Interactive Video Case Study: Arrhenius - Linearisation of 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

Data Analysis: 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 ēK 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.

Question 1

Is this a first order or second order reaction ?

Question 2

Assuming that the data follows the Arrhenius equation,

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

calculate the

ˇ         activation energy, Ea, of the reaction.

ˇ         the value of the constant, A, in the equation.

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

Study guide

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)

Question 1         It must be a first order reaction because the units of the rate constant, k, are given as: s-1.

The units of k for a second order reaction would be given as: s-1 (mol L-1)-1 or  L mol-1 s-1 .

Question 2         The correct answers are:  Ea = 87.9 kJ mol-1, and A = 13.9 × 103 s-1

Video Answers: - including specific links to revision/help in the relevant mathematical skills: