IBDP Chemistry HL Cheat sheet - Reactivity 2.2 - How fast? The rate of chemical change | IBDP Chemistry Cheatsheets

What rate of reaction means

Rate of reaction = change in concentration of a reactant or product per unit time.
For reactants, concentration decreases; for products, concentration increases.
Units often used: mol dm $^{-3}$ s $^{-1}$ , cm $^{3}$ s $^{-1}$ , g s $^{-1}$ depending on the data provided.
In exams, rate is commonly found from:
- gradient of a graph
- average rate over a time interval
- instantaneous rate using a tangent
Always check whether the graph is concentration–time, volume–time or mass–time before calculating.

Measuring rate experimentally

Rate is rarely measured directly as concentration change.
Common practical methods:
- Gas volume collected vs time
- Mass loss vs time when gas escapes
- Colour / opacity change vs time
- Sampling + titration at intervals
If time is the dependent variable, you often compare time taken for a fixed change.
If time is the independent variable, you track how some measurable quantity changes with time.
Steeper gradient = faster reaction.
A tangent gives instantaneous rate at one point; a chord between two points gives average rate.
In practical design, keep all other variables constant when testing one factor.

This image shows how reactant and product concentrations change with time and how the slope of a tangent gives instantaneous rate. It is useful for IB questions on reading rate from graphs and relating slopes to stoichiometric ratios. Source

Collision theory

A reaction happens only when particles collide.
Not every collision is successful.
A successful collision must have:
- sufficient energy to overcome activation energy, $E_a$
- correct orientation so bonds can break/form in the right way
Higher temperature means higher average kinetic energy, so more particles can react.
Collision geometry / orientation matters: even energetic collisions may fail if particles are aligned wrongly.

Factors that affect rate

Concentration: higher concentration means more particles per unit volume, so more frequent collisions.
Pressure (for gases): higher pressure means particles are closer together, so collision frequency increases.
Surface area: greater surface area means more exposed particles, so more collisions can occur.
Temperature: increases both collision frequency and the fraction of particles with energy $\geq E_a$ .
Catalyst: increases rate by giving an alternative pathway with lower $E_a$ .
Exam rule: when explaining any factor, link it to collision frequency, energy, or successful collisions.

Activation energy and Maxwell–Boltzmann distributions

Activation energy, $E_a$ = minimum energy needed for a collision to lead to reaction.
On an energy profile, $E_a$ is the energy gap from reactants to the peak.
The peak represents the transition state / activated complex.
A Maxwell–Boltzmann distribution shows the spread of particle energies in a sample.
Area under the curve to the right of $E_a$ = fraction of particles able to react.
When temperature increases:
- the curve becomes lower and broader
- the peak shifts right
- the area beyond $E_a$ increases a lot
This explains why a small increase in temperature can cause a large increase in rate.

This image shows that only particles with energy to the right of $E_a$ can react. It helps explain why raising temperature increases the fraction of successful collisions, not just the number of collisions. Source

Catalysts

A catalyst increases reaction rate by providing an alternative reaction pathway with lower $E_a$ .
A catalyst does not change $\Delta H$ of the reaction.
A catalyst is not used up overall.
In equilibrium contexts, catalysts speed up both forward and backward reactions equally.
On an energy profile:
- reactant and product energy stay the same
- the peak is lower
On Maxwell–Boltzmann diagrams, a catalyst is shown by moving the $E_a$ line left, increasing the area beyond it.
Enzymes are biological catalysts.

This image shows that a catalyst lowers $E_a$ but does not change the overall energy difference between reactants and products. It is very useful for explaining catalyst questions in both SL and HL. Source

HL only – Reaction mechanisms, intermediates and the rate-determining step

Many reactions occur in a series of elementary steps.
The slowest step is the rate-determining step (RDS).
The overall mechanism must be consistent with:
- the overall equation
- the experimental rate equation
- any stated kinetic data
An intermediate:
- is formed in one step and used up in a later step
- does not appear in the overall equation
A transition state:
- is the highest-energy state during a step
- appears at the peak of an energy profile
- is not isolatable
Be able to distinguish:
- intermediate = species between steps
- transition state = energy maximum during a step
The RDS is not always the first step.
Molecularity of an elementary step:
- unimolecular = 1 reacting particle
- bimolecular = 2 reacting particles
- termolecular = 3 reacting particles

HL only – Rate equations and reaction order

A rate equation has the form: rate = $k[A]^m[B]^n$
The exponents are the orders with respect to each reactant.
Overall order = sum of all exponents.
Orders are determined experimentally, not from the balanced equation.
Order can suggest how many particles are involved in the RDS, but only for a proposed mechanism.
Typical graph shapes:
- Zero order:
  - rate–concentration graph = horizontal line
  - concentration–time graph = straight decreasing line
- First order:
  - rate–concentration graph = straight line through origin
  - concentration–time graph = curved exponential decay
- Second order:
  - rate–concentration graph = upward curve
  - concentration–time graph = steeper curve at start, then levels off
Strategy for experimental data:
- compare trials where only one concentration changes
- see how the rate changes
- deduce the exponent from the pattern
Rate constant, $k$ depends on temperature.
Units of $k$ depend on overall order.

HL only – Arrhenius equation

The Arrhenius equation links rate constant and temperature:
- $k = Ae^{-E_a/RT}$
Meanings:
- $k$ = rate constant
- $A$ = Arrhenius factor / frequency factor
- $E_a$ = activation energy
- $R$ = gas constant
- $T$ = temperature in K
As temperature increases, $k$ increases.
$A$ reflects how often collisions occur with correct orientation.
Linear form:
- $\ln k = -\dfrac{E_a}{R}\left(\dfrac{1}{T}\right) + \ln A$
For a graph of $\ln k$ against $1/T$ :
- slope = $-E_a/R$
- intercept = $\ln A$
Therefore you can calculate:
- $E_a$ from the slope
- $A$ from the intercept
Exam warning: use Kelvin, and keep units consistent for $E_a$ and $R$ .

This image shows the linear Arrhenius plot used to calculate activation energy from the gradient. It is the key diagram for HL data analysis on temperature dependence of rate. Source

Checklist: can you do this?

Calculate rate from a graph, including using a tangent for instantaneous rate.
Explain rate changes using collision theory, $E_a$ , and successful collisions.
Sketch and interpret energy profiles and Maxwell–Boltzmann distributions with and without a catalyst.
HL: Deduce a rate equation and reaction order from experimental data.
HL: Use an Arrhenius plot to determine $E_a$ and interpret $A$ .

Common exam traps

Do not say rate increases just because particles move faster; link it to more frequent and/or more successful collisions.
Do not confuse $\Delta H$ with $E_a$ .
Do not derive reaction order from the balanced equation unless told the reaction is elementary.
Do not forget that a catalyst changes rate, not the position of equilibrium.
In HL data questions, always check units of $k$ , slope, $E_a$ , and temperature in K.

Written by:

Dr Shubhi Khandelwal

Qualified Dentist and Expert Science Educator

Shubhi is a seasoned educational specialist with a sharp focus on IB, A-level, GCSE, AP, and MCAT sciences. With 6+ years of expertise, she excels in advanced curriculum guidance and creating precise educational resources, ensuring expert instruction and deep student comprehension of complex science concepts.