Activation Energy & Arrhenius (Edexcel International A Level Chemistry)

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Activation Energy & Arrhenius

  • The rate equation shows how each of the reactants in a reaction effects the rate of the reaction and it includes the rate constant, k
  • However, k only remains constant if the concentration of the reactants is the only factor which is changed
    • If the temperature is changed or a catalyst is used or changed, then the rate constant, k, changes

  • At higher temperatures, a greater proportion of molecules have energy greater than than the activation energy
  • Since the rate constant and rate of reaction are directly proportional to the fraction of molecules with energy equal or greater than the activation energy, then at higher temperatures:
    • The rate of reaction increases
    • The rate constant increases

  • The relationship between the rate constant, the temperature and also the activation energy is given by the Arrhenius equation:

Arrhenius Equation, downloadable AS & A Level Chemistry revision notes

    • Ea and A are constants that are characteristic of a specific reaction
      • A does vary slightly with temperature but it can still be considered a constant

    • R is a fundamental physical constant for all reactions
    • k and T are the only variables in the Arrhenius equation

  • The Arrhenius equation is used to describe reactions that involve gases, reactions occurring in solution or reactions that occur on the surface of a catalyst

Finding the Activation Energy

  • Very often, the Arrhenius equation is used to calculate the activation energy of a reaction
  • A question will either give sufficient information for the Arrhenius equation to be used or a graph can be plotted and the calculation done from the plot

Using the Arrhenius Equation

  • The Arrhenius equation is easier to use if you take natural logarithms of each side of the equation, which results in the following equation:

ln of Arrhenius Equation, downloadable AS & A Level Chemistry revision notes

  • The Arrhenius Equation can be used to show the effect that a change in temperature has on the rate constant, k, and thus on the overall rate of the reaction
    • An increase in temperature (higher value of T) gives a greater value of ln k and therefore a higher value of k
    • Since the rate of the reaction depends on the rate constant, k, an increase in k also means an increased rate of reaction

  • The equation can also be used to show the effect of increasing the activation energy on the value of the rate constant, k
    • An increase in the activation energy, Ea, means that the proportion of molecules which possess at least the activation energy is less
    • This means that the rate of the reaction, and therefore the value of k, will decrease

  • The values of k and T for a reaction can be determined experimentally
    • These values of k and T can then be used to calculate the activation energy for a reaction
    • This is the most common type of calculation you will be asked to do on this topic

Worked example

Calculate the activation energy of a reaction which takes place at 400 K, where the rate constant of the reaction is 6.25 x 10-4 s-1.

A = 4.6 x 1013 and R = 8.31 J mol-1 K-1.

Answer

WE calculate Ea answer, downloadable AS & A Level Chemistry revision notes

Using an Arrhenius plot:

  • A graph of ln k against 1/T can be plotted, and then used to calculate Ea
    • This gives a line which follows the form y = mx + c

The graph of ln k against 1/T is a straight line with gradient -Ea/R

  • From the graph, the equation in the form of y = mx + c is as follows:

5.2.5 Y = mx + c from Arrhenius graph_2, downloadable AS & A Level Chemistry revision notes

Worked example

  1. Complete the following table
  2. Plot a graph of ln k against 1/T
  3. Use this to calculate the activation energy, Ea, and the Arrhenius constant, A, of the reaction.

Calculate the activation energy from the Arrhenius plot - WE, downloadable AS & A Level Chemistry revision notes

Answer 1:

5.2.5 Using Arrhenius plot to calculate Ea - calculation answer complete table (WE)_1, downloadable AS & A Level Chemistry revision notes

Answer 2:

5.2.5 using Arrhenius plot to calculate Ea - plotted graph (WE)_2, downloadable AS & A Level Chemistry revision notes

Answer 3: 5.2.5 WE Arrhenius plot calculate Ea 1_1, downloadable AS & A Level Chemistry revision notes

5.2.5 WE Arrhenius plot calculate Ea 2_2, downloadable AS & A Level Chemistry revision notes

5.2.5 WE Arrhenius plot - calculate A (part 1)_1, downloadable AS & A Level Chemistry revision notes

5.2.5 WE Arrhenius plot - calculate A (part 2)_2, downloadable AS & A Level Chemistry revision notes

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Richard

Author: Richard

Expertise: Chemistry

Richard has taught Chemistry for over 15 years as well as working as a science tutor, examiner, content creator and author. He wasn’t the greatest at exams and only discovered how to revise in his final year at university. That knowledge made him want to help students learn how to revise, challenge them to think about what they actually know and hopefully succeed; so here he is, happily, at SME.