How Fast? The Rate of Chemical Change

How Fast? The Rate of Chemical Change
Table of Contents
1. Rate of Reaction
Definition, formula, and concentration–time graphs
2. Measuring Rates
Gas collection, colorimetry, and titration methods
3. Collision Theory
Successful vs. unsuccessful collisions, orientation, and energy
4. Factors Affecting Rate
Concentration, pressure, temperature, surface area, catalysts
5. Activation Energy (Eₐ)
Minimum energy for reaction; energy profiles
6. Energy Profiles
Exothermic & endothermic; effect of catalysts on Eₐ
7. Maxwell-Boltzmann Distribution
Energy distribution curves; effect of temperature & catalysts
8. Summary
Key points and examiner tips






Rate of Reaction
Definition
The rate of reaction is the change in concentration of a reactant or product per unit of time. Units: mol dm⁻³ s⁻¹
As a reaction progresses, reactant concentration decreases while product concentration increases.
The Formula
The rate can be found graphically by calculating the gradient of a tangent to the concentration–time curve at a specific point.
Rate is always a positive value — negate the gradient when reading from a reactants graph.
Rate of Reaction ( In Detail )
What is Rate of Reaction?
Definition
The rate of a reaction refers to how quickly a chemical reaction occurs. It is defined as the change in concentration of a reactant or product per unit of time.
Units: mol dm⁻³ s⁻¹
Key Points
Some reactions happen instantly; most occur more slowly
Reactant concentration decreases over time
Product concentration increases over time
Note: Reversible reactions — at dynamic equilibrium, concentrations remain constant
How to Calculate Rate of Reaction
The rate of reaction is given by:
Rate of Reaction Graphs
As the reaction proceeds, the concentration of reactants and products change with time
Steeper Gradient
Faster rate of reaction
Reactant Curve
Shows a negative gradient as concentration decreases
Product Curve
Shows a positive gradient as concentration increases
Examiner Tips & Tricks 
Reactant Graph
Shows a negative gradient — you must flip the sign to obtain a positive rate.
E.g. gradient = –20.6 mol dm⁻³ s⁻¹ → rate = 20.6 mol dm⁻³ s⁻¹
Product Graph
Shows a positive gradient — the rate is already positive. No sign change needed.
Worked Example

The rate of reaction can be found by measuring the volume of CO₂ produced per unit time and plotting a graph as shown:
Calculate the rate of reaction at 20 seconds.
01
Draw a tangent
Draw a tangent to the curve at t = 20 s
02
Reference graph
See the tangent drawn on the graph below
03
Complete the triangle
Read off Δy and Δx values: Δy = 27 − 3 = 24 cm³, Δx = 40 − 0 = 40 s
04
Apply the gradient formula

05
Calculate the rate
Rate = 24 / 40 = 0.60 cm³ s⁻¹
Examiner Tips for Drawing Tangents
Make the triangle large
A larger triangle reduces errors of precision when reading off values
Intersect with gridlines
Try to make the triangle corners land on gridlines to get exact values
Minimise errors
These steps reduce the chance of accidentally misreading graph values
✅ Success Summary — Rate of Reaction 
Rate of reaction = change in concentration ÷ time (units: mol dm⁻³ s⁻¹)
Reactant concentration decreases; product concentration increases over time
At dynamic equilibrium (reversible reactions), concentrations remain constant
Steeper gradient on a concentration–time graph = faster rate
To find rate at a point: draw a tangent, calculate gradient = Δy / Δx
Reactant graph has negative gradient → flip sign to get positive rate
Product graph has positive gradient → rate is already positive
Worked example: rate at 20 s = 24/40 = 0.60 cm³ s⁻¹
Tangent tips: make triangle large, intersect gridlines to minimise error
Measuring Rates of Reaction
Overview
What Are We Measuring?
Track how quickly reactants are used up OR products are formed
Method chosen depends on the substances involved
Each method monitors a property proportional to concentration (e.g. colour, mass, volume)
Continuous vs. Non-Continuous
Continuous Monitoring
Tracked throughout the reaction → Provides a detailed data set
Non-Continuous (Single Point)
Measured once reaction is complete → Calculates average rate from overall data
Useful in fast reactions
🎨 Colorimetry
Measures light intensity through a solution
⚖️ Mass Loss
Tracks decrease in mass as gas escapes
🧪 Gas Volume
Collects and measures gas produced
Method 1 — Colorimetry
Colorimetry measures the light intensity of light passing through a sample
How It Works
A colorimeter or spectrophotometer measures light passing through a solution
If solution changes colour during reaction → used to measure rate
Light intensity measured every few seconds
Data plotted → concentration of reactants/products vs. time
Light intensity is proportional to concentration
Sketch graph of colour intensity against time (the coloured species is a reactant in this case)
⚠️ Limitation
Cannot monitor coloured precipitates — light is scattered or blocked by the precipitate
Absorbance vs. Light Intensity
💡 Light Intensity
Measures how much light passes through the solution to the detector
As a coloured reactant is used up → solution becomes less coloured → more light passes through → intensity increases
If a coloured product forms → solution becomes more coloured → less light passes through → intensity decreases
Inversely proportional to concentration
Graph shape: decreasing curve (if reactant is coloured)
📊 Absorbance
Measures how much light is absorbed by the solution
More concentrated coloured solution → more light absorbed → absorbance increases
Directly proportional to concentration
Graph shape: decreasing curve (mirrors light intensity — same shape, same information)
Preferred measurement because of its direct linear relationship with concentration

🔄 Key Relationship: The two graphs are mirror images of each other — both convey the same concentration information, just measured differently.
