Reactivity 2.1 | Rate of Reaction

📋 IB Content Statements (R2.1)

This topic covers the following syllabus points from the IB Chemistry 2025 guide:

R2.1.1: Species react as a result of collisions of sufficient energy and proper orientation.
R2.1.2: Activation energy ($E_a$) is the minimum energy that colliding molecules need for a successful collision.
R2.1.3: Factors that influence the rate of reaction include temperature, concentration (or pressure for gases), surface area, and the use of a catalyst.
R2.1.4: The Maxwell-Boltzmann distribution curve shows the number of particles at different kinetic energies. It can be used to explain the effect of temperature changes and catalysts on rate.
R2.1.5: A catalyst increases the rate of reaction by providing an alternative reaction pathway with a lower activation energy. It is not consumed in the reaction.

⏱️ Measuring Rates

Definition

The rate of reaction is the change in concentration of a reactant or product per unit time.

$$Rate = \frac{-\Delta [\text{Reactants}]}{\Delta t} = \frac{\Delta [\text{Products}]}{\Delta t}$$

Units: $mol \ dm^{-3} \ s^{-1}$

Methods of Measurement

Method	What is Measured	Suitable When…	Example Reaction
Gas syringe	Volume of gas produced over time	A gas is a product	$Mg + 2HCl → MgCl_2 + H_2↑$
Mass loss	Decrease in mass (gas escapes)	A gas is a product	$CaCO_3 + 2HCl → CaCl_2 + H_2O + CO_2↑$
Disappearing cross	Time for precipitate to obscure a cross	A precipitate forms	$Na_2S_2O_3 + 2HCl → 2NaCl + H_2O + SO_2 + S↓$
Colorimetry	Change in absorbance / light transmission	A coloured species is consumed or produced	$Br_2$ (brown) decolourized by alkenes
Conductivity	Change in electrical conductivity	Number or type of ions changes	Ester hydrolysis (produces ions)

Lab setups for measuring reaction rate: gas syringe, mass loss, and precipitate methods

Reading rate from a graph: Plot [reactant] or [product] vs time. The gradient (slope) of the tangent at any point gives the instantaneous rate at that moment. The initial rate is measured from the tangent at $t = 0$.

💥 Collision Theory

Two Conditions for a Successful Collision

For a reaction to occur, particles must:

Collide with sufficient energy ($E ≥ E_a$)
Collide with the correct orientation (geometry)

A collision meeting both conditions is called an effective collision or successful collision.

Activation Energy ($E_a$)

The minimum energy that colliding particles must possess for a reaction to occur. It represents the energy barrier that must be overcome to break existing bonds and form new ones.

🎛️ Factors Affecting Rate

📺 R2.2.6 — Intermediates vs Transition States

Factor	Change	Effect on Rate	Explanation (Collision Theory)
Temperature	Increase ↑	Rate increases ↑	Main effect: Greater proportion of particles have $E ≥ E_a$. Minor effect: More frequent collisions.
Concentration	Increase ↑	Rate increases ↑	More particles per unit volume → more frequent collisions → more successful collisions per second.
Pressure (gases)	Increase ↑	Rate increases ↑	Same as concentration — particles are forced closer together, increasing collision frequency.
Surface area	Increase ↑ (smaller pieces)	Rate increases ↑	More particles exposed at the surface → more collisions per second.
Catalyst	Add catalyst	Rate increases ↑	Provides an alternative pathway with lower $E_a$. More particles now have sufficient energy.

⚠️ Temperature is special: For temperature, the main reason rate increases is that a greater proportion of particles have energy exceeding $E_a$ (shown by the Maxwell-Boltzmann curve). The increase in collision frequency alone is a minor contribution. This distinction is heavily tested!

