To calculate the enthalpy of polymerization for the reaction of ethylene to polyethylene, we need to determine the enthalpy change per mole of ethylene used in the reaction. Since the enthalpy of combustion for ethylene is given, we can use this information to determine the enthalpy change for the polymerization reaction.Enthalpy of combustion of ethylene H_combustion = -1411 kJ/molNumber of moles of ethylene n = 4.5 molThe enthalpy of combustion represents the energy released when one mole of ethylene is completely combusted. However, we are interested in the enthalpy change for the polymerization reaction, which is a different process. To find the enthalpy of polymerization H_polymerization , we can use the following relationship:H_polymerization = -H_combustionThis relationship is based on the assumption that the enthalpy change for the polymerization reaction is equal in magnitude but opposite in sign to the enthalpy change for the combustion reaction.Now we can calculate the enthalpy of polymerization:H_polymerization = - -1411 kJ/mol = 1411 kJ/molThis value represents the enthalpy change per mole of ethylene used in the polymerization reaction. To find the total enthalpy change for the 4.5 moles of ethylene used, we can multiply the enthalpy change per mole by the number of moles:Total enthalpy change = H_polymerization n = 1411 kJ/mol 4.5 mol = 6349.5 kJTherefore, the enthalpy of polymerization for the reaction of ethylene to polyethylene using 4.5 moles of ethylene is 6349.5 kJ.