📐 Beer-Lambert Law
A
Absorbance
No units
ε
Molar absorption coefficient
dm³ mol⁻¹ cm⁻¹
l
Path length of light through solution
cm
c
Concentration of solution
mol dm⁻³
Doubling concentration → doubles absorbance (linear relationship)
Only valid for dilute solutions and a fixed wavelength of light
The wavelength used should be the complementary colour to the solution's colour (e.g. blue solution → use orange/red light)
📈 Calibration Curve
What Is a Calibration Curve?
A graph of absorbance vs. known concentration for standard solutions
Prepared using solutions of known concentration measured in the colorimeter
Gives a straight line through the origin (Beer-Lambert Law)
Used to determine the unknown concentration of a sample
How to Use It — Step by Step
01
Prepare Standards
Make a series of solutions with known concentrations
02
Measure Absorbance
Record absorbance of each standard in the colorimeter
03
Plot the Graph
Plot absorbance (y-axis) vs. concentration (x-axis) → draw line of best fit
04
Read Off Unknown
Measure absorbance of unknown sample → read off concentration from the graph
✅ Why Use a Calibration Curve?
Accounts for any systematic errors in the colorimeter; more accurate than using Beer-Lambert Law alone; gives a visual check for linearity
⚠️ Important Note
The calibration curve is only valid for the same wavelength and same substance it was prepared with
Method 2 — Mass Loss
Cotton wool allows gas to escape whilst preventing reactants/products from leaving
How It Works
Gas produced escapes from vessel → mass of vessel decreases
Example: CaCO₃ + HCl → CO₂ escapes
Mass measured every few seconds
Change in mass plotted over time
Graph = amount of reactant remaining vs. time
Mass loss of a product against time
⚠️ Limitation
Gas must be sufficiently dense — change in mass must be detectable on a 2–3 decimal place balance
✅ Suitable Gas
CO₂ (Mr = 44) ✓ | H₂ (Mr = 2) ✗ — too light to detect
Method 3 — Gas Volume
Using a Gas Syringe
Collecting gases experimental set up
Gas produced is trapped and volume measured over time
Example: Mg + HCl → hydrogen gas
Volume measured every few seconds
Graph shows amount of product vs. time
Alternative — Inverted Measuring Cylinder
Alternative gas collection set up
Gas collected through water by displacement
Only works if gas has low water solubility
Hydrogen can be collected this way
The volume of gas increases with time. The reaction has stopped when the volume of gas plateaus
Method 4 — Titration (Quenching)
01
Take Samples
Samples of reaction mixture taken at regular intervals
02
Quench the Reaction
Reaction deliberately stopped — 'freezes' it at a specific point in time
03
Perform Titration
Measure concentration of sample
04
Calculate Rate
Determine change in concentration with time
⚠️ Limitation
Titration cannot be done continuously — taking a sample can affect the rate of reaction
Method 5 — Conductivity
Principle
Monitors changes in electrical conductivity of reaction mixture over time
As reaction proceeds, ion concentration changes → affects conductivity
Rate determined by how quickly conductivity changes
Example Reaction
HCl (aq) + NaOH (aq) → NaCl (aq) + H₂O (l)
HCl and NaOH dissociate into ions → increases conductivity
As reaction progresses, ion concentration changes → conductivity changes
Method 6 — Clock Reactions
What Is a Clock Reaction?
