner on heating, so this is a favourite question.
Molar mass of the S₈ molecule. Atomic mass of sulphur = 32.06.
M(S₈) = 8 × 32.06 = 256.48 g/mol
So 1 g of sulphur contains 1 ÷ 256.48 = 3.899 × 10⁻³ mol of S₈ molecules — but 1 ÷ 32.06 = 3.119 × 10⁻² mol of sulphur atoms. Whether a question means moles of atoms or moles of molecules changes the answer eightfold, and that is precisely where marks are lost.
Phosphorus — three forms with wildly different reactivity
| White phosphorus | Red phosphorus | Black phosphorus | |
|---|---|---|---|
| Structure | Discrete tetrahedral P₄ molecules | Polymeric — P₄ units linked into chains | Layered, sheet-like |
| P–P–P bond angle | 60° — highly strained | Normal, unstrained | Normal |
| Reactivity | Very high; ignites in air at around 30 °C | Much lower; does not ignite in air at room temperature | Least reactive; the most thermodynamically stable form |
| Appearance | Waxy white or pale yellow solid | Dark red powder | Black, metallic-looking; a semiconductor |
| Solubility in CS₂ | Soluble | Insoluble | Insoluble |
| Toxicity | Highly toxic | Essentially non-toxic | Low |
| Storage | Under water | Ordinary container | Ordinary container |
| Prepared by | — | Heating white phosphorus at about 573 K in an inert atmosphere | Heating under high pressure, or by other controlled routes |
The whole comparison follows from the 60° bond angle. A P₄ tetrahedron forces the bond angles down to 60°, far from the roughly 109° a p-block atom with lone pairs prefers. That angle strain stores energy and makes white phosphorus desperate to react. Heating breaks one bond of each tetrahedron and links the units into chains, which relieves the strain — and red phosphorus is correspondingly placid. The conversion white → red does not reverse on cooling; a one-way change like this is called monotropy, the contrast with sulphur's reversible enantiotropy.
Safety, stated plainly. White phosphorus is highly toxic and can ignite in air near room temperature, which is why it is kept under water. It is not a substance for a school or home laboratory under any circumstances. Read about it; do not obtain or handle it. Any demonstration belongs to a properly equipped laboratory with trained supervision.
Counting P₄ molecules. Atomic mass of phosphorus = 30.974.
M(P₄) = 4 × 30.974 = 123.90 g/mol
Moles in 1.00 g = 1.00 ÷ 123.90 = 8.071 × 10⁻³ mol
Molecules = 8.071 × 10⁻³ × 6.022 × 10²³ = 4.86 × 10²¹ P₄ molecules
Atoms = 4 × 4.86 × 10²¹ = 1.94 × 10²² phosphorus atoms
Cross-check by the atom route: 1.00 ÷ 30.974 = 3.229 × 10⁻² mol of P atoms; 3.229 × 10⁻² × 6.022 × 10²³ = 1.944 × 10²² atoms ✓ — the two routes agree.
Two more allotropes worth naming in an answer
- Oxygen: dioxygen O₂ and ozone O₃. Same element, different molecule — one supports life and the other is a pungent, reactive gas that shields the Earth from ultraviolet light.
- Tin: white (metallic) tin and grey tin. Below about 13 °C the metallic form slowly converts to the powdery grey form, a change historically nicknamed "tin pest".
Mistakes that cost marks
- Calling isotopes allotropes. Isotopes differ in neutrons; allotropes differ in structure. This is the single most common confusion in this topic.
- Saying diamond does not conduct because it has no electrons. It has plenty — all four valence electrons per atom are tied up in localised sigma bonds, so none is free to move. Say localised, not absent.
- Writing "graphite is soft because its bonds are weak". The covalent bonds inside a layer are strong — shorter than diamond's. It is the forces between layers that are weak.
- Claiming diamond has the higher melting point by a wide margin. Both are extremely high because both are giant covalent structures; do not treat graphite as a low-melting solid just because it is soft.
- Confusing the transition temperature with a melting point. 95.3 °C is where rhombic and monoclinic sulphur interconvert, not where sulphur melts.
- Forgetting S₈ and P₄ when doing mole calculations. Sulphur vapour and solid sulphur are molecular; using 32.06 where 256.48 is required is an eightfold error.
- Saying red phosphorus is made by heating white phosphorus in air. It must be heated in an inert atmosphere — in air it would simply burn.
Where this is asked in exams
| Exam | Typical question |
|---|---|
| ICSE / CBSE Class 10 | Define allotropy; give the allotropes of carbon and their uses |
| CBSE Class 11 | Structure and bonding in diamond, graphite and fullerene; p-block group 15 and 16 elements |
| CBSE Class 12 | Allotropes of phosphorus and sulphur in the p-block chapter; preparation and properties |
| JEE / NEET | Compare hybridisation, conductivity and bond lengths; identify the correct statement about an allotrope |
| IIT-JAM / CUET-PG | Solid-state structures, enantiotropy versus monotropy, phase behaviour of sulphur |
| GATE / CSIR-NET | Solid-state and materials chemistry, catenation in group 14–16, structures of P₄, S₈ and their derivatives |
Look the elements up while you revise. Allotropy is a property of particular elements — carbon, phosphorus, sulphur, oxygen, tin — and it helps to see where they sit and how they relate to their neighbours down each group. The Interactive Periodic Table in the suite covers all 118 elements in one screen.
Open the Interactive Periodic Table →The p-block is the chapter where careful, structured revision pays off most. ABC Chemistry runs Class 11–12 chemistry coaching at the Gurugram centre plus online classes across India — details at abcchemistry.in. Students in Delhi, Noida or Gurgaon who want one-to-one teaching at home can arrange it through delhihometutor.com.