1. Reversible Reactions

What Is a Reversible Reaction?

Many chemical reactions appear to travel in only one direction.

Reactants combine or change to form products:

reactants → products

For example, when a fuel burns in oxygen, new substances are produced. Under ordinary conditions, those products do not simply react to recreate the original fuel and oxygen.

However, some chemical reactions can occur in both directions.

These are called reversible reactions.

In a reversible reaction:

• reactants form products
• the products can react to form the original reactants again

We can represent this as:

reactants ⇌ products

The special double arrow ⇌ shows that the reaction can proceed in both directions.

---

Forward and Reverse Reactions

A reversible reaction actually involves two reactions.

Consider:

A + B ⇌ C + D

The forward reaction is:

A + B → C + D

The reactants A and B form products C and D.

The reverse reaction is:

C + D → A + B

The products of the forward reaction react to recreate the original substances.

Therefore, the words reactant and product depend partly on which direction we are considering.

---

The Reversible Reaction Symbol

Reversible reactions are represented using:

⇌

rather than the ordinary reaction arrow:

→

For example:

A + B → C

means that the reaction is being represented as proceeding from A and B toward C.

By contrast:

A + B ⇌ C

means that:

A + B can form C

and:

C can form A + B

The double arrow is therefore an important part of a reversible chemical equation.

---

Reversible vs Irreversible Reactions

An irreversible reaction is represented as proceeding essentially in one direction under the conditions being considered.

reactants → products

A reversible reaction can proceed in both directions.

reactants ⇌ products

---

Why Can Some Reactions Reverse?

For a reaction to reverse, the products must be capable of reacting to recreate the original reactants.

Imagine:

A + B ⇌ C + D

Initially, there may be mostly A and B.

Their particles collide and react:

A + B → C + D

As C and D accumulate, there are more opportunities for C and D particles to collide.

Some of these collisions can cause the reverse reaction:

C + D → A + B

Eventually, both directions may be occurring at the same time.

This leads to the important idea of dynamic equilibrium, which is closely connected to reversible reactions.

---

A Simple Particle Model

Imagine a closed container containing particles A and B.

At first, there are many A and B particles, so the forward reaction occurs frequently:

A + B → C

As C is produced, its concentration increases.

Now C particles are available to undergo the reverse reaction:

C → A + B

Over time:

• the forward reaction continues
• the reverse reaction begins
• both reactions can occur simultaneously

This does not mean that individual particles constantly move backward and forward in a predictable pattern.

Instead, some particle collisions produce products while other collisions produce reactants.

---

Example: Hydrated Copper(II) Sulfate

A useful classroom example involves hydrated copper(II) sulfate.

Hydrated copper(II) sulfate is blue.

When heated, it loses water and forms white anhydrous copper(II) sulfate.

This can be represented as:

hydrated copper(II) sulfate ⇌ anhydrous copper(II) sulfate + water

Heating favours the removal of water.

Adding water to the anhydrous copper(II) sulfate can recreate the blue hydrated substance.

This provides visible evidence that the chemical change can proceed in opposite directions under suitable conditions.

---

Forward Direction: Removing Water

When hydrated copper(II) sulfate is heated:

hydrated copper(II) sulfate → anhydrous copper(II) sulfate + water

The colour changes approximately:

blue → white

Water is removed from the hydrated crystals.

---

Reverse Direction: Adding Water

If water is added to anhydrous copper(II) sulfate:

anhydrous copper(II) sulfate + water → hydrated copper(II) sulfate

The colour changes:

white → blue

Together, the two reactions can be represented using the reversible reaction symbol.

---

Example: Ammonium Chloride

Another example involves ammonium chloride.

When heated strongly, ammonium chloride vapour can dissociate into ammonia and hydrogen chloride:

NH₄Cl(g) ⇌ NH₃(g) + HCl(g)

Under suitable conditions, ammonia and hydrogen chloride can combine again to form ammonium chloride.

This demonstrates that decomposition reactions are not necessarily irreversible.

Whether a reaction is reversible depends on the chemistry of the substances and the conditions.

---

Example: Formation of Hydrogen Iodide

Hydrogen gas and iodine vapour can react to form hydrogen iodide:

H₂(g) + I₂(g) ⇌ 2HI(g)

The reverse reaction can also occur:

2HI(g) ⇌ H₂(g) + I₂(g)

In a closed system under suitable conditions, both reactions can occur simultaneously.

---

Example: The Haber Process

One of the most important industrial reversible reactions is the production of ammonia.

Nitrogen reacts with hydrogen:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

The forward reaction produces ammonia.

The reverse reaction breaks ammonia back into nitrogen and hydrogen.

This reversible reaction is extremely important because ammonia is used to manufacture many nitrogen-containing products, especially fertilizers.

Industrial chemists carefully control reaction conditions to obtain a useful rate and yield.

---

Reversible Reactions and Closed Systems

Reversible reactions are particularly important in closed systems.

A closed system allows energy to be transferred but prevents the reacting substances from freely entering or leaving.

Imagine:

A + B ⇌ C + D

If C and D remain inside the container, they can react to recreate A and B.

But suppose C escapes continuously.

There may then be much less C available for the reverse reaction.

Keeping all reacting substances together allows the forward and reverse reactions to continue and makes it possible for dynamic equilibrium to become established.

---

Reversible Reactions and Dynamic Equilibrium

A reversible reaction in a closed system may eventually reach dynamic equilibrium.

At dynamic equilibrium:

rate of forward reaction = rate of reverse reaction

This does not mean the reactions have stopped.

Both reactions continue.

Imagine that every second:

• 50 forward reactions occur
• 50 reverse reactions occur

There is no overall change in the amounts of reactants and products because they are being produced and consumed at equal rates.

The system looks unchanged at the macroscopic level, even though reactions are still occurring at the particle level.

---

Equilibrium Does Not Mean Equal Amounts

A very important point is that equilibrium does not necessarily mean:

amount of reactants = amount of products

Suppose:

A ⇌ B

At equilibrium, there might be:

• 80% A
• 20% B

Or there might be:

• 30% A
• 70% B

Both could represent equilibrium.

What must be equal is the rate of the forward reaction and the rate of the reverse reaction, not the concentrations of the substances.

---

How Equilibrium Develops

Consider a reversible reaction that begins with only reactants:

A + B ⇌ C + D

At the beginning

There are many reactant particles and almost no products.

Therefore:

• forward reaction is relatively fast
• reverse reaction is very slow or initially absent

As the reaction continues

Reactants are consumed and products accumulate.

Therefore:

• forward reaction tends to slow
• reverse reaction becomes faster

At equilibrium

Eventually:

forward rate = reverse rate

The concentrations then remain constant as long as the conditions remain unchanged.

---

Reversible Reactions Can Respond to Conditions

Changing the conditions of a reversible reaction can change the relative amounts of reactants and products.

