1. Breaking Chemical Bonds

What Is a Chemical Bond?

A chemical bond is an attractive interaction that holds atoms or ions together.

In a covalent bond, electrons are shared between atoms. The positively charged nuclei are attracted to the shared electrons, helping hold the atoms together.

Because bonded atoms attract one another, separating them requires energy.

The central idea for this topic is:

Breaking bonds requires energy.

Therefore:

bond breaking = endothermic

This is one of the most important rules in chemical energetics.

If the image above does not load from the source, the potential-energy diagram below shows the same principle particularly clearly.

Why Does Breaking a Bond Require Energy?

Imagine two atoms joined by a chemical bond.

At the normal bond distance, attractive interactions hold the atoms together. To separate the atoms, we must work against these attractions.

That requires an input of energy.

As the atoms move farther apart, the potential energy of the system increases until the atoms are effectively separated.

Therefore:

bonded atoms + energy → separated atoms

The chemical system has gained energy.

That is why bond breaking is an endothermic process.

Notice the upward arrow labelled energy absorbed when bond breaks. Moving upward out of the potential-energy well requires energy.

The Potential-Energy Well

A useful way of understanding a chemical bond is to imagine the bonded atoms sitting in an energy well.

At the bottom of the well, the atoms are at their most stable separation.

To separate them completely, energy must be supplied to move the system out of the well.

For the H–H bond, the minimum occurs at a bond length of approximately 74 pm.

The vertical distance from the minimum to the separated-atoms energy level represents the bond dissociation energy. For H₂, this is about 436 kJ mol⁻¹.

A useful general rule is:

deeper energy well → more energy required to escape → stronger bond

Bond Breaking Is Endothermic

An endothermic process absorbs energy from its surroundings.

Breaking a chemical bond requires exactly this kind of energy input.

For example:

H₂(g) → 2H(g)

requires approximately:

+436 kJ mol⁻¹

The positive value indicates that energy has entered the chemical system.

The same principle applies to every covalent bond:

A–B + energy → A + B

Bond breaking always requires energy.

Bond Breaking and Bond Formation Are Opposites

Now imagine the reverse process.

Instead of separating bonded atoms, two separated atoms move together and form a bond.

When the bond forms, the system moves into a lower-energy, more stable arrangement.

Energy is released to the surroundings.

Therefore:

Breaking bonds → energy absorbed

Forming bonds → energy released

For hydrogen:

H₂ → 2H

requires approximately:

+436 kJ mol⁻¹

The reverse process:

2H → H₂

releases approximately:

−436 kJ mol⁻¹

Bond breaking and bond formation are opposite processes.

A Very Important Misconception

One of the most common mistakes in chemical energetics is saying:

"Breaking bonds releases energy."

It does not.

Breaking bonds always requires energy.

Students sometimes develop this misconception because reactions such as combustion release large amounts of energy.

But the energy released by combustion does not come from breaking the reactant bonds.

During a reaction:

Energy IN → break reactant bonds

Energy OUT → form product bonds

If more energy is released during bond formation than was required for bond breaking, the overall reaction is exothermic.

This distinction becomes extremely important when we begin calculating reaction energies.

What Is Bond Energy?

The strength of a covalent bond can be described using its bond energy.

Bond energy is the energy required to break one mole of a particular type of covalent bond in gaseous molecules.

Bond energies are usually expressed in:

kJ mol⁻¹

For example:

H–H = 436 kJ mol⁻¹

This means approximately 436 kJ of energy must be supplied to break one mole of H–H bonds.

The stronger the bond, the more energy is required to break it.

Therefore:

large bond energy → strong bond

small bond energy → weaker bond

Interpreting Bond Energy Values

Consider some approximate average bond energies:

Bond-energy values allow us to compare the strengths of different bonds.

For example:

N≡N = 945 kJ mol⁻¹

while:

Cl–Cl = 243 kJ mol⁻¹

Much more energy is required to break the N≡N bond.

Therefore:

N≡N is much stronger than Cl–Cl.

What Does 436 kJ mol⁻¹ Actually Mean?

Consider hydrogen gas.

Each H₂ molecule contains one H–H bond.

H–H bond energy ≈ 436 kJ mol⁻¹

Therefore:

H₂(g) → 2H(g)

requires:

436 kJ for every mole of H–H bonds broken

The bond-energy value is positive when describing bond breaking because energy must be supplied.

Average Bond Energies

Many bond-energy tables actually contain average bond energies.

A particular bond type does not have exactly the same strength in every molecule.

For example, the energy required to break a C–H bond depends somewhat on the other atoms surrounding that bond.

Chemists therefore use average values obtained from many compounds.

This is why calculations using average bond energies usually provide an estimate of the reaction enthalpy rather than a perfectly exact value.

Comparing Single, Double and Triple Bonds

Bond order affects bond strength.

Consider carbon-carbon bonds:

C–C ≈ 345 kJ mol⁻¹

C=C ≈ 611 kJ mol⁻¹

C≡C ≈ 837 kJ mol⁻¹

Therefore:

C≡C > C=C > C–C

in bond strength.

In general, for bonds between the same pair of elements:

single bond → weaker

double bond → stronger

triple bond → strongest

However, a double bond is not exactly twice as strong as a single bond, and a triple bond is not exactly three times as strong.

Bond Strength and Bond Length

Bond strength is also related to bond length.

For carbon-carbon bonds, approximate values are:

As bond order increases:

bond length decreases

and:

bond strength increases.

So the overall trend is:

C–C → longest and weakest

C=C → shorter and stronger

C≡C → shortest and strongest

The bond length corresponds to the stable separation of the two nuclei near the bottom of the energy well.

Why Is the N≡N Bond So Strong?

Nitrogen gas consists of two nitrogen atoms joined by a triple covalent bond:

N≡N

Its bond energy is approximately:

945 kJ mol⁻¹

This is one of the strongest common covalent bonds.

A large amount of energy must therefore be supplied to separate the nitrogen atoms.

The strength of this bond helps explain why atmospheric nitrogen is relatively unreactive under ordinary conditions.

Strong Bonds Require More Energy to Break

Imagine two bonds:

Bond A = 250 kJ mol⁻¹

Bond B = 700 kJ mol⁻¹

Bond B requires much more energy to break.

Therefore:

Bond B is stronger.

The difference is:

700 − 250 = 450 kJ mol⁻¹

So breaking one mole of Bond B requires 450 kJ more energy than breaking one mole of Bond A.

This gives us a simple way of interpreting bond-energy tables:

higher number = stronger bond

Worked Example 1: Breaking Hydrogen Bonds

Consider:

H₂ → 2H

One H–H bond must be broken.

H–H bond energy:

436 kJ mol⁻¹

Therefore:

Energy required = 436 kJ mol⁻¹

Because energy enters the system:

ΔH = +436 kJ mol⁻¹

The process is:

endothermic

Worked Example 2: Breaking Chlorine Bonds

Consider:

Cl₂ → 2Cl

Cl–Cl bond energy:

243 kJ mol⁻¹

Therefore:

Energy required = 243 kJ mol⁻¹

So:

ΔH = +243 kJ mol⁻¹

Again:

bond breaking is endothermic

Comparing H–H and Cl–Cl

H–H:

436 kJ mol⁻¹

Cl–Cl:

243 kJ mol⁻¹

Which bond is stronger?

H–H

Which requires more energy to break?

H–H

Difference:

436 − 243 = 193 kJ mol⁻¹

Therefore, approximately 193 kJ mol⁻¹ more energy is required to break H–H bonds than Cl–Cl bonds.

Breaking Several Bonds

Chemical reactions often require many bonds to be broken.

If several bonds must be broken, their energies can be added.

Suppose we need to break:

2 C–H bonds

and:

1 C–C bond

Using:

C–H = 413 kJ mol⁻¹

C–C = 345 kJ mol⁻¹

Energy required:

2(413) + 345

= 826 + 345

= 1171 kJ mol⁻¹

Because these bonds are being broken, this represents an energy input.

Bond Breaking During Chemical Reactions

Chemical reactions rearrange atoms.

Existing bonds in the reactants are disrupted, and new bonds form to produce the products.

A simplified reaction might be represented as:

AB + CD → AC + BD

First:

A–B and C–D bonds are broken

Energy is required.

Then:

A–C and B–D bonds form

Energy is released.

The overall energy change depends on the balance between these two processes.

The Energy Balance of a Reaction

The overall reaction energy can be estimated using:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

In words:

reaction energy = energy required to break bonds − energy released when bonds form

If breaking bonds requires more energy than bond formation releases:

ΔH > 0

The reaction is:

endothermic

If forming bonds releases more energy than was required for bond breaking:

ΔH < 0

The reaction is:

exothermic

Example: Combustion of Methane

Consider the combustion of methane:

CH₄ + 2O₂ → CO₂ + 2H₂O

This reaction involves both breaking and forming bonds.