📈 Maxwell-Boltzmann Distribution

📺 R2.1 — The Boltzmann Distribution

What It Shows

The Maxwell-Boltzmann distribution shows the number of particles (y-axis) at each kinetic energy (x-axis) in a sample of gas. Key features:

The curve starts at the origin (no particles have zero energy)
It has a peak (most probable energy)
It is asymptotic — the tail never touches the x-axis (a few particles always have very high energy)
The area under the curve equals the total number of particles

Maxwell-Boltzmann distribution curve showing effect of temperature on particle energy distribution

Effect of Temperature on the Distribution

Feature	Lower Temperature	Higher Temperature
Peak height	Taller (more particles at peak energy)	Shorter and broader
Peak position	Further left (lower most probable energy)	Shifts right (higher most probable energy)
Area beyond $E_a$	Smaller (fewer successful collisions)	Larger (more successful collisions)
Total area	Same (total number of particles unchanged)

Effect of a Catalyst on the Distribution

A catalyst does not change the distribution curve. Instead, it lowers $E_a$, meaning the $E_a$ line moves to the left. This means a greater proportion of the same distribution now has enough energy to react.

🧪 Catalysts

Definition

A catalyst is a substance that increases the rate of reaction by providing an alternative reaction pathway with a lower activation energy. It is not consumed and is regenerated at the end of the reaction.

Type	Description	Example
Homogeneous	Same phase as reactants	$H^+$ catalysing ester hydrolysis (all aqueous)
Heterogeneous	Different phase from reactants	Iron in the Haber process ($Fe(s)$ with gases)

Important: A catalyst does not change $\Delta H$ for the reaction. It lowers $E_a$ for both the forward and reverse reactions equally, so it does not shift the position of equilibrium.

🧠 Memory Aids

🔤 Two Requirements — "Energy + Orientation = Success"

Think of a key in a lock. The key needs to be turned with enough force (energy ≥ $E_a$) AND inserted in the correct direction (orientation). Only then will it unlock (react).

🔤 Factors — "TCSC" (Temperature, Concentration, Surface area, Catalyst)

All four factors increase rate by increasing successful collisions. But remember: Temperature works mainly through energy (more particles ≥ $E_a$), while C, S, and Catalyst work through frequency or lower $E_a$.

🔤 Maxwell-Boltzmann — "SANA" (Starts At zero, Never touches Axis)

The curve starts at the origin (0,0) and the tail never touches the x-axis. Higher temperature: peak goes down and right, but the total area stays the same.

🔤 Temperature vs Catalyst — "Curve Change vs Line Shift"

Temperature changes the curve (flattens and shifts right). Catalyst doesn't change the curve — it shifts the $E_a$ line left. Both result in more particles beyond $E_a$, but by different mechanisms.

🌍 Real-World Applications

🚗 Catalytic Converters — Heterogeneous Catalysis

Context: Car exhausts contain catalytic converters with platinum, palladium, and rhodium catalysts on a honeycomb structure.

Science: The large surface area of the honeycomb maximizes contact between exhaust gases and the catalyst. The catalyst lowers $E_a$ for the conversion of toxic $CO$ and $NO_x$ into harmless $CO_2$ and $N_2$: $2CO + 2NO → 2CO_2 + N_2$.

Impact: Reduces air pollution from vehicles. This is why leaded petrol was banned — lead poisons the catalyst by blocking active sites.

🥛 Storing Milk — Temperature and Rate

Context: Milk is refrigerated at ~4°C to extend its shelf life.

Science: At lower temperatures, bacterial enzymes have less kinetic energy. Fewer enzyme-substrate collisions have $E ≥ E_a$, so the rate of decomposition decreases dramatically. This illustrates the Maxwell-Boltzmann effect of temperature on reaction rate.

Impact: Refrigeration extends the lifespan of perishable foods from hours to days/weeks — a direct application of kinetics.

💥 Dust Explosions — Surface Area and Rate

Context: Flour mills and coal mines can experience devastating dust explosions.

Science: Fine particles of combustible material (flour, coal dust) have an enormous surface area. When suspended in air and ignited, the reaction rate is so fast that it becomes an explosion. A block of coal burns slowly; the same mass as fine dust can explode.

Impact: Industrial safety regulations require dust control, ventilation, and spark prevention in flour mills and coal mines.

