Grade by Grade
D. Energy Changes and Rates of Reaction · Energy Changes and Rates of Reaction

Activation Energy and Potential Energy Diagrams

D3.6 D3.5 D2.1 A1.12About 65 minutes
Learning goals
  • I can describe the energy changes during a collision and explain what an activated complex is.
  • I can draw and label potential energy diagrams for exothermic and endothermic reactions.
  • I can read Ea(fwd), Ea(rev) and ΔH from a diagram and use ΔH = Ea(fwd) − Ea(rev).
  • I can explain the difference between what Ea tells us (rate) and what ΔH tells us (energy change).

Words to know

potential energy diagram
A graph of the potential energy of a reacting system against reaction progress.
activated complex (transition state)
The unstable, highest-energy arrangement of atoms at the peak of the diagram, with bonds partly broken and partly formed.
activation energy, forward (Ea(fwd))
The energy difference between the reactants and the activated complex.
activation energy, reverse (Ea(rev))
The energy difference between the products and the activated complex.
reaction progress
The horizontal axis of a potential energy diagram, showing the change from reactants to products.

Over the hill

Imagine pushing a toboggan from a hollow, over a snowy ridge, and down into a lower valley on the other side. You have to push it up first, even though it ends up lower than where it started. Most reactions are like that: even very exothermic ones need an initial "push" of energy, the activation energy, before they can go downhill. A potential energy diagram draws this journey and shows both how fast a reaction might be (the height of the hill) and how much energy it releases or absorbs (the difference between the valleys).

What happens during a collision

As two reactant particles approach, their electron clouds repel. The particles slow down, and their kinetic energy is converted into potential energy (Eₚ), stored in the stretched and squeezed bonds. If the collision has enough energy, the particles get close enough for old bonds to start breaking while new bonds start forming.

At the very top of the energy hill is an unstable arrangement called the activated complex (or transition state). In it, old bonds are partly broken and new bonds are partly formed. It lasts for an extremely short time (about the time of one molecular vibration), and it can go either way: forward to products or back to reactants. As the products separate, potential energy is converted back into kinetic energy.

ABCreactants: A–B + CABC[A···B···C]‡activated complex: A–B half broken,B–C half formedABCproducts: A + B–C
The activated complex, marked with a double dagger (‡), is a short-lived arrangement in which the old bond is partly broken (dashed) and the new bond partly formed (dashed).

Reading a potential energy diagram

The horizontal axis is the reaction progress (from reactants on the left to products on the right). The vertical axis is potential energy.

  • The activation energy of the forward reaction, Ea(fwd), is the height from the reactants up to the peak.
  • The activation energy of the reverse reaction, Ea(rev), is the height from the products up to the peak.
  • The enthalpy change, ΔH, is the height of the products minus the height of the reactants.

These three are related:

ΔH = Ea(fwd) − Ea(rev)

For an exothermic reaction the products are lower than the reactants, so ΔH < 0 and Ea(rev) > Ea(fwd). For an endothermic reaction the products are higher, ΔH > 0 and Ea(rev) < Ea(fwd).

reaction progress →Eₚreactantsproductsactivated complexEa(fwd) = 75 kJΔH =−100 kJEa(rev) = 175 kJ
An exothermic reaction: products lower than reactants. Ea(fwd) = 75 kJ, ΔH = −100 kJ, and the reverse reaction must climb Ea(rev) = 75 + 100 = 175 kJ. (Drawn to scale.)
reaction progress →Eₚreactantsproductsactivated complexEa(fwd) = 200 kJΔH =+100 kJ
An endothermic reaction: products higher than reactants. Ea(fwd) = 200 kJ and ΔH = +100 kJ, so Ea(rev) = 100 kJ (drawn to scale). For an endothermic reaction, Ea(fwd) is always at least as large as ΔH.

What the diagram tells you, and what it does not

The height of the hill (Ea) relates to rate: the higher the barrier, the smaller the fraction of collisions that can get over it, and the slower the reaction at a given temperature. The difference in the valleys (ΔH) tells you whether energy is released or absorbed. The two are independent: a very exothermic reaction can be extremely slow (methane and oxygen mixed at room temperature, with no spark), and an endothermic one can be fast (an instant cold pack).

Worked example

Example 1: Reading values from a diagram

On a potential energy diagram, the reactants are at 50 kJ, the peak at 140 kJ, and the products at 20 kJ. Find Ea(fwd), Ea(rev) and ΔH, and classify the reaction.

  1. Ea(fwd) = peak − reactants = 140 − 50 = 90 kJ.
  2. Ea(rev) = peak − products = 140 − 20 = 120 kJ.
  3. ΔH = products − reactants = 20 − 50 = −30 kJ. Check: Ea(fwd) − Ea(rev) = 90 − 120 = −30 kJ. ✓

Ea(fwd) = 90 kJ, Ea(rev) = 120 kJ, ΔH = −30 kJ: exothermic.

Worked example

Example 2: Finding the reverse activation energy

The decomposition of a compound has Ea(fwd) = 183 kJ and ΔH = +9 kJ. Find Ea(rev) and sketch the diagram.

  1. ΔH = Ea(fwd) − Ea(rev), so Ea(rev) = Ea(fwd) − ΔH = 183 − 9 = 174 kJ.
  2. Sketch: reactants on the left; products slightly higher (by 9 kJ) on the right; a tall peak 183 kJ above the reactants.

Ea(rev) = 174 kJ. The diagram looks almost symmetrical, with products just a little higher than reactants.

