1. Concentration-Time Graphs

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:

2. Product Formation Graphs

What Is a Product Formation Graph?

As a chemical reaction occurs:

reactants are consumed

and:

products are formed

A product formation graph shows how the amount or concentration of a product changes as time passes.

The graph can help us determine:

• how much product has formed
• how quickly product is being produced
• how the reaction rate changes
• when the reaction stops producing additional product
• how different reaction conditions affect reaction rate

These graphs are closely related to concentration-time graphs, but instead of focusing on disappearing reactants, we focus on:

appearing products

---

Understanding the Axes

A typical product formation graph has:

x-axis → time

y-axis → amount or concentration of product

The y-axis might show:

• concentration in mol/L
• mass in grams
• volume of gas in cm³
• amount in moles

Always read the:

axis label + units

before interpreting the graph.

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Product Concentration Increases

At the beginning of many reactions, there may be:

little or no product

As reactant particles react:

product particles are formed

Therefore:

product concentration increases with time

A typical pattern is:

rapid increase → slower increase → plateau

---

A Typical Product Formation Graph

Consider these illustrative data:

3. Determining Rate from Graphs

Reaction Graphs Tell Us More Than What Happened

Reaction graphs do more than show how the amount of a substance changes.

They can also tell us:

how quickly the change is happening

This is the:

reaction rate

The key mathematical idea is:

gradient

A steep graph represents a rapid change.

A shallow graph represents a slower change.

A horizontal graph represents:

no net change

By calculating gradients, we can turn the shape of a graph into a numerical measurement of reaction rate.

---

The Basic Rate Equation

Reaction rate compares:

change in a measured quantity

with:

change in time

The general relationship is:

average rate = change in quantity ÷ change in time

This can also be written as:

Average rate = Δy / Δt

where:

• Δy = change in the quantity shown on the y-axis
• Δt = change in time
• Δ means "change in"

The quantity might be:

• concentration
• mass
• gas volume
• amount of substance

---

What Is Gradient?

The gradient of a graph tells us how quickly the y-value changes compared with the x-value.

For reaction graphs:

gradient = change in measured quantity / change in time

or:

gradient = Δy / Δx

Because time is normally on the x-axis:

gradient = Δy / Δt

This makes gradient extremely useful for measuring:

reaction rate

---

Rise Over Run

Another way to remember gradient is:

gradient = rise / run

where:

rise = vertical change

and:

run = horizontal change

For a reaction graph:

vertical change = change in concentration, mass, or volume

horizontal change = change in time

---

Average Rate

An average rate describes how quickly something changes over a:

time interval

Suppose a reaction produces:

60 cm³ of gas

during:

30 seconds

Average rate:

60 cm³ ÷ 30 s

= 2.0 cm³/s

Therefore:

average rate = 2.0 cm³/s

---

Finding Average Rate from a Graph

Consider this illustrative product-formation data:

The graph would rise rapidly at first and gradually become horizontal.

To calculate the average rate between:

10 s and 30 s

read the corresponding values:

At 10 s:

28 cm³

At 30 s:

57 cm³

---

Step 1: Calculate the Change in Product

Δvolume = final volume − initial volume

Δvolume = 57 − 28

Δvolume = 29 cm³

---

Step 2: Calculate the Change in Time

Δtime = final time − initial time

Δtime = 30 − 10

Δtime = 20 s

---

Step 3: Calculate the Average Rate

average rate = 29 / 20

average rate = 1.45 cm³/s

Therefore:

Average rate from 10–30 s = 1.45 cm³/s

---

A Common Calculation Error

Suppose we want the average rate between:

20 s and 50 s

Do not divide the product amount at 50 s by 50.

Instead, calculate the:

change between the two selected points

At 20 s:

46 cm³

At 50 s:

66 cm³

Change in product:

66 − 46 = 20 cm³

Change in time:

50 − 20 = 30 s

Therefore:

average rate = 20 / 30

= 0.67 cm³/s

approximately.

The rule is:

always calculate change in y and change in x

---

Units of Reaction Rate

Rate units depend on:

what the graph measures

If the graph shows:

gas volume in cm³

and:

time in seconds

then rate units are:

cm³/s

If the graph shows:

concentration in mol/L

then:

mol L⁻¹ s⁻¹

If the graph shows:

mass in grams

then:

g/s

Always derive rate units from:

y-axis unit ÷ x-axis unit

---

Positive Gradients

A product formation graph usually rises.

For example:

gas volume increases with time

Therefore:

Δy is positive

and:

gradient is positive

A positive gradient means the measured quantity is:

increasing

For a product graph, this usually represents:

product formation

---

Negative Gradients

A reactant concentration usually:

decreases

as the reaction proceeds.

Therefore, its graph may slope downward.

For example:

At 10 s:

[A] = 0.80 mol/L

At 30 s:

[A] = 0.50 mol/L

Gradient:

(0.50 − 0.80) / (30 − 10)

= −0.30 / 20

= −0.015 mol L⁻¹ s⁻¹

The negative sign tells us:

reactant concentration is decreasing

---

Rate of Disappearance

Although a reactant concentration graph has a negative gradient, we often report its:

rate of disappearance

as a positive magnitude.

So if:

gradient = −0.015 mol L⁻¹ s⁻¹

we may say:

rate of disappearance = 0.015 mol L⁻¹ s⁻¹

The negative gradient describes:

direction of change

The positive magnitude describes:

how quickly the reactant disappears

---

Straight-Line Graphs

If a reaction graph is a straight line, its gradient is:

constant

This means the measured quantity changes at a:

constant rate

For example:

0 s → 0 cm³

10 s → 20 cm³

20 s → 40 cm³

30 s → 60 cm³

Every 10 seconds:

20 cm³ more product forms

Therefore:

rate = 20 / 10 = 2 cm³/s

throughout that interval.

---

Curved Reaction Graphs

Most reaction graphs are not perfectly straight.