Non-continuous method
'Stop the clock' when a specific visible point is reached
Time taken to reach a fixed point is measured
Example: magnesium dissolves completely in HCl
Sodium Thiosulfate + HCl (Disappearing Cross)
Na₂S₂O₃ (aq) + 2HCl (aq) → 2NaCl (aq) + SO₂ (g) + H₂O (l) + S (s)
Yellow precipitate of sulfur slowly forms → obscures a cross viewed through the solution
The disappearing cross experiment
⚠️ Limitation
Only generates one piece of data for analysis
Examiner Tips & Tricks
Graph Interpretation
Be familiar with graphs of concentration, volume or mass against time
Calculate Rate from Tangent
Draw a tangent to the curve → calculate gradient = Δy / Δx
Absorbance vs. Intensity
Colorimeter can measure absorbance OR light intensity — both give concentration vs. time plots
✅ Success Summary — Measuring Rates of Reaction
 • Rate is measured by tracking reactants used up OR products formed over time
 • The monitored property (colour, mass, volume) is proportional to concentration
 • Colorimetry: measures light intensity through solution; proportional to concentration; cannot be used for coloured precipitates; can also measure absorbance
 • Mass loss: gas escapes → mass decreases; graph = reactant amount vs. time; gas must be dense enough (CO₂ ✓, H₂ ✗)
 • Gas volume: gas trapped and measured; graph = product amount vs. time; alternative = inverted measuring cylinder (low solubility gases only)
 • Titration: samples taken at intervals → quenched (reaction stopped) → titrated to find concentration; cannot be done continuously
 • Conductivity: monitors ion concentration changes; rate = how quickly conductivity changes
 • Clock reactions: non-continuous; time to reach a visible fixed point; Na₂S₂O₃ + HCl → disappearing cross experiment; limitation = only one data point
 • Always be able to interpret concentration/volume/mass vs. time graphs and calculate rate from a tangent
 • Light intensity is inversely proportional to concentration; absorbance is directly proportional — graphs are mirror images
 • Beer-Lambert Law: A = εlc — absorbance is directly proportional to concentration; only valid for dilute solutions at a fixed wavelength
 • Calibration curve: plot absorbance vs. known concentration → straight line through origin → used to find unknown concentrations from absorbance readings
Collision Theory
For a reaction to occur, reactant particles must collide with sufficient energy and correct orientation. The rate of reaction depends on the frequency of successful collisions.
Collision Frequency
How often particles collide per unit time — affected by concentration, pressure, temperature, and surface area.
Collision Energy
The combined kinetic energy of colliding particles. Must meet or exceed the activation energy for a reaction to occur.
Collision Geometry
Particles must collide in the correct orientation. Critical for large, complex molecules where only specific active sites can react.
Successful vs. Unsuccessful Collisions
What Makes a Collision Successful?
A successful collision requires both:
Correct orientation of the colliding particles
Collision energy ≥ activation energy (Ea)
Most collisions fail due to insufficient energy rather than wrong orientation.
 At the same temperature, lighter particles move faster — explaining why lower-mass substances diffuse more quickly.
Collision Theory — In Detail
Kinetic Energy & Temperature
What is Kinetic Energy?
Kinetic theory accounts for properties of solids, liquids and gases in terms of particle interactions and relative energies
Kinetic energy = energy associated with movement or motion
Particles in a substance have a range of kinetic energies due to random motion
The KE Equation
m
mass of the particle
v
velocity of the particle
At the same temperature, KE of particles is equal
→ Inverse relationship between mass and velocity
Lower mass → diffuses faster at same temperature
What is Collision Theory?
💥 Collision Frequency
How often particles collide per unit time
⚡ Collision Energy
The combined energy of colliding particles
🔋 Activation Energy
Minimum energy needed for a reaction to occur
🔄 Collision Geometry
The orientation/angle at which particles collide
For a reaction to occur, reactant particles must collide with sufficient kinetic energy AND in the correct orientation. The rate depends on how often successful collisions happen.
Collision Frequency
Definition
The number of collisions between particles per unit time
Particles must first collide before a reaction can take place
What Affects Collision Frequency?
Concentration
More particles in same volume → more frequent collisions
Pressure
Higher pressure → particles closer together → more collisions
Temperature
Faster moving particles → more frequent collisions
Surface Area
More exposed surface → more collisions possible
Collision Energy
Successful vs. Unsuccessful
✅ Successful Collision
Particles have sufficient energy to break bonds → reaction occurs
❌ Unsuccessful Collision
Particles bounce off each other → no reaction → not enough energy to break bonds
The combined energy of colliding particles = collision energy
Most collisions are unsuccessful — particles simply bounce off
Collision energy is the combined energy of two colliding particles
Activation Energy (Ea)
Definition
The minimum energy colliding particles need in order to react
The Ea of any specific reaction is fixed
The Rule
Collision energy < Ea
Collision is unsuccessful → no reaction
Collision energy ≥ Ea
Collision is successful → reaction takes place
Effect of a Catalyst
❌ Does NOT change Ea
The activation energy of the reaction itself stays fixed
✅ Provides Alternative Route
A different, lower activation energy pathway → more successful collisions
Collision Geometry
Why Orientation Matters
Particles must have the correct orientation when they collide for a reaction to be successful
Especially important for large molecules with complex shapes