Before the products can form, bonds in the reactants must be disrupted.

These include:

C–H bonds in CH₄

and:

O=O bonds in O₂

Breaking these bonds requires energy.

Then new bonds form:

C=O bonds in CO₂

and:

O–H bonds in H₂O

Forming these bonds releases energy.

More energy is released when the product bonds form than is required overall to break the reactant bonds.

Therefore methane combustion is exothermic.

But notice:

breaking the bonds was still endothermic.

The overall reaction becomes exothermic because of the energy released during bond formation.

Where Does the Energy of Combustion Come From?

It is tempting to say that fuels contain bonds that "release energy when broken."

That explanation is misleading.

Breaking the C–H bonds in methane requires energy.

Breaking O=O bonds also requires energy.

The large energy release occurs because the products contain a very stable set of bonds, particularly strong C=O and O–H bonds.

Formation of these product bonds releases a large amount of energy.

So:

energy absorbed breaking reactant bonds

is smaller than:

energy released forming product bonds

The difference is transferred to the surroundings.

Bond Breaking and Activation Energy

Bond breaking also helps us understand activation energy.

At the beginning of many reactions, existing bonds must stretch, distort or partially break as the reacting particles move toward the transition state.

This requires energy.

The reaction profile therefore initially rises toward the transition state.

However, there is an important distinction:

Activation energy is not simply the energy required to completely break every bond in the reactants.

Activation energy is the energy barrier required to reach the transition state.

Some bonds may only be partially broken at this point while new interactions may already be developing.

Bonds and Molecular Stability

Strong bonds generally require large amounts of energy to break.

This can contribute to the stability of molecules.

For example, the very strong N≡N bond helps make nitrogen gas relatively unreactive.

However, we should not judge the reactivity of an entire substance from just one bond.

Reactivity also depends on:

• all the bonds involved
• molecular structure
• possible products
• temperature
• reaction mechanism
• catalysts
• activation energy

Bond energy is therefore one important part of understanding chemical reactions.

Energy Is Conserved

Energy is not created or destroyed during a chemical reaction.

Instead, energy is transferred and transformed.

During bond breaking:

energy enters the chemical system

During bond formation:

energy leaves the chemical system

The overall reaction energy depends on the difference between these transfers.

This is an application of the law of conservation of energy.

Did You Know?

The N≡N bond in nitrogen gas has an average bond energy of about:

945 kJ mol⁻¹

That enormous bond strength creates an interesting biological problem.

Earth's atmosphere contains a huge amount of nitrogen gas, but most organisms cannot directly use N₂ because breaking and rearranging the N≡N bond is difficult.

Special processes called nitrogen fixation convert atmospheric nitrogen into compounds that living organisms can use.

This is why nitrogen-fixing bacteria are so important in ecosystems and agriculture.

Common Misconceptions

"Breaking bonds releases energy."

Incorrect. Breaking bonds requires energy.

"Strong bonds contain more energy, so they release more energy when broken."

Incorrect. Strong bonds require more energy to break.

"A double bond requires exactly twice the energy of a single bond."

Incorrect. Bond energies do not increase in simple whole-number ratios.

"Bond energy is identical in every molecule."

Not usually. Many tabulated values are average bond energies because the molecular environment affects bond strength.

"If a reaction releases energy, breaking the reactant bonds must have released it."

Incorrect. Bond breaking absorbs energy. Energy is released when new bonds form.

"Activation energy is the energy needed to completely break every bond in the reactants."

Incorrect. Activation energy is the barrier to reaching the transition state.

Key Terms

Chemical bond – An attractive interaction that holds atoms or ions together.

Bond breaking – Separation of bonded atoms, requiring an input of energy.

Endothermic process – A process in which the system absorbs energy.

Bond energy – Energy required to break one mole of a particular type of covalent bond in gaseous molecules.

Average bond energy – An average energy required to break a particular bond type across different molecular environments.

Bond strength – A measure of how strongly two atoms are held together.

Bond length – The equilibrium distance between the nuclei of two bonded atoms.

Bond order – The number of bonding interactions between two atoms, such as single, double or triple.

Activation energy – The energy barrier that must be overcome for a reaction to proceed.

Transition state – A temporary high-energy arrangement of atoms along a reaction pathway.

Key Takeaways

• Breaking chemical bonds requires energy.
• Bond breaking is an endothermic process.
• Energy must be supplied to overcome the attractive interactions holding bonded atoms together.
• Bond formation releases energy.
• Bond energy is usually measured in kJ mol⁻¹.
• A larger bond energy generally indicates a stronger bond.
• Stronger bonds require more energy to break.
• Average bond energies are approximations because bond strength depends somewhat on molecular environment.
• For the same pair of atoms, triple bonds are generally stronger and shorter than double bonds, which are generally stronger and shorter than single bonds.
• Chemical reactions involve both breaking reactant bonds and forming product bonds.
• The overall energy change can be estimated using:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

• Exothermic reactions do not release energy because bonds are broken.
• They release energy overall when forming the new bonds releases more energy than breaking the original bonds requires.
• Bond breaking and bond distortion contribute to the energy requirements involved in reaching a reaction's transition state.

2. Forming Chemical Bonds

What Happens When a Chemical Bond Forms?

A chemical bond forms when atoms or ions become attracted strongly enough to create a more stable arrangement.

When two atoms that can bond move toward one another, attractive interactions between their nuclei and electrons lower the potential energy of the system.

The atoms move from a:

higher-energy, less stable arrangement

to a:

lower-energy, more stable arrangement

The difference in energy is transferred to the surroundings.

Therefore:

forming bonds releases energy

and:

bond formation is exothermic.

Why Does Bond Formation Release Energy?

Consider two atoms that are initially far apart.

When they are far apart, there is little attractive interaction between them.

As they approach one another, attractive forces develop between:

• each positively charged nucleus
• the electrons associated with the other atom

If the atoms are at an appropriate distance, these attractions lower the potential energy of the system.

The atoms become more stable.

The decrease in potential energy must appear somewhere else.

It is released to the surroundings, often as thermal energy.

Therefore:

separated atoms → bonded atoms + energy

or more generally:

A + B → A–B + energy

The bottom of the energy well represents the most stable bond distance. Moving into that lower-energy state releases energy.

Bond Formation Is Exothermic

An exothermic process transfers energy from the chemical system to its surroundings.

Because bond formation lowers the potential energy of the atoms, energy leaves the system.

Therefore:

bond formation → exothermic

The enthalpy change associated with forming a bond is negative.

For example:

2H(g) → H₂(g)

releases approximately:

436 kJ mol⁻¹

We can express the energy change as approximately:

ΔH = −436 kJ mol⁻¹

The negative sign indicates that energy has been released from the chemical system.

Bond Breaking and Bond Formation Are Opposites

The two processes can be compared directly.

Bond breaking:

A–B + energy → A + B

Energy absorbed

Endothermic

Bond formation:

A + B → A–B + energy

Energy released

Exothermic

The amount of energy required to break a particular bond is approximately equal in magnitude to the energy released when that same bond forms under corresponding conditions.

For example:

H₂ → 2H

requires approximately:

+436 kJ mol⁻¹

while:

2H → H₂

releases approximately:

−436 kJ mol⁻¹.

Why Is the Bonded State More Stable?

In chemistry, a system tends to be more stable when it has lower potential energy.

Consider a ball rolling downhill.

At the top of a hill, it has relatively high gravitational potential energy.

At the bottom, it has lower potential energy and is more stable.

Bond formation is similar.

Separated atoms begin at a higher potential energy.

As a stable bond forms, the system moves to a lower potential energy.

The energy difference is transferred to the surroundings.

This is why we can summarize bond formation as:

higher energy → lower energy + released energy

Bond Energy and Bond Formation

A bond energy is commonly defined as the energy required to break one mole of a particular type of bond in gaseous molecules.

Bond energy can also tell us approximately how much energy is released when that bond forms.

For example:

H–H bond energy ≈ 436 kJ mol⁻¹

Breaking H–H:

+436 kJ mol⁻¹

Forming H–H:

−436 kJ mol⁻¹

The magnitudes are approximately the same, but the direction of energy transfer is opposite.

Stronger Bonds Release More Energy When They Form

A stronger bond has a greater bond energy.

Therefore, forming a stronger bond generally releases more energy than forming a weaker comparable bond.

Consider these approximate average bond energies:

If one mole of N≡N bonds forms from separated nitrogen atoms, a very large amount of energy is released because the N≡N bond is extremely strong.

