Energy Profiles and Activation Energy

What Is an Endothermic Reaction?

An endothermic reaction is a chemical reaction that absorbs energy from the surroundings.

The reacting system gains energy, usually as heat.

In simple terms:

surroundings lose energy → reacting system gains energy

Because the system has gained energy, the products finish at a higher energy level than the reactants. Endothermic reactions therefore have a positive enthalpy change, ΔH.

Recognizing an Endothermic Reaction Profile

An energy profile diagram normally has:

Vertical axis: Energy, potential energy or enthalpy

Horizontal axis: Reaction progress or reaction coordinate

The horizontal axis represents the progress of the reaction from reactants to products. It does not normally represent time.

For an endothermic reaction:

reactants start lower → curve rises to a peak → products finish higher

The quickest way to identify an endothermic profile is therefore:

Products above reactants = endothermic

Why Do the Products Have More Energy?

Chemical reactions involve both:

• breaking existing bonds
• forming new bonds

Breaking bonds requires energy.

Bond breaking → energy absorbed

Forming bonds releases energy.

Bond making → energy released

In an endothermic reaction, more energy is required to break bonds than is released when new bonds form. The system therefore gains energy overall.

For example:

Energy required to break bonds = 500 kJ mol⁻¹

Energy released when new bonds form = 350 kJ mol⁻¹

Overall energy change:

ΔH = 500 − 350

ΔH = +150 kJ mol⁻¹

The reaction absorbs:

150 kJ mol⁻¹

Enthalpy Change, ΔH

The overall energy change of a reaction is represented by the enthalpy change, ΔH.

The equation is:

ΔH = Hproducts − Hreactants

For an endothermic reaction:

Hproducts > Hreactants

Therefore:

ΔH > 0

The enthalpy change is positive.

For example:

Reactants = 80 kJ mol⁻¹

Products = 140 kJ mol⁻¹

Then:

ΔH = 140 − 80

ΔH = +60 kJ mol⁻¹

The reaction absorbs:

60 kJ mol⁻¹

Energy Absorbed

The amount of energy absorbed is shown by the vertical difference between the reactant and product energy levels.

Suppose:

Reactants = 120 kJ mol⁻¹

Products = 210 kJ mol⁻¹

Energy absorbed:

210 − 120 = 90 kJ mol⁻¹

Therefore:

ΔH = +90 kJ mol⁻¹

and the reaction absorbs:

90 kJ mol⁻¹

Notice the wording:

ΔH = +90 kJ mol⁻¹

but:

energy absorbed = 90 kJ mol⁻¹

The positive sign shows that the reacting system has gained energy.

Activation Energy Is Still Required

Like exothermic reactions, endothermic reactions also have an activation energy, Eₐ.

Activation energy is the minimum energy barrier that reacting particles must overcome before products can form.

On an energy profile, activation energy is measured from:

reactant energy level → highest point of the profile

The highest point represents the transition state or activated complex.

The activation energy should not be measured from the bottom of the graph.

It is always measured relative to the reactants.

Worked Example 1: Activation Energy and ΔH

Suppose an endothermic reaction has:

Reactants = 60 kJ mol⁻¹

Peak = 240 kJ mol⁻¹

Products = 130 kJ mol⁻¹

Activation energy:

Eₐ = 240 − 60

Eₐ = 180 kJ mol⁻¹

Enthalpy change:

ΔH = 130 − 60

ΔH = +70 kJ mol⁻¹

Therefore:

• activation energy = 180 kJ mol⁻¹
• energy absorbed = 70 kJ mol⁻¹
• ΔH = +70 kJ mol⁻¹
• reaction = endothermic

This shows that activation energy and energy absorbed are different quantities.

Activation Energy vs Energy Absorbed

A reaction can have:

• a large activation energy but a small ΔH
• a small activation energy but a large ΔH
• similar ΔH values but very different activation energies

These quantities should always be considered separately.

A Real-World Example: Instant Cold Packs

Some instant cold packs use an endothermic dissolving process.

When the internal barrier is broken, water mixes with a substance such as ammonium nitrate.

The dissolving process absorbs energy from the surroundings.

As thermal energy is removed from the surroundings, the pack feels cold.

This is an important point:

The reaction or process does not create cold.

Instead:

energy is absorbed from the surroundings

→ surroundings lose thermal energy

→ temperature falls

Endothermic Does Not Simply Mean "Cold"

An endothermic reaction is defined by energy transfer, not by temperature alone.

A reaction is endothermic when the reacting system absorbs energy from its surroundings.

