It is a well known fact that the process of formation of a chemical bond is accompanied by the release of energy. Conversely, the energy has to be supplied for the breaking of a bond. The energy required to break a particular bond in a gaseous molecule is referred to as bond dissociation energy. It is a definite quantity and is expressed in kJ mol-1.

In a diatomic molecule, the bond dissociation energy is same as bond energy. For example, the energy required to break one mol of H-H bonds in gaseous state is 435.4 kJ.

Therefore, bond enthalpy of H-H bond is 435.4 kJ mol- 1 This may be expressed as:

It is quite clear that dissociation of H_{2} molecule leads to the formation of gaseous atoms. Therefore, this is also known as enthalpy of atomization of hydrogen.

The enthalpy of atomization (ΔaH^{0}) may be defined as the enthalpy change accompanying the dissociation of a one mole of the substance completely into its atoms in the gaseous state. For example, enthalpy of atomization of CH_{4} is represented as

Similarly enthalpy of atomization of Na(s) is 108.4 Kj moi-1 which also represents enthalpy of sublimation of Na(s).

However, in a polyatomic molecule having more than one similar bonds the bond dissociation enthalpy is not the same for successive bonds. Therefore, in such a case the bond energy is not equal to the bond dissociation energy. For example, in water, H_{2}O, the bond dissociation energies of the two O-H bonds differ from one another as described as follows:

HO – H (g) à H(g) + OH(g) ; ΔH = 498 KJ

O – H (g) à H(g) + O(g) ; ΔH = 430 KJ

In such a case, therefore, the bond energy is expressed as the average of the bond dissociation energies of various similar bonds. For example, the average bond energy of O-H bond is expressed as

Thus, mean bond energy, in general, may be defined as the average amount of energy required to break one mole bonds of that type in gaseous molecules.

**CALCULATION OF BOND ENERGIES**

The thermochemical data makes it possible to calculate the bond energies of different bonds. As an illustration the bond enthalpy of C-H bond in methane can be obtained if ΔH of the following chemical reaction is known

CH_{4}(g) à C(g) + 4H(g) ; ΔH = ?

The bond enthalpy of C-H bond is one fourth of the ΔH value for the above reaction. The value of HΔ can be calculated from the type of data available to us.

(a) Direct use of Hess’s law if Δ _{f} H^{0} values of H(g), C(g) and CH_{4}(g) are given.

Δ _{f} H^{0} ‘ values of H(g); C(g) and CH4(g) are 218.0, 717.0 and 750 kJ moi^{-1} respectively

= 4(218) + 717 – (-75.0) = 1664 KJ

(b) Use of thermochemical calculations if the data has values other than Δ_{F}H.

Let the given data be:

Let us now write thermochemical equation of each of the above.

(i) Enthalpy of combustion of methane

CH_{4}(g) + 2O_{2} (g) àCO_{2}(g) + 2H_{2}O(l) ; ΔH1 = – 891 KJ

(ii) Enthalpy of combustion of carbon

C(s) + O_{2} (g) à CO_{2}(g) ; ΔH_{2} = – 394 KJ

(iii) Enthalpy of combustion of hydrogen

H_{2}(g) + 1/2 + O_{2}(g) à H_{2}O(l) ; ΔH_{3} = – 286 KJ

(iv) Enthalpy of sublimation of carbon

C(s) à C(g) ; ΔH_{4} = + 717 KJ

(v) Enthalpy of dissociation of hydrogen molecule

H_{2}(g) à 2H(g); ΔH_{5} = + 436 KJ

can be calculated as follows:

Multiply equation (v) and also equation (iii) by 2. Now add equation (i), equation (iv) and twice of equation (v). From the resulting expression subtract equation (ii) and twice of equation (iii). The resulting value of enthalpy change comes out to be

ΔH = ΔH_{1} – ΔH_{2} – (2 x ΔH_{3} ) + ΔH_{4} + ( 2x ΔH_{5})

= 891 – (-394) – ( -2 x 286) + (717) + ( 2 x 436) = + 1664 kj

This represents the energy required for the cleavage of four C-H bonds.

Therefore , ΔH _{C-H} = 1664 / 4 = 416 KJ mol^{-1}

* These bond enthalpies are the dissociation energies of diatomic molecules that have only one bond, they are, therefore, exact values.

** These bond enthalpies are obtained from molecules that contain more than one bond, therefore, they are average values.

**USE OF BOND ENTHALPY DATA**

The bond enthalpy data given in Table 17.2 is quite useful in determining the standard enthalpies of the reactions. The chemical reaction involves the cleavage of old bonds in reacting species and formation of new bonds· to give product molecules. In general,

The bond enthalpies of various bonds are given Table 17 A

**Table 17 .4. Bond Enthalpies of Some Bonds**

Thus, the values given in bond enthalpy data can help us

(i) calculating standard enthalpy of reactions.

(ii) calculation of bond enthalpies of some specific bond in the molecule.

(iii) comparing the strength of various bonds.