The Arrhenius Equation (HL) (DP IB Chemistry): Revision Note

The Arrhenius Equation

• The rate equation shows how each of the reactants in a reaction affects 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 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

What is the Arrhenius equation?

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

• Where:

  • k = Rate constant

  • A = Arrhenius factor (also known as the frequency factor or pre-exponential factor) which is a constant that takes into account the frequency of collisions with proper orientations

  • E_a = Activation energy (J mol^-1)

  • R = Gas constant (8.31 J K^-1 mol^-1)

  • T = Temperature (Kelvin, K)

  • e = Mathematical constant (can be found on your calculator - it has the approximate value of 2.718)

• 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

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

Graphing the Arrhenius Equation

Finding the activation energy and Arrhenius factor

• A graph of experimental data can be used to determine the activation energy and the Arrhenius factor

Arrhenius equation graph

• 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
    

  Graph of ln k against 1/T

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

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

• Where:

  • y = ln k

  • x = 

  • m =  (the gradient)

  • c = ln A (the y-intercept)

• E_a can be calculated by:
  

  • E_a = - gradient x R

• As the slope has a negative gradient, the minus signs cancel giving E_a as a positive value

• The Arrhenius factor, A, can be calculated by:

  • A = e^y-intercept