e.g. proteins and carbohydrates — active sites can only be accessed in one orientation
Note: Most collisions fail because they don't reach Ea — not because of wrong geometry
Orientation becomes increasingly important in large complex biomolecules such as proteins and carbohydrates where active sites can only be accessed in one orientation
Successful vs. Unsuccessful Collisions
Diagram (A) shows an ineffective collision due to the particles not having enough energy whereas (B) shows an effective collision where the particles have the correct orientation and enough energy for a chemical reaction to take place
✅ Successful Collision
Correct orientation of particles
Collision energy ≥ activation energy (Ea)
Both conditions must be met
Results in a chemical reaction
❌ Unsuccessful Collision
Wrong orientation OR insufficient energy
Particles simply bounce off each other
No chemical reaction occurs
Most collisions are unsuccessful
Rate of reaction depends on the number of successful collisions per unit time
✅ Success Summary — Collision Theory
Kinetic energy = energy of motion; KE = ½mv² — at same temperature, KE is equal → inverse relationship between mass and velocity
Lower mass particles diffuse faster at the same temperature
Collision theory: reactions occur when particles collide with sufficient KE and correct orientation
4 factors affecting collision frequency: concentration, pressure, temperature, surface area
Collision energy = combined energy of colliding particles; most collisions are unsuccessful (particles bounce off)
Activation energy (Ea) = minimum energy needed for reaction; fixed for a specific reaction
Collision energy < Ea → unsuccessful; collision energy ≥ Ea → successful reaction
A catalyst does NOT change Ea — it provides an alternative route with a lower Ea
Collision geometry: particles must collide in the correct orientation — especially important for large/complex molecules
Most failed collisions are due to insufficient energy, not wrong geometry
Successful collision = correct orientation AND energy ≥ Ea → reaction occurs
Factors Affecting Rate of Reaction
Any factor that changes the number of successful collisions will alter the rate. Five key factors are:
1
Concentration
More particles per unit volume → increased collision frequency → faster rate.
2
Pressure
For gases: higher pressure compresses particles into a smaller volume, increasing collision frequency.
3
Temperature
Particles move faster AND a greater proportion exceed Ea — both effects increase the rate.
4
Surface Area
Only surface particles react. Grinding a solid into powder dramatically increases exposed surface area.
5
Catalysts
Provide an alternative pathway with lower Ea, increasing successful collisions without being consumed.
Examiner tip: Increasing particle size decreases surface area and reduces the rate — a common trick question. Increasing pressure and temperature both increase rate.
Factors Affecting Rates of Reaction ( In Detail )
The rate of reaction depends on any factor that changes the number of successful collisions. There are 5 key factors.
🧪 Concentration
More particles → more collisions
🔵 Pressure
Less space → more collisions (gases)
🌡️ Temperature
Faster particles + more energy → more successful collisions
📐 Surface Area
More exposed particles → more collisions
⚗️ Catalysts
Lower Ea → more successful collisions
1. Concentration
The Effect
Higher concentration → more particles in a given volume
→ Increased collision frequency
→ More successful collisions
→ Increased rate of reaction
Why It Works
More particles in the same volume = particles are closer together
Particles collide more often
More total collisions → more that meet or exceed Ea
Higher concentration (b) means more particles in the same volume → increased collision frequency → increased rate
2. Pressure
The Effect
Applies to reactions involving gases
Same effect as increasing concentration
Higher pressure → particles have less space to move
→ Increased collision frequency
→ Increased rate of reaction
Why It Works
Same number of particles in a smaller volume
Particles are closer together
More frequent collisions → more successful collisions
Higher pressure (b) — same particles in smaller volume → increased collision frequency → increased rate
3. Temperature
Two Ways Temperature Increases Rate
01
Faster Particles
Higher temperature → particles move faster → collide more frequently → more total collisions → more successful collisions
02
More Energy
Higher proportion of particles have energy ≥ activation energy (Ea) → higher proportion of collisions are successful
Key Point
Effect 1 — Frequency
More collisions per unit time → more chances for successful collisions
Effect 2 — Energy
More particles exceed Ea → greater proportion of collisions are successful
4. Surface Area
The Effect
Only particles on the surface of a solid can collide with other reactants
Increasing surface area → more particles exposed
→ More total collisions → more successful collisions
→ Increased rate of reaction
How to Increase Surface Area
Large Pieces
Small surface area → fewer collisions → slower rate
Fine Powder
Very large surface area → many more collisions → faster rate
Decreasing particle size increases surface area → more particles exposed → increased collision frequency
5. Catalysts
How Catalysts Work
Provides an alternative reaction pathway
This pathway has a lower activation energy than the uncatalysed reaction
→ More collisions have sufficient energy to react
→ More successful collisions
→ Increased rate of reaction
Catalyst is chemically unchanged at the end of the reaction — no permanent chemical change
✅ What a Catalyst DOES
Provides alternative route with lower Ea → increases rate
❌ What a Catalyst Does NOT Do
Does NOT get permanently used up; does NOT change the overall energy of reactants or products

Worked Example
Which of the following factors can result in the rate of a chemical reaction increasing?
