Estimate the heat of the formation of each of the following molecules useing the bond dissociation energies provided (in KJ/mol)
(a) NH3 (b) H2O (C) H2O2
D(NÎN)=944; D(H-H)=436; D(OÎO)=498; D(O-O)= 142; D(N-N)=391; D(O-H)=464
NB>all the brackets are foot note
To estimate the heat of formation of a molecule using bond dissociation energies, we use the concept of Hess's Law. Hess's Law states that the overall enthalpy change in a chemical reaction is independent of the pathway taken.
The heat of formation (ΔHf) is defined as the enthalpy change when one mole of a compound is formed from its elements in their standard states. In this case, we need to determine the heat of formation of NH3, H2O, and H2O2 using the given bond dissociation energies.
(a) NH3:
The balanced equation for the formation of NH3 from its elements (N2 and H2) would be:
N2(g) + 3H2(g) → 2NH3(g)
To calculate the heat of formation of NH3:
ΔHf(NH3) = Σ(ΔHbonds broken) - Σ(ΔHbonds formed)
Breaking the bonds:
Σ(ΔHbonds broken) = D(N≡N) + 3D(H-H)
Forming the bonds:
Σ(ΔHbonds formed) = 2D(N-H)
Substituting the given values:
Σ(ΔHbonds broken) = 944 + 3(436) = 2252 KJ/mol
Σ(ΔHbonds formed) = 2(391) = 782 KJ/mol
ΔHf(NH3) = 2252 - 782 = 1470 KJ/mol
Therefore, the estimated heat of formation of NH3 is 1470 KJ/mol.
(b) H2O:
The balanced equation for the formation of H2O from its elements (H2 and O2) is:
H2(g) + 1/2 O2(g) → H2O(g)
To calculate the heat of formation of H2O:
ΔHf(H2O) = Σ(ΔHbonds broken) - Σ(ΔHbonds formed)
Breaking the bonds:
Σ(ΔHbonds broken) = D(H-H) + 1/2D(O=O)
Forming the bonds:
Σ(ΔHbonds formed) = 2D(O-H)
Substituting the given values:
Σ(ΔHbonds broken) = 436 + 1/2(498) = 685 KJ/mol
Σ(ΔHbonds formed) = 2(464) = 928 KJ/mol
ΔHf(H2O) = 685 - 928 = -243 KJ/mol
Therefore, the estimated heat of formation of H2O is -243 KJ/mol.
(c) H2O2:
The balanced equation for the formation of H2O2 from its elements (H2 and O2) is:
H2(g) + O2(g) → H2O2(g)
To calculate the heat of formation of H2O2:
ΔHf(H2O2) = Σ(ΔHbonds broken) - Σ(ΔHbonds formed)
Breaking the bonds:
Σ(ΔHbonds broken) = D(H-H) + D(O=O)
Forming the bonds:
Σ(ΔHbonds formed) = 2D(O-H)
Substituting the given values:
Σ(ΔHbonds broken) = 436 + 498 = 934 KJ/mol
Σ(ΔHbonds formed) = 2(464) = 928 KJ/mol
ΔHf(H2O2) = 934 - 928 = 6 KJ/mol
Therefore, the estimated heat of formation of H2O2 is 6 KJ/mol.
Please note that these values are approximate estimates calculated using bond dissociation energies and should be verified through experimental data for accuracy.