Reaction Rate Graphs and Applications
1. Concentration-Time Graphs
Learning outcomes
- I can interpret concentration-time graphs.
- I can describe changes in reactant concentration during a reaction.
- I can explain how graph shape relates to reaction rate.
- I can compare reactions using concentration-time graphs.
- I can identify when a reaction has reached completion.
What Is a Concentration-Time Graph?
Chemical reactions change substances over time.
As a reaction occurs:
- reactants are used up
- products are formed
One way to follow these changes is to measure the concentration of a substance at different times.
A concentration-time graph shows how the concentration of a reactant or product changes as a reaction proceeds.
These graphs provide useful information about:
- how quickly a reaction occurs
- how reactant concentration changes
- how product concentration changes
- when the reaction slows down
- when concentrations stop changing
- how two reactions compare
Understanding the Axes
A typical concentration-time graph has:
x-axis → time
y-axis → concentration
Concentration may be measured in units such as:
mol/L
or:
mol dm⁻³
Time may be measured in:
- seconds
- minutes
- hours
depending on how quickly the reaction occurs.
What Is Concentration?
Concentration describes how much of a substance is present in a particular volume.
For solutions, concentration is often expressed as:
moles of solute per litre of solution
A higher concentration means there are:
more particles per unit volume
A lower concentration means there are:
fewer particles per unit volume
Reactant Concentration During a Reaction
Reactants are:
consumed
during a chemical reaction.
Therefore, their concentrations usually:
decrease with time
Consider the reaction:
A → B
At the beginning, there is a high concentration of A.
As the reaction proceeds:
A particles are converted into B particles
Therefore:
[A] decreases
while:
[B] increases
Square brackets are commonly used to mean:
concentration
So:
[A] = concentration of A
A Typical Reactant Concentration-Time Graph
Suppose a reactant begins at a concentration of 1.0 mol/L.
Illustrative data might look like this:
| Time (s) | Reactant Concentration (mol/L) |
|---|---|
| 0 | 1.00 |
| 10 | 0.70 |
| 20 | 0.50 |
| 30 | 0.38 |
| 40 | 0.32 |
| 50 | 0.30 |
| 60 | 0.30 |
Notice two important features:
The concentration decreases.
and:
The graph becomes less steep with time.
Both features tell us something about the reaction.
Why Does Reactant Concentration Decrease?
Reactant particles are converted into:
products
Therefore, as time passes:
number of reactant particles decreases
which causes:
reactant concentration to decrease
For example:
hydrogen + iodine → hydrogen iodide
As the reaction proceeds, hydrogen and iodine are consumed.
Their concentrations decrease while the concentration of hydrogen iodide:
increases
Product Concentration During a Reaction
Products behave differently.
At the beginning of a reaction, there may be:
little or no product
As the reaction proceeds:
product concentration increases
Eventually, the graph may level off.
Therefore:
reactant concentration → generally decreases
product concentration → generally increases
Reading Concentration from a Graph
Suppose you are asked:
What is the reactant concentration at 20 seconds?
Use the graph like this:
- Find 20 s on the x-axis.
- Move vertically until you reach the curve.
- Move horizontally toward the y-axis.
- Read the concentration.
For our example:
at 20 s, concentration = 0.50 mol/L
Graph reading should always include:
the correct units
Describing a Concentration-Time Graph
When describing a graph, avoid vague statements such as:
"The graph goes down."
Instead say:
"The concentration of the reactant decreases with time."
An even stronger description might be:
"The reactant concentration decreases rapidly at first and then decreases more slowly before becoming constant."
This describes both:
the direction of change
and:
how the rate of change varies
Concentration-Time Graphs and Reaction Rate
A concentration-time graph can also tell us about:
reaction rate
Reaction rate describes:
how quickly reactants are consumed or products are formed
For a reactant, the average rate of disappearance can be written as:
average rate = decrease in concentration ÷ time interval
More generally:
average rate = change in concentration ÷ change in time
or:
rate = Δconcentration / Δtime
For a disappearing reactant, the concentration change itself is negative, so the rate of disappearance is often reported as a positive magnitude.
