Question

Calculate the enthalpy change for the following polymerization reaction: 2 C2H4 (g) → C4H8 (g) Given the following bond enthalpies: C-H = 413 kJ/mol, C-C = 348 kJ/mol, C=C = 611 kJ/mol Assume all reactants and products are gases at 298 K and 1 atm.

Answer 1

To calculate the enthalpy change for the polymerization reaction, we need to determine the energy required to break the bonds in the reactants and the energy released when new bonds are formed in the products. The enthalpy change  H  can be calculated using the following equation:H =  Bond enthalpies of bonds broken  -  Bond enthalpies of bonds formed First, let's identify the bonds that are broken and formed in the reaction:Reactants: 2 C2H4  g  - Each molecule of C2H4 has 1 C=C bond and 4 C-H bonds.Products: 1 C4H8  g  - The molecule of C4H8 has 1 C=C bond, 6 C-H bonds, and 3 C-C bonds.Now, let's calculate the energy required to break the bonds in the reactants:Energy to break 2 C=C bonds: 2 * 611 kJ/mol = 1222 kJ/molEnergy to break 8 C-H bonds: 8 * 413 kJ/mol = 3304 kJ/molTotal energy to break bonds in reactants: 1222 kJ/mol + 3304 kJ/mol = 4526 kJ/molNext, let's calculate the energy released when new bonds are formed in the products:Energy released by forming 1 C=C bond: 1 * 611 kJ/mol = 611 kJ/molEnergy released by forming 6 C-H bonds: 6 * 413 kJ/mol = 2478 kJ/molEnergy released by forming 3 C-C bonds: 3 * 348 kJ/mol = 1044 kJ/molTotal energy released by forming bonds in products: 611 kJ/mol + 2478 kJ/mol + 1044 kJ/mol = 4133 kJ/molFinally, let's calculate the enthalpy change  H  for the reaction:H = Energy to break bonds in reactants - Energy released by forming bonds in productsH = 4526 kJ/mol - 4133 kJ/mol = 393 kJ/molThe enthalpy change for the polymerization reaction is 393 kJ/mol.