The surroundings may become colder, but that temperature change is a consequence of the energy transfer.

So the best definition is:

An endothermic reaction absorbs energy from the surroundings.

Not simply:

"An endothermic reaction gets cold."

Comparing Endothermic and Exothermic Profiles

The position of the products provides the quickest comparison.

For an endothermic reaction:

• products are above reactants
• ΔH is positive
• energy is absorbed

For an exothermic reaction:

• products are below reactants
• ΔH is negative
• energy is released

This difference can be summarized as:

Endothermic: energy goes in

Exothermic: energy goes out

Comparing Different Endothermic Reactions

Suppose Reaction A has:

Reactants = 50 kJ mol⁻¹

Products = 90 kJ mol⁻¹

Then:

ΔH = +40 kJ mol⁻¹

Reaction B has:

Reactants = 50 kJ mol⁻¹

Products = 150 kJ mol⁻¹

Then:

ΔH = +100 kJ mol⁻¹

Both reactions are endothermic.

However, Reaction B absorbs more energy because the vertical difference between reactants and products is greater.

Therefore:

larger upward energy difference → greater energy absorbed

Comparing Activation Energies

Now consider two endothermic reactions with the same ΔH.

Reaction X:

Reactants = 70 kJ mol⁻¹

Peak = 150 kJ mol⁻¹

Products = 110 kJ mol⁻¹

Reaction Y:

Reactants = 70 kJ mol⁻¹

Peak = 230 kJ mol⁻¹

Products = 110 kJ mol⁻¹

For Reaction X:

Eₐ = 150 − 70

Eₐ = 80 kJ mol⁻¹

For Reaction Y:

Eₐ = 230 − 70

Eₐ = 160 kJ mol⁻¹

Both reactions have:

ΔH = 110 − 70

ΔH = +40 kJ mol⁻¹

Therefore:

• both absorb the same amount of energy
• Reaction X has the lower activation-energy barrier
• Reaction Y has the higher activation-energy barrier

This shows that the amount of energy absorbed does not determine the activation energy.

Endothermic Does Not Mean Slow

Another common misconception is:

"Endothermic reactions are always slow."

This is incorrect.

Whether a reaction is endothermic or exothermic tells us about its overall energy change.

Reaction rate depends on factors such as:

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

An endothermic reaction can be relatively fast if its activation-energy barrier is sufficiently low.

Catalysts and Endothermic Profiles

A catalyst lowers the activation energy of an endothermic reaction by providing an alternative pathway.

However, the catalyst does not change:

• the energy of the reactants
• the energy of the products
• ΔH
• the amount of energy absorbed

Therefore:

same reactant level + same product level + lower peak

The reaction remains endothermic.

Only the activation-energy barrier changes.

Worked Example 2: A Catalyzed Endothermic Reaction

Suppose:

Reactants = 100 kJ mol⁻¹

Products = 170 kJ mol⁻¹

Uncatalyzed peak = 300 kJ mol⁻¹

Catalyzed peak = 220 kJ mol⁻¹

Without catalyst:

Eₐ = 300 − 100

Eₐ = 200 kJ mol⁻¹

With catalyst:

Eₐ = 220 − 100

Eₐ = 120 kJ mol⁻¹

But:

ΔH = 170 − 100

ΔH = +70 kJ mol⁻¹

in both cases.

The catalyst lowers Eₐ but does not change the 70 kJ mol⁻¹ absorbed.

Forward and Reverse Reactions

Suppose an endothermic profile has:

Reactants = 90 kJ mol⁻¹

Peak = 250 kJ mol⁻¹

Products = 140 kJ mol⁻¹

For the forward reaction:

ΔH = 140 − 90

ΔH = +50 kJ mol⁻¹

The forward reaction is endothermic.

Forward activation energy:

Eₐ = 250 − 90

Eₐ = 160 kJ mol⁻¹

Now consider the reverse reaction.

Reverse activation energy:

Eₐ(reverse) = 250 − 140

Eₐ(reverse) = 110 kJ mol⁻¹

The reverse enthalpy change is:

ΔH(reverse) = −50 kJ mol⁻¹

Therefore:

forward reaction = endothermic

reverse reaction = exothermic

The energy changes are equal in magnitude but opposite in sign.

Why Is Reverse Activation Energy Smaller Here?

In this example, the products of the forward reaction are already higher in energy than the reactants.

Therefore, when the reaction runs backward, the starting point is closer to the transition-state peak.