Gradient and Reaction Rate
The gradient or slope of a concentration-time graph tells us how quickly concentration is changing.
A:
steep slope = rapid change in concentration
A:
shallow slope = slower change in concentration
A:
horizontal line = no change in concentration
Therefore:
the steeper the concentration-time graph, the greater the magnitude of the reaction rate
Why Is the Graph Usually Steepest at the Beginning?
At the beginning of many reactions, reactant concentration is:
highest
There are many reactant particles available.
This generally leads to:
more frequent successful collisions
Therefore, the reaction is often:
fastest near the beginning
The concentration changes quickly.
The graph is therefore:
steep
Why Does the Graph Become Less Steep?
As the reaction continues:
reactants are consumed
Their concentrations decrease.
There are fewer reactant particles available for collisions.
Successful collisions generally occur:
less frequently
The reaction slows down.
Therefore:
the graph becomes less steep
Linking Graph Shape to Particle Collisions
The graph can be connected directly to:
collision theory
At the beginning:
high concentration → many particles → frequent collisions → faster reaction
Later:
lower concentration → fewer reactant particles → fewer successful collisions → slower reaction
Therefore:
concentration decreases → collision frequency decreases → reaction rate decreases
This explains the curved shape commonly seen on concentration-time graphs.
Calculating Average Rate
Suppose a reactant concentration decreases from:
0.80 mol/L
to:
0.50 mol/L
during a period of:
15 seconds
Decrease in concentration:
0.80 − 0.50 = 0.30 mol/L
Average rate of disappearance:
rate = 0.30 ÷ 15
rate = 0.020 mol/L/s
Therefore:
average rate = 0.020 mol L⁻¹ s⁻¹
Average Rate Over a Time Interval
Suppose this information is obtained from a graph:
At 10 seconds:
[A] = 0.80 mol/L
At 30 seconds:
[A] = 0.40 mol/L
Change in time:
30 − 10 = 20 s
Decrease in concentration:
0.80 − 0.40 = 0.40 mol/L
Average rate:
0.40 ÷ 20 = 0.020 mol/L/s
The average rate of disappearance of A is:
0.020 mol L⁻¹ s⁻¹
Average Rate vs Instantaneous Rate
The rate of a reaction often changes continuously.
An average rate describes the rate over:
a time interval
An instantaneous rate describes the rate at:
one particular moment
The instantaneous rate can be estimated by drawing:
a tangent to the curve
at the required point.
Tangents
A tangent is a straight line that touches a curve at a particular point and follows the direction of the curve there.
The gradient of the tangent gives the:
instantaneous rate of change
For a decreasing reactant graph:
steeper tangent → faster disappearance
shallower tangent → slower disappearance
Calculating a Tangent Gradient
Suppose a tangent passes through two convenient points:
(20 s, 0.70 mol/L)
and:
(40 s, 0.30 mol/L)
Gradient:
gradient = change in concentration / change in time
gradient = (0.30 − 0.70) / (40 − 20)
gradient = −0.40 / 20
gradient = −0.020 mol L⁻¹ s⁻¹
The negative sign indicates that the reactant concentration is:
decreasing
The magnitude of its instantaneous rate of disappearance is:
0.020 mol L⁻¹ s⁻¹
Why Is Reactant Gradient Negative?
For a reactant:
concentration decreases as time increases
Therefore:
Δconcentration is negative
So the mathematical gradient is:
negative
This does not mean the reaction has a "negative rate."
It means the measured reactant concentration is:
decreasing
Product Graphs Have Positive Gradients
For a product:
concentration usually increases with time
Therefore:
Δconcentration is positive
and the concentration-time graph has a:
positive gradient
At the beginning, the product curve may be steep.
Later, it becomes less steep as the reaction slows.
Eventually, it may become:
horizontal
Reactant and Product on the Same Graph
For a simple reaction:
A → B
the graphs may look like this:
- A begins high and decreases.
- B begins low and increases.
- Both curves gradually flatten.
The graph makes it easy to see how reactant disappearance is connected to:
product formation
When Has a Reaction Reached Completion?