Important conditions include:

• temperature
• pressure for reactions involving gases
• concentration

For example, changing the temperature may favour one direction more than the other.

Changing the concentration of one substance can also affect the balance between the forward and reverse reactions.

This behaviour is extremely important in industrial chemistry because manufacturers often want to maximize the production of a particular product.

---

Everyday Example: Carbon Dioxide in Fizzy Drinks

Carbon dioxide dissolved in a carbonated drink provides a useful example of processes that can occur in opposite directions.

In a sealed bottle, carbon dioxide exists both in the gas above the liquid and dissolved in the liquid.

A simplified representation is:

CO₂(g) ⇌ CO₂(aq)

where:

• (g) means gas
• (aq) means dissolved in water

When the bottle is opened, carbon dioxide can escape from the system. This changes the conditions and dissolved carbon dioxide leaves the liquid, producing bubbles.

This is why fizzy drinks gradually become flat after being left open.

---

Reversible Physical Changes

The idea of processes occurring in opposite directions is also familiar from physical changes.

For example:

liquid water ⇌ water vapour

In a closed container:

• some liquid molecules evaporate
• some gas molecules condense

This is a physical equilibrium, rather than a chemical reaction, because no new chemical substances are formed.

However, it provides a useful model for understanding how two opposing processes can occur simultaneously.

---

Reversible and Irreversible Examples

Some familiar processes can be compared.

Often treated as irreversible under ordinary conditions

• combustion of fuels
• many reactions that produce gases which escape
• many precipitation reactions when considered under fixed classroom conditions
• many reactions in which products are continually removed

Reversible under suitable conditions

• hydration and dehydration of some salts
• formation and decomposition of hydrogen iodide
• ammonia formation in the Haber process
• some dissociation reactions

It is important to include the phrase under suitable conditions. Whether a reaction behaves reversibly can depend strongly on the conditions.

---

Worked Example 1: Identifying the Reaction Type

Consider:

A + B ⇌ C

Is this reaction reversible?

Step 1: Examine the arrow

The equation contains:

⇌

Step 2: Interpret the symbol

This means:

A + B → C

can occur, and:

C → A + B

can also occur.

Answer

Yes. The equation represents a reversible reaction.

---

Worked Example 2: Writing Forward and Reverse Reactions

Consider:

N₂ + 3H₂ ⇌ 2NH₃

Forward reaction

N₂ + 3H₂ → 2NH₃

Nitrogen and hydrogen form ammonia.

Reverse reaction

2NH₃ → N₂ + 3H₂

Ammonia forms nitrogen and hydrogen.

The double arrow combines these two processes into one reversible equation.

---

Worked Example 3: Interpreting Equilibrium

Suppose the following reaction reaches equilibrium:

A ⇌ B

Measurements show:

[A] = 0.80 mol/dm³

[B] = 0.20 mol/dm³

A student says:

"The system cannot be at equilibrium because there is more A than B."

This reasoning is incorrect.

Equilibrium does not require equal concentrations.

The system can be at equilibrium if:

rate of A → B = rate of B → A

The amounts of A and B can be different.

---

How to Recognize a Reversible Reaction

When examining a chemical equation, look first at the reaction arrow.

Single arrow

→

Usually indicates that the reaction is being represented as proceeding in one direction.

Double reversible arrow

⇌

Indicates that both forward and reverse reactions can occur.

Then ask:

• Can the products react to recreate the reactants?
• Are the substances kept together in a closed system?
• Do the conditions allow both reactions to occur?
• Could the system establish dynamic equilibrium?

These questions help explain the behaviour rather than simply identifying the symbol.

---

Common Mistakes

Mistake 1: Using → for a reversible reaction

If both directions are important, use:

⇌

rather than:

→

---

Mistake 2: Thinking the reverse reaction is a different, unrelated reaction

The reverse reaction uses the products of the forward reaction to recreate the original reactants.

For:

A + B ⇌ C + D

Forward:

A + B → C + D

Reverse:

C + D → A + B

---

Mistake 3: Thinking equilibrium means the reaction stops

At dynamic equilibrium, reactions continue in both directions.

The system appears unchanged because the rates are equal.

---

Mistake 4: Thinking equilibrium means equal concentrations

At equilibrium:

forward rate = reverse rate

It does not necessarily mean:

reactant concentration = product concentration

---

Mistake 5: Thinking all chemical reactions are reversible

Many reactions do not readily reverse under the same conditions.

For example, the products of combustion do not normally reform the original fuel simply by remaining together.

---

Mistake 6: Ignoring the importance of a closed system

If substances continuously escape from a reaction mixture, the conditions required for dynamic equilibrium may not be maintained.

Closed systems are therefore important when studying reversible reactions and equilibrium.

---

Key Terms

Reversible reaction — A chemical reaction that can proceed in both the forward and reverse directions.

Irreversible reaction — A reaction treated as proceeding essentially in one direction under the conditions considered.

Forward reaction — The reaction in which the substances written on the left side of a reversible equation form those on the right.

Reverse reaction — The reaction in which the products of the forward reaction recreate the original reactants.

Dynamic equilibrium — A state in a closed system in which the forward and reverse reactions continue at equal rates.

Closed system — A system in which matter does not freely enter or leave.

Reaction rate — How quickly reactants are converted into products.

Equilibrium — A state in which opposing processes occur at equal rates, producing no overall change in macroscopic composition.

---

Check Your Understanding

1. Define a reversible reaction.

2. What symbol is used to represent a reversible chemical reaction?

3. Explain the difference between:

→

and:

⇌

4. For the reaction:

A + B ⇌ C + D

write the forward reaction and the reverse reaction separately.

5. Explain why products must remain available for a reverse reaction to occur.

6. Is the following equation reversible or irreversible as written?

X + Y → Z

Explain your answer.

7. Consider:

H₂ + I₂ ⇌ 2HI

What substances react in the forward direction?

8. What substances react in the reverse direction?

9. Explain why a closed system is important when establishing dynamic equilibrium.

10. At equilibrium, a system contains 70% reactants and 30% products. Can the system still be at equilibrium? Explain.

11. A student says, "At equilibrium, the forward and reverse reactions have stopped." Explain why this statement is incorrect.

12. Hydrated copper(II) sulfate can form anhydrous copper(II) sulfate and water. Explain how this example demonstrates reversibility.

13. Explain what happens to the number of forward and reverse reactions per second when dynamic equilibrium is reached.

14. Why might opening a closed container affect a reversible system involving gases?

15. Explain the difference between a reversible reaction and an irreversible reaction.

---

Key Takeaways

• A reversible reaction can proceed in both directions.
• The products of the forward reaction can react to recreate the original reactants.
• Reversible reactions are represented using the symbol ⇌.
• The forward reaction proceeds from reactants toward products.
• The reverse reaction proceeds from products toward reactants.
• Not all reactions are readily reversible under the same conditions.
• Reversibility depends on the substances involved and the reaction conditions.
• Reversible reactions are especially important in closed systems.
• A reversible reaction can eventually establish dynamic equilibrium.
• At dynamic equilibrium, the forward and reverse reactions continue.
• The rates of the forward and reverse reactions are equal at equilibrium.
• Equilibrium does not mean that the concentrations of reactants and products are equal.
• Reversible reactions are important in laboratory chemistry, environmental systems, and industrial processes such as ammonia production.