I. Increasing the total pressure in reactions involving gases
II. Raising the temperature in reactions involving gases
III. Increasing the particle size of a solid in a reaction
A. I and II only
B. I and III only
C. II and III only
D. I, II and III
✅ Answer: A — I and II only
Increasing pressure → particles closer → more collisions → faster rate ✓
Raising temperature → faster particles + more exceed Ea → faster rate ✓
Increasing particle size → decreases surface area → fewer collisions → slower rate ✗
✅ Success Summary — Factors Affecting Rate of Reaction
Rate depends on the number of successful collisions per unit time — 5 factors affect this
Concentration ↑ → more particles in same volume → more frequent collisions → faster rate
Pressure ↑ (gases only) → same effect as concentration → particles closer → more collisions → faster rate
Temperature ↑ → (1) particles move faster → more frequent collisions; (2) more particles have energy ≥ Ea → greater proportion of successful collisions
Surface area ↑ → more particles exposed on surface → more collisions → faster rate; fine powder has much greater surface area than large pieces
Catalyst → provides alternative pathway with lower Ea → more collisions are successful → faster rate; catalyst is chemically unchanged at end
Worked example: Pressure ↑ ✓, Temperature ↑ ✓, Particle size ↑ ✗ (decreases surface area) → Answer: A (I and II only)
Activation Energy (Eₐ)
What is Activation Energy?
Definition
For a reaction to take place, reactant particles must overcome a minimum amount of energy
This energy is called the activation energy (Eₐ)
Even with correct orientation, reaction will NOT occur unless particles have at least Eₐ
The Golden Rule
Collision energy < Eₐ
Reaction does NOT occur — even with correct orientation
Collision energy ≥ Eₐ
Reaction occurs — provided orientation is also correct
For a successful collision, particles must BOTH:
✓ Collide in the correct orientation
✓ Have energy ≥ Eₐ
Energy Profiles
⬇️ Exothermic Reaction
Reactants are higher in energy than products
Energy is released during the reaction
ΔH is negative
The diagram shows that the reactants are higher in energy than the products in the exothermic reaction
⬆️ Endothermic Reaction
Reactants are lower in energy than products
Energy is absorbed during the reaction
ΔH is positive
The diagram shows that the reactants are lower in energy than the products in the endothermic reaction
Reverse Reaction — Finding Eₐ
The reverse reaction has a different Eₐ from the forward reaction. It is always measured from the products' energy level up to the peak (transition state).
⬇️ Exothermic (forward)
Eₐ (reverse) = ΔH + Eₐ (forward)
Note: ΔH is negative for exothermic, so use the magnitude (absolute value)
⬆️ Endothermic (forward)
Eₐ (reverse) = Eₐ (forward) − ΔH
Note: ΔH is positive for endothermic
Why Do the Formulas Work? — The Logic
01
Identify the peak energy
The peak = transition state = highest point on the energy profile. Both forward and reverse Eₐ are measured TO this peak.
02
Forward Eₐ
Measured from reactants → peak. This is given on the diagram.
03
Reverse Eₐ
Measured from products → peak. Since peak = reactants + Eₐ(fwd), and products = reactants + ΔH, the reverse Eₐ = Eₐ(fwd) − ΔH (endothermic) or |ΔH| + Eₐ(fwd) (exothermic)
📊 Worked Example 1 — Exothermic Reaction
Given: Eₐ (forward) = 50 kJ mol⁻¹, ΔH = −30 kJ mol⁻¹
Find: Eₐ (reverse)
01
Identify reaction type
ΔH = −30 kJ mol⁻¹ → Exothermic reaction
02
Write the formula
Eₐ (reverse) = ΔH + Eₐ (forward)
03
Note: use magnitude of ΔH
|ΔH| = 30 kJ mol⁻¹
04
Substitute values
Eₐ (reverse) = 30 + 50
05
Calculate
Eₐ (reverse) = 80 kJ mol⁻¹ ✓
💡 Why is Eₐ(reverse) > Eₐ(forward) for exothermic reactions?
Because the products are at a lower energy than the reactants — so the reverse reaction has to climb a bigger energy hill to reach the peak.
📊 Worked Example 2 — Endothermic Reaction
Given: Eₐ (forward) = 80 kJ mol⁻¹, ΔH = +50 kJ mol⁻¹
Find: Eₐ (reverse)
01
Identify reaction type
ΔH = +50 kJ mol⁻¹ → Endothermic reaction
02
Write the formula
Eₐ (reverse) = Eₐ (forward) − ΔH
03
Substitute values
Eₐ (reverse) = 80 − 50
04
Calculate
Eₐ (reverse) = 30 kJ mol⁻¹ ✓
💡 Why is Eₐ(reverse) < Eₐ(forward) for endothermic reactions?
Because the products are at a higher energy than the reactants — so the reverse reaction only has to climb a smaller energy hill to reach the peak.