They are:

curved

A curved graph means:

the gradient is changing

Therefore:

the reaction rate is changing

This is why we need to distinguish between:

average rate

and:

instantaneous rate

---

Average Rate vs Instantaneous Rate

Average Rate

Measures the rate over:

a time interval

For example:

average rate between 10 s and 30 s

Instantaneous Rate

Measures the rate at:

one particular moment

For example:

rate at exactly 20 s

These are different quantities.

---

Why Do We Need Instantaneous Rate?

Imagine driving a car.

Your average speed during a one-hour journey might be:

60 km/h

But at one particular moment, your speedometer might show:

85 km/h

Reaction rates work similarly.

An average rate tells us about:

an interval

An instantaneous rate tells us about:

one moment

---

Finding Instantaneous Rate

For a curved graph, we cannot simply use the gradient of the entire curve.

Instead, we draw:

a tangent

at the point we want to investigate.

A tangent is a straight line that touches the curve at that point and follows its direction there.

The gradient of the tangent estimates:

the instantaneous rate

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How to Draw a Tangent

Suppose you want to find the reaction rate at:

30 seconds

Step 1

Find:

30 s

on the x-axis.

Step 2

Find the corresponding point on the reaction curve.

Step 3

Draw a straight line that:

just touches the curve at that point

and follows the direction of the curve.

Step 4

Extend the tangent so that you can select:

two widely separated points

on the tangent.

Step 5

Calculate:

gradient = Δy / Δt

The result estimates the:

instantaneous rate at 30 s

---

Use Points on the Tangent

This is extremely important.

When calculating instantaneous rate:

use points on the tangent

not necessarily points on the original curve.

The tangent is a:

straight line

so its gradient can be calculated accurately.

---

Use a Large Triangle

When finding the gradient of a tangent, choose points that are:

far apart

on the tangent.

Why?

A larger gradient triangle generally reduces the effect of:

small reading errors

So instead of choosing two points very close together:

use as much of the tangent as practical

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Worked Example: Instantaneous Rate

Suppose a tangent drawn at 20 s passes through:

(10 s, 25 cm³)

and:

(30 s, 55 cm³)

Change in product:

55 − 25 = 30 cm³

Change in time:

30 − 10 = 20 s

Gradient:

30 / 20

= 1.5 cm³/s

Therefore:

instantaneous rate at 20 s ≈ 1.5 cm³/s

The approximation symbol is useful because the tangent itself is:

an estimate

---

Comparing Rates at Different Times

A reaction often begins quickly and then slows.

Suppose the instantaneous rates are:

At 10 s:

2.8 cm³/s

At 30 s:

1.4 cm³/s

At 50 s:

0.3 cm³/s

We can conclude:

reaction rate decreases with time

The graph becomes progressively:

less steep

---

Why Does Rate Decrease?

As the reaction proceeds:

reactants are consumed

Therefore:

reactant concentrations decrease

There are fewer reactant particles available for:

successful collisions

As a result:

successful collision frequency decreases

and:

reaction rate decreases

This produces the typical curved shape.

---

Connecting Gradient to Collision Theory

The relationship can be summarized:

high reactant concentration

↓

frequent successful collisions

↓

fast reaction

↓

steep graph

As the reaction proceeds:

lower reactant concentration

↓

fewer successful collisions

↓

slower reaction

↓

shallower graph

---

Comparing Early and Late Gradients

Consider a product graph.

Near the beginning:

large gradient

Later:

smaller gradient

Finally:

gradient ≈ 0

This corresponds to:

fast → slower → no further net product formation

The gradient therefore provides a mathematical description of:

reaction progress

---

The Gradient at Completion

When a product graph becomes horizontal:

Δy = 0

Therefore:

gradient = 0 / Δt

and:

gradient = 0

For a simple irreversible reaction, this means:

no additional product is being formed

The reaction has effectively:

reached completion

---

Reaction Graph Regions

A typical reaction graph can be interpreted in three regions.

Region 1 — Steep

large gradient

The reaction is:

fast

Region 2 — Curving

decreasing gradient

The reaction is:

slowing

Region 3 — Plateau

gradient ≈ 0

There is:

no further net change

---

Comparing Two Reactions

Suppose Reaction A and Reaction B are plotted on the same graph.

Reaction A has a steeper initial slope.

Reaction B has a shallower initial slope.

We can conclude:

Reaction A has a greater initial rate

provided the graphs show comparable measured quantities and scales.

---

Same Final Amount, Different Rates

Suppose both reactions eventually produce:

80 cm³ of gas

but:

Reaction A reaches 80 cm³ in 40 s

while:

Reaction B reaches 80 cm³ in 90 s

Reaction A is:

faster

but both produce:

the same final amount

This demonstrates:

gradient → rate

while:

plateau height → final amount

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Different Rates at the Same Time

Suppose at 20 s:

Reaction A has a tangent gradient of:

2.0 cm³/s

Reaction B has a tangent gradient of:

1.1 cm³/s

Therefore, at 20 s:

Reaction A is producing gas more rapidly

This is a comparison of:

instantaneous rates

---

Different Rates Within the Same Reaction

We can also compare the reaction with:

itself

at different times.

For example:

At 10 s:

rate = 3.0 cm³/s

At 30 s:

rate = 1.5 cm³/s

At 50 s:

rate = 0.4 cm³/s

This tells us:

the reaction is slowing down

---

Percentage Decrease in Rate

Sometimes we can quantify how much the rate changes.

Suppose:

Initial rate:

2.0 cm³/s

Later rate:

0.5 cm³/s

Decrease:

2.0 − 0.5 = 1.5 cm³/s

Percentage decrease:

1.5 / 2.0 × 100

= 75%

The rate has decreased by:

75%

---

Product Graphs

For a product formation graph:

positive gradient → product forming

large positive gradient → rapid product formation

small positive gradient → slow product formation

zero gradient → no further net product formation

The gradient generally decreases as the reaction progresses.

