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.

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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?

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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.

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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.

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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.

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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.

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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

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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

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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.

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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.

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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.

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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.

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Comparing the Two Types of Graph

This distinction is extremely useful when interpreting equilibrium diagrams.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.

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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.