Did You Know?

The arrows used in chemical equations carry important scientific information. A single arrow → describes a reaction in the direction shown, while the equilibrium arrow ⇌ tells a chemist that both forward and reverse reactions are important. That tiny change in notation can completely change how we analyze a chemical system.

2. Dynamic Equilibrium

What Is Dynamic Equilibrium?

A dynamic equilibrium can occur when a reversible reaction takes place in a closed system.

Recall that a reversible reaction can proceed in both directions:

reactants ⇌ products

The reactants form products in the forward reaction, while the products can react to reform the original reactants in the reverse reaction.

At first, these reactions usually occur at different rates. Over time, however, the system can reach a state where:

rate of forward reaction = rate of reverse reaction

This state is called dynamic equilibrium.

The word dynamic is important. The reactions have not stopped. Both reactions continue to occur, but because they occur at equal rates, there is no overall change in the amounts of reactants and products.

The Key Features of Dynamic Equilibrium

For a chemical system to be at dynamic equilibrium:

• the reaction must be reversible
• the system must be closed
• the forward reaction must continue
• the reverse reaction must continue
• the forward and reverse reaction rates must be equal
• the concentrations of reactants and products remain constant

Notice that constant concentration does not mean equal concentration.

A system might contain much more product than reactant and still be at equilibrium.

---

Forward and Reverse Reactions

Consider the general reversible reaction:

A + B ⇌ C + D

The forward reaction is:

A + B → C + D

The reverse reaction is:

C + D → A + B

At dynamic equilibrium, both reactions continue simultaneously.

At the particle level, A and B particles continue forming C and D, while C and D particles continue forming A and B.

There is continuous chemical activity even though the overall composition of the mixture appears unchanged.

---

How Is Equilibrium Established?

Imagine that a reversible reaction begins with only reactants:

A + B ⇌ C + D

At the beginning:

• there are many A and B particles
• there are almost no C and D particles
• the forward reaction occurs rapidly
• the reverse reaction is very slow or cannot yet occur

As the reaction continues:

• A and B are consumed
• C and D are produced
• the concentrations of A and B decrease
• the concentrations of C and D increase

As more products accumulate, the reverse reaction becomes increasingly important.

Eventually:

forward reaction rate = reverse reaction rate

Dynamic equilibrium has now been established.

---

Stage 1: At the Beginning

Suppose we start with reactants A and B:

A + B ⇌ C

Initially, there may be no C present.

Therefore:

Forward reaction: fast

Reverse reaction: essentially zero at the very beginning

Why?

There are plenty of A and B particles available to collide, but there are initially no C particles available to undergo the reverse reaction.

---

Stage 2: Products Begin to Accumulate

As A and B react:

A + B → C

the concentration of C increases.

Now C particles can undergo the reverse reaction:

C → A + B

As time passes:

• the forward reaction tends to become slower
• the reverse reaction tends to become faster

This happens because the relative numbers and concentrations of the particles are changing.

---

Stage 3: Dynamic Equilibrium

Eventually, the two reaction rates become equal:

rate of forward reaction = rate of reverse reaction

At this point:

• reactants continue forming products
• products continue forming reactants
• concentrations stop changing overall
• the system has reached dynamic equilibrium

If 100 forward reactions occur during a certain period, approximately 100 reverse reactions occur during the same period.

There is therefore no net change in composition.

---

What Happens to Concentrations?

Consider:

A ⇌ B

Suppose the system begins with mostly A.

Initially:

[A] is high

and:

[B] is low

As the forward reaction occurs:

• [A] decreases
• [B] increases

Eventually both concentrations become constant.

The graph levels off because there is no longer any net change in concentration.

However, A and B are still continuously being converted into each other.

---

Constant Does Not Mean Equal

This is one of the most important ideas about equilibrium.

At equilibrium:

reactant concentrations are constant

and:

product concentrations are constant

But they do not have to be equal.

For example, an equilibrium mixture might contain:

80% reactants and 20% products

or:

20% reactants and 80% products

or:

50% reactants and 50% products

All three could represent equilibrium.

What matters is:

forward rate = reverse rate

not:

amount of reactants = amount of products

---

Dynamic vs Static

The word dynamic means that change or activity is still occurring.

A static system, in contrast, has no ongoing change.

Static situation

Imagine a book resting on a table.

Its position remains unchanged because it is not moving.

Dynamic situation

Imagine two escalators carrying exactly 20 people per minute in opposite directions between two floors.

The number of people on each floor could remain constant even though people are continuously moving.

That is similar to dynamic equilibrium.

There is activity at the microscopic level, but no overall change at the macroscopic level.

---

A Useful Analogy: Two Rooms

Imagine two rooms connected by doors.

There are:

40 people in Room A

and:

20 people in Room B

Suppose every minute:

• 5 people move from A to B
• 5 people move from B to A

After one minute:

Room A still has 40 people.

Room B still has 20 people.

But people have definitely moved.

This represents a dynamic system.

Notice something else important:

The number of people in the rooms is not equal.

Yet the numbers remain constant because the rates of movement are equal.

This is similar to chemical equilibrium.

---

Particle Behaviour at Equilibrium

At equilibrium, particles are still:

• moving
• colliding
• reacting
• forming products
• reforming reactants

Suppose:

A₂ + B₂ ⇌ 2AB

At equilibrium, some A₂ and B₂ molecules collide successfully and form AB.

At the same time, some AB molecules react to recreate A₂ and B₂.

Because these processes occur at equal rates, the concentrations remain constant.

---

Why Don't We See Anything Happening?

Chemical reactions happen at the level of atoms, ions, and molecules.

At equilibrium, enormous numbers of particles may still be reacting every second.

However, because the forward and reverse reactions balance one another, there is no overall change that we can easily observe.

For example:

• colour may remain constant
• pressure may remain constant
• concentrations may remain constant
• visible amounts of substances may remain constant

This can make equilibrium appear static even though it is actually highly dynamic.

---

The Importance of a Closed System

Dynamic equilibrium normally requires a closed system.

A closed system prevents matter from freely entering or leaving.

Consider:

A(g) ⇌ B(g)

If B can escape from the container, then B is continually removed.

There may not be enough B available to maintain the reverse reaction at the equilibrium rate.

In a sealed container, both A and B remain available.

The forward and reverse reactions can therefore establish equilibrium.

---

Open and Closed Systems

Open system

Matter can enter or leave.

Examples might include:

• an uncovered beaker
• an open bottle
• a reaction vessel releasing gas

Closed system

Matter cannot freely enter or leave.

