AP | A-Level | IB | NCERT 11 + 12 – FREE NOTES, RESOURCES AND VIDEOS!
S1.1 - Introduction to the particulate nature of matter S1.2 - The nuclear atom S1.3 - Electron configurations S1.4 - Counting particles by mass - The mole S1.5 - Ideal gases S2.1 - The ionic model S2.2 - The covalent model S2.3 - The metallic model S2.4 - From models to materials S3.1 - The periodic table - Classification of elements S3.2 - Functional groups - Classification of organic compounds R1.1 - Measuring enthalpy changes R1.2 - Energy cycles in reactions R1.3 - Energy from fuels R1.4 - Entropy and spontaneity AHL R2.1 - How much? The amount of chemical change R2.2 - How fast? The rate of chemical change R2.3 - How far? The extent of chemical change R3.1 - Proton transfer reactions R3.2 - Electron transfer reactions R3.3 - Electron sharing reactions R3.4 - Electron-pair sharing reactions

R2.2 - How fast? The rate of chemical change

2.2.1 Rate of Reaction 2.2.2 Collision Theory 2.2.3 Factors Affecting Reaction Rate 2.2.4 Activation Energy and Temperature 2.2.5 Catalyst and Activation Energy 2.2.6 Reaction Mechanism and Intermediates (AHL) 2.2.7 Energy Profile and Rate Determining Step (AHL) 2.2.8 Molecularity in Reaction Mechanism (AHL) 2.2.9 Rate Equations and Experimental Data (AHL) 2.2.10 Reaction Orders and Graphs (AHL) 2.2.11 Rate Constant, K (AHL) 2.2.12 Arrhenius Reaction and Temperature (AHL) 2.2.13 Arrhenius Factor and Activation Energy (AHL)

The Arrhenius Factor (A) HL Only

Specification Reference R2.2.13

Quick Notes

  • In the Arrhenius equation, A is the frequency factor – it reflects how often collisions occur with the correct orientation to react.
  • Arrhenius equation:
    IB Chemistry Arrhenius equation showing k = Ae^-Ea/RT
  • Linear form (used for graphing):
    IB Chemistry linear form of Arrhenius equation ln k = -Ea/R (1/T) + ln A
  • A graph of ln k vs 1/T gives a straight line:
    • Slope = –Ea / R
    • Intercept = ln A

Full Notes

Background theory to the Arrhenius Equation has been covered here - make sure you are comfortable with it before tackling this page.

What Is the Arrhenius Factor, A?

A (the pre-exponential factor) reflects how often particles collide with the correct orientation to react.

While Ea (activation energy) represents the energy barrier, A indicates the frequency and effectiveness of collisions.

Photo of Matt
Matt’s exam tip

You can think of A as the maximum possible theoretical rate — if all particles had enough energy, the rate would simply be A × [reactants]. See this video for more: https://youtu.be/kj4laup0kvs

Performing Arrhenius Equation Calculations

Worked Example

Calculate Activation Energy (Ea) Using Two Rate Constants

  1. A reaction has the following rate constants, k, at 300K and 350K. Determine the activation energy, Ea, for the reaction.
    At 300K, k = 2.5 × 10−3 s−1
    At 350K, k = 5.0 × 10−3 s−1
  2. Use:
    ln (k2 / k1) = (−Ea / R) × (1/T2 − 1/T1)
    ln (5.0 × 10−3 / 2.5 × 10−3) = (−Ea / 8.31) × (1/350 − 1/300)
    ln 2 = (−Ea / 8.31) × (−4.76 × 10−4)
  3. Ea = (ln 2 × 8.31) / (4.76 × 10−4)
    Ea = 12 110 J mol−1 = 12.1 kJ mol−1

Photo of Matt
Matt’s exam tip

when using the Arrhenius equation in calculations, don’t forget units of activation energy (Ea) are kJ mol−1! The gas constant, R, has units of J K−1 mol−1, meaning you must convert any calculated Ea value to kJ (divide by 1000).

Using Arrhenius Graph to Find Ea and A

The gradient of an Arrhenius plot is −Ea÷R which can be rearranged to find activation energy (Ea).

By plotting ln k vs. 1÷T, we can also use the intercept of the line across the y axis to find A.

IB Chemistry Arrhenius plot showing ln k versus 1/T with gradient −Ea/R and intercept ln A for HL kinetics.

Summary