Quick Reference — Eₐ Comparison
⬇️ Exothermic Forward Reaction
Products lower in energy than reactants
ΔH is negative
Eₐ(reverse) > Eₐ(forward)
Formula: Eₐ(rev) = |ΔH| + Eₐ(fwd)
Example: 30 + 50 = 80 kJ mol⁻¹
⬆️ Endothermic Forward Reaction
Products higher in energy than reactants
ΔH is positive
Eₐ(reverse) < Eₐ(forward)
Formula: Eₐ(rev) = Eₐ(fwd) − ΔH
Example: 80 − 50 = 30 kJ mol⁻¹
📚 Level Note
Calculations of Eₐ from experimental data are NOT required at Standard Level but ARE required at Higher Level Chemistry
Examiner Tips & Tricks
Correct Orientation Alone Is Not Enough
Particles must ALSO have energy ≥ Eₐ — both conditions must be met simultaneously
Reading Energy Profiles
Eₐ is the energy difference between the reactants and the peak (transition state) of the curve
Reverse Reaction Eₐ
Always measured from the products energy level up to the peak — use the appropriate formula
✅ Success Summary — Activation Energy
Activation energy (Eₐ) = minimum energy particles must have to react
Even with correct orientation, reaction will NOT occur if collision energy < Eₐ
Successful collision requires BOTH: correct orientation AND collision energy ≥ Eₐ
Exothermic reaction: reactants higher in energy than products; ΔH is negative
Endothermic reaction: reactants lower in energy than products; ΔH is positive
Eₐ on energy profile = energy difference between reactants and the peak (transition state)
Reverse reaction Eₐ: Exothermic → Eₐ(rev) = ΔH + Eₐ(fwd) | Endothermic → Eₐ(rev) = Eₐ(fwd) − ΔH
Eₐ calculations from experimental data: NOT required at SL; required at HL
Reverse Eₐ (exothermic): Eₐ(rev) = |ΔH| + Eₐ(fwd) → reverse Eₐ is larger (products at lower energy → bigger hill to climb)
Reverse Eₐ (endothermic): Eₐ(rev) = Eₐ(fwd) − ΔH → reverse Eₐ is smaller (products at higher energy → smaller hill to climb)
Worked example 1 (exothermic): Eₐ(fwd) = 50, ΔH = −30 → Eₐ(rev) = 30 + 50 = 80 kJ mol⁻¹
Worked example 2 (endothermic): Eₐ(fwd) = 80, ΔH = +50 → Eₐ(rev) = 80 − 50 = 30 kJ mol⁻¹
Energy Profiles: Exothermic & Endothermic
Exothermic Reaction
Products are lower in energy than reactants. ΔH is negative. Ea is the energy barrier from reactants to the transition state.
Endothermic Reaction
Products are higher in energy than reactants. ΔH is positive. The activation energy barrier must still be overcome.
Energy Profiles With & Without Catalysts
How Do Catalysts Increase Rate?
The Mechanism
Provides reactants with an alternative reaction pathway
This pathway has a lower activation energy (Eₐ) than the uncatalysed reaction
→ More particles have sufficient energy to react
→ More successful collisions
→ Increased rate of reaction
Catalyst remains chemically unaltered at the end of the reaction
What Changes vs. What Stays the Same
✅ CHANGES
Activation energy (Eₐ) is lowered → alternative pathway provided → faster rate
❌ UNCHANGED
Enthalpy change (ΔH) stays the same → overall energy of reactants and products is unaffected
The catalyst speeds up a reaction that would normally be slow due to high activation energy. The catalyst is NOT used up and does NOT take part in the chemical reaction
Environmental Benefits of Catalysts
⚡ Lower Energy Requirements
Enable reactions at lower temperatures and pressures → less energy consumed → reduced carbon footprint
♻️ Reduced Waste
Can be reused and used in small quantities → increases atom economy → less waste produced
🎯 Increased Selectivity
Promote specific reactions → suppress undesired side reactions → cleaner, more efficient processes
Types of Catalysts
🔵 Homogeneous Catalyst
Catalyst is in the same phase as the reactants
Example: reactants and catalyst are all liquids
Mixes uniformly with reactants → good contact
🔴 Heterogeneous Catalyst
Catalyst is in a different phase to the reactants
Example: reactants are gases, catalyst is a solid
Reaction occurs at the surface of the catalyst
Homogeneous
Same phase as reactants (e.g. liquid catalyst + liquid reactants)
Heterogeneous
Different phase to reactants (e.g. solid catalyst + gas reactants)
Energy Profile — With & Without Catalyst
A catalyst lowers the activation energy (Eₐ) by providing an alternative reaction pathway, making the reaction faster without affecting the enthalpy change (ΔH)
📖 How to Read the Profile
Without catalyst: higher peak → higher Eₐ → fewer particles can react
With catalyst: lower peak → lower Eₐ → more particles can react
ΔH (reactants → products energy difference) is identical in both cases
The catalyst creates a new, lower energy route to the same products
Key Labels on the Diagram
Eₐ (uncatalysed)
Energy from reactants to the higher peak
Eₐ (catalysed)
Energy from reactants to the lower peak
ΔH
Energy difference between reactants and products — unchanged
Examples of Catalysts
🧬 Enzymes — Biological Catalysts
Act as catalysts in biological systems
Control many biochemical reactions within cells
Also important in industry
Allow industrial reactions at lower temperatures and pressures → saves money and energy
Example: enzymes in fermentation, digestion, pharmaceutical production
⚙️ Transition Metals
Commonly used as industrial catalysts
Can form variable oxidation states
This allows them to provide alternative pathways in redox reactions
Example: Iron (Fe) in the Haber process (N₂ + H₂ → NH₃)
Example: Platinum/Rhodium in catalytic converters
Worked Example
The energy profile below shows the energy changes for a reaction with and without a catalyst.
