To find the enthalpy of polymerization of ethylene, we can use Hess's Law, which states that the total enthalpy change for a reaction is the same, regardless of the path taken. In this case, we can consider the combustion of ethylene gas and polyethylene as two separate reactions, and then find the difference in their enthalpies to determine the enthalpy of polymerization.Let's represent the combustion reactions as follows:1. Ethylene gas combustion: C2H4 g + 3O2 g 2CO2 g + 2H2O l H1 = -1411 kJ/mol2. Polyethylene combustion: [C2H4]n s + 3nO2 g 2nCO2 g + 2nH2O l H2 = -5120 kJ/molWe want to find the enthalpy change for the polymerization reaction:3. Polymerization of ethylene gas: nC2H4 g [C2H4]n s H3 = ?To find H3, we can manipulate the combustion reactions 1 and 2 to get the desired reaction 3 . We can do this by reversing reaction 1 and adding it to reaction 2 :-1 * [C2H4 g + 3O2 g 2CO2 g + 2H2O l ] -H1 = 1411 kJ/mol+ [C2H4]n s + 3nO2 g 2nCO2 g + 2nH2O l H2 = -5120 kJ/mol--------------------------------------------------------------nC2H4 g [C2H4]n s H3 = ?Now, we can add the enthalpy changes for the manipulated reactions to find H3:H3 = -H1 + H2H3 = 1411 kJ/mol - 5120 kJ/molH3 = -3709 kJ/molHowever, this value is for the polymerization of n moles of ethylene. To find the enthalpy change per mole of ethylene, we need to divide by n:H3 per mole of ethylene = -3709 kJ/mol / nSince we are considering the polymerization of one mole of ethylene n=1 , the enthalpy change for the polymerization of ethylene gas to form polyethylene is:H3 per mole of ethylene = -3709 kJ/mol