If one mole of Cl–Cl bonds forms, less energy is released.

Therefore:

stronger bond → larger energy release when formed

and:

weaker bond → smaller energy release when formed

Single, Double and Triple Bonds

For bonds between the same kinds of atoms, bond order usually affects bond strength.

Consider carbon-carbon bonds:

C–C ≈ 345 kJ mol⁻¹

C=C ≈ 611 kJ mol⁻¹

C≡C ≈ 837 kJ mol⁻¹

So:

C≡C > C=C > C–C

in bond strength.

Because stronger bonds correspond to a greater lowering of potential energy when formed, forming stronger bonds generally releases more energy.

However, a double bond is not simply twice as strong as a single bond, and a triple bond is not exactly three times as strong.

Bond Strength and Bond Length

Bond strength is also related to bond length.

For carbon-carbon bonds:

For the same pair of atoms:

shorter bonds are generally stronger

and:

stronger bonds release more energy when they form

Worked Example 1: Forming Hydrogen

Two separated hydrogen atoms combine:

H(g) + H(g) → H₂(g)

The H–H bond energy is approximately:

436 kJ mol⁻¹

Therefore, forming one mole of H–H bonds releases approximately:

436 kJ

The energy change can be written as:

ΔH ≈ −436 kJ mol⁻¹

The negative sign indicates an exothermic process.

Worked Example 2: Comparing Bond Formation

Suppose Bond A has a bond energy of:

250 kJ mol⁻¹

and Bond B has a bond energy of:

600 kJ mol⁻¹

Which bond releases more energy when formed?

Bond B

Approximately:

600 − 250 = 350 kJ mol⁻¹

more energy would be released when one mole of Bond B forms compared with one mole of Bond A.

Bond B is also the stronger bond.

Bond Formation During a Chemical Reaction

Chemical reactions involve rearranging atoms.

Existing bonds in the reactants are disrupted, while new bonds form in the products.

A simplified reaction might be:

AB + CD → AC + BD

During the first part:

A–B and C–D are broken

Energy is absorbed.

During the second part:

A–C and B–D are formed

Energy is released.

The overall reaction energy depends on the balance between these two energy changes.

The Overall Energy Change

The enthalpy change of a reaction can be estimated from bond energies using:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

Remember:

Breaking bonds → energy IN

Forming bonds → energy OUT

Suppose:

Energy required to break reactant bonds = 700 kJ mol⁻¹

Energy released forming product bonds = 900 kJ mol⁻¹

Then:

ΔH = 700 − 900

ΔH = −200 kJ mol⁻¹

The reaction is exothermic.

Why?

Because forming the product bonds released more energy than was required to break the reactant bonds.

Exothermic Reactions and Bond Formation

An exothermic reaction occurs when:

energy released forming bonds > energy absorbed breaking bonds

In the diagram, energy must first be supplied to disrupt the reactant bonds.

A larger amount of energy is then released when the product bonds form.

The products finish at a lower energy than the reactants.

Therefore:

ΔH < 0

This is the energetic basis of many exothermic reactions.

Endothermic Reactions and Bond Formation

Bond formation always releases energy, even during an overall endothermic reaction.

The difference is that an endothermic reaction requires more energy to break the reactant bonds than is released when product bonds form.

For example:

Energy required for bond breaking:

900 kJ mol⁻¹

Energy released during bond formation:

650 kJ mol⁻¹

Therefore:

ΔH = 900 − 650

ΔH = +250 kJ mol⁻¹

The reaction is endothermic.

Notice:

bond formation still released 650 kJ mol⁻¹.

It simply did not release enough energy to compensate for the energy required to break the original bonds.

A Crucial Rule

Do not say:

"Bond formation is exothermic only in exothermic reactions."

Bond formation itself is always energy-releasing.

Similarly:

Bond breaking itself is always energy-requiring.

The overall reaction may be either exothermic or endothermic depending on the balance between the two.

Formation of Water

Consider:

2H₂ + O₂ → 2H₂O

To begin the reaction, bonds in the reactants must be disrupted:

• H–H bonds
• O=O bonds

This requires energy.

The atoms then rearrange and form O–H bonds in water.

Formation of the O–H bonds releases energy.

The newly formed O–H bonds are sufficiently strong that their formation releases more energy than was required overall to break the H–H and O=O bonds.

Therefore, the formation of water from hydrogen and oxygen is strongly exothermic.

Worked Example 3: Formation of HCl

Consider:

H₂ + Cl₂ → 2HCl

Approximate bond energies:

H–H = 436 kJ mol⁻¹

Cl–Cl = 243 kJ mol⁻¹

H–Cl = 431 kJ mol⁻¹

Step 1: Energy needed to break bonds

Break one H–H bond:

436 kJ mol⁻¹

Break one Cl–Cl bond:

243 kJ mol⁻¹

Total:

436 + 243 = 679 kJ mol⁻¹

Step 2: Energy released forming bonds

Two H–Cl bonds form:

2 × 431 = 862 kJ mol⁻¹

Step 3: Calculate ΔH

ΔH ≈ 679 − 862

ΔH ≈ −183 kJ mol⁻¹

So the reaction is exothermic.

The key reason is:

forming the H–Cl bonds releases more energy than breaking H–H and Cl–Cl requires.

Combustion and Bond Formation

Consider the combustion of methane:

CH₄ + 2O₂ → CO₂ + 2H₂O

Reactant bonds include:

• C–H
• O=O

Product bonds include:

• C=O
• O–H

The C–H and O=O bonds must first be disrupted.

That requires energy.

Then strong C=O and O–H bonds form.

That releases a large amount of energy.

The formation of the product bonds releases more energy than is required to break the reactant bonds.

Therefore:

methane combustion is exothermic

This is why combustion reactions can transfer large amounts of energy to the surroundings.

Does Energy Come From "Breaking Fuel Bonds"?

A common explanation says:

"Fuel releases energy because its bonds are broken."

That is incorrect.

Breaking bonds in the fuel requires energy.

Breaking O=O bonds in oxygen also requires energy.

Energy is released when new, more stable product bonds form.

In methane combustion, much of the energy release is associated with forming strong:

C=O bonds

and:

O–H bonds

So the more accurate explanation is:

Combustion releases energy because the new product bonds are energetically more favourable than the original set of reactant bonds.

Strong Product Bonds and Exothermic Reactions

Suppose two hypothetical reactions require the same amount of bond-breaking energy.

Reaction A forms relatively weak product bonds.

Reaction B forms much stronger product bonds.

Reaction B will release more energy during bond formation.

It may therefore have a more negative ΔH.

This leads to an important connection:

strong product bonds can contribute to a strongly exothermic reaction

But remember that the overall energy change always depends on both sides of the calculation:

• energy required to break reactant bonds
• energy released forming product bonds

Bond Formation and Reaction Profiles

On an energy profile diagram, the system initially climbs toward the transition state.

As products form and new bonds become established, the energy of the system decreases.

For an exothermic reaction, the new bonding arrangement in the products has a lower energy than the original reactants.

The difference is transferred to the surroundings.

For an endothermic reaction, bond formation still lowers energy from the high-energy transition-state region, but the final products remain above the original reactants.

Bond Formation and Catalysts

A catalyst changes the pathway of a reaction.

It can make it easier for bonds to reorganize by providing a pathway with a lower activation energy.

However, a catalyst does not change:

• which reactants begin the reaction
• which products are formed
• their initial and final energy levels
• the overall ΔH

Therefore, it does not change the overall energy released through the difference between reactant and product bonding.

Bond Formation and Stability

Stronger bonding arrangements usually correspond to lower potential energy and greater stability.

This is why reactions that produce particularly stable molecules can release substantial amounts of energy.

For example, nitrogen contains an extremely strong N≡N bond.

The N≡N bond has an average bond energy of approximately:

945 kJ mol⁻¹

Forming such a strong bond from separated nitrogen atoms would produce a very large decrease in potential energy and therefore a large release of energy.

Energy Is Conserved

When bonds form, energy does not disappear.

The decrease in the chemical potential energy of the atoms is transferred into other forms.

It may appear as:

• thermal energy
• light
• kinetic energy of surrounding particles

The total energy remains conserved.

So when we say:

"bond formation releases energy"

we mean that energy is transferred from the chemical system to the surroundings.

Worked Example 4: Comparing Energy Released

Suppose three bonds form:

Bond A = 250 kJ mol⁻¹

Bond B = 460 kJ mol⁻¹

Bond C = 800 kJ mol⁻¹

Which releases the most energy per mole when formed?

Bond C

Approximate energy released:

800 kJ mol⁻¹

Which releases the least?