Which symbols represent the enthalpy change, ΔH, and the activation energy, Eₐ, for the reaction using a catalyst?
01
Identify ΔH
ΔH = difference in energy between reactants and products = arrow c (the vertical gap between start and end of the profile)
02
Identify Eₐ (with catalyst)
Eₐ = energy from reactants to the lower peak (catalysed pathway) = arrow a
✅ Answer: C — ΔH = c | Eₐ (with catalyst) = a
✅ Success Summary — Energy Profiles With & Without Catalysts 
A catalyst provides an alternative reaction pathway with a lower Eₐ → more particles can react → faster rate
The catalyst is chemically unchanged at the end of the reaction
ΔH is unchanged by a catalyst — only Eₐ changes
Environmental benefits: lower energy requirements, reduced waste (reusable), increased selectivity
Homogeneous catalyst: same phase as reactants (e.g. both liquid)
Heterogeneous catalyst: different phase to reactants (e.g. solid catalyst + gas reactants)
On an energy profile: catalysed pathway shows a lower peak (lower Eₐ) but same start and end points (same ΔH)
Enzymes: biological catalysts; control biochemical reactions; used in industry at lower T and P
Transition metals: variable oxidation states → provide alternative redox pathways (e.g. Fe in Haber process, Pt/Rh in catalytic converters)
Worked example: ΔH = arrow c (reactants to products); Eₐ (catalysed) = arrow a (reactants to lower peak) → Answer: C
Maxwell-Boltzmann Distribution Curves
What is a Maxwell-Boltzmann Distribution Curve?
Definition
A graph showing the distribution of energies of particles at a certain temperature
Shows how many particles have each energy level
The curve is never symmetrical — it has a long tail to the right
Energy Distribution in a Sample
🔵 Very Low Energy
A few particles have very low energy
🟡 Middle Energy
Most particles have energy in between
🔴 Very High Energy
A few particles have very high energy
The Maxwell-Boltzmann distribution curve shows the distribution of energies and the activation energy
Key Features of the Curve
Starts at the origin (no particles have zero energy)
Rises to a peak (most probable energy)
Falls away with a long tail to the right
Tail never touches the x-axis (some particles always have very high energy)
Total area under curve = total number of particles
Key Labels
EMP
Most probable energy → highest point on the peak
Eₐ
Activation energy → marked on x-axis; only particles to the RIGHT of Eₐ can react
Shaded Area
Particles with energy ≥ Eₐ → proportion that can react
Effect of Temperature on the Curve
What Happens When Temperature Increases?
01
Particles gain kinetic energy
Move around faster
02
More frequent collisions
Particles collide more often
03
Curve flattens & shifts right
Peak moves right and becomes lower
04
More particles exceed Eₐ
Greater proportion of successful collisions → faster rate
Two Reasons Rate Increases with Temperature
⚡ More Frequent Collisions
Particles move faster → collide more often per unit time
🔋 More Successful Collisions
Greater proportion of particles have energy ≥ Eₐ → more reactions occur per collision
As temperature increases, the curve flattens and shifts right — more particles exceed Eₐ
Important: The area under the curve stays the same (same number of particles). Only the shape changes — flatter and shifted right.
