IB DP Chemistry Reactivity 2.2: How fast? Rates and collision theory – Revision Notes

These notes condense Reactivity 2.2.1 to 2.2.5, the rate and collision theory part of Reactivity 2.2, How fast? The rate of chemical change, from the February 2023 IB Diploma Programme Chemistry guide, whose first exams ran in 2025. All of it is examined at both SL and HL. The HL-only material that follows in the guide (Reactivity 2.2.6 to 2.2.13) is not included here.

Each idea is set out in full, with longer worked examples, in the study guide; afterwards, test yourself on the practice questions. The IB DP chemistry hub lists every unit, and the checklist prints the whole course on one page. If you are not sure where your gaps are, try our free diagnostics.

Key definitions

Term	Meaning
Rate of reaction	How fast the concentration of a named reactant or product changes, per unit time (mol dm⁻³ s⁻¹)
Instantaneous rate	Gradient of the tangent to a concentration–time (or volume or mass–time) curve at one moment
Initial rate	Gradient of the tangent at t = 0
Successful collision	A collision with energy ≥ Ea and proper orientation, which leads to reaction
Activation energy, Ea	Smallest energy a collision must bring for the particles to react
Catalyst	Increases the rate by providing an alternative pathway with lower Ea; not used up overall
Enzyme	A biological catalyst
Kinetically stable	Reacts very slowly because Ea is high, even if the reaction is exothermic

Rate (2.2.1): method in steps

Average rate over an interval

1. Read the property at the start and end of the interval.
2. Divide the change by the time taken.
3. Give units: mol dm⁻³ s⁻¹, cm³ s⁻¹ or g s⁻¹.

Rate at one moment (tangent)

1. Draw a long straight tangent touching the curve at that time.
2. Pick two well-separated points on the tangent, not on the curve.
3. Gradient = Δy/Δx. Quote rate as positive, with units.

Converting between species. Use the equation’s coefficients. For 2SO₂ + O₂ → 2SO₃, SO₃ forms twice as fast as O₂ is used up.

Converting units. Mass of gas: divide by molar mass to get moles. Gas volume: divide by the molar volume you are given for the conditions.

Worked reminder. Sodium carbonate solution is poured into excess hydrochloric acid in an open flask, and the balance reading drops by 0.88 g in 25 s. Average rate = 0.88/25 = 0.035 g s⁻¹. In moles of CO₂: 0.88/44.01 = 0.0200 mol, so the rate = 0.0200/25 = 8.0 × 10⁻⁴ mol s⁻¹.

Why the curve flattens. As reactants are used up their concentration falls, collisions become less frequent and the gradient decreases. The curve becomes horizontal when a reactant is used up.

Ways to follow a reaction

Measure against time	Suits
Gas volume	Any reaction that gives off a gas
Mass loss	CO₂ or another heavy gas leaving an open flask
Absorbance (colorimeter)	A coloured reactant or product
Conductivity or pH	Ions used up or made
Time for a fixed change	Colour change or precipitate; rate ∝ 1/t

Time is the independent variable when you take readings at set times. It is the dependent variable when you time a fixed change.

Collision theory (2.2.2)

• Reaction needs a collision with E ≥ Ea and the proper orientation (collision geometry).
• Average kinetic energy ∝ absolute temperature (kelvin). K = °C + 273.15.
• Doubling the kelvin temperature doubles the average kinetic energy. Raising 20 °C to 40 °C increases it by only about 7% (293.15 K → 313.15 K).

Factors (2.2.3): what changes and why

Factor	Collision frequency	Fraction with E ≥ Ea
Concentration ↑	↑	no change
Pressure ↑ (gases)	↑	no change
Surface area ↑	↑	no change
Temperature ↑	↑ (small effect)	↑ (main effect)
Catalyst added	no change	↑ (because Ea is lower)

Controlled variables in a rate investigation: temperature, volumes and concentrations of solutions, mass and particle size of solids, stirring, apparatus.

Errors from graphs. Scatter about the line → random error (reduce by repeats). All points displaced the same way, or an unexpected intercept → systematic error (repeats do not help).

Maxwell–Boltzmann curves (2.2.4 and 2.2.5)

Sketch checklist

• Axes labelled: kinetic energy (x); number or fraction of particles (y).
• Curve starts at the origin.
• Single peak, then a long tail that approaches but never meets the x-axis.
• Ea marked as a vertical line to the right of the peak; shade the area beyond it.

Higher temperature (T₂ > T₁)

• Peak lower and shifted right; curve broader.
• Same area under both curves (same number of particles).
• Much more area beyond Ea → far more successful collisions per unit time.