For many simple reactions that effectively proceed to completion, the reaction is complete when the limiting reactant has been:
used up
On a concentration-time graph, this is often indicated when the measured concentrations:
stop changing
The curves become:
horizontal
This means:
gradient = 0
and there is no further net concentration change.
Does Reactant Concentration Always Reach Zero?
No.
A graph can level off while some measured reactant remains.
This can happen because:
- another reactant was the limiting reactant
- the measured reactant was present in excess
- the reaction is reversible and has reached equilibrium
Therefore:
a horizontal graph does not automatically mean every reactant has been completely consumed
This is an important distinction.
Completion vs Equilibrium
These ideas should not be confused.
Reaction completion
A limiting reactant has effectively been consumed and the reaction no longer proceeds significantly because the required reactant is unavailable.
Dynamic equilibrium
In a reversible reaction:
forward reaction continues
and:
reverse reaction continues
but they occur at equal rates.
Therefore, concentrations remain:
constant
A concentration-time graph can become horizontal in both situations.
Context is needed to decide:
why
the concentrations have stopped changing.
Identifying Completion from a Simple Graph
For an introductory irreversible reaction, suppose the product concentration rises and then becomes constant after:
50 seconds
We can say:
The reaction is effectively complete by about 50 s because the product concentration no longer changes.
Likewise, if the limiting reactant reaches zero concentration:
that reactant has been completely consumed
Comparing Reaction Rates
Concentration-time graphs are particularly useful for comparing:
different reactions or different conditions
Suppose two experiments use the same reaction.
Reaction A has a much steeper initial curve than Reaction B.
We can conclude:
Reaction A initially has the greater rate
because its concentration changes more quickly.
Comparing Two Reactions
Consider these illustrative results:
| Time (s) | Reactant A (mol/L) | Reactant B (mol/L) |
|---|---|---|
| 0 | 1.00 | 1.00 |
| 10 | 0.55 | 0.80 |
| 20 | 0.32 | 0.63 |
| 30 | 0.25 | 0.50 |
| 40 | 0.25 | 0.40 |
| 50 | 0.25 | 0.34 |
| 60 | 0.25 | 0.30 |
| 70 | 0.25 | 0.27 |
| 80 | 0.25 | 0.25 |
Reaction A:
- has a steeper initial slope
- changes concentration more rapidly
- reaches its final concentration sooner
Therefore:
Reaction A is faster under these conditions.
Notice that both eventually reach the same final concentration.
Same Final Concentration, Different Rates
Two reactions can produce graphs that level off at the:
same final concentration
but reach that value at different times.
This means they may have:
different rates
but the same overall concentration change.
For example:
fast reaction → reaches plateau in 30 s
slow reaction → reaches plateau in 80 s
The final amount changed is the same.
Only the:
time required
is different.
Rate Does Not Mean Amount
This distinction is very important.
Reaction rate tells us:
how fast
a reaction occurs.
It does not necessarily tell us:
how much product is ultimately formed
A faster reaction does not automatically produce:
more product
It may simply produce the same amount:
more quickly
Different Final Concentrations
Now imagine two product curves.
Reaction A levels off at:
0.80 mol/L
Reaction B levels off at:
0.50 mol/L
This tells us that the final product concentrations are:
different
But we cannot determine the reason from graph shape alone.
Possible reasons might include:
- different starting quantities
- different limiting reactants
- different reaction conditions
- different equilibrium positions
Always use the information provided with the graph.
Effect of Temperature
Increasing temperature often increases reaction rate.
Particles have:
more kinetic energy
They move faster and collide more frequently.
A greater fraction of collisions also have enough energy to overcome:
activation energy
Therefore, a higher-temperature reaction may show:
a steeper concentration-time curve
and reach its final concentration:
sooner
Effect of Concentration
Increasing the concentration of a reactant places:
more reactant particles in a given volume
This generally increases:
collision frequency
and can increase reaction rate.
Therefore, under otherwise identical conditions, a higher reactant concentration may produce:
a greater initial rate
However, if starting concentrations differ, be careful when comparing raw slopes because the graphs may begin at different values.