---

Reactant Graphs

For a reactant concentration graph:

negative gradient → reactant being consumed

steep negative gradient → rapid reactant consumption

shallow negative gradient → slower consumption

zero gradient → concentration no longer changing

---

Mass-Loss Graphs

Some reactions release gas.

If the gas escapes from the reaction vessel:

measured mass decreases

For example:

acid + carbonate → salt + water + carbon dioxide

As CO₂ escapes:

mass decreases

The graph therefore slopes:

downward

The magnitude of the gradient tells us:

how quickly mass is being lost

---

Gas Volume Graphs

If the gas is collected instead:

gas volume increases

The graph slopes:

upward

Even though one graph decreases and the other increases, both can measure the rate of:

the same reaction

This is why you must always read:

the axes

before interpreting the graph.

---

Units from Different Graphs

The units come directly from:

y-axis units ÷ x-axis units

---

Graph Scale Matters

Two graphs can look very different simply because they use:

different axis scales

A visually steeper curve does not automatically mean a faster reaction if the graphs use different scales.

For reliable comparisons:

• check the x-axis scale
• check the y-axis scale
• check the units
• calculate gradients when necessary

Never compare graph steepness without first checking:

the axes

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Worked Example 1: Average Rate

A gas-producing reaction gives:

Calculate the average rate from:

20 s to 60 s

Change in volume:

76 − 40 = 36 cm³

Change in time:

60 − 20 = 40 s

Rate:

36 / 40

= 0.90 cm³/s

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Worked Example 2: Overall Average Rate

Using the same data, calculate the average rate from:

0 to 80 s

Change in volume:

80 − 0 = 80 cm³

Change in time:

80 − 0 = 80 s

Average rate:

80 / 80

= 1.0 cm³/s

Notice that this does not mean the reaction rate was:

1.0 cm³/s at every moment

It is only the:

average over the entire interval

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Worked Example 3: Reactant Concentration

A reactant concentration decreases from:

1.20 mol/L

at 10 s to:

0.60 mol/L

at 40 s.

Gradient:

(0.60 − 1.20) / (40 − 10)

= −0.60 / 30

= −0.020 mol L⁻¹ s⁻¹

Therefore:

gradient = −0.020 mol L⁻¹ s⁻¹

and the average rate of disappearance is:

0.020 mol L⁻¹ s⁻¹

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Worked Example 4: Tangent

A tangent drawn at 25 s passes through:

(10 s, 18 cm³)

and:

(40 s, 60 cm³)

Change in volume:

60 − 18 = 42 cm³

Change in time:

40 − 10 = 30 s

Gradient:

42 / 30

= 1.4 cm³/s

Therefore:

instantaneous rate at 25 s ≈ 1.4 cm³/s

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Worked Example 5: Comparing Rates

Reaction A has an initial gradient of:

2.4 cm³/s

Reaction B has an initial gradient of:

1.6 cm³/s

Difference:

2.4 − 1.6 = 0.8 cm³/s

Therefore, Reaction A initially produces product:

0.8 cm³/s faster

than Reaction B.

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Worked Example 6: Rate at Completion

A product graph becomes horizontal after:

70 seconds

What is the gradient after 70 seconds?

Because the product amount remains constant:

Δy = 0

Therefore:

gradient = 0

For a simple irreversible reaction:

no further product is being formed

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Experimental Data and Scatter

Real experimental results rarely produce perfectly smooth curves.

Data may contain:

scatter

Small variations may occur because of:

• measurement uncertainty
• timing uncertainty
• temperature fluctuations
• reading errors
• limitations of equipment

Scientists therefore often draw:

a smooth curve of best fit

rather than connecting every data point with straight lines.

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Tangents and Experimental Data

When using experimental data:

1. Draw an appropriate curve of best fit.
2. Identify the required time.
3. Draw a tangent to the curve.
4. Choose two widely separated points on the tangent.
5. Calculate the gradient.

This provides an estimate of:

instantaneous reaction rate

---

Why Tangent Rates Are Estimates

A tangent drawn by hand will not be:

perfectly exact

Two students may draw slightly different tangents and calculate slightly different rates.

This is acceptable if:

• the tangent is reasonable
• a large gradient triangle is used
• calculations are correct
• units are included

Therefore, instantaneous rates obtained graphically are often reported as:

approximate values

---

Interpreting Graphical Evidence

Calculations are only part of graph analysis.

You should also be able to explain:

what the graph tells us about the reaction

For example:

The curve is steepest during the first 10 seconds, indicating the greatest reaction rate. The gradient decreases with time as reactants are consumed. After approximately 60 seconds, the graph becomes horizontal, showing that there is no further net product formation.

This combines:

observation + calculation + chemical explanation

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A Strong Graph Analysis Structure

Use:

Observe → Quantify → Explain

Observe

Describe what the graph does.

"The curve becomes less steep."

Quantify

Use numbers or gradients.

"The rate decreases from approximately 2.5 cm³/s to 0.6 cm³/s."

Explain

Use chemistry.

"Reactants are being consumed, so successful collisions become less frequent."

This creates a much stronger scientific response.

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Comparing Reaction Conditions

Suppose two curves represent the same reaction:

Curve A: higher temperature

Curve B: lower temperature

If Curve A has a greater initial gradient:

higher temperature produced a faster initial reaction

This can be explained because particles have:

greater kinetic energy

and a larger fraction of collisions can overcome:

activation energy

---

Catalyst Graphs

Suppose two experiments differ only by the presence of a catalyst.

The catalyzed reaction generally has:

a greater gradient

and reaches the plateau:

sooner

If both experiments contain the same reactant amounts and reach the same completion:

final product amount remains the same

The catalyst changes:

rate

not the stoichiometric amount of product available.

---

Concentration and Graph Gradient

Higher reactant concentration usually increases:

collision frequency

Therefore, the initial gradient may be:

greater

A graph can therefore provide evidence about how concentration affects:

reaction rate

---

Surface Area and Graph Gradient

For reactions involving solids:

greater surface area

means more particles are exposed.

This increases collision opportunities.