Examples include:

• a sealed flask
• a sealed reaction vessel
• a closed bottle

Energy may still be transferred between a closed system and its surroundings.

This distinction is important because equilibrium depends on keeping the reacting substances available.

---

Example: Hydrogen and Iodine

A classic reversible reaction is:

H₂(g) + I₂(g) ⇌ 2HI(g)

Hydrogen and iodine react to form hydrogen iodide.

At the same time, hydrogen iodide can decompose to form hydrogen and iodine.

In a closed system at equilibrium:

rate of H₂ + I₂ → 2HI

equals:

rate of 2HI → H₂ + I₂

The concentrations of H₂, I₂, and HI therefore remain constant.

---

Example: The Haber Process

The industrial production of ammonia involves the reversible reaction:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

In a closed reaction system:

• nitrogen and hydrogen form ammonia
• ammonia can decompose back into nitrogen and hydrogen

Eventually, equilibrium can be established.

Understanding this equilibrium is extremely important because ammonia is widely used to manufacture fertilizers and other chemicals.

---

Example: Carbon Dioxide in a Sealed Drink

A familiar analogy involves carbon dioxide in a sealed carbonated drink.

A simplified process can be represented as:

CO₂(g) ⇌ CO₂(aq)

Carbon dioxide moves between:

• the gas above the liquid
• carbon dioxide dissolved in the liquid

In a sealed bottle, opposing processes can reach a dynamic balance.

When the bottle is opened, the system is changed and carbon dioxide can escape into the surroundings.

That is why bubbles form and the drink eventually becomes flat.

---

Physical Dynamic Equilibrium

Dynamic equilibrium can also occur in physical processes.

Consider water in a sealed container:

H₂O(l) ⇌ H₂O(g)

Some liquid water molecules evaporate:

liquid → gas

At the same time, some water vapour molecules condense:

gas → liquid

Eventually:

rate of evaporation = rate of condensation

The amount of liquid and vapour remains constant even though molecules continue moving between the two states.

This is an excellent example of a dynamic physical equilibrium.

---

Reaction Rate at Equilibrium

Consider a reaction beginning with mostly reactants.

At first:

forward rate > reverse rate

As products accumulate:

• forward rate decreases
• reverse rate increases

Eventually:

forward rate = reverse rate

At that point, equilibrium has been established.

The important detail is that both rates are greater than zero.

If both rates were zero, the system would be static rather than dynamically reacting.

---

Worked Example 1: Is It at Equilibrium?

Suppose a reversible reaction has:

Forward rate = 8 mol/s

Reverse rate = 3 mol/s

Is the system at equilibrium?

No.

The rates are different.

There is still a net change toward the products.

Later:

Forward rate = 5 mol/s

Reverse rate = 5 mol/s

Now:

forward rate = reverse rate

Answer

The system is at dynamic equilibrium.

---

Worked Example 2: Constant Concentrations

A reaction mixture contains:

0.60 mol/dm³ reactant

and:

0.20 mol/dm³ product

Measurements show that both concentrations remain constant.

The forward and reverse reactions are occurring at equal rates.

Is the system at equilibrium?

Yes.

The concentrations do not need to be equal.

They only need to remain constant while the forward and reverse reactions occur at equal rates.

---

Worked Example 3: Particle Behaviour

Consider:

A ⇌ B

During one second:

• 150 A particles become B
• 150 B particles become A

What happens to the total amounts of A and B?

There is no overall change.

For every 150 A particles consumed, another 150 A particles are produced.

The same is true for B.

Therefore, the system is at dynamic equilibrium.

---

Worked Example 4: Not Yet at Equilibrium

Suppose:

A ⇌ B

During one second:

• 200 A particles become B
• 80 B particles become A

The reactions are occurring in both directions, but the rates are not equal.

There is a net conversion of:

200 − 80 = 120 particles

from A toward B.

Therefore:

the system is not yet at equilibrium.

This is an important distinction.

A reaction can be reversible without currently being at equilibrium.

---

Reversible Reaction vs Dynamic Equilibrium

These terms are related but do not mean exactly the same thing.

Reversible reaction

A reaction that can occur in both directions.

Dynamic equilibrium

A particular state of a reversible system in which:

forward rate = reverse rate

Therefore:

reversible does not automatically mean at equilibrium.

A reversible reaction may need time to reach equilibrium.

---

Static Equilibrium vs Dynamic Equilibrium

The word equilibrium is used in different areas of science.

Static equilibrium

Nothing is changing.

For example, an object resting with balanced forces may be described as being in static equilibrium.

Dynamic equilibrium

Opposing processes continue, but they occur at equal rates.

In chemical dynamic equilibrium:

• particles continue reacting
• forward and reverse reactions continue
• no overall concentration change occurs

The system appears unchanged even though microscopic activity continues.

---

Macroscopic and Microscopic Views

Dynamic equilibrium becomes easier to understand when we distinguish between two scales.

Macroscopic level

This is what we can observe or measure directly.

At equilibrium:

• concentration appears constant
• colour may remain constant
• pressure may remain constant
• other measurable properties remain constant

Microscopic level

This describes atoms, molecules, and ions.

At equilibrium:

• particles continue moving
• collisions continue
• bonds continue breaking and forming
• forward reactions continue
• reverse reactions continue

So:

macroscopically constant does not mean microscopically inactive.

---

How Do We Know Equilibrium Has Been Reached?

Suppose scientists monitor the concentration of reactants and products over time.

Initially, the concentrations change.

Eventually, they become constant.

If the reaction is reversible and the system is closed, this constant composition can indicate that dynamic equilibrium has been established.

Scientists can also consider the reaction rates.

At equilibrium:

forward rate = reverse rate

This provides the microscopic explanation for the constant concentrations.

---

Common Mistakes

Mistake 1: Thinking equilibrium means the reaction has stopped

Incorrect.

At dynamic equilibrium:

forward reaction continues

and:

reverse reaction continues

The reactions occur at equal rates.

---

Mistake 2: Thinking reactant and product concentrations must be equal

They do not.

For example:

[reactant] = 0.80 mol/dm³

and:

[product] = 0.20 mol/dm³

could still represent equilibrium.

What must be equal are the reaction rates.

---

Mistake 3: Thinking a reversible reaction is always at equilibrium

A reaction may be reversible but not yet have reached equilibrium.

Before equilibrium:

forward rate ≠ reverse rate

At equilibrium:

forward rate = reverse rate

---

Mistake 4: Thinking nothing happens at equilibrium

A great deal can be happening at the particle level.

Particles continue colliding and reacting.

There is simply no net change.

---

Mistake 5: Thinking equilibrium can only happen with equal numbers of particles

Equal numbers are not required.

The equilibrium composition depends on the particular reaction and conditions.

---

Mistake 6: Ignoring the closed system

If substances continuously leave the system, the reverse reaction may not be able to balance the forward reaction.