Bond A

Approximate energy released:

250 kJ mol⁻¹

Which is strongest?

Bond C

Therefore:

greater bond energy → stronger bond → greater energy release when that bond forms

Worked Example 5: Several Bonds Forming

Suppose a reaction forms:

2 O–H bonds

Average O–H bond energy:

463 kJ mol⁻¹

Energy released:

2 × 463

= 926 kJ mol⁻¹

Because this is bond formation, the energy change associated with that step is approximately:

−926 kJ mol⁻¹

If four O–H bonds form:

4 × 463 = 1852 kJ mol⁻¹

Approximately 1852 kJ mol⁻¹ would be released during formation of those bonds.

Worked Example 6: Is the Overall Reaction Exothermic?

Suppose:

Energy absorbed breaking bonds = 1250 kJ mol⁻¹

Energy released forming bonds = 1620 kJ mol⁻¹

Calculate:

ΔH = 1250 − 1620

ΔH = −370 kJ mol⁻¹

Therefore:

370 kJ mol⁻¹ is released overall

and the reaction is:

exothermic

Why?

Because:

bond formation released 370 kJ mol⁻¹ more than bond breaking required.

Worked Example 7: Is the Overall Reaction Endothermic?

Suppose:

Energy absorbed breaking bonds = 980 kJ mol⁻¹

Energy released forming bonds = 720 kJ mol⁻¹

Then:

ΔH = 980 − 720

ΔH = +260 kJ mol⁻¹

The reaction absorbs:

260 kJ mol⁻¹ overall

and is:

endothermic

However, the bond-formation stage was still exothermic.

It released:

720 kJ mol⁻¹

The reaction is endothermic only because even more energy was needed for bond breaking.

Did You Know?

The enormous energy released by some explosions is not caused by chemical bonds "containing explosive energy" that escapes when they break.

In fact, breaking the original bonds requires energy.

The rapid energy release occurs when atoms rearrange and form a new collection of strongly bonded, stable products.

For many explosive reactions, stable gaseous molecules such as:

N₂

CO₂

and:

H₂O

can be produced very rapidly.

The combination of energy release and rapid gas production produces the dramatic expansion associated with an explosion.

Common Misconceptions

"Forming bonds requires energy."

Incorrect. Stable bond formation releases energy.

"Breaking a strong bond releases lots of energy."

Incorrect. Breaking a strong bond requires a large amount of energy.

"Only exothermic reactions contain bond formation."

Incorrect. Both exothermic and endothermic chemical reactions normally involve bond formation.

"Bond formation in an endothermic reaction absorbs energy."

Incorrect. Bond formation is still exothermic. The overall reaction is endothermic because bond breaking requires more energy than bond formation releases.

"Bond energy only tells us how difficult a bond is to break."

Bond energy is defined using bond breaking, but it also tells us approximately how much energy is released when the same bond forms under corresponding conditions.

"If strong bonds are present in a fuel, breaking them releases energy."

Incorrect. Energy must be supplied to break them. The overall release depends on forming an even more favourable set of product bonds.

Key Terms

Bond formation – The process in which atoms or ions become joined through attractive interactions.

Exothermic process – A process that transfers energy from the system to the surroundings.

Bond energy – The energy required to break one mole of a particular bond in gaseous molecules.

Bond strength – A measure of how strongly bonded atoms are held together.

Potential energy – Energy associated with the arrangement and interactions of particles.

Bond length – The equilibrium distance between the nuclei of two bonded atoms.

Bond order – The number of bonding interactions between two atoms.

Enthalpy change, ΔH – The overall energy change of a reaction under constant-pressure conditions.

Reactant bonds – Bonds present before a chemical reaction.

Product bonds – New bonds present after the reaction.

Key Takeaways

• Forming chemical bonds releases energy.
• Bond formation is an exothermic process.
• Bond formation lowers the potential energy of the chemical system.
• The bonded arrangement is generally more stable than the separated atoms.
• The decrease in chemical potential energy is transferred to the surroundings.
• Stronger bonds generally release more energy when they form.
• A bond's energy can be used to estimate both the energy required to break it and the energy released when it forms.
• Bond breaking absorbs energy.
• Bond formation releases energy.
• Both processes occur during chemical reactions.
• An exothermic reaction occurs when more energy is released forming product bonds than is required to break reactant bonds.
• An endothermic reaction occurs when more energy is required to break reactant bonds than is released during bond formation.
• Bond formation remains exothermic even when the overall reaction is endothermic.
• The overall reaction energy can be estimated using:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

• Energy released in reactions does not come from breaking bonds. It results from the overall change to a more energetically favourable bonding arrangement.

3. Bond Energy Data Tables

What Is a Bond Energy Table?

A bond energy table is a reference table containing the average amount of energy required to break different types of covalent bonds.

Bond energies are normally given in:

kilojoules per mole, kJ mol⁻¹

For example:

H–H = 436 kJ mol⁻¹

This means approximately 436 kJ of energy is required to break one mole of H–H bonds in gaseous molecules.

Because breaking bonds requires energy:

bond energy values are listed as positive numbers.

The depth of the energy well represents the energy needed to separate the bonded atoms. A deeper well corresponds to a stronger bond.

A Typical Bond Energy Table

The following values are useful approximate average bond energies.

These are average values, not exact values for every molecule containing that bond.

How to Read a Bond Energy Table

Suppose you are asked:

What is the bond energy of an O–H bond?

Find:

O–H

Then read across:

463 kJ mol⁻¹

This means approximately 463 kJ of energy is required to break one mole of O–H bonds.

Likewise:

C=C = 611 kJ mol⁻¹

means approximately:

611 kJ is required to break one mole of C=C bonds.

The larger the value, the stronger the bond.

Bond Energy and Bond Strength

Bond energy provides a useful measure of bond strength.

A large bond energy means that a large amount of energy must be supplied to separate the atoms.

Therefore:

high bond energy → strong bond

low bond energy → weaker bond

Consider:

Cl–Cl = 243 kJ mol⁻¹

O=O = 498 kJ mol⁻¹

N≡N = 945 kJ mol⁻¹

The strongest of these is:

N≡N

The weakest is:

Cl–Cl

A stronger bond generally corresponds to a deeper potential-energy well.

Comparing Bonds in a Data Table

Suppose a table gives:

The ranking from strongest to weakest is:

C≡C > C=C > C–C

This illustrates an important trend:

For the same pair of atoms:

triple bonds are generally stronger than double bonds

and:

double bonds are generally stronger than single bonds.

Bond Strength and Bond Length

Bond energy tables are sometimes combined with bond length data.

For carbon-carbon bonds:

Notice the pattern:

As bond strength increases:

bond length decreases

So:

C–C → longest and weakest

C=C → shorter and stronger

C≡C → shortest and strongest

This general relationship is especially useful when comparing bonds between the same two elements.

Worked Example 1: Identifying the Strongest Bond

Consider:

H–H = 436 kJ mol⁻¹

O=O = 498 kJ mol⁻¹

N≡N = 945 kJ mol⁻¹

Which bond is strongest?

Look for the largest bond-energy value.

N≡N = 945 kJ mol⁻¹

Therefore:

N≡N is the strongest bond.

Which requires the least energy to break?

H–H, because 436 kJ mol⁻¹ is the smallest value in this particular set.

Worked Example 2: Comparing Bond Strength

Compare:

C–H = 415 kJ mol⁻¹

C–C = 345 kJ mol⁻¹

Difference:

415 − 345 = 70 kJ mol⁻¹

Therefore, approximately:

70 kJ mol⁻¹ more energy

is required to break a C–H bond than a C–C bond.

The C–H bond is therefore stronger according to these average values.

Do Not Confuse Bond Energy with Total Molecular Energy

Bond energy refers to one mole of a particular type of bond.

A molecule can contain many bonds.

For example, methane:

CH₄

contains:

4 C–H bonds

If all four C–H bonds are considered using an average value of 415 kJ mol⁻¹:

4 × 415 = 1660 kJ mol⁻¹

This does not mean a single C–H bond has an energy of 1660 kJ mol⁻¹.

Each bond is approximately:

415 kJ mol⁻¹

There are simply four of them.

Using Bond Energy Tables in Calculations

Bond-energy tables become especially useful when estimating the overall energy change of a reaction.

The key equation is:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

where:

Σ means "sum of"

and:

E represents bond energy.

Remember:

Bonds broken → energy absorbed

Bonds formed → energy released

Bond-energy calculations provide an approximate reaction enthalpy because the values in most tables are averages.

Step-by-Step Bond Energy Calculations

A useful method is:

Step 1: Draw or identify all bonds in the reactants

Determine which bonds must be broken.

Step 2: Use the table

Find the bond energy of each bond.

