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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Measurement of the Activation Energy of a Reaction
(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:
where T is in degrees Kelvin and k is measured in units of s-1.
Answer the following questions:
Is this a first order or second order reaction ?
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,
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
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
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:
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