2.2.3

The Arrhenius Equation (A2 Only)

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The Arrhenius Equation

The rate constant can be expressed in terms of the activation energy by using the Arrhenius equation.

The Arrhenius equation

The Arrhenius equation

  • The Arrhenius equation is: k=Ae−EaRT k = Ae^{\frac{-E_a}{RT}}
    • In this equation, k is the rate constant.
    • A is the Arrhenius constant.
    • R is the gas constant.
    • T is the temperature.
    • Ea is the activation energy.
Using the Arrhenius equation

Using the Arrhenius equation

  • The Arrhenius equation lets us find the rate constant at different temperatures.
  • More importantly, if we measure the rate constant at a bunch of different temperatures, we can calculate the activation energy.
Key points about the equation

Key points about the equation

  • As the activation energy rises, the rate constant gets smaller (so the rate is slower).
    • This is what you expect - think back to the Maxwell Boltzmann distribution.
    • The higher the activation energy, the fewer the number of molecules with enough energy to react.
  • As temperature rises, the rate constant gets larger, so the rate is faster.
    • Again, you can understand this by thinking about the Maxwell Boltzmann distribution.

Arrhenius Plots

An Arrhenius plot is the name given to the graph used to find the activation energy.

The activation energy

The activation energy

  • You can rearrange the Arrhenius plot to find the activation energy.
    • The Arrhenius equation is:
      • k=Ae−EaRT k =Ae^{\frac{-E_a}{RT}}
    • This can be rearranged to:
      • ln(k)=−EaRT+ln(A)ln(k) = \frac{-E_a}{RT} + ln(A)
  • This means that if we plot the graph of ln(k) against 1/T, you have a graph with the gradient as −EaR{\frac{-E_a}{R}}.
An example

An example

  • The gradient of the above graph is -6.014.
  • This means that the activation energy is:
    • 6.014 × R = 50 J

Arrhenius Calculations

You need to be able to calculate the activation energy given a rate constant and vice versa.

Calculating the activation energy

Calculating the activation energy

  • The Arrhenius equation is:
    • k=Ae−EaRT k = Ae^{\frac{-E_a}{RT}}
  • If you want to calculate the activation energy, the easiest way is to rearrange the equation into:
    • ln(k)=−EaRT+ln(A)ln(k) = \frac{-E_a}{RT} + ln(A)
  • You can then substitute in the values for k and A that you’re given to get the activation energy out.
Calculating the rate constant

Calculating the rate constant

  • To calculate the rate constant, you can just use the original Arrhenius equations and throw all of the values into your calculator.
Jump to other topics
1

Physical Chemistry

1.1

Atomic Structure

1.1.1Fundamental Particles1.1.2Isotopes & Mass Number1.1.3Mass Spectrometry1.1.4Electron Shells, Sub-Shells & Orbitals1.1.5Electron Configuration1.1.6Ionisation Energy1.1.7Factors Affecting Ionisation Energies1.1.8Trends of Ionisation1.1.9Specific Impacts on Ionisation Energies1.1.10End of Topic Test - Atomic Structure1.1.11A-A* (AO3/4) - Atomic Structure
1.2

Amount of Substance

1.2.1Relative Masses1.2.2The Mole1.2.3The Ideal Gas Equation1.2.4Empirical & Molecular Formulae1.2.5Balanced Equations1.2.6Percentage Yield1.2.7A-A* (AO3/4) - Percentage Yield1.2.8Atom Economy1.2.9End of Topic Test - Amount of Substance1.2.10A-A* (AO3/4) - Substances & Yield1.2.11Diagnostic Misconceptions - Moles
1.3

Bonding

1.3.1Ionic Bonding1.3.2Covalent & Dative Bonding1.3.3Carbon Structures1.3.4Metallic Bonding1.3.5Physical Properties1.3.6Shapes of Molecules1.3.7Polarity1.3.8Intermolecular Forces1.3.9Intermolecular Forces 21.3.10End of Topic Test - Bonding1.3.11Exam-Style Question - Shape of Molecules1.3.12A-A* (AO3/4) - Bonding1.3.13Diagnostic Misconceptions - Ions1.3.14Diagnostic Misconceptions - Ionic & Covalent1.3.15Diagnostic Misconceptions - Phase Change1.3.16Diagnostic Misconceptions - Boiling1.3.17Diagnostic Misconceptions - Polar Bonds
1.4

Energetics

1.4.1Enthalpy Changes1.4.2Bond Breaking and Making1.4.3Enthalpy Changes: Standard Conditions1.4.4Calorimetry1.4.5Hess' Law1.4.6Bond Enthalpies1.4.7End of Topic Test - Energetics1.4.8Diagnostic Misconceptions - Calorimetry
1.5

