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

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Data Analysis: Measurement of the Activation Energy of a Reaction (Arrhenius equation)
(download the following question as a Word document for educational use)

 

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.

You can then follow study links to other resources to help you with the mathematics.

 

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 0.10 0.38 s-1

 

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

 

Answer the following questions:

 

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

 

You can click here for the answers and for study help with the relevant calculations.


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)

 

 

 

Answers

 

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:


 

Please send any comments and suggestions to:
graham.currell@uwe.ac.uk
17/09/09