Drawing Rules — Temperature Curves
Higher T peak is LOWER
The peak of the higher temperature curve is lower than the lower temperature curve
Higher T peak is to the RIGHT
The peak shifts right — higher most probable energy
Curves cross ONCE only
The two curves should only intersect once
Higher T tail is HIGHER
The tail of the higher temperature curve sits above the lower temperature tail
⚠️ Examiner Warning
Examiners often ask about reducing temperature — apply the same logic in reverse (curve shifts left, peak rises, fewer particles exceed Eₐ)
Effect of a Catalyst on the Curve
How a Catalyst Changes the Curve
A catalyst provides an alternative pathway with a lower Eₐ
The curve shape does NOT change — same temperature, same distribution
The Eₐ line shifts LEFT on the x-axis (lower activation energy)
→ A greater proportion of particles now have energy ≥ new lower Eₐ
→ More successful collisions → increased rate
Catalyst vs. Temperature — Key Difference
🌡️ Temperature Increase
Changes the shape of the curve (flattens, shifts right) AND lowers Eₐ relative to particles
⚗️ Catalyst
Does NOT change the curve shape → only lowers Eₐ → more particles already on the curve can react
The total shaded area shows particles with energy ≥ Eₐ with catalyst. The light purple area shows the extra particles that now have enough energy to react due to the lower Eₐ
✅ Shaded Area to Show Catalyst Effect
Highlight the TOTAL shaded area (both dark and light) — NOT just the light-shaded area
⚠️ Common Mistake
Students often only shade the extra area — you must shade all particles with energy ≥ new Eₐ
Examiner Tips & Tricks
Curve starts at origin
No particles have zero energy — curve begins at (0, 0)
Tail never touches x-axis
Always approaches but never reaches the x-axis — some particles always have very high energy
Catalyst shading
Show the total shaded area ≥ new Eₐ, not just the extra light-shaded portion
Reducing temperature
Examiners prefer this — curve shifts left, peak rises, fewer particles exceed Eₐ → slower rate
✅ Success Summary — Maxwell-Boltzmann Distribution Curves
Maxwell-Boltzmann curve = graph of distribution of particle energies at a given temperature
Few particles have very low or very high energy; most have intermediate energy
EMP = most probable energy = highest point on the peak
Only particles with energy ≥ Eₐ can react — shown by shaded area to the right of Eₐ
Temperature increase → curve flattens and shifts right → more particles exceed Eₐ → faster rate (two reasons: more frequent collisions AND greater proportion exceed Eₐ)
Drawing rules: higher T curve has lower peak, shifted right, crosses lower T curve once, tail is higher
Area under curve = constant (same number of particles) regardless of temperature
Catalyst → lowers Eₐ (shifts Eₐ line left) → curve shape unchanged → greater proportion of particles can react → faster rate
Catalyst effect on curve: shade the TOTAL area ≥ new Eₐ (not just the extra light-shaded area)
Reducing temperature: opposite effect — curve shifts left, peak rises, fewer particles exceed Eₐ → slower rate
Curve must start at origin and tail must never touch the x-axis
Summary: The Rate of Chemical Change
📏 Rate of Reaction
Change in concentration of a reactant or product per unit time
Measured by tracking reactants used up or products formed
Units: mol dm⁻³ s⁻¹
💥 Collision Theory
For a reaction to occur, particles must:
Collide with correct orientation
Have energy ≥ activation energy (Eₐ)
Only then is the collision successful
⚡ Activation Energy (Eₐ)
The minimum energy required for a reaction to occur
Only particles with energy ≥ Eₐ can react
Shown as a shaded area on the Maxwell-Boltzmann curve
Factors Affecting Rate of Reaction
🧪 Concentration ↑
More particles in same volume → more frequent collisions → faster rate
🔵 Pressure ↑ (gases)
Particles pushed closer together → more frequent collisions → faster rate
🌡️ Temperature ↑
Particles move faster (more KE) AND greater proportion exceed Eₐ → faster rate (two reasons!)
🧱 Surface Area ↑
More particles exposed at the surface → more collisions → faster rate
⚗️ Catalyst
Provides an alternative pathway with a lower Eₐ → greater proportion of particles can react → faster rate
📈 Energy Profiles
🔴 Exothermic
Products lower than reactants → ΔH is negative → energy released
🔵 Endothermic
Products higher than reactants → ΔH is positive → energy absorbed
⚗️ Catalyst Effect
Lowers the peak (transition state) but ΔH is unchanged — start and end points stay the same
📊 Maxwell-Boltzmann Distribution
Curve Shape
Starts at origin, rises to a peak, long tail to the right that never touches the x-axis
Temperature Increase
Curve flattens and shifts right → peak moves right and lowers → more particles exceed Eₐ
Catalyst Effect
Curve shape unchanged → only the Eₐ line shifts left → greater shaded area → more successful collisions
✅ Full Topic Summary
Rate of reaction = change in concentration per unit time; measured via reactants used or products formed
Collision theory: successful collision requires correct orientation AND energy ≥ Eₐ
Concentration/Pressure ↑ → more frequent collisions → faster rate
Temperature ↑ → more frequent collisions AND greater proportion exceed Eₐ → faster rate (two reasons)
Surface area ↑ → more exposed particles → more collisions → faster rate
Catalyst → lowers Eₐ via alternative pathway → more successful collisions → faster rate; curve shape unchanged
Exothermic: ΔH negative; endothermic: ΔH positive; catalyst lowers peak but ΔH unchanged
Maxwell-Boltzmann: area under curve beyond Eₐ = fraction of particles that can react; temperature shifts curve right and flattens it; area under curve stays constant
Drawing rules: higher T curve has lower, right-shifted peak; curves cross once only; tail of higher T curve sits above lower T tail
⚠️ Examiner Trick Question — Particle Size!
Increasing particle size decreases surface area — fewer particles are exposed at the surface → slower rate. Examiners often phrase questions about "larger pieces" or "grinding into a powder" to catch students out. Smaller pieces = greater surface area = faster rate.