Worked example

Example 3: Which reaction is faster?

Reaction X: Ea = 40 kJ, ΔH = −10 kJ. Reaction Y: Ea = 90 kJ, ΔH = −300 kJ. At the same temperature and concentrations, which is likely to be faster, and which releases more heat?

  1. Rate depends on Ea: the lower barrier lets a larger fraction of collisions react. X has the lower Ea.
  2. Energy released depends on ΔH: Y releases 300 kJ, X only 10 kJ.

X is likely faster; Y releases more heat. Rate and energy change are separate properties.

Hands-on activity

Build a potential energy diagram you can roll

You need: a strip of thin cardboard about 60 cm long and 10 cm wide (from a cereal box), tape, a stack of books, a marble, and a ruler.

  1. Tape one end of the strip to a stack of books about 6 cm high (the reactants), and the other end to a stack about 2 cm high (the products). Push the middle of the strip up into a hump about 12 cm high, supported by a rolled-up piece of cardboard, so the strip forms a smooth hill.
  2. Place the marble on the reactant end and give it gentle pushes of increasing strength. Note the weakest push that gets it over the hump.
  3. Now try from the product end. Is a stronger push needed?
  4. Lower the hump to 8 cm and repeat.

What to look for: the marble needs a minimum push to get over the hill (activation energy); from the lower product side, a bigger push is needed (Ea(rev) > Ea(fwd) for an exothermic reaction); lowering the hump makes it easier in both directions, which is exactly what a catalyst does. Measure the heights to label your model: Ea(fwd) ≈ 12 − 6 = 6 cm, Ea(rev) ≈ 12 − 2 = 10 cm, "ΔH" ≈ 2 − 6 = −4 cm.

Just for fun

An activated complex lasts roughly as long as one molecular vibration, about 10⁻¹³ s. If you blinked, you would miss about a trillion of them. Chemists have caught glimpses of transition states only with laser pulses lasting femtoseconds (10⁻¹⁵ s).

Your turn

1

Define activated complex.

2

Reactants 80 kJ, peak 200 kJ, products 150 kJ. Find Ea(fwd), Ea(rev) and ΔH.

3

A reaction has Ea(fwd) = 62 kJ and ΔH = −45 kJ. Find Ea(rev).

4

Describe the energy changes as two molecules collide and react.

5

Can the activation energy of an endothermic reaction be smaller than its ΔH? Explain.

6

Sketch (describe) the diagram for a reaction with Ea(fwd) = 30 kJ and ΔH = −80 kJ.

More practice: warm-up

1

What is on the vertical axis of a potential energy diagram?

2

What does the height from the reactants to the peak represent?

3

In an exothermic reaction, which are higher: reactants or products?

4

Write the equation linking ΔH, Ea(fwd) and Ea(rev).

5

What symbol is often used to label an activated complex?

More practice: on your own

1

For a reaction, Ea(fwd) = 125 kJ and Ea(rev) = 85 kJ. Find ΔH and classify the reaction.

2

The combustion of methane is very exothermic, yet natural gas does not burn until a spark or flame is applied. Explain using a potential energy diagram.

3

Two reactions have the same ΔH = −50 kJ, but A has Ea = 20 kJ and B has Ea = 100 kJ. Sketch both on one diagram and say which is faster.

4

Explain why the activated complex cannot be isolated and put in a bottle.

5

The reverse reaction of an exothermic process has Ea(rev) = 210 kJ and the forward has Ea(fwd) = 90 kJ. Which direction is faster at the same temperature and concentrations, and why?

Challenge

1

A student claims that any reaction with ΔH = −400 kJ must have a reverse activation energy greater than 400 kJ. Is she right? Explain with the equation and a sketch.

2

Use bond energies to explain why Ea for H₂ + Cl₂ → 2HCl is much smaller than the energy needed to break both reactant bonds completely (678 kJ).

3

A diagram shows two humps with a small valley between them. What does the valley represent, and which hump controls the rate?

Check your understanding

Quiz

1.

On a potential energy diagram, reactants are at 40 kJ, the peak at 110 kJ and products at 90 kJ. What is Ea(fwd)?

2.

Using the same diagram (reactants 40 kJ, peak 110 kJ, products 90 kJ), ΔH is

3.

An exothermic reaction has Ea(fwd) = 50 kJ and ΔH = −120 kJ. Ea(rev) is

4.

Which statement about the activated complex is correct?

5.

A reaction with a very large activation energy will be

6.

As two reactant molecules approach each other during a collision,

For parents and teachers

Big ideas (D3.6, D3.5): a potential energy diagram shows the energy of the reacting system as it changes from reactants, through an activated complex at the peak, to products. The activation energy (reactants to peak) relates to how fast a reaction is; ΔH (reactants to products) shows whether energy is released or absorbed. ΔH = Ea(fwd) − Ea(rev).

How to help: Build the cardboard-and-marble model together. Then draw a diagram on paper with numbers and quiz your teen: "Point to Ea(fwd). Point to ΔH. Is it exothermic?"

Common difficulties:

  • Measuring Ea from zero (the bottom of the graph) instead of from the reactants.
  • Measuring ΔH from the peak instead of between reactants and products.
  • Believing that exothermic reactions must be fast, or that a large ΔH means a large Ea.
  • Sign errors in Ea(rev) = Ea(fwd) − ΔH.

Activity safety: marbles are a choking hazard for small children; keep them away from younger siblings.