Answer :
Final answer:
The bond energy for the C=C double bond in ethene (C2H4) is calculated using the given enthalpy of formation, atomisation energy for carbon, and bond energies for H2 and C-H. After considering the energy required to break the bonds of the reactants and the energy released to form the products, the bond energy of C=C is found to be 141.1 kcal, which matches option A, 140.9 kcal.
Explanation:
To find the C=C bond energy, we need to consider the given thermochemical data for ethene (C2H4) and use Hess's Law which relates the change in enthalpy of a reaction to the sum of the energies of the bonds broken minus the energy of the bonds formed.
Given:
- ΔHf for C2H4 = 12.5 kcal
- Heat of atomisation for C = 171 kcal (this is the energy required to break the bonds in one mole of solid carbon atoms)
- Bond energy of H2 = 104.3 kcal
- C-H bond energy = 99.3 kcal
First, we consider the formation of ethene from its elements in their standard states:
- 2C (graphite) + 2H2 (gas) → C2H4
- ΔHf for this reaction is the energy change when one mole of ethene is formed from elements in their standard states, which is given as +12.5 kcal.
The total energy input is the sum of the heat of atomisation of 2 moles of carbon and the bond energy of 2 moles of H2, which totals to 2(171) + 2(104.3) = 550.6 kcal. This input is required to break the bonds in the reactants.
The energy output is the formation of 1 mole of ethene, which includes forming 4 C-H bonds and 1 C=C bond. Given that ΔHf for the reaction is +12.5 kcal, we can set up the equation:
550.6 kcal (input) - (bond energy of 4 C-H + bond energy of C=C) = 12.5 kcal (output)
To find the bond energy of C=C, we rearrange the equation:
Bond energy of C=C = 550.6 kcal - bond energy of 4 C-H - 12.5 kcal
Since we have the C-H bond energy (99.3 kcal), we can calculate as:
Bond energy of C=C = 550.6 kcal - 4(99.3 kcal) - 12.5 kcal
Bond energy of C=C = 550.6 kcal - 397.2 kcal - 12.5 kcal
Bond energy of C=C = 141.1 kcal
Therefore, the bond energy of the C=C double bond is 141.1 kcal, which is closest to option A, 140.9 kcal.
