Edexcel A Level Chemistry:复习笔记5.5.9 Arrhenius & Activation Energy

Arrhenius & Activation Energy

 

  • 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:

5.2.4-Arrhenius-Equation_2

    • 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:

5.2.4-ln-of-Arrhenius-Equation_2

 

  • 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

5.2.5-WE-calculate-Ea-answer

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

     

5.2.5-Arrhenius-sketch-of-ln-k-against-1_T_2

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

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.

5.2.5-Calculate-the-activation-energy-from-the-Arrhenius-plot-WE

 

Answer 1:

5.2.5-Using-Arrhenius-plot-to-calculate-Ea-calculation-answer-complete-table-WE_1

Answer 2:

 

5.2.5-using-Arrhenius-plot-to-calculate-Ea-plotted-graph-WE_2

 

Answer 3:

5.2.5-WE-Arrhenius-plot-calculate-Ea-1_1

 

5.2.5-WE-Arrhenius-plot-calculate-Ea-2_2

 

5.2.5-WE-Arrhenius-plot-calculate-A-part-1_1

 

5.2.5-WE-Arrhenius-plot-calculate-A-part-2_2

 

 

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