Step 3: Add the bond-breaking energies

This is the energy input.

Step 4: Identify all bonds formed in the products

Find their bond energies.

Step 5: Add the bond-forming energies

This represents the magnitude of energy released.

Step 6: Calculate

ΔH ≈ bonds broken − bonds formed

Worked Example 3: H₂ + Cl₂ → 2HCl

Consider:

H₂ + Cl₂ → 2HCl

Bond energies:

H–H = 436 kJ mol⁻¹

Cl–Cl = 243 kJ mol⁻¹

H–Cl = 431 kJ mol⁻¹

Bonds Broken

One H–H:

436 kJ mol⁻¹

One Cl–Cl:

243 kJ mol⁻¹

Total energy required:

436 + 243 = 679 kJ mol⁻¹

Bonds Formed

Two H–Cl bonds:

2 × 431 = 862 kJ mol⁻¹

Overall Energy Change

ΔH ≈ 679 − 862

ΔH ≈ −183 kJ mol⁻¹

The negative value indicates an:

exothermic reaction

Why Do We Count Every Bond?

A common error in bond-energy calculations is to identify the types of bonds but forget how many of each bond are present.

For example:

2H₂O

contains four O–H bonds in total.

Each H₂O molecule contains:

2 O–H bonds

Therefore:

2 × 2 = 4 O–H bonds

If O–H = 463 kJ mol⁻¹, the energy associated with four such bonds is:

4 × 463 = 1852 kJ mol⁻¹

Always count the bonds before performing the calculation.

Worked Example 4: Forming Water

Consider:

2H₂ + O₂ → 2H₂O

Average bond energies:

H–H = 436 kJ mol⁻¹

O=O = 498 kJ mol⁻¹

O–H = 463 kJ mol⁻¹

Bonds Broken

2 H–H bonds:

2 × 436 = 872 kJ mol⁻¹

1 O=O bond:

498 kJ mol⁻¹

Total:

872 + 498 = 1370 kJ mol⁻¹

Bonds Formed

Two H₂O molecules contain four O–H bonds:

4 × 463 = 1852 kJ mol⁻¹

Calculate ΔH

ΔH ≈ 1370 − 1852

ΔH ≈ −482 kJ mol⁻¹

The reaction is:

exothermic

because forming the O–H bonds releases more energy than is required to break the H–H and O=O bonds.

Using Structural Formulae

Sometimes a chemical equation alone does not make all the bonds obvious.

For example:

C₂H₄ + H₂ → C₂H₆

It is useful to draw the structures:

H₂C=CH₂ + H–H → H₃C–CH₃

Now we can identify what actually changes.

The reaction:

• breaks an H–H bond
• changes C=C to C–C
• forms two new C–H bonds

Drawing the molecules makes it much easier to use the bond-energy table correctly.

A Useful Shortcut: Count Only Bonds That Change

In many reactions, some bonds appear unchanged in both reactants and products.

Because identical unchanged bonds would appear on both sides of the calculation, they effectively cancel.

For simple reactions, we can sometimes calculate ΔH using only bonds that are broken, formed or changed.

However, this shortcut should be used carefully.

When first learning bond-energy calculations, it is often safer to:

draw all structures → count all relevant bonds → check your work

Worked Example 5: Hydrogenation of Ethene

Consider:

C₂H₄ + H₂ → C₂H₆

Relevant average bond energies:

C=C = 611 kJ mol⁻¹

H–H = 436 kJ mol⁻¹

C–C = 345 kJ mol⁻¹

C–H = 415 kJ mol⁻¹

Bonds effectively broken or replaced

1 C=C:

611

1 H–H:

436

Total:

1047 kJ mol⁻¹

Bonds formed

1 C–C:

345

2 additional C–H:

2 × 415 = 830

Total:

1175 kJ mol⁻¹

Calculate

ΔH ≈ 1047 − 1175

ΔH ≈ −128 kJ mol⁻¹

The reaction is approximately:

exothermic

Bond Energy Tables and Combustion

Bond-energy data are particularly useful for understanding combustion reactions.

Consider methane combustion:

CH₄ + 2O₂ → CO₂ + 2H₂O

We must consider:

Reactant bonds:

• 4 C–H
• 2 O=O

Product bonds:

• 2 C=O in CO₂
• 4 O–H

Bond-energy calculations allow us to estimate why the reaction is strongly exothermic: forming the strong product bonds releases more energy than breaking the reactant bonds requires.

Average Bond Energies Are Not Exact

The word average is extremely important.

A C–H bond does not have exactly the same bond energy in every molecule.

For example, the chemical surroundings of a C–H bond in methane differ from those of a C–H bond in another organic compound.

The surrounding atoms affect electron distribution and therefore bond strength.

The value listed in a table is therefore usually an average measured across many molecular environments. OpenStax notes, for example, that the listed C–H value is an average and individual C–H bond dissociation energies can differ significantly.

Why Can Two Tables Give Slightly Different Values?

You may notice that different textbooks give slightly different numbers.

One table might give:

C–H = 413 kJ mol⁻¹

while another gives:

C–H = 415 kJ mol⁻¹

Likewise, one source may list:

C–C = 347 kJ mol⁻¹

while another uses:

345 kJ mol⁻¹

This is not necessarily an error.

Differences can arise because:

• bond energies are averages
• different sets of compounds were used
• values may be rounded differently
• different reference data may be used

For calculations, use the values supplied in the question or the table being used in your course.

Bond Dissociation Energy vs Average Bond Energy

These two terms are related but are not always identical.

A bond dissociation energy refers to the energy required to break a particular bond in a particular molecule.

An average bond energy is an average value for a bond type across several molecules.

For example, different C–H bonds can have slightly different dissociation energies.

A bond-energy table simplifies this by giving one useful average value.

This makes calculations easier but reduces precision.

Why Bond Energy Calculations Are Estimates

Suppose a bond-energy calculation gives:

ΔH ≈ −125 kJ mol⁻¹

An experimentally measured value might be somewhat different.

This does not necessarily mean the calculation is wrong.

The difference may occur because average bond energies were used instead of the exact energies of the bonds in those specific molecules. Bond-energy calculations are therefore typically estimates rather than exact reaction enthalpies.

Gas-Phase Values

Average bond energies are normally defined for gaseous molecules.

That matters because real chemical reactions may involve:

• solids
• liquids
• dissolved substances
• gases

Changes of state and intermolecular interactions can also involve energy.

A simple bond-energy calculation may therefore not capture every energy contribution present in a real experimental reaction.

This is another reason calculated values can differ from measured enthalpy changes.

Comparing Bond Strengths from a Table

Suppose you are given:

Which is strongest?

C≡O

Which is weakest?

C–O

How much more energy is required to break C=O than C–O?

741 − 350 = 391 kJ mol⁻¹

How much more energy is required to break C≡O than C–O?

1080 − 350 = 730 kJ mol⁻¹

The table therefore provides both qualitative and quantitative information about bond strength.

A Pattern Down a Group

Bond-energy tables can also reveal trends.

Consider:

H–F = 567 kJ mol⁻¹

H–Cl = 431 kJ mol⁻¹

H–Br = 366 kJ mol⁻¹

H–I = 299 kJ mol⁻¹

The bond strength decreases:

H–F > H–Cl > H–Br > H–I

As the halogen atom becomes larger, the bond generally becomes longer and weaker.

Bond-energy data can therefore reveal patterns that connect chemical structure with chemical properties.

Another Interesting Pattern

Compare:

F–F = 160 kJ mol⁻¹

Cl–Cl = 243 kJ mol⁻¹

Br–Br = 190 kJ mol⁻¹

I–I = 150 kJ mol⁻¹

You might expect F–F to be the strongest simply because fluorine atoms are small.

But the F–F bond is unusually weak because the small fluorine atoms bring several lone pairs very close together, increasing electron-electron repulsion.

This reminds us that chemical trends often have interesting exceptions.

Bond Energy and Reaction Profiles

Bond-energy calculations and reaction-profile diagrams describe related ideas, but they are not identical.

Bond energies help us estimate:

overall reaction energy, ΔH

Reaction profiles show:

• reactant energy
• activation energy
• transition state
• product energy

A bond-energy table cannot by itself tell you the activation energy of the reaction.

This is an important distinction.

What Bond Energy Tables Can Tell Us

A bond-energy table can help us:

• identify approximate bond strengths
• compare different bonds
• estimate energy required for bond breaking
• estimate energy released by bond formation
• calculate approximate ΔH values
• predict whether a reaction is likely to be exothermic or endothermic

What Bond Energy Tables Cannot Tell Us

A bond-energy table alone does not directly tell us:

• how fast a reaction occurs
• the activation energy
• the reaction mechanism
• whether a catalyst is present
• the exact enthalpy of a real reaction
• the exact strength of a bond in every molecular environment

Bond energies are powerful tools, but they provide only part of the energetic picture.

