Interactive Case Study:    Arrhenius - Linearizing an exponential equation

Produced by Graham Currell, University of the West of England, Bristol, in association with:
Royal Society of Chemistry, 'Discover Maths for Chemists' website
, and

Essential Mathematics and Statistics for Science, 2nd Edition
Graham Currell and Antony Dowman, Wiley-Blackwell, 2009

Measurement of the Activation Energy of a Reaction (Arrhenius equation)

The Arrhenius equation

gives the rate constant, k, of a chemical reaction as a function of temperature, T, where Ea is the activation energy of the reaction and R is the gas constant.

The following exercise gives a worked example with video answers to illustrate the mathematics of this problem.

The rate constant, k, of a chemical reaction is measured at several temperatures, T, as given in the table below:

 T 600 700 800 900 1000 ºK k 0.00034 0.0031 0.029 0.1 0.38 s-1

where T is in degrees Kelvin and k is measured in units of s-1.

The above data can be downloaded in the Excel (2003) file ArrheniusData

Question 1

Is this a first order or a second order reaction?

Question 2

Assuming the data follows the Arrhenius equation:

where R is the gas constant with a value of 8.314 J K-1 mol-1,
calculate:

• activation energy, Ea, of the reaction, and
• the value of the constant, A, in the equation.

Study guide:

The numerical and video answers are given in the sections below.
The following techniques are relevant to the calculations in this problem:

Standard techniques of rearranging equations (study guide)
Key properties of exponentials and logarithms (study guide)
Linear regression for the slope and intercept of a straight line (study guide)
Excel for data analysis (web): X-Y graphs using Excel (video), Linear regression using Excel (video)