The Arrhenius Equation (Oxford AQA International A Level (IAL) Chemistry): Revision Note

The Arrhenius Equation

• The rate equation shows how each reactant affects the rate of the reaction

• 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

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

$\mathit{k}\mathbf{=}\mathit{A}{\mathit{e}}^{\left(\frac{-E_a}{\mathrm{RT}}\right)}$

• Terms in 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 that occur in solution

  • Reactions that occur on the surface of a catalyst

Activation Energy Calculations

• The Arrhenius Equation is often used to calculate:

  • The activation energy, E_a, of a reaction

  • The Arrhenius constant, A, for a reaction

• A question will give sufficient information for:

  • The Arrhenius equation to be used

  • Or, a graph to 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:

$\mathbf{ln}\mathit{k}\mathbf{=}\mathbf{ln}\mathit{A}\mathbf{-}\frac{{\mathit{E}}_{\mathit{a}}}{\mathit{R}\mathit{T}}$

• How temperature affects the rate constant and rate of reaction:

  • An increase in temperature gives a greater value of ln k

  • This results in a higher value for the rate constant, k

  • Since the rate of the reaction depends on the rate constant, k, an increase in k also means an increased rate of reaction

• How activation energy affects the rate constant:

  • An increase in the activation energy, E_a, means a smaller proportion of molecules has the required activation energy

  • This results in a lower value for the rate constant, k

  • Since the rate of the reaction depends on the rate constant, k, a decrease in k also means a decreased rate of reaction

• 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

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

$\mathbf{ln}\mathit{k}\mathbf{=}\frac{\mathbf{-}{\mathit{E}}_{\mathbf{a}}}{\mathit{R}}\frac{\mathbf{1}}{\mathbf{T}}\mathbf{+}\mathbf{ln}\mathit{A}$

• Where:

  • y = ln k 

  • x = $\frac{1}{T}$

  • m = $\frac{-E_{\mathrm{a}}}{R}$ (the gradient)

  • c = ln A (the y-intercept)

• The equation shows that 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

Example graph of ln k over 1/T