Effect of a Catalyst
A catalyst increases reaction rate by providing an alternative reaction pathway with:
lower activation energy
With a catalyst:
- concentration changes more quickly
- the initial curve is steeper
- the reaction reaches its final state sooner
For a reaction that proceeds to the same completion under both conditions, a catalyst does not change:
the final amount produced
It changes:
how quickly that state is reached
Catalyst Graph
Suppose the same reaction is performed:
with a catalyst
and:
without a catalyst
The catalyzed reaction would generally show:
steeper initial concentration change
and reach the plateau:
earlier
If the catalyst does not change the overall reaction outcome, both curves eventually reach:
the same final concentration
Surface Area and Concentration-Time Graphs
For reactions involving a solid, increasing surface area can increase reaction rate.
For example:
powdered calcium carbonate
usually reacts faster than:
large calcium carbonate pieces
because more particles are exposed for collisions.
On an appropriate concentration-time graph, the faster reaction would show:
a steeper initial concentration change
Three Important Features to Examine
Whenever you see a concentration-time graph, look for:
1. Direction
Is concentration:
increasing or decreasing?
This can help identify whether the substance is behaving as a product or reactant.
2. Gradient
How steep is the graph?
This tells you about:
reaction rate
3. Plateau
When does the graph become horizontal?
This tells you when:
the measured concentrations stop changing
A Simple Graph-Reading Strategy
Use:
D-G-P
D — Direction
Is the concentration increasing or decreasing?
G — Gradient
Is the graph steep, shallow, or horizontal?
P — Plateau
When does the concentration stop changing?
This gives a quick method for interpreting most introductory concentration-time graphs.
Steep, Shallow, Flat
A concentration-time curve can often be divided into three stages.
Early reaction
steep
The reaction is relatively fast.
Middle of reaction
less steep
The reaction is slowing.
Final stage
horizontal
Concentration is no longer changing.
So:
steep → fast
shallow → slower
flat → zero net concentration change
Reading Numerical Information
Suppose a graph shows:
[A] at 0 s = 1.20 mol/L
and:
[A] at 40 s = 0.60 mol/L
The change is:
1.20 − 0.60 = 0.60 mol/L
If the concentration later becomes constant at:
0.40 mol/L
then the total decrease is:
1.20 − 0.40 = 0.80 mol/L
Graphs therefore provide both:
qualitative information
and:
quantitative information
Qualitative vs Quantitative Interpretation
A qualitative description might say:
"The reactant concentration decreases rapidly at first and then more slowly."
A quantitative description might say:
"The reactant concentration decreases from 1.0 mol/L to 0.5 mol/L during the first 20 seconds."
Strong scientific analysis often combines:
both
Comparing Initial Rates
When comparing reactions, examine the graph:
near time = 0
The reaction with the steeper initial slope has the:
greater initial rate
For a decreasing reactant graph, this means the curve drops more sharply.
For an increasing product graph, it means the curve rises more sharply.
Comparing Completion Times
Suppose:
Reaction A becomes horizontal at 25 s
and:
Reaction B becomes horizontal at 70 s
If the graphs represent comparable irreversible reactions, Reaction A reaches its final state:
sooner
This provides evidence that Reaction A proceeds more rapidly overall under those conditions.
Initial Rate vs Average Rate
Be careful with these terms.
Initial rate
is the rate:
right at the beginning of the reaction
It can be estimated from a tangent near:
t = 0
Average rate
is calculated over:
a chosen time interval
These values may differ because the reaction rate changes with time.
Why Rate Changes During a Reaction
For many reactions:
reactants are gradually consumed
Therefore:
reactant concentration decreases
which often causes:
collision frequency to decrease
Therefore:
reaction rate decreases
This creates the characteristic curved concentration-time graph.
Reversible Reactions
Some reactions can occur in:
both directions
For example:
A + B ⇌ C + D
Initially, the forward reaction may dominate.
As products accumulate, the reverse reaction becomes more significant.
Eventually:
forward rate = reverse rate
The system reaches:
dynamic equilibrium
Concentration-Time Graph at Equilibrium
At equilibrium:
reactant concentrations remain constant
and:
product concentrations remain constant
Therefore, concentration-time curves become:
horizontal
But the reaction has not stopped.
At the particle level:
forward and reverse reactions continue
at equal rates.
Completion and Equilibrium Look Similar
Both can produce:
horizontal concentration-time curves
But they mean different things.
Completion
A limiting reactant is effectively used up.
Equilibrium
Reactants and products continue interconverting, but their concentrations remain constant because:
forward rate = reverse rate
Always consider whether the reaction is described as:
irreversible or reversible
Common Misconception: A Flat Line Means Concentration Is Zero
A horizontal line means:
concentration is constant
It does not necessarily mean:
concentration = zero
For example, a reactant concentration might level off at:
0.30 mol/L
That substance is still present.
Its concentration simply is not changing.
Common Misconception: The Highest Graph Means the Fastest Reaction
Reaction rate is determined by:
gradient
not simply the height of the curve.
A high concentration does not automatically mean:
a high reaction rate
When interpreting rate from a graph, examine:
how quickly concentration is changing
Common Misconception: A Faster Reaction Makes More Product
A faster reaction produces product:
more quickly
It does not necessarily produce:
more product overall
Two reactions may reach exactly the same final product concentration but at:
different times
Common Misconception: The Reaction Rate Is Constant
If a concentration-time graph is curved, its gradient changes.
Therefore:
the reaction rate is changing
A straight sloping line would indicate a constant rate of concentration change.
Most reactions do not maintain exactly the same rate throughout.
Common Misconception: A Reaction Stops Because Time Has Passed
Time itself does not cause a reaction to stop.
A reaction may stop changing because:
- a limiting reactant has been consumed
- suitable reactants are no longer available
- equilibrium has been reached
The explanation must come from:
the chemistry of the system
Worked Example 1
A reactant concentration changes as follows:
| Time (s) | Concentration (mol/L) |
|---|---|
| 0 | 1.00 |
| 20 | 0.65 |
| 40 | 0.45 |
| 60 | 0.35 |
| 80 | 0.30 |
| 100 | 0.30 |
Question 1
Describe the concentration change.
Answer:
The reactant concentration decreases from 1.00 mol/L to 0.30 mol/L. It decreases rapidly at first, then more slowly, and becomes constant at approximately 80 seconds.
Question 2
When does the measured concentration stop changing?
Answer:
Approximately:
80 seconds
Question 3
Why does the curve become less steep?
Answer:
Reactant concentration decreases, so there are fewer reactant particles available for successful collisions. The reaction rate therefore decreases.
Worked Example 2
A reactant decreases from:
0.90 mol/L
to:
0.60 mol/L
during the first:
10 seconds
Calculate the average rate of disappearance.
Change in concentration:
0.90 − 0.60 = 0.30 mol/L
Rate:
0.30 ÷ 10 = 0.030 mol/L/s
Therefore:
average rate = 0.030 mol L⁻¹ s⁻¹
Worked Example 3
Two reactions begin with the same reactant concentration.
After 20 seconds:
Reaction A: 0.30 mol/L remaining
Reaction B: 0.65 mol/L remaining
Assuming the reactions are otherwise comparable, which has consumed reactant faster?
Reaction A
More reactant has disappeared during the same time interval.
Its concentration-time graph would have a:
greater average downward gradient magnitude
over that interval.
Worked Example 4
A product concentration rises quickly and then becomes constant at:
0.75 mol/L
after approximately:
45 seconds
What does this tell us?
For a simple irreversible reaction, it suggests:
- product formed rapidly at first
- product formation slowed
- no further net product formation is occurring after about 45 s
The final product concentration is:
0.75 mol/L
Exam-Style Graph Analysis
Suppose a question asks:
"Explain why the reaction rate decreases between 20 s and 60 s."
A weak answer:
"The graph gets flatter."
A better answer:
"The graph becomes less steep, showing that concentration changes more slowly."
A strong answer:
"As reactants are consumed, their concentrations decrease. This reduces the frequency of successful collisions between reactant particles, so the reaction rate decreases and the concentration-time curve becomes less steep."