Catalyst

• Same single curve (temperature unchanged).
• Second Ea line further left, labelled Ea(cat).
• Larger area beyond Ea(cat) → larger fraction of successful collisions.

Energy profiles (2.2.5)

Feature	Exothermic	Endothermic
Products vs reactants	Lower	Higher
Sign of ΔH	Negative	Positive
Ea(reverse)	Ea(forward) + size of ΔH	Ea(forward) − ΔH
With catalyst	Lower hump, same ΔH	Lower hump, same ΔH

A catalyst lowers the forward and reverse barriers by the same amount. That is why it speeds both directions equally and leaves the equilibrium position unchanged (Reactivity 2.3).

Worked reminder. An endothermic reaction has Ea = 140 kJ mol⁻¹ and ΔH = +35 kJ mol⁻¹. Ea(reverse) = 140 − 35 = 105 kJ mol⁻¹.

Linking questions to have an answer for

• Kinetic molecular theory (Structure 1.1): collision theory adds Ea and orientation to the idea that particles are always moving, with a spread of kinetic energies.
• Fuels (Reactivity 1.3): a fuel–air mixture is safe to store because its combustion has a high Ea; a spark supplies the energy to start it.
• Alkanes (Reactivity 3.3): strong, essentially non-polar C–C and C–H bonds give a high Ea, so alkanes are kinetically stable even though their combustion is exothermic.
• Equilibrium (Reactivity 2.3): a catalyst increases the forward and backward rates by the same factor.
• HL link (Structure 3.1): transition elements are often used as catalysts.

Must-know distinctions

• Average rate vs instantaneous rate: the first is an interval average; the second is a tangent gradient.
• More collisions vs more frequent collisions: rate depends on collisions per unit time.
• Temperature vs catalyst on a Maxwell–Boltzmann curve: temperature changes the curve; a catalyst moves the Ea line.
• Kinetic vs thermodynamic stability: a high Ea makes a reaction slow; a positive or negative ΔH says nothing about speed. A high Ea is a useful property of a fuel, because it will not ignite until energy is supplied.
• Celsius vs kelvin: only kelvin temperatures are proportional to average kinetic energy.

Quick self-test

1. State the definition of rate of reaction.
2. A tangent to a gas volume–time curve passes through (10 s, 16 cm³) and (50 s, 64 cm³). Calculate the rate at that point.
3. In 2SO₂ + O₂ → 2SO₃, O₂ is used at 1.5 × 10⁻³ mol dm⁻³ s⁻¹. Find the rate of formation of SO₃.
4. Convert 127 °C to kelvin.
5. Give the two conditions for a successful collision.
6. Why does crushing a solid reactant speed up the reaction?
7. Why does a temperature rise increase rate much more than the rise in average kinetic energy suggests?
8. On a Maxwell–Boltzmann curve, what stays the same when the temperature is raised?
9. How do you show a catalyst on a Maxwell–Boltzmann curve?
10. A time-to-colour-change run takes 40 s. Give a value proportional to the rate.
11. State what an enzyme is.

Answers

1. How fast the concentration of a named reactant or product changes, per unit time.
2. Gradient = (64 − 16)/(50 − 10) = 1.2 cm³ s⁻¹.
3. 2 × 1.5 × 10⁻³ = 3.0 × 10⁻³ mol dm⁻³ s⁻¹.
4. 400.15 K (400 K).
5. Energy at least equal to Ea, and proper orientation.
6. More of the solid’s particles are exposed, so collisions happen more often.
7. A larger fraction of collisions now have E ≥ Ea; the extra collision frequency is a small effect.
8. The total area under the curve (the number of particles).
9. One curve only; add a second Ea line to the left of the first.
10. 1/40 = 0.025 s⁻¹.
11. A biological catalyst.

Where marks are usually lost

• Reading a single point off a curve when the question asks for the rate at a time: you need a tangent.
• Taking the two gradient points from the curve instead of from the tangent line.
• Missing or wrong units: cm³ s⁻¹ for gas volume, mol dm⁻³ s⁻¹ for concentration.
• Forgetting the stoichiometric ratio when asked for the rate of a different species.
• Explaining a temperature effect only through collision frequency.
• Using Celsius in a kinetic energy comparison.
• Maxwell–Boltzmann sketches that start above the origin, touch the x-axis, or show a larger area at higher temperature.
• Adding a second curve for a catalyst, or changing ΔH on an energy profile when a catalyst is added.
• Saying a catalyst changes the yield at equilibrium.

Official syllabus

Condensed from the International Baccalaureate’s Diploma Programme Chemistry guide (February 2023; first assessment 2025). These notes follow Reactivity 2.2, How fast? The rate of chemical change, understandings 2.2.1 to 2.2.5, which are common to SL and HL.