A closed system is therefore an important condition for establishing chemical dynamic equilibrium.

---

Key Terms

Dynamic equilibrium — A state in a closed reversible system where the forward and reverse reactions occur at equal rates.

Reversible reaction — A reaction that can proceed in both directions.

Forward reaction — The reaction converting reactants into products as the equation is written.

Reverse reaction — The reaction converting products back into reactants.

Reaction rate — How quickly reactants are converted into products.

Closed system — A system in which matter does not freely enter or leave.

Static — Not changing or moving.

Dynamic — Involving continuing activity or change.

Macroscopic — Describing properties observable on a large scale.

Microscopic — Describing behaviour at the particle level.

Concentration — The amount of a substance present per unit volume.

Net change — The overall change after opposing processes are considered together.

---

Check Your Understanding

1. Define dynamic equilibrium.

2. What two reaction rates are equal at dynamic equilibrium?

3. Does a chemical reaction stop when equilibrium is reached? Explain.

4. Explain why equilibrium is described as dynamic.

5. What is the difference between a static system and a dynamic system?

6. Consider:

A + B ⇌ C

Describe what particles are doing at equilibrium.

7. A reaction has a forward rate of 12 mol/s and a reverse rate of 7 mol/s. Is it at equilibrium? Explain.

8. Later, both rates become 9 mol/s. Is the system now at equilibrium? Explain.

9. At equilibrium, a mixture contains 75% reactants and 25% products. Explain why this is possible.

10. Explain why reactant and product concentrations remain constant at equilibrium.

11. Why is a closed system important for dynamic equilibrium?

12. Explain how equilibrium develops when a reversible reaction begins with only reactants.

13. What happens to the forward reaction rate as reactants are consumed?

14. What happens to the reverse reaction rate as products accumulate?

15. Explain the difference between a reversible reaction and a system that has actually reached dynamic equilibrium.

16. In one second, 300 particles undergo the forward reaction while 300 particles undergo the reverse reaction. Explain what happens to the overall composition.

17. In another system, 300 particles undergo the forward reaction while only 100 undergo the reverse reaction. Is the system at equilibrium? Explain.

18. Use evaporation and condensation in a sealed container to explain dynamic equilibrium.

---

Key Takeaways

• Dynamic equilibrium occurs in a closed reversible system.
• The forward and reverse reactions continue at equilibrium.
• At equilibrium, forward reaction rate = reverse reaction rate.
• Both reaction rates remain greater than zero.
• There is therefore no net change in the amounts of reactants and products.
• Reactant and product concentrations remain constant, but they do not have to be equal.
• Equilibrium is dynamic, not static.
• At the microscopic level, particles continue moving, colliding, breaking bonds, and forming bonds.
• At the macroscopic level, the system appears unchanged.
• A reversible reaction is not necessarily at equilibrium.
• Equilibrium develops as the forward reaction slows relative to its initial rate and the reverse reaction becomes increasingly significant until their rates become equal.
• A closed system is important because the reacting substances must remain available for both forward and reverse reactions.

Did You Know?

At chemical equilibrium, an apparently unchanged mixture can contain an enormous amount of microscopic activity. Countless molecules may react in the forward direction every second while a matching number react in the reverse direction. To an observer, nothing seems to change—but at the molecular level, the system is continuously active.

3. Equilibrium in Closed Systems

Why Does Equilibrium Need a Closed System?

A reversible reaction can reach dynamic equilibrium when the forward and reverse reactions occur at equal rates.

For example:

A + B ⇌ C + D

At equilibrium:

rate of forward reaction = rate of reverse reaction

For this balance to be maintained, the substances involved in the reaction must remain available to react.

If products escape from the system, there may no longer be enough of them to maintain the reverse reaction. If reactants are continually added, the balance is also disturbed.

For this reason, chemical dynamic equilibrium is established and maintained in a closed system.

---

What Is a System?

In chemistry, a system is the particular part of the universe that we choose to study.

Everything outside the system is called the surroundings.

For example, if we are studying a chemical reaction inside a sealed flask:

• the chemicals inside the flask are the system
• the flask helps form the boundary
• the air and laboratory outside are the surroundings

Understanding exactly where the system begins and ends is important when discussing equilibrium.

---

What Is a System Boundary?

A system boundary separates the system from its surroundings.

The boundary may be physical, such as:

• the walls of a flask
• the lid of a container
• the walls of a reaction vessel
• a sealed bottle

Or it may be an imaginary boundary chosen by a scientist when analyzing a process.

The important question is:

What can cross the boundary?

In particular, we need to consider matter and energy.

---

Open Systems

An open system can exchange both matter and energy with its surroundings.

Matter can:

• enter the system
• leave the system

Energy can also be transferred between the system and surroundings.

Examples include:

• an uncovered beaker
• an open bottle
• a reaction vessel with gas escaping
• a cup of hot water without a lid
• many living organisms

Suppose a reaction produces a gas:

A ⇌ B(g)

If the container is open, B may escape.

Once B leaves, it is no longer available to undergo the reverse reaction.

This can prevent equilibrium from being maintained.

---

Closed Systems

A closed system does not allow matter to freely enter or leave.

However, energy may still cross the system boundary.

For example, a sealed flask can still:

• gain thermal energy from a heater
• lose thermal energy to the surroundings
• absorb light
• transfer energy through its walls

But the reacting substances remain inside.

This allows products to remain available for the reverse reaction.

---

Closed Does Not Mean Insulated

This is an important distinction.

A closed system prevents the transfer of matter across its boundary, but it can still exchange energy.

Imagine a sealed glass flask being heated.

The flask is closed because chemicals cannot freely escape.

However, thermal energy can enter through the glass.

Therefore:

closed system ≠ no energy transfer

---

What Is an Isolated System?

A third type of system is sometimes considered.

An isolated system ideally exchanges neither matter nor energy with its surroundings.

Perfectly isolated systems are difficult to create in reality, but the concept is useful when studying energy and thermodynamics.

For chemical equilibrium, we normally focus on closed systems rather than requiring perfect isolation.

---

Why Does Matter Need to Stay Inside?

Consider:

A ⇌ B

Suppose we begin with A.

The forward reaction produces B:

A → B

As B accumulates, the reverse reaction becomes increasingly important:

B → A

Eventually:

forward rate = reverse rate

and equilibrium is established.

Now imagine that B continuously escapes from the system.

There are now fewer B particles available for the reverse reaction.

Removing B therefore interferes with the balance between the forward and reverse reactions.

---

Particle View of a Closed System

Consider:

A₂(g) + B₂(g) ⇌ 2AB(g)

Inside a sealed container:

• A₂ and B₂ particles collide
• some successful collisions produce AB
• AB particles also collide and undergo the reverse reaction
• all substances remain inside the container

Eventually:

rate of A₂ + B₂ → 2AB

equals:

rate of 2AB → A₂ + B₂

Because the substances remain inside the system, both reactions can continue.