This means:

Eₐ(reverse) < Eₐ(forward)

For a simple single-step endothermic profile, this relationship is expected because:

Eₐ(forward) − Eₐ(reverse) = ΔH

Reading an Endothermic Profile Step by Step

When interpreting a reaction profile, follow this sequence.

First, identify the reactant energy level.

Next, identify the product energy level.

Ask:

Are the products above the reactants?

If yes:

The reaction is endothermic.

Then calculate:

ΔH = Hproducts − Hreactants

Next, locate the peak.

Calculate:

Eₐ = Hpeak − Hreactants

Finally, compare ΔH and Eₐ with those of other reactions if required.

Worked Example 3

An energy profile shows:

Reactants = 120 kJ mol⁻¹

Peak = 350 kJ mol⁻¹

Products = 200 kJ mol⁻¹

Step 1: Identify the reaction.

Products are higher than reactants.

Endothermic

Step 2: Calculate ΔH.

ΔH = 200 − 120

ΔH = +80 kJ mol⁻¹

Step 3: Determine the energy absorbed.

80 kJ mol⁻¹

Step 4: Calculate activation energy.

Eₐ = 350 − 120

Eₐ = 230 kJ mol⁻¹

Worked Example 4: Comparing Two Reactions

Reaction A:

Eₐ = 70 kJ mol⁻¹

ΔH = +90 kJ mol⁻¹

Reaction B:

Eₐ = 150 kJ mol⁻¹

ΔH = +40 kJ mol⁻¹

Which reaction absorbs more energy?

Reaction A

because +90 kJ mol⁻¹ is a larger energy gain.

Which has the smaller activation-energy barrier?

Reaction A

Which reactions are endothermic?

Both

This illustrates why a reaction comparison should consider both ΔH and Eₐ.

Other Examples of Endothermic Processes

Common examples include:

• some dissolving processes
• thermal decomposition reactions
• photosynthesis overall
• melting
• evaporation

For example, the thermal decomposition of calcium carbonate requires continued energy input:

CaCO₃ → CaO + CO₂

Energy must be supplied to drive the process.

Photosynthesis also requires energy input, provided by sunlight, to build higher-energy molecules from lower-energy starting materials.

Did You Know?

An instant cold pack feels cold for exactly the opposite energetic reason that a hand warmer feels hot.

A cold pack contains a process that absorbs thermal energy from its surroundings.

A hand warmer contains a process that releases thermal energy to its surroundings.

So the temperature you feel is evidence of energy moving between the chemical system and the surroundings.

Common Misconceptions

"Endothermic means the reaction contains cold energy."

Incorrect. The system absorbs energy from the surroundings.

"Products are higher, so activation energy equals ΔH."

Incorrect. Activation energy is measured from the reactants to the peak. ΔH is measured from reactants to products.

"The energy absorbed is measured from the reactants to the peak."

Incorrect. That is activation energy.

"All endothermic reactions are slow."

Incorrect. Reaction rate and overall energy change are different ideas.

"A catalyst makes an endothermic reaction exothermic."

Incorrect. A catalyst lowers activation energy but does not change ΔH.

"The x-axis shows how long the reaction takes."

Usually incorrect. It represents reaction progress.

Key Terms

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

Energy profile – A diagram showing how the energy of a reacting system changes as the reaction progresses.

Reactants – Substances present at the beginning of a reaction.

Products – Substances formed by a reaction.

Enthalpy, H – A measure of the energy content of a system under constant-pressure conditions.

Enthalpy change, ΔH – The difference between product and reactant enthalpy.

Activation energy, Eₐ – The energy barrier that reacting particles must overcome.

Transition state – The high-energy arrangement at the peak of a reaction profile.

Reaction coordinate – A conceptual representation of progress from reactants to products.

Key Takeaways

• An endothermic reaction absorbs energy from the surroundings.
• On an endothermic profile, the products are higher in energy than the reactants.
• Endothermic reactions have positive ΔH.
• ΔH = Hproducts − Hreactants.
• The vertical difference between reactants and products represents the energy absorbed.
• Products have more energy because the reaction absorbs more energy during bond breaking than it releases overall during bond formation.
• Endothermic reactions still require activation energy.
• Activation energy is measured from the reactant level to the peak.
• Activation energy and energy absorbed are different quantities.
• Two endothermic reactions can absorb different amounts of energy.
• Two reactions can absorb the same amount of energy but have different activation energies.
• An endothermic reaction is not necessarily slow.
• A catalyst lowers activation energy but does not change ΔH.
• The reverse of an endothermic reaction is exothermic.
• Cold packs are a familiar real-world example of an endothermic process.