*Interactive Video
Case Study:
Arrhenius - Linearisation of an exponential equation*

Produced by Graham Currell, University of the
West of England, Bristol in association with:, and

● Royal Society of Chemistry, 'Discover Maths for Chemists' website

**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 *E _{a}* is the
activation energy of the reaction and

**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},

calculatetheˇ

activation energy,of the reaction.E,_{a}ˇ the value of the

constant,in the equation.A,

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

**S****tudy
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)

**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: *E _{a }*=
87.9 kJ mol

**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