---

Conditions Needed for Dynamic Equilibrium

Several conditions are needed for chemical dynamic equilibrium.

1. The reaction must be reversible

There must be both a forward and reverse reaction:

reactants ⇌ products

2. The system must be closed

Reactants and products must not freely escape.

3. The reaction must be given time

The forward and reverse rates may initially be different.

They need time to become equal.

4. Conditions must remain constant

Once equilibrium has been established, changing conditions such as:

• temperature
• pressure
• concentration

can disturb the existing equilibrium state.

5. Both reactions must continue

At dynamic equilibrium:

forward rate = reverse rate ≠ 0

The reactions have not stopped.

---

Establishing Equilibrium Step by Step

Consider:

A + B ⇌ C

Suppose the system initially contains mostly A and B.

Stage 1

There are many reactant particles.

The forward reaction is relatively fast.

There is little or no C, so the reverse reaction is initially very slow.

Stage 2

C begins to accumulate.

The reverse reaction becomes faster because more C particles are available.

Stage 3

Eventually:

forward rate = reverse rate

Dynamic equilibrium has been established.

The concentrations of A, B, and C then remain constant as long as the equilibrium conditions are maintained.

---

What Happens in an Open System?

Now imagine that C is a gas and the container is open.

A + B ⇌ C(g)

As C forms, it escapes into the surroundings.

The concentration of C inside the system remains lower than it would in a closed container.

That reduces the opportunity for:

C → A + B

to occur.

The system therefore cannot maintain the same dynamic equilibrium that would exist if all substances were retained.

---

Example: Carbonated Drinks

A sealed bottle of carbonated drink provides a useful example of why system boundaries matter.

Carbon dioxide can move between the gas above the liquid and the dissolved state:

CO₂(g) ⇌ CO₂(aq)

Bottle closed

Carbon dioxide remains within the bottle.

Opposing processes can establish a dynamic balance.

Bottle opened

The boundary changes.

Carbon dioxide gas can now escape into the surroundings.

As CO₂ leaves the system, more dissolved CO₂ can leave the liquid.

Eventually, the drink becomes less fizzy.

Opening the bottle has changed the system from effectively closed to open with respect to carbon dioxide.

---

Example: Water in a Sealed Container

Consider liquid water in a sealed container.

Some molecules evaporate:

H₂O(l) → H₂O(g)

Some water-vapour molecules condense:

H₂O(g) → H₂O(l)

Together:

H₂O(l) ⇌ H₂O(g)

Eventually:

rate of evaporation = rate of condensation

The amount of liquid and vapour remains constant.

This is a physical dynamic equilibrium.

---

What If the Container Is Open?

Now remove the lid.

Water molecules can evaporate and escape into the surrounding air.

Many of those molecules never return to the liquid.

The system therefore does not maintain the same balance between evaporation and condensation that exists in the sealed container.

Over time, the amount of liquid can decrease.

This demonstrates how changing the system boundary changes the behaviour of the system.

---

Example: Hydrogen Iodide Equilibrium

Consider:

H₂(g) + I₂(g) ⇌ 2HI(g)

In a sealed reaction vessel, all three gases remain available.

Hydrogen and iodine form hydrogen iodide.

Hydrogen iodide can also decompose into hydrogen and iodine.

At equilibrium:

forward rate = reverse rate

If one of the gases were continuously removed, the original equilibrium could not be maintained.

---

Example: The Haber Process

The Haber process uses the reversible reaction:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

Nitrogen and hydrogen react to produce ammonia.

Ammonia can also undergo the reverse reaction.

Industrial systems carefully control:

• temperature
• pressure
• gas flow
• reactant supply
• product removal

This demonstrates that real industrial equilibrium systems can be more complicated than a simple sealed classroom flask. Engineers control what enters and leaves different parts of the process to obtain useful production while managing the reversible reaction.

---

Equilibrium and Constant Conditions

A closed system alone is not enough to guarantee that an existing equilibrium remains unchanged.

Conditions also matter.

Important factors include:

• temperature
• pressure
• concentration

Suppose a system has reached equilibrium.

If its temperature changes, the rates of the forward and reverse reactions may change differently.

If pressure changes in a gaseous system, the equilibrium composition may change.

If the concentration of a substance changes, the system may respond.

The system may then establish a new equilibrium under the new conditions.

This idea leads into Le Chatelier's principle.

---

Predicting Whether Equilibrium Can Be Maintained

When given a situation, ask the following questions.

Is the reaction reversible?

If not, dynamic chemical equilibrium cannot be established between the forward and reverse reactions.

Is matter able to escape?

If important reactants or products continuously leave, equilibrium may not be maintained.

Is matter being added?

Continually adding substances changes the composition and can disturb the existing equilibrium.

Are the conditions constant?

Changes in temperature, pressure, or concentration can disturb the equilibrium.

Are both reactions still occurring?

Dynamic equilibrium requires both directions to continue.

---

Worked Example 1: Sealed Flask

A reversible gaseous reaction occurs in a sealed flask:

A(g) ⇌ B(g)

After some time, the forward and reverse rates become equal.

Can equilibrium be maintained?

Analysis

• The reaction is reversible.
• The flask is sealed.
• A and B cannot freely escape.
• Both reactions can continue.

Answer

Yes. Dynamic equilibrium can be maintained if the conditions remain constant.

---

Worked Example 2: Open Flask

Consider the same reaction:

A(g) ⇌ B(g)

but the flask is open and B escapes continuously.

Can the original equilibrium be maintained?

Analysis

B is being removed from the system.

There are therefore fewer B particles available for the reverse reaction.

Answer

No. The original equilibrium cannot be maintained while B continuously escapes.

---

Worked Example 3: Heating a Closed System

A reversible reaction has reached equilibrium in a sealed flask.

The flask is then heated.

Is the system still closed?

Yes.

Matter still cannot freely enter or leave.

But has a condition changed?

Yes. Temperature has changed.

Therefore, although the system remains closed, the original equilibrium may be disturbed and the system may establish a new equilibrium.

This shows that:

closed system ≠ equilibrium can never change

---

Worked Example 4: Removing Product

Consider:

A ⇌ B

The system is initially at equilibrium.

A device continuously removes B.

What happens?

Removing B means the system is no longer closed with respect to B.

The original equilibrium cannot simply remain unchanged.

This demonstrates why the system boundary matters.

If material crosses the boundary, the chemical behaviour of the system can change.

---

System Boundaries in Real Situations

A boundary does not always have to be the wall of a glass flask.

Scientists define boundaries depending on what they are studying.

For example:

Aquarium

If the entire aquarium is the system, matter may enter through:

• food
• added water
• gases exchanged with air

and leave through:

• evaporation
• waste removal
• gas exchange

Therefore, it is an open system.

