# Applications of Bond Energies

Applications of Bond Energies are listed below:-

1. Determination of enthalpy of reaction

The bond energies can be used for determining enthalpies of reactions $Delta H_{Reaction} = E(B.E)_R- E(B.E.)_P$ for example, we want to determine the enthalpy of the following reaction:

$HC \equiv CH(g) +2H_2(g) \to H_3C- CH_3(g) \hspace{5mm}\Delta H = ?$

In this reaction a triple bond $(C \equiv C)$ breaks in acetylene and two H — H bonds break in 4H. In turn, one C C- bond and four C — H bonds are formed in$C_2H_6$. Therefore

$\Delta H = [\Delta H_{C- C} +4 \Delta H_{C-H}] + [\Delta H_{C \equiv C} + 2\Delta H_{H- H}]$

$= -[3.47.3 + 4 \times 416.2] + [811.7 + 2 \times 435.1] \\[3mm] =-2.12.1 + 1681.9 \\[3mm] = -330.2 kJ mol^{-1}$

2. Determination of enthalpies of formation of compounds

The bond energies can be used for determining enthalpies of formation of compounds. For example, we want to determine the enthalpy of formation of ethyl alcohol:

Determination of enthalpies of formation of compounds

The formation of ethyl alcohol involves:

(i) Breaking of 3H-H bonds to give 6H, breaking bf 1/2O-O bond to give O and sublimation of 2 atoms of C(s) to give 2C(g).

(ii) Formation of one C-C bond, five bonds, one C-0 bond and one bond.

Therefore,

$\Delta H_f = [3 \Delta H_{H- H} + \dfrac{1}{2} \Delta H_{O- O} + 2 \Delta H_{C(s) \to C(g)}]- [\Delta H_{C- C} + 5\Delta H_{C- H} + \Delta H_{C-O} + \Delta H_{O- H}]$

$= 3 \times 435.1 + \dfrac{1}{2} \times 489.5 + 2 \times 719.6]- [347.3 + 5 \times 416.2 + 351.4 + 464.4]$

$2989.2- 3244.1 = -254.9 k J mol^{-1}$

3. Determination of resonance energy

Resonance energy is taken to be equal to the difference between the actual bond energy of the molecule and that of the most stable of the resonating structures. Let us determine the resonance energy of benzene.

The dissociation of benzene may be given as:

$C_6H_6(g) \to 6C(g) + 6H(g)$

According to Kekule's structure there are three C-C bonds, three C = C bonds and six C-H bonds in benzene. Therefore dissociation energy of benzene may be given as:

$\Delta H_d = 3 \Delta H_{C-C} + 3 \Delta H_{C = C} + 6\Delta H_{C-H}$

$= 3 \times 347.3 + 3 \times 615.0 + 6 \times 416.2 \\[3mm] = 5384.1 k J mol^{-1}$

Thus, dissociation energy of benzene is $5384.1 kJ mol^{-1}$. But experimental value is known to be $5535.1 kJ mol^{-1}$. Evidently, the resonance energy of benzene is $5384.1 = 151 kJ \hspace{2mm} mol^{-1}$.

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