Worked Example 6: Reading a Table Carefully

Suppose a table contains:

C–N = 290 kJ mol⁻¹

C=N = 615 kJ mol⁻¹

C≡N = 891 kJ mol⁻¹

Question 1: Which bond is easiest to break?

C–N

Question 2: Which is strongest?

C≡N

Question 3: How much more energy is required to break C≡N than C–N?

891 − 290

= 601 kJ mol⁻¹

Question 4: Which bond is probably shortest?

C≡N

Worked Example 7: Using Several Table Values

Suppose a reaction requires breaking:

• 2 C–H bonds
• 1 O=O bond

Using:

C–H = 415 kJ mol⁻¹

O=O = 498 kJ mol⁻¹

Energy required:

2(415) + 498

= 830 + 498

= 1328 kJ mol⁻¹

If the reaction then forms bonds whose total bond energy is:

1540 kJ mol⁻¹

then:

ΔH ≈ 1328 − 1540

ΔH ≈ −212 kJ mol⁻¹

Therefore the reaction is approximately:

exothermic

A Reliable Calculation Strategy

When using a bond-energy table, ask four questions:

1. What bonds are broken?

Count them carefully.

2. What bonds are formed?

Count those carefully too.

3. What are their bond energies?

Read the correct values from the table.

4. Which total is larger?

Then calculate:

ΔH ≈ bonds broken − bonds formed

This simple routine prevents most errors.

Did You Know?

The N≡N bond in nitrogen is one of the strongest common bonds, with an average bond energy of about:

945 kJ mol⁻¹

That large value helps explain why nitrogen gas is relatively unreactive.

Yet nitrogen is essential for amino acids, proteins and DNA.

Nature solves this problem through processes such as nitrogen fixation, while industry uses catalysts and carefully controlled conditions in processes such as the Haber process.

Common Mistakes

"A larger bond-energy value means the bond contains more energy to release when broken."

Incorrect. A larger bond-energy value means more energy must be supplied to break the bond.

"Bond energy tables give exact values."

Usually incorrect. Most tables contain average bond energies.

"I only need to identify the bond type."

Not enough. You must also count how many of each bond are involved.

"Double bonds have twice the energy of single bonds."

Incorrect. For example, C=C is stronger than C–C, but it is not exactly twice as strong.

"Bond-energy calculations give activation energy."

Incorrect. They estimate the overall energy change, not the activation barrier.

"Different tables must agree exactly."

Not necessarily. Slight differences are normal because average values and rounding can differ.

Key Terms

Bond energy – Energy required to break one mole of a particular covalent bond in gaseous molecules.

Average bond energy – An average energy value for a particular bond type across different molecules.

Bond dissociation energy – Energy required to break a specified bond in a particular molecule.

Bond strength – A measure of how strongly two bonded atoms are held together.

Bond length – The equilibrium distance between the nuclei of bonded atoms.

Bond order – The number of bonding interactions between two atoms.

Enthalpy change, ΔH – The overall energy change of a reaction at constant pressure.

Exothermic – Describes a process that transfers energy to the surroundings.

Endothermic – Describes a process that absorbs energy from the surroundings.

Key Takeaways

• Bond-energy tables list energies in kJ mol⁻¹.
• A bond-energy value tells us approximately how much energy is required to break one mole of that bond.
• Higher bond energy generally means a stronger bond.
• Bond-energy tables can be used to compare bond strengths.
• Triple bonds are generally stronger than corresponding double bonds, which are generally stronger than corresponding single bonds.
• Stronger bonds between the same elements are generally shorter.
• Bond energies can be used to estimate reaction enthalpy:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

• Bonds must be counted carefully before calculations are performed.
• Most tabulated bond energies are average values.
• The exact strength of a bond depends on its molecular environment.
• Different reference tables may give slightly different values.
• Bond-energy calculations therefore produce estimates rather than exact reaction enthalpies.
• Bond-energy data do not directly tell us reaction rate or activation energy.
• When solving problems, use the bond-energy values provided in the question whenever possible.

4. Calculating Reaction Energies

Energy Changes During Chemical Reactions

Every chemical reaction involves a rearrangement of atoms.

During this rearrangement:

existing bonds are broken

and:

new bonds are formed

These two processes have opposite energy effects:

Breaking bonds → requires energy → endothermic

Forming bonds → releases energy → exothermic

The overall energy change of a reaction depends on the balance between these two processes.

The Central Idea

Think of a reaction as having two energy calculations.

Energy IN

Energy must be supplied to break bonds in the reactants.

Energy OUT

Energy is released when bonds form in the products.

We compare these two quantities to determine the overall reaction energy.

The Bond Energy Equation

The main equation for this topic is:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

In simpler language:

overall energy change = energy required to break bonds − energy released when bonds form

The symbol Σ means "the sum of."

Average bond energies are used, so the calculated ΔH is normally an estimate of the actual reaction enthalpy.

Understanding the Signs

The sign of ΔH tells us whether the overall reaction releases or absorbs energy.

If:

ΔH < 0

the reaction is:

exothermic

Energy is released overall.

If:

ΔH > 0

the reaction is:

endothermic

Energy is absorbed overall.

In an exothermic reaction, the products finish at a lower energy than the reactants.

In an endothermic reaction, the products finish at a higher energy than the reactants.

A Useful Bond Energy Table

The exact table supplied in a problem should always be used, because average bond-energy values can differ slightly between sources.

Here are some useful approximate values:

Remember:

larger bond energy → stronger bond → more energy required to break it

Step 1: Start With a Balanced Equation

Before doing any bond-energy calculation, make sure the chemical equation is balanced.

For example:

H₂ + Cl₂ → 2HCl

The coefficients tell us how many molecules — and therefore how many bonds — are involved.

This matters because bond energies must be multiplied by the number of bonds.

Step 2: Draw the Bonds

It is often much easier to calculate bond energies if you draw the displayed or structural formulae.

For:

H₂ + Cl₂ → 2HCl

we can write:

H–H + Cl–Cl → H–Cl + H–Cl

Now we can clearly see:

Bonds broken:

1 H–H

1 Cl–Cl

Bonds formed:

2 H–Cl

Drawing the bonds is one of the best ways to prevent counting errors.

Step 3: Calculate Energy Required to Break Bonds

Bond breaking requires energy.

Suppose:

H–H = 436 kJ mol⁻¹

Cl–Cl = 243 kJ mol⁻¹

We break:

1 H–H bond:

1 × 436 = 436 kJ mol⁻¹

and:

1 Cl–Cl bond:

1 × 243 = 243 kJ mol⁻¹

Total energy required:

436 + 243 = 679 kJ mol⁻¹

So:

Energy IN = 679 kJ mol⁻¹

Step 4: Calculate Energy Released When Bonds Form

The products contain two H–Cl bonds.

H–Cl bond energy:

431 kJ mol⁻¹

Two bonds form:

2 × 431 = 862 kJ mol⁻¹

Therefore:

Energy OUT = 862 kJ mol⁻¹

Approximately 862 kJ mol⁻¹ is released when these bonds form.

Step 5: Calculate the Overall Energy Change

Now use:

ΔH ≈ bonds broken − bonds formed

Therefore:

ΔH ≈ 679 − 862

ΔH ≈ −183 kJ mol⁻¹

Because the answer is negative:

the reaction is exothermic

This calculation is a standard example of determining reaction enthalpy from bond energies.

Visualizing the H₂ + Cl₂ Calculation

We can think of the reaction as:

H–H + Cl–Cl

Energy must first enter:

+679 kJ mol⁻¹

The atoms can then rearrange.

When two H–Cl bonds form:

862 kJ mol⁻¹ is released

Therefore:

679 IN

versus:

862 OUT

Difference:

183 kJ mol⁻¹ OUT

So:

ΔH ≈ −183 kJ mol⁻¹

A Reliable Calculation Method

For almost every basic bond-energy problem, use this sequence:

1. Balance the equation.

2. Draw the structures.

3. Count bonds broken.

4. Multiply each by its bond energy.

5. Add to find total energy absorbed.

6. Count bonds formed.

7. Multiply each by its bond energy.

8. Add to find total energy released.

9. Calculate:

ΔH ≈ broken − formed

10. Interpret the sign.

This method works for both exothermic and endothermic reactions.

Worked Example 1: Formation of Water

Consider:

2H₂ + O₂ → 2H₂O

The structures can be represented as:

2(H–H) + O=O → 2(H–O–H)

Bonds broken:

• 2 H–H
• 1 O=O

Bonds formed:

• 4 O–H

This is an excellent example because it makes bond counting especially important.