Sealed reaction vessel

Matter is contained inside, but thermal energy may pass through the walls.

This is a closed system.

Open cup of water

Water can evaporate and energy can enter or leave.

This is an open system.

Understanding the boundary tells us what interactions with the surroundings are possible.

---

Open and Closed Systems Compared

The key difference is the movement of matter across the boundary.

---

Macroscopic and Particle Views

At equilibrium, the system can look unchanged.

Macroscopic view

We may observe:

• constant colour
• constant pressure
• constant concentration
• constant amounts of substances

Particle view

Particles continue:

• moving
• colliding
• reacting
• forming products
• reforming reactants

The closed boundary keeps the particles within the system so these opposing reactions can continue.

---

Why System Boundaries Matter in Chemistry

Defining the system boundary helps chemists determine:

• what substances are included in the system
• whether matter can enter
• whether matter can leave
• whether energy can be transferred
• whether equilibrium can be established
• whether equilibrium can be maintained

Without clearly defining the boundary, statements such as "the system is closed" or "the amount of matter remains constant" may be unclear.

The boundary tells us exactly what we are tracking.

---

Common Mistakes

Mistake 1: Thinking a closed system exchanges nothing

A closed system can exchange energy with its surroundings.

It does not freely exchange matter.

---

Mistake 2: Confusing closed and isolated systems

Closed:

no matter transfer, but energy transfer is possible

Isolated:

ideally no matter or energy transfer

They are not the same.

---

Mistake 3: Thinking a lid automatically guarantees equilibrium

A closed container allows equilibrium to be established, but other requirements still matter.

The reaction must be reversible and enough time must pass for the forward and reverse rates to become equal.

---

Mistake 4: Thinking equilibrium cannot change in a closed system

Changing temperature, pressure, or concentration can disturb an equilibrium even if the container remains closed.

The system may then establish a new equilibrium.

---

Mistake 5: Ignoring escaping gases

If a gaseous product escapes from an open container, it is no longer available for the reverse reaction.

This can prevent equilibrium from being maintained.

---

Mistake 6: Thinking equilibrium means equal amounts

A closed system may reach equilibrium with very different concentrations of reactants and products.

The important equality is:

forward rate = reverse rate

---

Key Terms

System — The part of the universe selected for study.

Surroundings — Everything outside the system.

System boundary — The real or imaginary boundary separating a system from its surroundings.

Open system — A system that can exchange both matter and energy with its surroundings.

Closed system — A system that does not freely exchange matter with its surroundings but can exchange energy.

Isolated system — An idealized system that exchanges neither matter nor energy with its surroundings.

Dynamic equilibrium — A state in a closed reversible system where the forward and reverse reactions occur at equal rates.

Reversible reaction — A reaction that can proceed in both directions.

Forward reaction — The reaction converting reactants into products as written.

Reverse reaction — The reaction converting products back into reactants.

---

Check Your Understanding

1. Define a closed system.

2. Define an open system.

3. What is a system boundary?

4. Explain the difference between a closed system and an isolated system.

5. Why is a closed system important for dynamic equilibrium?

6. Consider:

A(g) ⇌ B(g)

Explain what could happen if B escapes from the container.

7. Give two examples of open systems.

8. Give two examples of closed systems.

9. Can energy enter or leave a closed system? Explain.

10. A reversible reaction occurs in a sealed flask. Is this enough to prove that the system is at equilibrium? Explain.

11. A reaction has reached equilibrium in a sealed container. The temperature is then changed. Can the original equilibrium be disturbed even though the system is still closed? Explain.

12. Explain why a carbonated drink behaves differently before and after the bottle is opened.

13. Describe what happens to water molecules in a sealed container when evaporation and condensation reach dynamic equilibrium.

14. A student says, "A closed system is the same as an isolated system." Explain the student's mistake.

15. A reversible reaction is at equilibrium. One product is then continuously removed. Predict whether the original equilibrium can be maintained and explain why.

16. Explain why identifying the system boundary is important when analyzing a chemical process.

---

Key Takeaways

• Dynamic equilibrium is established in a closed reversible system.
• A system is the part of the universe being studied.
• The surroundings are everything outside that system.
• A system boundary separates the system from its surroundings.
• An open system can exchange matter and energy with its surroundings.
• A closed system does not freely exchange matter, although energy can still be transferred.
• An isolated system ideally exchanges neither matter nor energy.
• Keeping reactants and products inside the system allows both the forward and reverse reactions to continue.
• If a reacting substance continuously escapes, the original equilibrium cannot be maintained.
• A closed system alone does not guarantee equilibrium; the reaction must also be reversible and have time to reach equilibrium.
• At equilibrium, the forward and reverse reaction rates are equal.
• Changing conditions can disturb an equilibrium even when the system remains closed.
• Clearly defining the system boundary allows chemists to determine what matter and energy can enter or leave.

Did You Know?

A sealed container is not necessarily completely inactive or cut off from its surroundings. A sealed glass flask can absorb heat, release heat, or even allow light to pass through while still being considered a closed system. In chemistry, the key feature of a closed system is not that nothing crosses the boundary—it is that matter is retained within the defined system.

4. Equilibrium Diagrams and Graphs

Why Do We Use Equilibrium Graphs?

Chemical equilibrium happens at the particle level, so we cannot usually see individual forward and reverse reactions taking place.

Instead, scientists measure quantities such as:

• concentration
• reaction rate
• pressure
• time

and represent the results using graphs.

One of the most useful is a concentration-time graph.

A concentration-time graph shows how the concentrations of reactants and products change as a reversible reaction approaches equilibrium.

For example:

A ⇌ B

At the beginning, there may be a high concentration of A and little or no B.

As the reaction proceeds:

• A is converted into B
• the concentration of A decreases
• the concentration of B increases

Eventually, both concentrations become constant.

That is evidence that the system has reached dynamic equilibrium.

---

Understanding the Axes

Before interpreting any graph, identify the axes.

On a typical concentration-time graph:

Horizontal axis

Time

This might be measured in:

• seconds
• minutes
• hours

Vertical axis

Concentration

This might be measured in:

mol/dm³

or:

mol/L

So the graph answers the question:

How does the concentration of each substance change over time?

---

A Typical Concentration-Time Graph

Consider:

A ⇌ B

Suppose we begin mainly with A.

An illustrative set of data might look like this:

Before equilibrium:

• [A] decreases
• [B] increases

From about 5 time units onward, both concentrations remain constant.

This indicates that equilibrium has been established.

---

What Does [A] Mean?

Chemists commonly use square brackets to represent concentration.

For example:

[A]

means:

the concentration of A

Similarly:

[H₂]

means:

the concentration of hydrogen

and:

[NH₃]

means:

the concentration of ammonia

Therefore, a graph labelled [A] against time is showing how the concentration of A changes over time.

---

Before Equilibrium

Before equilibrium is established, there is a net change in concentrations.