Kinetics

1.5.1Collision Theory1.5.2Maxwell-Boltzmann Distribution1.5.3Increasing Rates1.5.4End of Topic Test - Kinetics
1.6

Equilibria

1.6.1Le Chatelier1.6.2Equilibrium Constants1.6.3A-A* (AO3/4) - Energetics, Kinetics, Equilibria1.6.4End of Topic Test - Equilibria1.6.5Diagnostic Misconceptions - Solids
1.7

Redox

1.7.1Redox1.7.2End of Topic Test - Redox
2

Physical Chemistry 2 (A2 Only)

2.1

Thermodynamics (A2 Only)

2.1.1Born-Haber Cycles (A2 Only)2.1.2Born-Haber Cycle Calculations (A2 Only)2.1.3Entropy (A2 Only)2.1.4Free Energy (A2 Only)2.1.5End of Topic Test - Thermodynamics2.1.6A-A* (AO3/4) - Thermodynamics
2.2

Rate Equations (A2 Only)

2.2.1Rate Equations (A2 Only)2.2.2Rate Equations 2 (A2 Only)2.2.3The Arrhenius Equation (A2 Only)2.2.4Experimental Methods for Rates (A2 Only)2.2.5End of Topic Test - Rate Equations2.2.6Exam-Style Question - Rates2.2.7A-A* (AO3/4) - Rate Equations
2.3

The Equilibrium Constant Kp (A2 Only)

2.3.1Properties of Kp (A2 Only)
2.4

Electrochemical Cells (A2 Only)

2.4.1Electrochemical Cells (A2 Only)2.4.2Electrochemical Series (A2 Only)2.4.3Commercial Application (A2 Only)2.4.4End of Topic Test - Kp & Electrochemistry2.4.5A-A* (AO3/4) - Electrochemical Cells2.4.6Diagnostic Misconceptions - Salt Bridges2.4.7Diagnostic Misconceptions - Electrode, Electrolyte
2.5

Acids & Bases (A2 Only)

2.5.1Brønsted-Lowry Acids & Bases (A2 Only)2.5.2pH (A2 Only)2.5.3The Ionic Product of Water (A2 Only)2.5.4Weak Acids & Bases (A2 Only)2.5.5pH Curves & Titrations (A2 Only)2.5.6pH Curves & Titrations 2 (A2 Only)2.5.7Buffer Solutions (A2 Only)2.5.8End of Topic Test - Acids & Bases2.5.9Exam-Style Question - Weak Acids2.5.10A-A* (AO3/4) - Acids & Bases2.5.11Diagnostic Misconceptions - Ammonia is an Alkali2.5.12Diagnostic Misconceptions - Water's Neutrality2.5.13Diagnostic Misconceptions - Concentrate & Strength
3

Inorganic Chemistry

3.1

Periodicity & Trends

3.1.1The Periodic Table3.1.2Trends in the Periodic Table3.1.3End of Topic Test - Periodicity & Trends3.1.4Diagnostic Misconceptions - Atomic Radius
3.2

Group 2

3.2.1Group 2 Chemistry3.2.2End of Topic Test - Group 2
3.3

Group 7

3.3.1Introduction to Halogens3.3.2Reactions of Halogens3.3.3Chlorine & Chlorate(I)3.3.4End of Topic Test - Group 73.3.5Exam-Style Question - Group 73.3.6A-A* (AO3/4) - Periodicity, Group 2 & 7
4

Inorganic Chemistry 2 (A2 Only)

4.1

Period 3 (A2 Only)

4.1.1Period 3 Elements & Oxides (A2 Only)4.1.2Period 3 Oxides (A2 Only)4.1.3End of Topic Test - Period 3
4.2

Transition Metals (A2 Only)

4.2.1General Properties (A2 Only)4.2.2Substitution Reactions (A2 Only)4.2.3Shapes of Complex Ions (A2 Only)4.2.4Colours of Ions (A2 Only)4.2.5Variable Oxidation States (A2 Only)4.2.6Titrations (A2 Only)4.2.7Homogeneous Catalysts (A2 Only)4.2.8Heterogeneous Catalysts (A2 Only)4.2.9End of Topic Test - Transition Metals4.2.10A-A* (AO3/4) - Transition Metals
4.3

Reactions of Ions in Aqueous Solutions (A2 Only)

4.3.1Acidity (A2 Only)4.3.2Identification (A2 Only)4.3.3End of Topic Test - Reactions of Ions in Solution
5

