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Why is graphite a good conductor of electricity but not a diamond?

Answer
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Hint: We know that the electricity is a free flow of electrons. If the structure of the compound has free electrons, it is said to be a good conductor of electricity. Both diamond and graphite are allotropes of carbon. Allotropes are compounds which are chemically the same but vary in their physical properties. Different structures give rise to different properties.

Complete answer:
We define metals and non-metals based on various properties they possess like metals are lustrous while non-metals are dull, metals are malleable and ductile whereas non-metals are not and metals are a good conductor of electricity but non-metals are not a good conductor of electricity. Diamond and graphite are large molecules of carbon which do not have a specific formula. Their size completely depends on the extent of their physical structures. The structural difference in diamond and graphite leads to different physical as well as chemical properties. Graphite is a crystalline allotrope of carbon and it has a slippery surface. In graphite, the carbon atoms are arranged in a hexagonal structure and each carbon atom is attached to three other carbon atoms. We know that carbon has four valence electrons in its outermost shell. In graphite each carbon is bonded to three other carbon atoms hence leaving behind a free electron. Due to the presence of this one delocalized electron, graphite is a good conductor of electricity.
In a graphite molecule, one valence electron of each carbon atom remains free. Therefore, graphite gained the name of a good conductor of electricity. Whereas in diamond, they have no free mobile electrons. So it has been said that diamonds are bad conductor electricity

Note:
Remember that the diamond and graphite have different physical properties but the chemical properties are similar because both are composed of the same element (carbon). Carbon has many allotropes and forms, the electrical conductivity of each of them is Buckminster fullerenes is a good electric conductor and Graphene is a good electric conductor.