Consider:

A ⇌ B

If the reaction begins mainly with A:

[A] decreases

while:

[B] increases

Why?

Initially, the forward reaction occurs faster than the reverse reaction.

So:

forward rate > reverse rate

More A is being converted into B than B is being converted back into A.

---

Why Does the Reactant Curve Become Less Steep?

At the beginning, the reactant concentration may decrease quickly.

Later, the curve becomes less steep.

A steep curve means the concentration is changing rapidly.

A flatter curve means the concentration is changing more slowly.

As equilibrium approaches, the net change becomes smaller because the forward and reverse reaction rates are becoming closer.

Eventually, the concentration curve becomes horizontal.

---

Identifying the Equilibrium Point

On a concentration-time graph, equilibrium is reached when the concentrations become constant.

Look for the point where the curves:

level off and become horizontal

This does not mean the concentrations have become zero.

It does not mean the reactant and product concentrations have become equal.

It means their concentrations are no longer changing overall.

At this point:

rate of forward reaction = rate of reverse reaction

---

Equilibrium Does Not Mean Equal Concentrations

Suppose another reaction reaches the following equilibrium concentrations:

[A] = 0.70 mol/dm³

[B] = 0.30 mol/dm³

The concentrations are clearly not equal.

The system can still be at equilibrium.

Consider this illustrative graph:

The important observation is that both curves become horizontal.

At equilibrium:

concentrations are constant

not necessarily:

concentrations are equal

---

What Does a Horizontal Line Mean?

A horizontal section of a concentration-time graph means:

concentration is not changing with time

For an equilibrium system, this means that there is no net change in the amount of that substance.

However, particles are still reacting.

Suppose:

A ⇌ B

At equilibrium:

A → B

continues, and:

B → A

continues.

Because the rates are equal, [A] and [B] remain constant.

---

Constant Concentration Does Not Mean the Reaction Has Stopped

This is one of the most important ideas when interpreting equilibrium graphs.

If a concentration curve becomes horizontal, it is tempting to conclude:

"The reaction has stopped."

That is incorrect.

At dynamic equilibrium, reactions continue in both directions.

At the particle level:

• particles continue moving
• collisions continue
• bonds continue breaking
• bonds continue forming
• reactants continue becoming products
• products continue becoming reactants

The graph is horizontal because the two opposing reactions produce no net change in concentration.

---

Concentration Graphs vs Rate Graphs

Students sometimes confuse concentration-time graphs with reaction-rate graphs.

They show different things.

Concentration-time graph

Shows:

how much of each substance is present per unit volume

Rate-time graph

Shows:

how quickly the forward and reverse reactions are occurring

The graphs are related, but they should not be interpreted in exactly the same way.

---

Reaction-Rate Graphs

Suppose a reversible reaction begins mainly with reactants.

Initially:

• forward rate is high
• reverse rate is low

As products accumulate:

• forward rate decreases
• reverse rate increases

Eventually:

forward rate = reverse rate

On this type of graph, equilibrium is reached when the two reaction-rate curves become equal.

This is different from a concentration graph, where the curves do not need to meet.

---

Comparing the Two Types of Graph

This distinction is extremely useful when interpreting equilibrium diagrams.

---

Worked Example 1: Finding the Equilibrium Time

Suppose a graph shows:

When is equilibrium established?

At 30 s, the concentrations reach:

[A] = 0.55 mol/dm³

[B] = 0.45 mol/dm³

After this point, both remain constant.

Answer

Equilibrium is established at approximately 30 s.

---

Worked Example 2: Interpreting Unequal Concentrations

At equilibrium, a graph shows:

[X] = 0.80 mol/dm³

[Y] = 0.20 mol/dm³

A student says:

"The reaction is not at equilibrium because X and Y have different concentrations."

The student is incorrect.

Equilibrium requires:

forward rate = reverse rate

It does not require:

[X] = [Y]

The horizontal concentration curves indicate that both concentrations are constant.

---

Worked Example 3: What Happens Before Equilibrium?

Consider:

A ⇌ B

A graph shows that [A] is decreasing while [B] is increasing.

What can we conclude?

There is a net forward reaction.

This means:

forward rate > reverse rate

Both reactions may already be occurring, but the forward reaction is occurring faster overall.

---

Worked Example 4: Reading the Shape of a Curve

Suppose [A] falls very rapidly during the first 10 seconds and then decreases more slowly between 10 and 30 seconds.

This means:

First 10 seconds

The net change in concentration is large.

10–30 seconds

The net change becomes smaller.

After 30 seconds

The graph becomes horizontal.

The system has reached equilibrium.

This graphical pattern represents the system gradually approaching dynamic equilibrium.

---

Starting with Products Instead

A reversible reaction does not have to begin with reactants.

Consider:

A ⇌ B

Suppose we begin with mostly B.

Then:

• [B] may decrease
• [A] may increase

Eventually, both concentrations become constant.

The direction in which the concentrations initially change depends on the starting composition.

The important feature is that the system eventually approaches constant equilibrium concentrations.

---

Several Substances on One Graph

Real reversible reactions often involve more than two substances.

For example:

N₂(g) + 3H₂(g) ⇌ 2NH₃(g)

A concentration-time graph could contain three curves:

• [N₂]
• [H₂]
• [NH₃]

If the system begins with nitrogen and hydrogen:

• [N₂] decreases
• [H₂] decreases
• [NH₃] increases

Eventually, all three curves level off.

That indicates equilibrium.

Again, the concentrations do not need to become equal.

---

The Shape Can Tell Us About Stoichiometry

Consider:

N₂ + 3H₂ ⇌ 2NH₃

The coefficients tell us that substances are consumed and produced in specific mole ratios.

For every:

1 mol N₂ consumed

approximately:

3 mol H₂ are consumed

and:

2 mol NH₃ are produced

Therefore, changes in concentration can reflect the stoichiometric relationship in the balanced equation, provided the volume is constant.

This means equilibrium graphs can contain information not only about equilibrium but also about the reaction equation itself.

---

Equilibrium Points on Graphs

The phrase equilibrium point usually refers to the time when the system first reaches equilibrium.

On a concentration-time graph, look for the time when:

all concentration curves become constant

On a rate-time graph, look for the time when:

forward rate = reverse rate

After that point, the system remains at equilibrium as long as the conditions remain unchanged.

---

What Happens If Equilibrium Is Disturbed?

Suppose a system reaches equilibrium.

Its concentration curves are horizontal.

Then something changes.

For example:

• reactant is added
• product is removed
• volume changes
• pressure changes
• temperature changes

The graph may begin changing again.

Eventually, the system may establish a new equilibrium.

The concentrations then become constant again, although they may have different values from before.

---

A Graph with Two Equilibria

Consider an illustrative reaction:

A ⇌ B

Initially, the system reaches equilibrium.

Later, the conditions are changed.

The system then moves toward a new equilibrium.

5. Everyday Examples of Equilibrium