3.4 Bond Energy (Bond Enthalpy) | Chemical Bonding | Chemistry 11

Bond energy, also known as bond enthalpy, is the energy required to break one mole of a specific type of bond in a gaseous substance. It is a measure of the strength of a chemical bond.

Unit: Kilojoules per mole ( $k J m o l^{- 1}$ )
Bond breaking is always endothermic ( $Δ H = + v e$ )
Bond formation is always exothermic ( $Δ H = - v e$ )

Bond energy is influenced by several factors:

Electronegativity difference between the two bonded atoms
Size of the atoms
Bond order (single, double, triple bond)
Bond length

Effect of Electronegativity

The greater the electronegativity difference between two bonded atoms, the more polar the bond becomes, which in turn increases the bond energy. A more polar bond has stronger electrostatic attraction, requiring more energy to break.

This trend is clearly visible in the hydrogen halides (hydrides of Group VII).

Table 3.2: Bond Energy of Hydrogen Halides

Bond	Bond Energy ( $k J m o l^{- 1}$ )	Electronegativity Difference
$H - F$	562	1.8
$H - C l$	431	0.9
$H - B r$	366	0.7
$H - I$	299	0.4

From the data, as the electronegativity difference decreases from $H - F$ to $H - I$ , the bond energy also decreases. $H - F$ has the largest electronegativity difference and the highest bond energy.

Bond Length

Bond length is the average distance between the nuclei of two covalently bonded atoms. It is typically measured in Ångströms ( $\overset{˚}{A}$ ) or picometers ( $p m$ ).

$1 p m = 1 0^{- 12} m$

Relationship with Atomic Size and Bond Energy

Bond length is directly related to the size of the bonded atoms. Generally, smaller atoms form shorter bonds, and shorter bonds are stronger, meaning they have higher bond energy.

Example: The bond energy of $H - H$ is $436 k J m o l^{- 1}$ , while that of $H - B r$ is $366 k J m o l^{- 1}$ . This is because the hydrogen molecule ( $H_{2}$ ) has a much shorter bond length compared to hydrogen bromide ( $H B r$ ), as the bromine atom is significantly larger than a hydrogen atom.

Bond Properties of Halogens

The relationship between bond length and bond energy can be observed in the halogen group. For more details on these elements, see 12.1 Halogens→(/chemistry-11/12-halogens/12-1-halogens).

Table 3.3: Bond Energy and Bond Length of Halogens

Bond	Bond Energy ( $k J m o l^{- 1}$ )	Bond Length (pm)
$F - F$	158	149
$C l - C l$	242	199
$B r - B r$	193	228
$I - I$	151	266

As the atomic radius increases down the group from fluorine to iodine, the bond length increases. The bond energy generally decreases from chlorine to iodine.

The Fluorine Anomaly: An exception to the trend is fluorine ( $F_{2}$ ), which has a lower bond energy than chlorine ( $C l_{2}$ ). This is because fluorine atoms are very small and electron-dense. The lone pairs of electrons on the adjacent fluorine atoms repel each other strongly, which weakens the $F - F$ covalent bond. Consequently, less energy is required to break it.

Predicting Reactivity

Bond energy is a useful tool for predicting the reactivity of covalent molecules.

High Bond Energy: A high bond energy indicates a strong bond. Molecules with strong bonds are more stable and therefore less reactive.
Low Bond Energy: A low bond energy indicates a weak bond. Molecules with weak bonds are less stable and more reactive.

Example: In alkyl halides, the $C - F$ bond has a greater bond energy than the $C - C l$ bond. Therefore, alkyl fluorides are generally less reactive than alkyl chlorides.

Energy Transfer During Bond Breaking and Making

Chemical reactions involve the breaking of bonds in reactants and the formation of new bonds in products.

Bond breaking requires energy input → endothermic step
Bond formation releases energy → exothermic step

The overall enthalpy change ( $Δ H$ ) of a reaction depends on the balance between these two processes:

$Δ H_{r e a c t i o n} = \sum Bond Energies Broken - \sum Bond Energies Formed$

If energy released (bonds formed) > energy absorbed (bonds broken): exothermic ( $Δ H < 0$ )
If energy absorbed (bonds broken) > energy released (bonds formed): endothermic ( $Δ H > 0$ )

Calculating Enthalpy Change Using Bond Energies

Bond energies can be used to estimate the enthalpy change of a reaction.

Worked Example: Calculate $Δ H$ for the reaction: $H_{2} (g) + C l_{2} (g) \to 2 H C l (g)$

Bond energies: $H - H = 436 k J m o l^{- 1}$ , $C l - C l = 242 k J m o l^{- 1}$ , $H - C l = 431 k J m o l^{- 1}$

Step 1 — Bonds broken (endothermic): $H - H : + 436 k J + C l - C l : + 242 k J = + 678 k J$

Step 2 — Bonds formed (exothermic): $2 \times H - C l : 2 \times (- 431) = - 862 k J$

Step 3 — Calculate $Δ H$ : $Δ H = + 678 + (- 862) = - 184 k J m o l^{- 1}$

The negative value confirms the reaction is exothermic.

Exact vs. Average Bond Energies

Bond energies can be classified as:

Exact bond energies: Apply to a specific bond in a specific molecule. For example, the $H - H$ bond energy in $H_{2}$ is exactly $436 k J m o l^{- 1}$ .
Average (approximate) bond energies: The bond energy of a particular bond type (e.g., $C - H$ ) varies slightly depending on the molecular environment. An average value ( $\approx 413 k J m o l^{- 1}$ for $C - H$ ) is used as an approximation across different compounds.

Average bond energies are useful for estimating $Δ H$ when exact values are unavailable, but they introduce some error into calculations.

Bond

Bond Energy (

k J m o l^{- 1}

)

Electronegativity Difference

H - F

562

1.8

H - C l

431

0.9

H - B r

366

0.7

H - I

299

0.4

Bond

Bond Energy (

k J m o l^{- 1}

)

Bond Length (pm)

F - F

158

149

C l - C l

242

199

B r - B r

193

228

I - I

151

266