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How will you synthesize polystyrene from benzene?

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Hint: Polystyrene is one of the most widely used polymers which is synthesised from styrene. It is a thermoplastic polymer i.e., it becomes moldable when the temperature rises to a certain temperature and solidifies on cooling. Thus, polystyrene can exist in both solid as well as foamed states.

Complete answer: As the monomer of polystyrene is styrene, we need to first convert benzene into styrene then after polymerization reaction, polystyrene will be formed. Therefore, the synthesis of polystyrene from benzene is done as per following steps:
Step-1: Benzene reacts with ethene in the presence of aluminium chloride to give ethyl benzene. The reaction proceeds as follows:
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Step-2: Ethyl benzene when heated to ${650^ \circ }C$ in the presence of ferric oxide, then the formation of styrene takes place. The reaction proceeds as follows:
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Step-3: Styrene undergoes polymerisation reaction and formation of polystyrene takes place. The reaction proceeds as follows:
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Hence, Polystyrene is synthesised from benzene in three steps.

Note:
It is important to note that the polymerisation reaction of styrene follows a free radical mechanism to form polystyrene. The three steps involved in the process are as follows:
1.Initiation step: In the presence of peroxide, the homolytic cleavage of covalent bond takes place and respective alkyl group free radicals are produced in this step.
2.Propagation step: The free radicals formed react with n molecules of free radical styrene to produce a long chain polymer i.e., Polystyrene.