The Arrhenius Equation (AQA A Level 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 that 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

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

$k={\mathrm{Ae}}^{\frac{-{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}}$

$$\begin{gathered} \mathrm{KEY}: \\ k=\mathrm{Rate}\mathrm{constant} \\ \mathrm{A}=\mathrm{Arrhenius}\mathrm{constant}\left(\mathrm{a}\mathrm{constant}\mathrm{related}\mathrm{to}\mathrm{the}\mathrm{collision}\mathrm{frequency}\mathrm{and}\mathrm{orientation}\mathrm{of}\mathrm{the}\mathrm{molecules}\right) \\ {\mathrm{E}}_{\mathrm{a}}=\mathrm{Activation}\mathrm{energy}\left({\mathrm{Jmol}}^{-1}\right) \\ \mathrm{R}=\mathrm{Gas}\mathrm{constant}\left(8.314{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}\right) \\ \mathrm{T}=\mathrm{Temperature}\mathrm{in}\mathrm{Kelvin} \\ \mathrm{e}=\mathrm{Mathematical}\mathrm{constant}\left(\mathrm{can}\mathrm{be}\mathrm{found}\mathrm{on}\mathrm{your}\mathrm{calculator}-\mathrm{it}\mathrm{has}\mathrm{an}\mathrm{approximate}\mathrm{value}\mathrm{of}2.718\right) \end{gathered}$$

• A varies only slightly with temperature; it can be considered a constant

• e, E_a, and R are also constants

Using the Arrhenius Equation

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

$\ln k=\ln \mathrm{A}-\frac{{\mathrm{E}}_{\mathrm{a}}}{\mathrm{RT}}$

• In the exam, you could be asked to calculate any part of the Arrhenius Equation, and using it in this form will make it easier

• 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 that 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 can be used to calculate the activation energy for a reaction, which is the most common type of calculation you will be asked to do on this topic

Related topics

• Rate Equations

• Finding Activation Energy

• Maxwell–Boltzmann distribution