Therefore:

greater surface area → greater initial gradient

For example:

powdered calcium carbonate

will generally react faster than the same mass of:

large calcium carbonate pieces

under otherwise identical conditions.

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Common Misconception: Rate Is the Height of the Graph

Rate is not determined by:

how high the graph is

Rate is determined by:

gradient

A graph can be very high but completely horizontal.

In that case:

rate of change = 0

Remember:

height → amount

gradient → rate

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Common Misconception: Use y ÷ x for Every Gradient

This only works if your interval begins at:

(0,0)

For any two general points, you must calculate:

(y₂ − y₁) / (x₂ − x₁)

Always use:

change in y ÷ change in x

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Common Misconception: Use Curve Points to Calculate a Tangent Gradient

For instantaneous rate:

draw the tangent first

Then select two points:

on the tangent

They do not have to be points on the original reaction curve.

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Common Misconception: A Steep Downward Graph Means a Slow Reaction

A steep downward slope has a:

large negative gradient

Its magnitude is large.

Therefore, it represents:

rapid decrease

For a reactant:

steep downward slope = rapid reactant consumption

---

Common Misconception: Negative Rate Means the Reaction Is Going Backward

A negative gradient usually means:

the measured quantity is decreasing

For example:

reactant concentration decreases

or:

mass decreases because gas escapes

It does not automatically mean the chemical reaction is:

running backward

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Common Misconception: Average Rate Equals Rate at Every Moment

If the graph is curved:

rate changes continuously

The average rate describes the entire selected interval.

It does not necessarily equal the rate at:

any particular moment

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Common Misconception: The Steepest-Looking Graph Is Always Fastest

Before comparing curves on different graphs, check:

• axis scales
• units
• quantities measured
• time intervals

Visual appearance alone can be:

misleading

Calculating gradients provides stronger evidence.

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Graph Interpretation Checklist

When given a reaction graph, ask:

1. What is on the x-axis?

Usually:

time

2. What is on the y-axis?

Concentration? Mass? Gas volume?

3. Is the graph increasing or decreasing?

This tells you the:

direction of change

4. How steep is the graph?

This tells you the:

rate

5. Does the gradient change?

This tells you whether the reaction:

speeds up or slows down

6. Does the graph become horizontal?

This indicates:

no further net change in the measured quantity

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Check Your Understanding

1. What does the gradient of a reaction graph represent?

2. A reaction produces 48 cm³ of gas in 24 s. Calculate the average rate.

3. Product volume increases from 30 cm³ at 10 s to 70 cm³ at 30 s. Calculate the average rate between these times.

4. A reactant concentration decreases from 0.90 mol/L to 0.50 mol/L over 20 s. Calculate the gradient.

5. Why is the gradient of a reactant concentration graph usually negative?

6. Explain the difference between average rate and instantaneous rate.

7. Describe how a tangent can be used to estimate instantaneous reaction rate.

8. Why should two widely separated points be selected when calculating a tangent gradient?

9. A reaction graph is steep at 10 s but almost horizontal at 50 s. What does this tell you about how the reaction rate has changed?

10. Explain why reaction graphs often become less steep as the reaction proceeds.

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Key Terms

• Reaction rate: Measure of how quickly reactants are consumed or products are formed.
• Gradient: Change in the y-value divided by the corresponding change in the x-value.
• Average rate: Rate calculated over a specified time interval.
• Instantaneous rate: Rate at one particular moment.
• Initial rate: Reaction rate at the beginning of a reaction.
• Tangent: Straight line touching a curve at a particular point and following its direction there.
• Rate of formation: Speed at which a product is produced.
• Rate of disappearance: Speed at which a reactant is consumed.
• Positive gradient: Gradient produced when the measured quantity increases.
• Negative gradient: Gradient produced when the measured quantity decreases.
• Plateau: Horizontal region where the measured quantity remains approximately constant.
• Curve of best fit: Smooth curve representing the overall pattern of experimental data.
• Collision theory: Model explaining reaction rates through collisions between reacting particles.
• Successful collision: Collision that results in a chemical reaction.
• Activation energy: Minimum energy required for a successful reaction.

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Key Takeaways

• Reaction rates can be determined from the gradients of reaction graphs.
• Average rate = change in measured quantity ÷ change in time.
• Always calculate Δy ÷ Δt, not simply y ÷ t unless the interval begins at the origin.
• Rate units depend on the quantities shown on the graph.
• Gas-volume graphs may give rates in cm³/s.
• Concentration graphs may give rates in mol L⁻¹ s⁻¹.
• Mass graphs may give rates in g/s.
• Product formation graphs usually have positive gradients.
• Reactant concentration graphs usually have negative gradients.
• The magnitude of a gradient indicates how quickly the measured quantity is changing.
• Steep gradient = rapid change.
• Shallow gradient = slow change.
• Horizontal graph = zero net change in the measured quantity.
• A curved graph indicates that reaction rate is changing.
• Average rate describes a time interval.
• Instantaneous rate describes one particular moment.
• Instantaneous rate can be estimated by drawing a tangent to the curve.
• Calculate the gradient using two widely separated points on the tangent.
• Tangent-based rates are estimates and should usually be treated as approximate.
• Reaction rates often decrease with time because reactants are consumed.
• Lower reactant concentrations generally lead to fewer successful collisions.
• Different reaction rates can be compared using gradients at the same time or over equivalent intervals.
• Graph scales and units must be checked before comparing curves.
• Graph height tells us amount; graph gradient tells us rate.
• Strong graph analysis uses Observe → Quantify → Explain.

4. Industrial and Biological Reactions

5. Energy, Rates, and Real-World Applications

Bringing Energy and Reaction Rates Together

Chemical reactions involve two closely related ideas:

energy changes

and:

reaction rates

Energy changes tell us whether energy is:

released or absorbed

Reaction rates tell us:

how quickly a reaction occurs

These ideas are connected, but they are not the same.

A reaction can:

• release a large amount of energy but occur slowly
• release a small amount of energy but occur quickly
• absorb energy and occur quickly
• absorb energy and occur slowly

To understand real chemical processes, we often need to consider:

both energetics and kinetics

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Energetics and Kinetics

Two important branches of chemistry help us understand reactions.

Energetics

Concerned with:

energy changes during reactions

Questions include:

• Is energy released?
• Is energy absorbed?
• How much energy changes?

Kinetics

Concerned with:

reaction rates

Questions include:

• How quickly does the reaction occur?
• What factors affect its rate?
• What mechanism does it follow?

A complete understanding of a reaction often requires:

energetics + kinetics

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Exothermic Reactions

An exothermic reaction transfers energy from the reacting system to the surroundings.

The surroundings may become:

warmer

Examples include:

• combustion
• many oxidation reactions
• acid-base neutralization
• some respiration-related reactions

For an exothermic reaction:

energy released forming new bonds > energy required to break bonds

The overall energy change is:

energy released to the surroundings

---

Endothermic Reactions

An endothermic reaction absorbs energy from the surroundings.

The surroundings may become:

cooler

Examples include:

• some thermal decomposition reactions
• reactions used in certain instant cold packs
• some dissolution processes

For an endothermic reaction:

more energy is required to break bonds than is released when new bonds form

The reaction therefore requires a net input of:

energy

---

Energy Profile Diagrams

An energy profile diagram shows the energy changes occurring during a reaction.

The vertical axis represents:

energy

The horizontal axis represents:

reaction progress

Important features include:

• reactant energy
• product energy
• activation energy
• overall energy change

---

Activation Energy

Even reactions that release energy usually require some energy to:

get started

This minimum energy is called:

activation energy

Symbol:

Eₐ

Particles must collide with sufficient energy to overcome this barrier.

Therefore:

collision + sufficient energy + suitable orientation → successful reaction

---

A Hill Analogy

Imagine pushing a ball over a hill.

The ball may eventually roll down to a:

lower-energy position

But first, you must provide enough energy to push it:

over the hill

The hill represents:

activation energy

This helps explain why an energetically favorable reaction may still:

occur slowly

---

Energy Released Does Not Determine Rate

Consider a piece of wood.

Wood can react with oxygen:

wood + oxygen → combustion products + energy

The reaction releases substantial energy.

Yet a piece of wood can sit in air for:

years

without suddenly bursting into flames.

Why?

Because the reaction requires sufficient:

activation energy

A flame or spark can provide this energy.

This demonstrates:

exothermic does not automatically mean fast

---

Collision Theory

Reaction rate can be explained using:

collision theory

Reacting particles must:

1. collide
2. collide with sufficient energy
3. collide with suitable orientation

Only some collisions are:

successful collisions

The reaction rate depends on:

how frequently successful collisions occur

---

Temperature Connects Energy and Rate

Increasing temperature gives particles more:

kinetic energy

This affects reaction rate in two important ways.

Particles:

move faster

so collisions occur more frequently.

More importantly, a greater fraction of particles have enough energy to overcome:

activation energy

Therefore:

higher temperature → more successful collisions → faster reaction

---

Why Temperature Has Such a Strong Effect

Increasing temperature does not merely make particles:

slightly faster

It also increases the proportion of collisions that have enough energy to overcome the activation-energy barrier.

Therefore, even a moderate increase in temperature can sometimes produce:

a substantial increase in reaction rate

---

Catalysts Connect Energy and Rate

A catalyst increases reaction rate by providing:

an alternative reaction pathway

with a lower:

activation energy

This allows a greater proportion of collisions to become:

successful

Therefore:

lower Eₐ → more successful collisions → faster reaction

---

Catalysts and Energy Profile Diagrams

A catalyst changes the pathway between:

reactants and products

but does not change their starting and finishing energy levels.

Therefore, a catalyst:

lowers activation energy

but does not change the overall energy change of the reaction.

---

What a Catalyst Does NOT Change

A catalyst does not change:

• the energy of the reactants
• the energy of the products
• the overall energy change
• the stoichiometric amount of product possible from given starting amounts

For a reversible reaction, a catalyst also does not change:

the equilibrium position

It simply allows equilibrium to be reached:

more quickly

---

Why Catalysts Matter to Society

Catalysts are enormously important because many useful chemical reactions would otherwise be:

too slow

or require:

more extreme conditions

Catalysts are used in:

• fertilizer manufacture
• fuel processing
• polymer production
• pharmaceuticals
• food production
• vehicle exhaust systems
• biotechnology
• biological metabolism

---

Catalysts Can Save Energy

Suppose an industrial reaction is too slow at:

300°C

Without a catalyst, it might require:

500°C

to reach a useful rate.

If a catalyst allows an acceptable rate at 300°C, the factory may require:

less heating

This can reduce:

• energy consumption
• operating costs
• fuel use
• associated emissions

Catalysts can therefore contribute to:

more efficient chemical production

---

Catalysts Can Improve Selectivity

Some catalysts help favor a particular:

reaction pathway

This can increase production of the:

desired product

and reduce:

unwanted side products

Greater selectivity can mean:

• less waste
• easier purification
• better use of raw materials

This is especially important in:

pharmaceutical and fine-chemical manufacturing

---

Catalysts Also Have Limitations

Catalysts are extremely useful, but their use can involve challenges.

They may:

• be expensive
• require rare materials
• become contaminated
• lose activity
• require replacement
• require recovery after use

Therefore, evaluating a catalyst involves more than simply asking:

"Does it make the reaction faster?"

---

Catalytic Converters

Vehicle engines produce gases that can include harmful pollutants.

A catalytic converter contains catalysts that speed up reactions converting some harmful exhaust gases into:

less harmful products

Catalytic converters demonstrate how catalysts can be used for:

pollution reduction

---

Catalysts and Fertilizer Production

Ammonia is an important starting material for many:

fertilizers

It is manufactured industrially through the Haber process:

N₂ + 3H₂ ⇌ 2NH₃

An iron-based catalyst helps the system reach equilibrium:

more quickly

Without effective catalysis, ammonia production would be:

less practical and more energy-intensive

---

Biological Catalysts

Living organisms also depend on catalysts.

These biological catalysts are:

enzymes

Enzymes allow reactions to occur rapidly at the relatively mild temperatures found inside:

cells

Without enzymes, many reactions required for life would occur:

far too slowly

---

Energy and Respiration

Cells require energy for:

• muscle contraction
• active transport
• growth
• cell division
• protein synthesis
• nerve activity

Cells obtain usable energy through controlled biochemical pathways such as:

cellular respiration

The overall aerobic respiration reaction releases energy:

glucose + oxygen → carbon dioxide + water

But cells do not simply burn glucose in one uncontrolled step.

Instead, enzymes control:

a sequence of reactions

---

Why Controlled Energy Release Matters

Imagine releasing all the chemical energy in glucose:

instantly

Much of it would be released as:

heat

and could damage cells.

Biological pathways allow energy to be released through:

controlled reaction steps

This allows cells to capture useful energy for:

biological work

---

Everyday Example: Food Storage

Reaction rates explain why food is often stored in:

refrigerators

Lower temperatures reduce particle kinetic energy and generally slow:

• enzyme-controlled reactions
• microbial growth and metabolism
• many chemical reactions involved in food deterioration

Therefore:

lower temperature → slower deterioration → longer storage life

---

Refrigeration Does Not Stop Reactions

A refrigerator does not normally stop chemical and biological processes completely.

It:

slows them

This is why refrigerated food still eventually:

spoils

Freezing can slow many processes even further, although it also does not necessarily destroy all microorganisms or permanently stop all chemical change.

---

Everyday Example: Cooking

Cooking involves many chemical changes.

Increasing temperature increases reaction rates.

Processes include:

• protein denaturation
• browning reactions
• starch changes
• breakdown of plant tissues
• flavor-producing reactions

Higher temperatures can make these changes occur:

more quickly

But excessive temperature can cause:

• burning
• unwanted products
• nutrient loss
• undesirable textures

Again:

faster is not always better

---

Everyday Example: Baking

Baking depends on carefully controlled reaction rates.

For example:

baking soda or baking powder

can produce:

carbon dioxide

The gas expands and contributes to:

rising

If gas is produced too early, too late, too quickly, or too slowly, the final texture can be affected.

This demonstrates how reaction rate influences:

product quality

---

Everyday Example: Combustion

Combustion reactions release:

energy

Fuels include:

• natural gas
• gasoline
• diesel
• biomass

A combustion reaction needs:

• fuel
• oxygen
• sufficient activation energy

Once initiated, combustion may proceed rapidly because it releases:

heat

---

Why Fuels Need Ignition

Gasoline contains chemical energy.

Yet gasoline does not necessarily combust immediately simply because oxygen is present.

The reaction requires:

activation energy

A spark in an engine can provide the initial energy needed to begin:

combustion

This is another example showing the distinction between:

stored chemical energy

and:

reaction rate

---

Everyday Example: Hand Warmers

Some hand warmers use chemical reactions that:

release energy

A common type uses oxidation of iron.

The reaction is designed to occur:

slowly enough

to provide useful warmth over an extended period.

If the same energy were released almost instantly, the product would be:

less useful and potentially unsafe

This demonstrates:

usefulness depends on both energy released and rate of release

---

Energy Release: Slow vs Fast

Imagine two reactions release the same total amount of energy.

Reaction A

Releases the energy in:

5 seconds

Reaction B

Releases the energy in:

5 hours

The total energy change may be similar.

But their:

power and practical effects

are very different.

Reaction A releases energy:

much more rapidly

This could make it:

hotter or more difficult to control

---

Everyday Example: Instant Cold Packs

Some cold packs use processes that absorb:

thermal energy

from the surroundings.

The pack becomes:

cooler

This is an example of an:

endothermic process

The usefulness of the pack depends on both:

• the amount of energy absorbed
• how quickly that energy is absorbed

---

Everyday Example: Rusting

Rusting is an oxidation process involving:

iron

It is energetically possible under ordinary conditions, but usually occurs:

relatively slowly

Factors such as:

• water
• oxygen
• salts
• temperature

can affect the rate.

Rusting again shows that:

a reaction can be favorable but slow

---

Why Salt Can Accelerate Corrosion

Dissolved salts can increase the conductivity of water and help electrochemical corrosion processes proceed.

This is why corrosion can be particularly important in:

marine environments

or where roads are treated with:

de-icing salts

Understanding reaction rates helps engineers develop strategies to:

slow corrosion

---

Slowing Reactions Can Be Useful

We often discuss ways to:

increase reaction rate

But sometimes we want the opposite.

Examples include:

• slowing food spoilage
• reducing corrosion
• preventing unwanted oxidation
• slowing decomposition of medicines
• preventing fires
• extending product shelf life

Reaction-rate science is therefore about:

controlling rate

not simply increasing it.

---

Everyday Example: Medicines

Medicines can undergo chemical changes during:

storage

Temperature, light, moisture, and oxygen can affect these reactions.

This is why medicines may have instructions such as:

store below a specified temperature

or:

protect from light

The goal is often to:

slow unwanted chemical reactions

and preserve product quality.

---

Shelf Life

The shelf life of a product is the period during which it remains suitable for its intended use under specified storage conditions.

Reaction rates influence the shelf life of:

• foods
• medicines
• cosmetics
• batteries
• chemicals

Slowing unwanted reactions can:

extend shelf life

---

Everyday Example: Glow Sticks

Glow sticks produce light through:

chemiluminescence

A chemical reaction releases energy that ultimately appears partly as:

visible light

Temperature affects the reaction rate.

A warmer glow stick generally reacts:

faster and more brightly for a shorter time

A colder glow stick generally reacts:

more slowly and less brightly for longer

This is an excellent example of:

temperature → reaction rate → product performance

---

Batteries

Batteries rely on:

redox reactions

to convert chemical energy into electrical energy.

Reaction rates affect:

• current delivery
• performance
• charging and discharging
• temperature behavior

At low temperatures, some battery reactions proceed:

more slowly

This can reduce battery performance.

---

Reaction Rate and Safety

Some reactions can become dangerous if their rate increases too much.

For an exothermic reaction:

reaction releases heat

If heat cannot escape quickly enough:

temperature rises

Higher temperature can:

increase reaction rate

which releases:

even more heat

This positive feedback can lead to:

thermal runaway

---

Thermal Runaway

The basic pattern is:

reaction produces heat

↓

temperature increases

↓

reaction becomes faster

↓

more heat is produced

↓

temperature rises further

This is why temperature control is extremely important in:

industrial chemistry and battery systems

---

Surface Area and Energy Release

Surface area can dramatically affect reaction rate.

Consider:

a block of wood

and:

fine wood shavings

The shavings have a much greater:

surface-area-to-volume ratio

More material is exposed to oxygen.

Therefore, combustion can occur:

more rapidly

The chemical energy stored in the material may be similar per unit mass, but the:

rate of energy release

can be very different.

---

Concentration and Everyday Reactions

Increasing reactant concentration often increases:

collision frequency

This can increase reaction rate.

This principle is important in:

• cleaning products
• industrial manufacturing
• laboratory reactions
• combustion
• biological processes

However, higher concentration can also increase:

• cost
• hazards
• corrosiveness
• environmental impact

Therefore, concentration must be:

optimized

---

Pressure and Gas Reactions

For gaseous reactants, increasing pressure places particles:

closer together

This generally increases:

collision frequency

and can increase reaction rate.

Industrial gas reactions may therefore use:

elevated pressures

But higher pressure requires:

• stronger equipment
• more energy
• greater safety controls

Again, the practical question is:

What conditions provide the best balance?

---

Applying Ideas to an Unfamiliar Situation

Suppose you are told:

A company produces a chemical using a reaction that is too slow at room temperature. Heating greatly increases the rate, but temperatures above 150°C produce unwanted products.

How could the process be improved?

A strong response might consider:

Use a catalyst

because it may increase the rate without requiring such a high temperature.

Also consider:

• moderate heating
• optimized concentration
• improved mixing
• increased surface area if solids are involved

The goal is not simply:

maximum rate

but:

useful rate + desired product + acceptable cost and safety

---

Another Unfamiliar Situation

Suppose a food manufacturer discovers that a product spoils rapidly at:

25°C

but much more slowly at:

5°C

Explain why.

At lower temperature:

• particles have less kinetic energy
• collisions occur less energetically
• fewer collisions overcome activation energy
• enzyme and microbial processes generally slow

Therefore:

spoilage reactions occur more slowly

This applies reaction-rate theory to:

food preservation

---

Another Unfamiliar Situation

A manufacturer wants a hand warmer to remain warm for:

eight hours

rather than becoming extremely hot for:

ten minutes

What should engineers consider?

They need to control:

reaction rate

Possible approaches might involve controlling:

• oxygen availability
• reactant concentration
• surface area
• catalyst conditions
• heat transfer

The desired product requires:

controlled energy release

rather than simply a large energy change.

---

Another Unfamiliar Situation

A biological reaction works well at 35°C but becomes extremely slow at 5°C and almost stops at 70°C.

What might explain this?

At 5°C:

low kinetic energy reduces enzyme-substrate collision frequency

At 70°C:

the enzyme may be denatured

Therefore, the reaction has an:

optimum temperature range

This applies ideas about:

energy + collisions + enzyme structure

---

Evaluating a Catalyst

When evaluating whether a catalyst should be used, consider:

Benefits

• faster reaction
• lower activation energy
• potentially lower operating temperature
• lower energy use
• possible improved selectivity
• increased production rate

Limitations

• catalyst cost
• availability of catalyst materials
• possible toxicity
• catalyst deactivation
• recovery and recycling requirements

A strong evaluation considers:

both benefits and limitations

---

Evaluating Reaction Conditions

Suppose increasing temperature doubles production rate.

Is that automatically worthwhile?

Not necessarily.

We must also ask:

• How much additional energy is required?
• Does product yield change?
• Are unwanted reactions increased?
• Does the catalyst degrade?
• Does equipment need upgrading?
• Are safety risks increased?
• What is the environmental cost?

Real chemistry involves:

trade-offs

---

Rate, Energy, and Sustainability

Modern chemical processes increasingly aim to reduce:

• energy consumption
• waste
• hazardous materials
• greenhouse gas emissions
• unnecessary resource use

Catalysts can help because they may allow reactions to proceed efficiently at:

lower temperatures or pressures

Enzymes can sometimes allow industrial reactions to occur under:

mild conditions

These ideas contribute to:

green chemistry

---

Green Chemistry

Green chemistry focuses on designing chemical products and processes that reduce environmental harm.

Reaction-rate control can contribute through:

• efficient catalysts
• lower-energy pathways
• reduced waste
• greater selectivity
• renewable raw materials
• safer reaction conditions

The goal is not merely to make chemistry:

faster

but to make it:

more efficient, safer, and more sustainable

---

The Central Connection

We can now connect the major ideas of chemical energetics and reaction rates.

Reactants

↓

must overcome

activation energy

↓

through

successful collisions

↓

to form

products

The frequency of successful collisions determines:

reaction rate

The energy difference between reactants and products determines:

overall energy change

A catalyst:

lowers the activation-energy barrier

without changing the overall energy difference.

---

Energy Profile Summary

For an exothermic reaction:

reactants → activation-energy barrier → lower-energy products

For an endothermic reaction:

reactants → activation-energy barrier → higher-energy products

With a catalyst:

activation-energy barrier becomes lower

but:

reactant and product energy levels remain unchanged

This distinction is one of the most important concepts in:

chemical energetics

---

A Powerful Problem-Solving Framework

When given an unfamiliar reaction-rate situation, ask:

1. What reaction is occurring?

Identify:

reactants and products

2. What energy changes are involved?

Is the process:

exothermic or endothermic?

