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# Bond Energy

In chemical reactions the formation of a chemical bond is accompanied by the release of energy. Conversely energy has to be supplied for the breaking of a bond.

Bond strengths are commonly described by their bond dissociation energy which is the energy required to break one mole of a bond of a particular type. This is a definite quantity and is expressed in kJ mol-1. For diatomic molecules the bond dissociation energy is the same as bond energy, whereas in polyatomic molecules the bond energy is taken as the mean average of the various bond dissociation energies of the bonds of a given type.

In general the bond dissociation energy $\Delta$U is greater than the true bond dissociation energy, $\Delta$U by an amount corresponding to the zero point energy even at 0 k.

Bond energy is defined as  "It is the amount of energy required to break the covalent bond between the atoms and to separate them to an infinite distance in the gaseous state under standard conditions."
The thermochemical data is useful in determining the bond energies of different bonds.

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## Bond Energy Table

Bonds between the same type of atom are covalent bonds and bonds between atoms with slightly differing electronegativity are also predominantly covalent in character. Theoretically even ionic bonds have some covalent character. Thus the boundary between ionic and covalent bonds is not a clear line of demarcation.

For covalent bonds bond energies and bond lengths depend on many factors- electron affinities, sizes of atoms involved in the bond, differences in their electronegativity and the overall structure of the molecule. There is a general trend that the shorter the bond length, the higher the bond energy, but there is no formula to show this relationship because of the widespread variation in bond character.

## Calculating Bond Energy

Bond energies can be easily calculated from the knowledge of heat of formation of molecules from the atom and heat of combustion etc. Bond energies of a few
calculations are discussed below.

### C-H bond energy in methane

We have four C-H bonds in methane so the C-H bond energy will be the average of bond dissociation energies.

CH4(g) $\rightarrow$ C(g) + 4H(g); $\Delta$C-H = Î”H / 4

The value of heat of formation for methane, the heat of sublimation of C (graphite) and the heat of dissociation of H2(g) molecules are used to calculate the $\Delta$C-Hin methane.

C (graphite) + 2H2(g) $\rightarrow$ CH4(g) ; $\Delta$Ho = - 74.9 kJ

The $\Delta$H value is reversed when one mole of methane is split into separate atoms of carbon and hydrogen.

CH4(g) $\rightarrow$ C(graphite) + 2H2(g); $\Delta$Ho = +74.9 kJ

Further it is given that

C
(graphite) $\rightarrow$ C(g); $\Delta$Ho = +716.68kJ

2H2(g) $\rightarrow$ 4H(g); $\Delta$Ho = 2 x 435.9 = 871.8kJ

On adding the last three equations one gets

CH4(g) $\rightarrow$ C(g) + 4H(g) $\Delta$Ho = 1663.39kJ

Thus C-H bond energy $\Delta$C-H = $\Delta$H / 4 = 1663.39kJ / 4 = 415.8 kJ / mole

Some typical bond length and bond energies are listed below.

## Bond Energy Equation

The ionic contribution to bond energy may be calculated using Born-Mayer equation. The lattice energy for a purely ionic crystal is calculated in this way and multiplied by the fractional ionic character of the bonds. Covalent bond energies are estimated as follows.

For a homo polar covalent bond between like atoms Sanderson proposed the relation

E = CrS

between the covalent bond energy E the electronegativity S and non polar covalent radius r of the atoms. Where C is the empirical constant.

The covalent bond energy for a hetero nuclear bond Ec is given as

Ec = (Rc / Ro) √EAA x EBB

The correction factor for bond length for a bond between atoms A and B in a molecule is added. The bond energy is a geometric mean of the two homo nuclear bond energies EAA and EBB multiplied by the ratio Rc / Ro in which the Rc is the sum of covalent radius and Ro is the observed bond length.

## Bond Order

The bond order is the number of electron pairs shared between two atoms in the formation of a bond. The amount of energy required to break a bond is called bond dissociation energy, or simply bond energy. Because bond length is consistent, bond energies of similar bonds are also consistent.

For example, the bond energy of C-H bond in methane can be calculated from its heat of formation. The heat for formation of methane from carbon and hydrogen has been found to be -1663 kJ mol-1.

C(S) + 4H(g) $\rightarrow$ CH4(g) $\Delta$H = -1663 kJ

Methane has four C-H bonds and the energy required to break all the four C-H bonds is 1663 kJ. Therefore the average C-H bond energy is

$\frac{1663}{4}$ = 415.7 or 416kJ mol-1

## How to Calculate Bond Energy

Below you could see bond energy problem

### Solved Example

Question: Compute the average S-F bond energy in SF6. The values of standard enthalpy of formation of SF6(g), S(g), F(g) are, 100, 275 and 80 kJ mol-1 respectively.
Solution:

Consider the equation
$SF_{6(g)}\rightarrow S_(g) + 6F_{(g)}$

D $H_{reaction}$ = 6D $H_{f}$ (F) + D $H_{f}$ (S) - D $H_{f}$ ($SF_{6}$)

= 6 x 80 + 275 - (-1100) = 1855 kJ

$\Delta H_{S-F}\ bond$ = $\frac{1855}{6}$ = $309.17kJmol^{-1}$

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