⚠️ Common Mistakes

❌ "Temperature increases rate because particles collide more often" → ✅ This is only a minor effect. The main reason is that a greater proportion of particles have $E ≥ E_a$. You must mention this for full marks.
❌ "A catalyst gives particles more energy" → ✅ A catalyst does not change particle energy. It provides an alternative pathway with lower $E_a$. The distribution curve stays the same.
❌ Drawing the MB curve touching the x-axis → ✅ The curve is asymptotic — it approaches but never touches the x-axis. There are always a few particles with very high energy.
❌ "Rate = speed of reaction" → ✅ Rate has specific units ($mol \ dm^{-3} \ s^{-1}$) and is defined as the change in concentration per unit time. Don't use vague language like "speed".
❌ Saying a catalyst "shifts equilibrium" → ✅ A catalyst increases the rate of both forward and reverse reactions equally. It does not change the position of equilibrium — only how quickly it is reached.

🧪 Interactive Virtual Labs

Experiment 1: Disappearing Cross

Available

Simulate the reaction between Thiosulfate and Acid. Measure time for precipitate to obscure a cross.

→ Launch Simulation

Experiment 2: Gas Collection

Available

Measure the volume of hydrogen gas produced over time from Mg + HCl.

→ Launch Simulation

Maxwell-Boltzmann Distribution Simulator

Available

Visualize how temperature affects particle energy distribution.

→ Launch Simulation

📝 Exam-Style Questions

Question 1: Define the term "rate of reaction". [1 mark]

Mark Scheme:

[1 mark] The change in concentration of a reactant (or product) per unit time.

Question 2: Explain, using collision theory, why increasing temperature increases the rate of reaction. [3 marks]

Mark Scheme:

[1 mark] Particles gain kinetic energy / move faster.
[1 mark] (Minor) Collision frequency increases.
[1 mark] Crucially: A greater proportion of particles have energy ≥ $E_a$, so more collisions are successful.

Question 3: State two methods for measuring the rate of: $Mg(s) + 2HCl(aq) → MgCl_2(aq) + H_2(g)$. [2 marks]

Mark Scheme:

[1 mark] Measure volume of $H_2$ gas over time (gas syringe).
[1 mark] Measure decrease in mass over time (gas escapes).

Question 4: Sketch a Maxwell-Boltzmann distribution and label the axes. Show the effect of increasing temperature. [3 marks]

Mark Scheme:

[1 mark] Y-axis: Number of particles. X-axis: Kinetic Energy. Curve starts at origin, asymptotic at high energy.
[1 mark] Higher T curve: lower peak, shifted right.
[1 mark] Total area under both curves is the same.

Maxwell-Boltzmann Distribution showing effect of temperature

Question 5: Explain the effect of a catalyst on the rate of reaction. [2 marks]

Mark Scheme:

[1 mark] Provides an alternative reaction pathway.
[1 mark] With a lower activation energy ($E_a$), so a greater proportion of particles can react.

Question 6: Explain why powdered calcium carbonate reacts faster with hydrochloric acid than a lump of the same mass. [2 marks]

Mark Scheme:

[1 mark] Powder has a larger surface area.
[1 mark] More particles are exposed / available for collision with $HCl$ molecules → more frequent successful collisions.

Question 7: Using a Maxwell-Boltzmann diagram, explain why a catalyst increases the rate without changing the temperature. [2 marks]

Mark Scheme:

[1 mark] The catalyst lowers $E_a$ (the $E_a$ line moves left on the diagram).
[1 mark] The distribution curve does not change, but the area to the right of the new (lower) $E_a$ is greater → more particles can react.

Maxwell-Boltzmann Distribution showing effect of catalyst

Question 8: Distinguish between homogeneous and heterogeneous catalysts and give one example of each. [2 marks]

Mark Scheme:

[1 mark] Homogeneous: same phase as reactants (e.g. $H^+$ in ester hydrolysis, both aqueous).
[1 mark] Heterogeneous: different phase (e.g. $Fe(s)$ in the Haber process with gaseous reactants).