The rate of polymerization in the synthesis of polyethylene using the free radical polymerization technique can be controlled by manipulating various factors. Here are some key approaches to control the rate of polymerization:1. Monomer concentration: The rate of polymerization is directly proportional to the concentration of the monomer. By increasing or decreasing the concentration of ethylene, the rate of polymerization can be controlled.2. Initiator concentration: The concentration of the initiator free radical source also affects the rate of polymerization. Higher initiator concentrations lead to a higher rate of polymerization, while lower concentrations result in a slower rate.3. Temperature: The rate of polymerization is temperature-dependent. Higher temperatures increase the rate of polymerization due to the increased kinetic energy of the molecules, leading to more frequent collisions and faster reaction rates. However, at very high temperatures, the rate may decrease due to the increased rate of termination reactions. Optimal temperature control is crucial for maintaining the desired rate of polymerization.4. Pressure: In the case of gaseous monomers like ethylene, the pressure can also affect the rate of polymerization. Higher pressures generally lead to higher monomer concentrations, which in turn increase the rate of polymerization.5. Chain transfer agents: The use of chain transfer agents can help control the rate of polymerization by transferring the growing polymer chain to another molecule, effectively terminating the chain growth and starting a new chain. This can be used to control the molecular weight of the polymer and indirectly influence the rate of polymerization.6. Inhibitors and retarders: Inhibitors and retarders are chemicals that slow down or stop the polymerization process. They can be added to the reaction mixture to control the rate of polymerization. Inhibitors typically react with free radicals to form stable, non-reactive species, while retarders slow down the rate of initiation or propagation reactions.By carefully adjusting these factors, the rate of polymerization in the synthesis of polyethylene using the free radical polymerization technique can be effectively controlled to achieve the desired properties and molecular weight of the final polymer product.