3. What limits the rate?

Consider:

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

4. What could change the rate?

Apply:

collision theory

5. What are the consequences?

Consider:

• cost
• safety
• yield
• quality
• energy use
• environmental effects

This approach allows you to apply familiar chemistry to:

new situations

---

Common Misconception: Exothermic Means Fast

False.

Exothermic describes:

energy change

It does not describe:

reaction rate

Rusting is an example of an oxidation process that can occur:

slowly

while combustion can occur:

rapidly

Both can release energy.

---

Common Misconception: Endothermic Means Slow

Also false.

Endothermic describes:

energy transfer

not:

speed

An endothermic process can occur rapidly if conditions allow a sufficiently high:

reaction rate

---

Common Misconception: Catalysts Add Energy

Catalysts do not supply the reaction with extra energy.

They provide:

an alternative pathway with lower activation energy

This allows more collisions to be:

successful

---

Common Misconception: Catalysts Change the Energy Released

A catalyst does not change the overall energy difference between:

reactants and products

Therefore, it does not change the overall reaction energy change.

It changes:

the pathway and rate

---

Common Misconception: Higher Temperature Is Always Better

Higher temperature often increases reaction rate.

But it may also:

• increase energy costs
• cause unwanted reactions
• damage products
• denature enzymes
• increase safety risks

The best temperature depends on:

the purpose of the process

---

Common Misconception: We Always Want Faster Reactions

Sometimes we deliberately want reactions to be:

slower

Examples include:

• food spoilage
• corrosion
• medicine degradation
• oxidation
• battery self-discharge

Reaction-rate science is fundamentally about:

control

---

Check Your Understanding

1. Explain the difference between chemical energetics and chemical kinetics.

2. Why can an exothermic reaction still occur slowly?

3. Define activation energy.

4. Explain why increasing temperature usually increases reaction rate.

5. How does a catalyst affect activation energy?

6. Does a catalyst change the overall energy change of a reaction? Explain.

7. Explain why refrigeration slows food spoilage.

8. Why does a glow stick usually glow more brightly but for less time when warmed?

9. Explain why wood shavings may burn faster than a large block of wood.

10. Explain why catalysts can reduce industrial energy requirements.

11. Why might an industrial chemist deliberately avoid the highest possible reaction rate?

12. Explain how enzymes allow living organisms to carry out chemical reactions efficiently.

13. A reaction releases a large amount of energy but occurs very slowly at room temperature. Suggest two ways its rate might be increased.

14. Explain why slowing reaction rates can sometimes be useful.

15. Evaluate why catalysts are important for modern society.

---

Key Terms

• Energetics: Study of energy changes associated with chemical reactions.
• Kinetics: Study of reaction rates and the factors affecting them.
• Exothermic reaction: Reaction that transfers energy to the surroundings.
• Endothermic reaction: Reaction that absorbs energy from the surroundings.
• Activation energy: Minimum energy required for a successful reaction.
• Reaction rate: Measure of how quickly reactants are consumed or products are formed.
• Collision theory: Model explaining reactions through collisions between particles.
• Successful collision: Collision with sufficient energy and suitable orientation to produce a reaction.
• Catalyst: Substance that increases reaction rate by providing an alternative pathway with lower activation energy.
• Enzyme: Biological catalyst.
• Energy profile diagram: Diagram showing energy changes during the progress of a reaction.
• Reaction pathway: Sequence of steps through which reactants become products.
• Combustion: Rapid reaction with oxygen that releases energy.
• Corrosion: Chemical deterioration of a material through reactions with its environment.
• Shelf life: Period during which a product remains suitable for its intended use under specified storage conditions.
• Thermal runaway: Self-accelerating process in which heat increases reaction rate, causing still more heat production.
• Selectivity: Tendency of a reaction or catalyst to produce a particular desired product.
• Green chemistry: Design of chemical products and processes to reduce hazardous substances, waste, and environmental impact.
• Optimization: Selection of conditions that provide the best practical balance among competing factors.

---

Key Takeaways

• Chemical energetics describes energy changes, while kinetics describes reaction rates.
• Energy change and reaction rate are related but are not the same thing.
• Exothermic does not mean fast.
• Endothermic does not mean slow.
• Most reactions require particles to overcome an activation-energy barrier.
• Reaction rate depends on the frequency of successful collisions.
• Increasing temperature generally increases particle kinetic energy and the proportion of collisions that overcome activation energy.
• Catalysts provide alternative reaction pathways with lower activation energies.
• Catalysts increase reaction rate without changing the overall energy difference between reactants and products.
• Catalysts are essential in many industrial, environmental, and biological processes.
• Catalysts can reduce energy requirements by allowing useful rates under less extreme conditions.
• Enzymes are biological catalysts that allow life-sustaining reactions to proceed rapidly under mild conditions.
• Combustion demonstrates how activation energy and energy release interact.
• Refrigeration preserves food by slowing chemical and biological processes.
• Cooking uses increased temperature to accelerate chemical changes.
• Hand warmers depend on controlled rates of energy-releasing reactions.
• Cold packs depend on processes that absorb thermal energy.
• Glow sticks demonstrate how temperature can change reaction rate and product performance.
• Corrosion demonstrates why slowing reactions can be useful.
• Surface area, concentration, temperature, pressure, and catalysts can all influence reaction rates.
• The amount of energy released and the rate at which it is released are different quantities.
• Very rapid exothermic reactions can create safety risks, including thermal runaway.
• Industry must balance reaction rate with yield, cost, energy use, safety, quality, and environmental impact.
• Green chemistry uses catalysts and optimized reaction conditions to improve efficiency and sustainability.
• When faced with an unfamiliar situation, consider reaction → energy → rate factor → collision theory → practical consequences.
• The central relationship is activation energy → successful collisions → reaction rate, while the difference between reactant and product energy determines the overall energy change.