Step 1: Calculate Bonds Broken

H–H = 436 kJ mol⁻¹

O=O = 498 kJ mol⁻¹

Two H–H bonds:

2 × 436 = 872 kJ mol⁻¹

One O=O bond:

1 × 498 = 498 kJ mol⁻¹

Total:

872 + 498 = 1370 kJ mol⁻¹

Therefore:

Energy required = 1370 kJ mol⁻¹

Step 2: Calculate Bonds Formed

Each water molecule contains:

2 O–H bonds

There are two water molecules.

Therefore:

4 O–H bonds form

O–H = 463 kJ mol⁻¹

So:

4 × 463 = 1852 kJ mol⁻¹

Therefore:

Energy released = 1852 kJ mol⁻¹

Step 3: Calculate ΔH

ΔH ≈ 1370 − 1852

ΔH ≈ −482 kJ mol⁻¹

Therefore:

the reaction is exothermic

A worked calculation using these values gives the same approximate result.

The key energy comparison is:

1370 kJ required

versus:

1852 kJ released

More energy is released than absorbed.

Why Is Water Formation Exothermic?

The answer is not simply:

"because bonds form."

Both bond breaking and bond formation occur.

The better explanation is:

The formation of the O–H bonds releases more energy than is required to break the H–H and O=O bonds.

Therefore, energy is released overall.

This distinction is essential when explaining reaction energetics.

Worked Example 2: An Endothermic Reaction

Suppose a reaction has:

Energy required to break bonds:

1250 kJ mol⁻¹

Energy released when bonds form:

980 kJ mol⁻¹

Calculate:

ΔH = 1250 − 980

ΔH = +270 kJ mol⁻¹

Because ΔH is positive:

the reaction is endothermic

The reaction absorbs:

270 kJ mol⁻¹ overall

In this case:

energy IN > energy OUT

Worked Example 3: Another Exothermic Reaction

Suppose:

Bonds broken = 1600 kJ mol⁻¹

Bonds formed = 2050 kJ mol⁻¹

Then:

ΔH = 1600 − 2050

ΔH = −450 kJ mol⁻¹

Therefore:

450 kJ mol⁻¹ is released overall

and the reaction is:

exothermic

The products have less energy than the reactants because the system has transferred energy to the surroundings.

Calculating the Energy Needed to Break Several Bonds

Suppose a molecule contains:

4 C–H bonds

and we want to calculate the approximate energy required to break all four.

C–H = 413 kJ mol⁻¹

Therefore:

4 × 413

= 1652 kJ mol⁻¹

Approximately:

1652 kJ mol⁻¹

must be supplied.

The most common mistake here is forgetting to multiply by the number of bonds.

Calculating Energy Released When Several Bonds Form

Suppose four O–H bonds form.

O–H = 463 kJ mol⁻¹

Energy released:

4 × 463

= 1852 kJ mol⁻¹

Therefore:

1852 kJ mol⁻¹ is released

during bond formation.

When using the main equation, we normally use the magnitude 1852 and subtract it:

ΔH = broken − formed

Worked Example 4: Combustion of Methane

Consider:

CH₄ + 2O₂ → CO₂ + 2H₂O

This is a more substantial bond-energy calculation.

First identify the bonds.

Reactants

CH₄ contains:

4 C–H bonds

2O₂ contains:

2 O=O bonds

Products

CO₂ contains:

2 C=O bonds

2H₂O contains:

4 O–H bonds

This type of diagram is particularly useful because it shows that both the number and type of bonds must be considered.

Methane Combustion: Bonds Broken

Using:

C–H = 413 kJ mol⁻¹

O=O = 498 kJ mol⁻¹

Four C–H bonds:

4 × 413 = 1652 kJ mol⁻¹

Two O=O bonds:

2 × 498 = 996 kJ mol⁻¹

Total:

1652 + 996

= 2648 kJ mol⁻¹

Therefore:

Energy required = 2648 kJ mol⁻¹

Methane Combustion: Bonds Formed

For this calculation, use:

C=O in CO₂ ≈ 805 kJ mol⁻¹

O–H = 463 kJ mol⁻¹

Two C=O bonds:

2 × 805 = 1610 kJ mol⁻¹

Four O–H bonds:

4 × 463 = 1852 kJ mol⁻¹

Total:

1610 + 1852

= 3462 kJ mol⁻¹

Therefore:

Energy released = 3462 kJ mol⁻¹

Methane Combustion: Overall ΔH

Calculate:

ΔH ≈ 2648 − 3462

ΔH ≈ −814 kJ mol⁻¹

The precise estimate changes slightly depending on which average bond-energy table is used. For example, a source using C–H = 412 kJ mol⁻¹ obtains approximately −818 kJ mol⁻¹.

The important conclusion is:

ΔH is negative

Therefore:

methane combustion is exothermic

Where Does the Energy from Combustion Come From?

This calculation helps correct a major misconception.

Methane does not release energy because its C–H bonds are broken.

Breaking those C–H bonds required:

1652 kJ mol⁻¹

Breaking the O=O bonds required even more energy.

The reaction releases energy overall because formation of the strong:

C=O

and:

O–H

bonds releases a greater amount of energy.

So:

energy released forming products > energy required breaking reactants

This is why the reaction is exothermic.

Worked Example 5: Formation of Ammonia

Consider the Haber reaction:

N₂ + 3H₂ → 2NH₃

Now identify the bonds.

Reactants:

1 N≡N bond

3 H–H bonds

Products:

Each NH₃ contains 3 N–H bonds.

Therefore 2NH₃ contains:

6 N–H bonds

Ammonia: Bonds Broken

Use:

N≡N = 945 kJ mol⁻¹

H–H = 436 kJ mol⁻¹

One N≡N:

1 × 945 = 945

Three H–H:

3 × 436 = 1308

Total:

945 + 1308

= 2253 kJ mol⁻¹

Energy required:

2253 kJ mol⁻¹

Ammonia: Bonds Formed

N–H = 391 kJ mol⁻¹

Six N–H bonds form:

6 × 391

= 2346 kJ mol⁻¹

Energy released:

2346 kJ mol⁻¹

Ammonia: Overall Energy Change

ΔH ≈ 2253 − 2346

ΔH ≈ −93 kJ mol⁻¹

Therefore:

the reaction is exothermic

This approximate bond-energy calculation gives an energy release of about 93 kJ for the reaction as written.

Notice how much energy is required to break the:

N≡N triple bond

Its very high bond energy makes nitrogen particularly difficult to react.

Worked Example 6: Hydrogenation of Ethene

Consider:

C₂H₄ + H₂ → C₂H₆

Structurally:

H₂C=CH₂ + H–H → H₃C–CH₃

During this reaction:

• the C=C bonding arrangement changes to C–C
• H–H is broken
• two new C–H bonds form

This reaction provides a good example of using structural formulae to determine which bonds have changed.

Hydrogenation Calculation

Use:

C=C = 614 kJ mol⁻¹

H–H = 436 kJ mol⁻¹

C–C = 347 kJ mol⁻¹

C–H = 413 kJ mol⁻¹

Energy associated with bonds broken/replaced:

614 + 436 = 1050 kJ mol⁻¹

Energy associated with bonds formed:

347 + 2(413)

= 347 + 826

= 1173 kJ mol⁻¹

Therefore:

ΔH ≈ 1050 − 1173

ΔH ≈ −123 kJ mol⁻¹

So the reaction is:

exothermic

Again, the exact estimate depends somewhat on the average bond-energy values used.

Why Structural Formulae Matter

Consider:

C₂H₄ + H₂ → C₂H₆

If you look only at the molecular formulae, it is difficult to see which bonds change.

But drawing:

H₂C=CH₂ + H–H → H₃C–CH₃

makes the changes visible.

For more complicated molecules:

Always draw the structure before counting bonds.

Be Careful With Double and Triple Bonds

A double bond counts as a double bond type, not as two single bonds.

For example:

O=O

should use the O=O bond-energy value.

Do not calculate:

2 × O–O

Similarly:

N≡N

uses the N≡N bond-energy value.

It should not be treated as:

3 × N–N

Single, double and triple bonds have their own characteristic average bond energies.

A Shortcut: Count Only Bonds That Change

Sometimes many bonds remain unchanged during a reaction.

Because identical unchanged bonds appear on both sides of the calculation, their contributions cancel.

For example:

C₂H₄ + H₂ → C₂H₆

Four of the original C–H bonds remain present.

Rather than including those identical bonds on both sides, we can focus on the bonding changes.

This can make calculations much faster.

