To design a polymerization reaction to produce high-density polyethylene HDPE with a molecular weight of 1 million grams per mole using ethylene as the monomer and a Ziegler-Natta catalyst system, we need to consider the following steps:1. Selection of Ziegler-Natta catalyst: A typical Ziegler-Natta catalyst system consists of a transition metal compound e.g., titanium tetrachloride, TiCl4 and an organoaluminum compound e.g., triethylaluminum, Al C2H5 3 . These two components work together to initiate the polymerization of ethylene.2. Polymerization reaction: The polymerization of ethylene using the Ziegler-Natta catalyst system can be represented by the following reaction:n C2H4 [-CH2-CH2-]nwhere n is the degree of polymerization.3. Calculation of the degree of polymerization: To achieve a molecular weight of 1 million grams per mole, we need to determine the degree of polymerization n . The molecular weight of ethylene C2H4 is 28.05 g/mol. Therefore, the degree of polymerization can be calculated as:n = 1,000,000 g/mol / 28.05 g/mol 35,6584. Theoretical yield: Assuming 100% conversion of ethylene to HDPE, the theoretical yield of the reaction can be calculated as:Theoretical yield = Degree of polymerization Molecular weight of ethylene Theoretical yield = 35,658 28.05 g/mol 1,000,000 g/mol5. Factors affecting the percent yield: The actual yield of the reaction may be different from the theoretical yield due to several factors, including:a. Catalyst efficiency: The efficiency of the Ziegler-Natta catalyst system may vary depending on the specific catalyst components and reaction conditions.b. Reaction conditions: Temperature, pressure, and reaction time can affect the polymerization process and the molecular weight of the resulting HDPE.c. Chain transfer reactions: Side reactions, such as chain transfer to the catalyst or monomer, can lead to lower molecular weight polymers and reduce the overall yield of the desired HDPE.d. Termination reactions: The polymerization reaction may be terminated prematurely due to various factors, such as impurities or unfavorable reaction conditions, resulting in lower molecular weight polymers and reduced yield.In summary, to produce HDPE with a molecular weight of 1 million grams per mole using ethylene as the monomer and a Ziegler-Natta catalyst system, the degree of polymerization needs to be approximately 35,658. The theoretical yield of the reaction is 1,000,000 g/mol. However, the actual yield may be affected by factors such as catalyst efficiency, reaction conditions, chain transfer reactions, and termination reactions.