To calculate the enthalpy of polymerization for the synthesis of polyethylene from its monomer, we need to find the difference in enthalpy between the reactants and the products.The reaction can be represented as:n C2H4 [-CH2-]nwhere n is the number of moles of ethylene monomer.The enthalpy of polymerization H_polymerization can be calculated using the formula:H_polymerization = H_products - H_reactantsThe standard enthalpy of formation of ethylene C2H4 is given as +52.3 kJ/mol, and the standard enthalpy of formation of polyethylene -[-CH2-]n- is given as -256 kJ/mol.Since there are n moles of ethylene in the reaction, the total enthalpy of the reactants is:H_reactants = n * +52.3 kJ/mol The enthalpy of the product polyethylene is:H_products = -256 kJ/molNow, we can calculate the enthalpy of polymerization:H_polymerization = -256 kJ/mol - n * +52.3 kJ/mol However, we need to find the enthalpy of polymerization per mole of ethylene. To do this, we can divide the equation by n:H_polymerization/n = -256 kJ/mol / n - +52.3 kJ/mol Since the enthalpy of polymerization is for the synthesis of polyethylene from one mole of ethylene, n = 1:H_polymerization = -256 kJ/mol - 52.3 kJ/molH_polymerization = -308.3 kJ/molTherefore, the enthalpy of polymerization for the synthesis of polyethylene from its monomer is -308.3 kJ/mol.