Bond Energies

Overview

Bond energy (bond dissociation energy) is the energy required to break one mole of a particular bond in gaseous molecules. It can be used to estimate enthalpy changes for reactions.

Definition

$$\text{A-B}(g) \rightarrow \text{A}(g) + \text{B}(g) \quad \Delta H = D \text{ (Bond Energy)}$$

Bond energy is always positive (breaking bonds requires energy).

Common Bond Energies

Single Bonds (kJ/mol)

Bond	Energy	Bond	Energy
H-H	436	C-H	413
H-F	567	C-C	347
H-Cl	431	C-N	305
H-Br	366	C-O	358
H-I	298	C-F	485
H-O	463	C-Cl	339
H-N	391	C-Br	276
H-S	363	C-S	259
O-O	146	N-N	163
F-F	155	Cl-Cl	242
Br-Br	193	I-I	151
O-H	463	N-H	391

Multiple Bonds (kJ/mol)

Bond	Energy	Bond	Energy
C=C	614	C≡C	839
C=O	799	C≡O	1072
C=N	615	C≡N	891
N=N	418	N≡N	941
O=O	495	S=O	523

Calculating ΔH from Bond Energies

Formula

$$\Delta H_{rxn} = \sum D(\text{bonds broken}) - \sum D(\text{bonds formed})$$ $$\Delta H_{rxn} = \sum D_{\text{reactants}} - \sum D_{\text{products}}$$

Important Notes

• Breaking bonds: ABSORBS energy (+)
• Forming bonds: RELEASES energy (-)
• This gives an ESTIMATE (average bond energies used)

Example 1: Combustion of Methane

$$\text{CH}_4(g) + 2\text{O}_2(g) \rightarrow \text{CO}_2(g) + 2\text{H}_2\text{O}(g)$$

Bonds Broken:

$$4 \times \text{C-H} = 4 \times 413 = 1652 \text{ kJ}$$ $$2 \times \text{O=O} = 2 \times 495 = 990 \text{ kJ}$$ $$\text{Total broken} = 2642 \text{ kJ}$$

Bonds Formed:

$$2 \times \text{C=O} = 2 \times 799 = 1598 \text{ kJ}$$ $$4 \times \text{O-H} = 4 \times 463 = 1852 \text{ kJ}$$ $$\text{Total formed} = 3450 \text{ kJ}$$

ΔH Calculation:

$$\Delta H_{rxn} = 2642 - 3450 = -808 \text{ kJ}$$

(Actual value ≈ -802 kJ/mol, so estimate is reasonable)

Example 2: Formation of HCl

$$\text{H}_2(g) + \text{Cl}_2(g) \rightarrow 2\text{HCl}(g)$$

Bonds Broken:

$$1 \times \text{H-H} = 436 \text{ kJ}$$ $$1 \times \text{Cl-Cl} = 242 \text{ kJ}$$ $$\text{Total} = 678 \text{ kJ}$$

Bonds Formed:

$$2 \times \text{H-Cl} = 2 \times 431 = 862 \text{ kJ}$$

ΔH Calculation:

$$\Delta H_{rxn} = 678 - 862 = -184 \text{ kJ}$$

Example 3: Hydrogenation

$$\text{H}_2\text{C}=\text{CH}_2(g) + \text{H}_2(g) \rightarrow \text{H}_3\text{C}-\text{CH}_3(g)$$

Bonds Broken:

$$1 \times \text{C=C} = 614 \text{ kJ}$$ $$1 \times \text{H-H} = 436 \text{ kJ}$$ $$\text{Total} = 1050 \text{ kJ}$$

Bonds Formed:

$$1 \times \text{C-C} = 347 \text{ kJ}$$ $$2 \times \text{C-H} = 2 \times 413 = 826 \text{ kJ}$$ $$\text{Total} = 1173 \text{ kJ}$$

ΔH Calculation:

$$\Delta H_{rxn} = 1050 - 1173 = -123 \text{ kJ}$$

Bond Order and Bond Strength

Bond	Order	Length (pm)	Energy (kJ/mol)
C-C	1	154	347
C=C	2	134	614
C≡C	3	120	839
C-O	1	143	358
C=O	2	123	799
C≡O	3	113	1072

Trends

• Higher bond order → Stronger bond
• Higher bond order → Shorter bond
• Multiple bonds are NOT simple multiples of single bond energies

Limitations of Bond Energy Method

1. Average values: Bond energies are averages for many compounds
2. Environment effects: Same bond can have different energies in different molecules
3. Resonance: Delocalized bonds don't match simple bond energies
4. State matters: Values are for gaseous molecules only
5. Approximation: Results are estimates, not exact

Comparing Methods

Method	Accuracy	Use
Bond Energies	Approximate	Quick estimates
$\Delta H_f°$ values	More accurate	Standard conditions
Hess's Law	Exact	Combining reactions
Calorimetry	Measured	Direct measurement

Why Breaking Bonds Requires Energy

• Bonds are stable electron arrangements
• Energy must be supplied to separate atoms
• This is the basis of activation energy in reactions

Why Forming Bonds Releases Energy

• Atoms achieve more stable configurations
• Lower energy state is reached
• Energy is released to surroundings