5.1.7 The Arrhenius Equation

• 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:

• • E_a 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:

• 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, E_a, 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

Answer

Using an Arrhenius plot:

• A graph of ln k against 1/T can be plotted, and then used to calculate E_a
  • 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 -E_a/R

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

Worked Example

Answers

Answer 1:

Answer 2:

Answer 3: