Allotropes of Carbon - UNSOLVED PRACTICE SET

Q7. Explain why diamond is an electrical insulator while graphite is a good conductor, despite both being allotropes of carbon.

Q8. Why is diamond extremely hard, while graphite is soft and can be used as a lubricant? Explain with reference to their structures.

Q9. Describe the structure of C₆₀ (buckminsterfullerene). How many pentagonal and hexagonal faces does it contain?

Q10. Why does charcoal have a large surface area and adsorption capacity? What property makes activated charcoal useful in gas masks and water purifiers?

Q11. Your school uses graphite pencils for writing. Explain why graphite is suitable for this purpose, and why diamond cannot be used in pencils.

Q12. Graphene is called a "wonder material." Mention two properties of graphene that make it superior to steel and silicon for future applications.

Q13. Compare the structures and properties of diamond and graphite:

(a) Hybridisation of carbon atoms and geometry

(b) Bonding within and between layers/units

(c) Electrical conductivity and reasons

(d) Hardness and uses

Draw labelled diagrams showing the arrangement of carbon atoms in both allotropes.

Q14. Discuss the discovery, structure, and applications of:

(a) Fullerenes (C₆₀, C₇₀)

(b) Carbon nanotubes (single-walled and multi-walled)

(c) Graphene

For each, mention at least two unique properties and two potential applications in science and technology.

Q15. Carbon allotropes have transformed technology and industry in India and worldwide. Discuss:

(a) Why synthetic diamonds are grown in India (Surat is the world's diamond cutting hub) and their industrial uses

(b) The use of activated carbon in water purification systems commonly used in Indian households

(c) The potential of graphene-based sensors for detecting pollutants in Indian rivers

(d) Why carbon nanotubes are being researched for use in lightweight, strong materials for Indian defence applications

Q16. In a C₆₀ fullerene molecule:

(a) Calculate the number of C–C bonds present. (Hint: Each carbon forms 3 bonds, but each bond is shared by 2 carbons)

(b) If the average bond energy of a C–C bond in C₆₀ is 348 kJ/mol, calculate the total bond energy of the molecule.

(c) Compare this with the bond energy of diamond per mole of carbon atoms. Which is more thermodynamically stable?

Q17. A water purifier uses activated carbon to remove organic impurities. The carbon bed has a surface area of 1000 m² per gram.

(a) If the purifier contains 200 g of activated carbon, calculate the total surface area available for adsorption.

(b) If each impurity molecule occupies 2 × 10⁻¹⁹ m² of surface area, calculate the maximum number of impurity molecules that can be adsorbed.

(c) If the water flowing through contains 10¹⁸ impurity molecules per litre, and the flow rate is 5 litres per minute, calculate how long the carbon bed will remain effective.

Q18. Graphene has a hexagonal structure with a C–C bond length of 142 pm.

(a) Calculate the area of one hexagonal unit cell in graphene. (Hint: Area of regular hexagon = (3√3/2) × a², where a is the side length)

(b) If 1 g of graphene is spread as a single layer, calculate the approximate area it would cover.

(c) Compare this area with the area of a standard football field (about 7000 m²). How many football fields can 1 g of graphene cover?

[Given: Avogadro's number = 6.022 × 10²³, Atomic mass of C = 12]