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# Bond Dissociation Energy

## What is Bond Dissociation Energy?

Bond dissociation energy is the energy absorbed per mole when a particular kind of chemical bond is broken in a gaseous state of matter. It depends on the nature of atoms united by a bond or the nature of the molecule. For example, the dissociation energy for breaking the oxygen hydrogen bond in the water molecule will be 120 kcal. when the second hydrogen atom separated from the residual OH-group the dissociation energy = 101 kcal. ## What is bond energy?

Bond energy is the average value of dissociation energies of a given bond in a series of different dissociating species. In the above-noted example, the dissociation energy for two bonds in a water molecule is 120 and 101 kcal. Therefore, the average value of the dissociation energies = 110.5 kcal. It is practically equal to bond energy. Hence bond energy is the average dissociating energy of a given bond in a whole molecule. For a diatomic molecule, these two energies are equal values. The dissociation energy of the carbon-hydrogen bond in methane and benzene is different because the residual portion of these two molecules is different.

### Bond energy of methane

A methane molecule is formed by the overlap of four sp3 hybridized orbitals of carbon and four 1s orbitals of the hydrogen atom. Therefore, all carbon-hydrogen bonds are equivalent. But dissociation energy required to break the first bond is not the same as the second bond. Hence for calculating bond energy, we can take the average values of all the four bonds dissociation. Therefore, the bond energy for methane molecule = 397/4 = 99 kcal. The dissociation energy of some chemical bonds are given below the table,

 Chemical Bond Dissociation Energy kJ Kcal CH3 – H 426.8 102 CH3CH2 – H 405.8 97 Me2CH – H 393.3 94 Me3C – H 374.5 89.5 C – C 347.3 83 C = C 606.7 145 N – N 163.2 39 N = N 418.4 100

## Ionic resonance energy

The greater the polarity of a bond greater will be bond dissociation energies. This extra energy appearing in A – B molecules arise by electrostatic attraction between A and B dipole. Hence this extra energy possessed by molecules by electric polarization is called ionic resonance energy.

### Pauling scale of electronegativity formula

Ionic resonance energy values are used by pulling for the determination of electronegativity or electron affinity difference of elements in the periodic table. The empirical formula uses for the calculation of electronegativity of A – B molecule is, XA – XB = 0.208 √Δ + α. Where XA and XB = electronegativity of A and B and α = arbitrary constant which is nearly zero for chemical elements other than carbon, nitrogen, oxygen, and fluorine, and helium.

### What is atomization?

The quantity of heat required to produce one mole of atoms in the gaseous atomic state in the standard state is called the heat of atomization of the element It can be calculated from the spectrum measurement and some thermal data.

 Element Atomization Heat of atomization (kcal) Carbon C(s) → C(g) 170.9 Hydrogen H2(g) → 2H(g) 52.1 Oxygen O2(g) → 2O(g) 59.6 Nitrogen N2(g) → 2N(g) 113.0 Chlorine Cl2(g) → 2Cl(g) 28.9

### What is heat of formation?

The heat of formation is the heat change associated with the formation of 1 mole of a substance from its constituents elements in their stable forms. It is generally represented by ΔHf. When the elements are standard states, it is called standard heat of formation. For example, ΔHfo for CH4 = – 17.9 kcal. A positive value of ΔHfo of a compound indicates that the compound is less stable than its constituents. It is called an endothermic compound, While negative sign refers to that the compound is more stable.

## How to calculate bond energy?

The thermodynamics heat of formation and heat of atomization formula from the above table is used to calculate the bond energy of a molecule. Some workout examples are given below,

### C-H bond dissociation energy

The heat of formation of methane = -17.9 kcal and the heat of atomization solid carbon and four hydrogen element to the gaseous carbon and hydrogen atom = 170.9 kcal and 4 × 52.1 kcal.

 C(s) → C(g) ΔHC = 170.9 kcal 2H2(g) → 4H(g) ΔHH = 4 × 52.1 kcal CH4 → C(s) + 4H(g) ΔHd = +17.9 kcal CH4 → C(s) + 4H(g) ΔH = 397.2 kcal

From the above data required energy for breaking four carbon-hydrogen bonds = 170.9 + 4 × 51.1 + 17.9 = 397.2 kcal. Therefore, the carbon-hydrogen bond energy = 397.2/4 ≈ 99 kcal. Such calculation shows that carbon-hydrogen bond energy in a hydrocarbon like methane, ethane, ethylene, etc are the same but this is not strictly correct. The energy varies due to linking and the stereochemistry of molecules.

### How to calculate heat of formation?

Automation and dissociation energy data are used to calculate the heat of the formation of a molecule. For example, the formation of methyl alcohol from carbon, oxygen, and hydrogen.

C (s) + 2H2 (g) + ½O2 (g) → CH3OH (l)
Atomization of 1-mole carbon = 170.9
For 2-mole hydrogen = 4 × 52.1
For half-mole oxygen = 59.6
Formation of 3 carbon hydrogen bonds = – 3 × 99
For 1 C-O bond = – 84
For 1 O-H bond = -110.5
Liquefaction of 1 mole CH3OH = – 8.4

From the above data, the heat of formation of liquid alcohol = – 61 kcal. If there exist one or more resonating structure, the resonance energy is also taken for the bond these energies calculations.