The strongest answers connect:
graph evidence → particle explanation → reaction rate
A Useful Answer Structure
For graph interpretation, use:
Observation → Meaning → Explanation
For example:
Observation: The curve is steepest during the first 10 seconds.
Meaning: The reaction rate is greatest during this interval.
Explanation: Reactant concentration is highest near the beginning, producing more frequent successful collisions.
This structure produces clear scientific explanations.
Check Your Understanding
1. What quantity is normally shown on the x-axis of a concentration-time graph?
2. What normally happens to reactant concentration as a reaction proceeds?
3. What normally happens to product concentration?
4. What does a steep concentration-time curve indicate about reaction rate?
5. Why does a concentration-time curve often become less steep as a reaction proceeds?
6. A reactant decreases from 0.80 mol/L to 0.50 mol/L in 15 s. Calculate its average rate of disappearance.
7. Two reactions reach the same final concentration, but Reaction A reaches it in 30 s while Reaction B requires 70 s. What does this tell you about their rates?
8. What does a horizontal section of a concentration-time graph mean?
9. Explain why a horizontal curve does not necessarily mean that the concentration is zero.
10. Explain the difference between a reaction reaching completion and a reversible reaction reaching dynamic equilibrium.
Key Terms
- Concentration: Amount of a substance present per unit volume.
- Concentration-time graph: Graph showing how the concentration of a substance changes with time.
- Reactant: Starting substance consumed during a chemical reaction.
- Product: Substance formed during a chemical reaction.
- Reaction rate: Measure of how quickly reactants are consumed or products are formed.
- Gradient: Rate of change represented by the slope of a graph.
- Average rate: Change in concentration divided by a time interval.
- Instantaneous rate: Reaction rate at a particular moment.
- Tangent: Straight line touching a curve at a point and used to estimate instantaneous gradient.
- Initial rate: Reaction rate at the beginning of a reaction.
- Limiting reactant: Reactant that is consumed first and limits the amount of product that can form.
- Excess reactant: Reactant remaining after the limiting reactant has been consumed.
- Completion: Stage at which an irreversible reaction can no longer proceed significantly because the limiting reactant has effectively been consumed.
- Dynamic equilibrium: State in a reversible reaction where forward and reverse reactions continue at equal rates.
- Catalyst: Substance that increases reaction rate by providing an alternative pathway with lower activation energy.
- Collision theory: Model explaining reaction rates in terms of collisions between reacting particles.
- Activation energy: Minimum energy required for a successful reaction-producing collision.
Key Takeaways
- Concentration-time graphs show how the concentration of a substance changes as a reaction proceeds.
- Time is normally plotted on the x-axis and concentration on the y-axis.
- Reactant concentrations generally decrease as reactants are consumed.
- Product concentrations generally increase as products are formed.
- The gradient of a concentration-time graph provides information about reaction rate.
- Steeper gradient = faster concentration change.
- Shallower gradient = slower concentration change.
- Horizontal line = concentration is no longer changing.
- Reactions are often fastest near the beginning because reactant concentrations are highest.
- As reactants are consumed, concentrations decrease and successful collisions generally become less frequent.
- Average rate can be calculated using change in concentration ÷ change in time.
- A tangent can be used to estimate instantaneous reaction rate.
- Reactant concentration graphs have negative gradients because reactants are being consumed.
- Product concentration graphs usually have positive gradients while products are being formed.
- Two reactions can reach the same final concentration at different rates.
- A faster reaction does not necessarily produce more product; it may simply reach the same final state sooner.
- Temperature, concentration, catalysts, and surface area can affect the shape of concentration-time graphs by changing reaction rate.
- A plateau means the measured concentration has become constant, not necessarily zero.
- For a simple irreversible reaction, a plateau can indicate that the reaction has effectively reached completion.
- For a reversible reaction, a plateau can indicate dynamic equilibrium rather than completion.
- When interpreting graphs, use Direction → Gradient → Plateau.
- Strong explanations connect graph shape → reaction rate → particle collisions.