Exercises: Diamond, graphite, graphene and fullerenes

1. a) Define the term allotrope.
2. b) Name four allotropes of carbon.
3. c) State the type of bonding between atoms within each layer of graphite.

Diamond and graphite are both pure carbon.

1. a) State the number of covalent bonds formed by each carbon atom in diamond and the hybridisation of the carbon atoms.
2. b) State the number of covalent bonds formed by each carbon atom in graphite.
3. c) Explain why graphite conducts electricity but diamond does not.

Match each use to the most suitable allotrope (diamond, graphite, graphene, fullerene), giving a reason in each case.

1. a) The tip of a drill bit for cutting rock.
2. b) The "lead" in a pencil.
3. c) A flexible, transparent conducting layer for a touchscreen.
4. d) A hollow cage molecule investigated for drug delivery.

The buckminsterfullerene molecule has formula $\mathrm{C_{60}}$.

1. a) Calculate its relative molecular mass ($A_r$ C = 12).
2. b) Describe its shape and the arrangement of the carbon atoms.
3. c) Explain why $\mathrm{C_{60}}$ is soft and has a much lower melting point than diamond.
4. d) Calculate the number of molecules in $1.00\,\text{g}$ of $\mathrm{C_{60}}$ ($L = 6.02\times10^{23}\,\text{mol}^{-1}$).

Graphite is used as a dry lubricant and as electrodes in electrolysis.

1. a) Describe the structure of graphite, including the forces between layers.
2. b) Explain why graphite is a good lubricant.
3. c) Explain why graphite is a good electrode material.
4. d) Explain why graphite has a very high melting point even though it is soft.

Graphene is a single layer of carbon atoms. A sheet of graphene has a mass of $0.77\,\text{mg}\,\text{m}^{-2}$.

1. a) Describe the structure of graphene.
2. b) Calculate the number of carbon atoms in $1.00\,\text{m}^2$ of graphene ($A_r$ C = 12, $L = 6.02\times10^{23}\,\text{mol}^{-1}$).
3. c) Suggest, with reasons, two properties that make graphene useful in electronics or composites.

The densities of diamond and graphite are $3.51\,\text{g}\,\text{cm}^{-3}$ and $2.27\,\text{g}\,\text{cm}^{-3}$ respectively.

1. a) Explain, in terms of structure, why graphite is less dense than diamond.
2. b) Calculate the volume occupied by $12.0\,\text{g}$ of each allotrope.
3. c) The conversion of graphite to diamond requires very high pressure. Use the densities to explain why high pressure favours diamond.
4. d) Explain why diamond does not spontaneously convert to graphite at room temperature even though graphite is more stable.

Compare the structure and properties of diamond, graphite and graphene in a table or in prose, addressing:

1. a) hybridisation of carbon and number of delocalised electrons per atom;
2. b) electrical conductivity;
3. c) hardness and the reason for it;
4. d) one application for each, justified by a property.

Carbon nanotubes can be viewed as rolled-up sheets of graphene.

1. a) Explain why a nanotube has very high tensile strength along its axis.
2. b) Explain why nanotubes conduct electricity.
3. c) A research group proposes using nanotubes in a water-filtration membrane. Suggest one advantage of this and one concern about releasing nanomaterials into the environment.
4. d) Explain why $\mathrm{C_{60}}$, graphene and nanotubes are all described as having carbon in the same oxidation state, 0, and yet different properties.