The most efficient method for synthesizing polystyrene from styrene monomer is through free radical polymerization. This process involves the formation of free radicals, which initiate the polymerization of styrene monomers to form the polystyrene polymer.To achieve a high yield of the desired product, the following reaction conditions are necessary:1. Temperature: The reaction is typically carried out at elevated temperatures, ranging from 60 to 120C. Higher temperatures increase the rate of polymerization and help achieve a higher yield.2. Catalysts: Free radical initiators, such as benzoyl peroxide BPO or azobisisobutyronitrile AIBN , are used to initiate the polymerization process. These initiators decompose at elevated temperatures to generate free radicals, which then react with styrene monomers to form the polymer.3. Solvent: The reaction can be carried out in bulk without a solvent or in a suitable solvent, such as toluene or ethylbenzene. The choice of solvent depends on the desired properties of the final product and the ease of processing.4. Inhibitors: Polymerization inhibitors, such as hydroquinone or butylated hydroxytoluene BHT , are often added to the reaction mixture to prevent premature polymerization during storage and transportation of the styrene monomer.5. Reaction time: The reaction time depends on the desired molecular weight of the polystyrene product. Longer reaction times result in higher molecular weights.6. Pressure: The reaction can be carried out under atmospheric pressure or under an inert atmosphere such as nitrogen to minimize side reactions and improve the quality of the final product.By optimizing these reaction conditions, it is possible to achieve a high yield of polystyrene with the desired properties.