Organic Chemistry 1

5.1

Introduction

5.1.1Naming Conventions5.1.2Mechanism5.1.3Isomerism5.1.4End of Topic Test - Introduction to Organic Chem
5.2

Alkanes

5.2.1Fractional Distillation5.2.2Cracking5.2.3Combustion5.2.4Chlorination5.2.5End of Topic Test - Alkanes
5.3

Halogenoalkanes

5.3.1Substitution Reactions5.3.2Elimination Reactions5.3.3Ozone Depletion5.3.4End of Topic Test - Halogenoalkanes
5.4

Alkenes

5.4.1Introduction to Alkenes5.4.2Reactions of Alkenes5.4.3Polymerisation Reactions5.4.4Properties of Polymers5.4.5End of Topic Test - Alkenes
5.5

Alcohols

5.5.1Production of Alcohols5.5.2Oxidation of Alcohols5.5.3Oxidation of Alcohols - 25.5.4Elimination Reactions5.5.5End of Topic Test - Alcohols5.5.6Exam-Style Question - Alcohols
5.6

Organic Analysis

5.6.1Reactions5.6.2Reactions 25.6.3Mass Spectrometry5.6.4Infrared Spectroscopy5.6.5End of Topic Test - Organic Analysis
5.7

A-A* (AO3/4) - Organic 1

5.7.1A-A* (AO3/4) - Organic 1
6

Organic Chemistry 2 (A2 Only)

6.1

Optical Isomerism (A2 Only)

6.1.1Optical Isomerism (A2 Only)6.1.2End of Topic Test - Optical Isomerism
6.2

Aldehydes & Ketones (A2 Only)

6.2.1Aldehydes & Ketones (A2 Only)6.2.2End of Topic Test - Aldehydes & Ketones
6.3

Carboxylic Acids & Esters (A2 Only)

6.3.1Acids & Esters (A2 Only)6.3.2Acylation (A2 Only)6.3.3End of Topic Test - Carboxylic Acids & Esters
6.4

Aromatic Chemistry (A2 Only)

6.4.1Structure & Reactivity (A2 Only)6.4.2Reactions of Benzene (A2 Only)6.4.3End of Topic Test - Aromatic Chemistry
6.5

Amines (A2 Only)

6.5.1Nature & Preparation of Amines (A2 Only)6.5.2Basicity & Nucleophilicity (A2 Only)6.5.3End of Topic Test - Amines
6.6

Polymers (A2 Only)

6.6.1Condensation Polymers (A2 Only)6.6.2Biodegradability (A2 Only)
6.7

Biological Organic (A2 Only)

6.7.1Amino Acids (A2 Only)6.7.2Proteins (A2 Only)6.7.3DNA (A2 Only)6.7.4Anti-Cancer Drugs (A2 Only)6.7.5End of Topic Test - Biological Organic
6.8

Organic Synthesis (A2 Only)

6.8.1Organic Synthesis (A2 Only)6.8.2Examples of Synthetic Routes (A2 Only)6.8.3End of Topic Test - Polymers & Organic Synthesis
6.9

NMR Spectroscopy (A2 Only)

6.9.1Understanding NMR (A2 Only)6.9.2Carbon-13 NMR (A2 Only)6.9.3Hydrogen-1 NMR (A2 Only)6.9.4Hydrogen-1 NMR 2 (A2 Only)6.9.5End of Topic Test - NMR
6.10

Chromatography (A2 Only)

6.10.1Overview of Chromatography (A2 Only)6.10.2Thin-Layer Chromatography (A2 Only)6.10.3Column Chromatography (A2 Only)6.10.4Gas Chromatography (A2 Only)6.10.5End of Topic Test - Chromatography
6.11

A-A* (AO3/4) - Organic 2

6.11.1A-A* (AO3/4) - Organic 2

Practice questions on The Arrhenius Equation (A2 Only)

Can you answer these? Test yourself with free interactive practice on Seneca — used by over 10 million students.

  1. 1
    Variables in the Arrhenius equation:Fill in the list
  2. 2
    A reaction is less likely to happen if:True / false
  3. 3
    Considering the Maxwell-Boltzmann distribution, what best explains why a higher activation energy has a lower rate?Multiple choice
  4. 4
    What does E<sub>a</sub> represent in the Arrhenius equation?Multiple choice
  5. 5
    On a graph of 1/T vs ln(k), what feature represents the activation energy?Multiple choice
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Rate Equations 2 (A2 Only)

Experimental Methods for Rates (A2 Only)