However, when learning the method, it is often safer to:

draw everything → count everything → check which bonds cancel

before using the shortcut.

Interpreting a Negative Answer

Suppose:

ΔH = −250 kJ mol⁻¹

The negative sign means:

the chemical system loses energy

and:

the surroundings gain energy

Therefore:

250 kJ mol⁻¹ is released overall

and the reaction is:

exothermic

Do not say:

"The reaction releases −250 kJ."

It is clearer to say:

ΔH = −250 kJ mol⁻¹

or:

250 kJ mol⁻¹ is released.

Interpreting a Positive Answer

Suppose:

ΔH = +175 kJ mol⁻¹

The positive sign means:

the chemical system gains energy

Energy has been absorbed from the surroundings.

Therefore:

175 kJ mol⁻¹ is absorbed overall

and the reaction is:

endothermic

What If ΔH Is Close to Zero?

Suppose:

Energy required to break bonds:

1520 kJ mol⁻¹

Energy released forming bonds:

1510 kJ mol⁻¹

Then:

ΔH ≈ 1520 − 1510

ΔH ≈ +10 kJ mol⁻¹

The reaction is predicted to be slightly endothermic.

However, because average bond energies are approximate, a result very close to zero should be interpreted cautiously.

Small differences can be sensitive to the particular average bond-energy values used.

Why Are Bond Energy Calculations Approximate?

Most tables contain average bond energies.

For example, a C–H bond does not have exactly the same bond strength in every molecule.

Its exact energy depends on its molecular environment.

Therefore:

ΔH from average bond energies ≈ estimated ΔH

not necessarily the exact experimental value.

Bond-energy values also conventionally refer to gaseous species, so phase changes and intermolecular interactions can contribute to differences between an estimate and an experimentally measured reaction enthalpy.

Bond Energy Calculations vs Reaction Profiles

Bond-energy calculations tell us about:

overall reaction energy, ΔH

Reaction profiles show additional information such as:

activation energy

and:

transition state

A bond-energy calculation does not directly tell us the activation energy.

For example:

ΔH = −300 kJ mol⁻¹

does not mean:

Eₐ = 300 kJ mol⁻¹

These are different quantities.

Does a More Negative ΔH Mean a Faster Reaction?

No.

Suppose:

Reaction A:

ΔH = −500 kJ mol⁻¹

Reaction B:

ΔH = −100 kJ mol⁻¹

Reaction A releases more energy.

But that does not automatically mean Reaction A occurs faster.

Reaction rate depends strongly on factors including:

• activation energy
• temperature
• concentration
• pressure
• surface area
• catalysts
• reaction mechanism

Energy change and reaction rate describe different aspects of a reaction.

Worked Example 7: Find the Missing Energy

Suppose a reaction has:

ΔH = −180 kJ mol⁻¹

and:

Energy required to break bonds = 720 kJ mol⁻¹

We know:

ΔH = broken − formed

Therefore:

−180 = 720 − formed

Rearrange:

formed = 720 + 180

formed = 900 kJ mol⁻¹

Therefore:

900 kJ mol⁻¹ is released during bond formation.

Worked Example 8: Find the Bond-Breaking Energy

Suppose:

ΔH = +120 kJ mol⁻¹

and:

Energy released forming bonds = 650 kJ mol⁻¹

Use:

ΔH = broken − formed

Therefore:

120 = broken − 650

So:

broken = 770 kJ mol⁻¹

Therefore:

770 kJ mol⁻¹ is required to break the reactant bonds.

Worked Example 9: Comparing Two Reactions

Reaction A:

Bonds broken = 800 kJ mol⁻¹

Bonds formed = 1100 kJ mol⁻¹

Reaction B:

Bonds broken = 1200 kJ mol⁻¹

Bonds formed = 1350 kJ mol⁻¹

For Reaction A:

ΔH = 800 − 1100

ΔH = −300 kJ mol⁻¹

For Reaction B:

ΔH = 1200 − 1350

ΔH = −150 kJ mol⁻¹

Both reactions are:

exothermic

But Reaction A releases more energy overall.

Reaction A releases:

300 kJ mol⁻¹

Reaction B releases:

150 kJ mol⁻¹

A Quick Visual Way to Think About the Calculation

Imagine the bond-breaking and bond-forming energies as two competing totals.

Exothermic

Bond breaking: 600 kJ IN

Bond forming: 900 kJ OUT

Net:

300 kJ OUT

ΔH = −300 kJ mol⁻¹

Endothermic

Bond breaking: 900 kJ IN

Bond forming: 600 kJ OUT

Net:

300 kJ IN

ΔH = +300 kJ mol⁻¹

This is often the simplest conceptual way to check whether your mathematical answer makes sense.

Checking Your Answer

After every bond-energy calculation, ask:

Does the sign make sense?

If bond formation released more energy than bond breaking required:

Your answer should be:

negative

If bond breaking required more energy than bond formation released:

Your answer should be:

positive

This quick check catches many arithmetic and sign errors.

Common Mistake 1: Adding Instead of Subtracting

Suppose:

Broken = 700 kJ mol⁻¹

Formed = 900 kJ mol⁻¹

Incorrect:

700 + 900 = 1600

Correct:

700 − 900 = −200 kJ mol⁻¹

Remember:

broken − formed

Common Mistake 2: Forgetting Coefficients

Consider:

2H₂ + O₂ → 2H₂O

There are:

2 H–H bonds

not one.

There are:

4 O–H bonds

not two.

The coefficients in the balanced equation affect the total number of bonds.

Common Mistake 3: Counting Atoms Instead of Bonds

Consider CH₄.

It contains:

1 carbon atom

4 hydrogen atoms

but:

4 C–H bonds

Bond-energy calculations require us to count bonds, not simply atoms.

Common Mistake 4: Using the Wrong Bond Type

Do not confuse:

C–C

with:

C=C

or:

C≡C

Their bond energies are very different.

The same applies to:

C–O

versus:

C=O

Always examine the structural formula carefully.

Common Mistake 5: Reversing the Equation

The correct equation is:

ΔH ≈ bonds broken − bonds formed

Not:

formed − broken

A useful memory aid is:

Break – Make

B − M

Common Mistake 6: Saying Bonds "Contain Energy That Is Released When Broken"

Breaking a bond requires energy.

Energy release during an exothermic reaction occurs because the formation of product bonds releases more energy than is required to break the reactant bonds.

This distinction is fundamental to chemical energetics.

Did You Know?

Bond-energy calculations can explain why two fuels may release different amounts of energy even if both undergo combustion.

The important question is not simply:

"How many bonds does the fuel contain?"

Instead, chemists compare:

the complete set of reactant bonds that must be broken

with:

the complete set of product bonds that form

The difference between these totals determines the approximate energy released by the reaction.

Calculation Summary

For any bond-energy calculation:

Balanced equation

↓

Draw structures

↓

Count bonds broken

↓

Calculate total energy required

↓

Count bonds formed

↓

Calculate total energy released

↓

ΔH ≈ broken − formed

↓

If ΔH < 0 → exothermic

If ΔH > 0 → endothermic

Key Terms

Bond energy – Energy required to break one mole of a particular type of covalent bond in gaseous molecules.

Bond breaking – An endothermic process requiring an input of energy.

Bond formation – An exothermic process that releases energy.

Enthalpy change, ΔH – The overall energy change associated with a reaction at constant pressure.

Exothermic reaction – A reaction that releases energy overall to the surroundings.

Endothermic reaction – A reaction that absorbs energy overall from the surroundings.

Average bond energy – An average value for a particular bond type across different molecular environments.

Structural formula – A representation showing how atoms are bonded within a molecule.

Key Takeaways

• Chemical reactions involve breaking bonds and forming bonds.
• Breaking bonds requires energy.
• Forming bonds releases energy.
• The energy required to break several bonds is calculated by multiplying each bond energy by the number of those bonds.
• The energy released when several bonds form is calculated in the same way.
• Overall reaction energy can be estimated using:

ΔH ≈ ΣE(bonds broken) − ΣE(bonds formed)

• If ΔH is negative, the reaction is exothermic.
• If ΔH is positive, the reaction is endothermic.
• A negative ΔH means energy is released overall.
• A positive ΔH means energy is absorbed overall.
• Structural formulae help identify and count the bonds involved.
• Double and triple bonds must use their own bond-energy values.
• Average bond energies make these calculations estimates, not perfectly exact experimental values.
• Bond-energy calculations determine approximate overall energy change; they do not directly determine activation energy or reaction rate.
• Exothermic reactions release energy because forming the product bonds releases more energy than breaking the reactant bonds requires.
• Always finish a calculation by interpreting the sign and explaining what it means chemically.

5. Predicting Energy Changes