# Chapter 3 Example

## Determination of the Activation Energy

This is Example 3-1 from the book page 95.

Calculate the activation energy for the decomposition of benzene diazonium chloride to give chlorobenzene and nitrogen:

using the information in Table E3-1.1 for this first order reaction.

Solution

__Solution__

We start by recalling Equation (3-20)
We can use the data in Table E3-1.1 to determine the activation energy, E, and frequency factor, A, in two different ways. One way is to make a semilog plot of k vs. (1/T) and determine E from the slope. Another way is to use Excel or Polymath to regress the data. The data in Table E3-1.1 was entered in Excel and is shown in Figure E3-1.1 which was then used to obtain Figure E3-1.2.

A step-by-step tutorial to construct both an Excel and a Polymath spread sheet is given in the Chapter 3 Summary Notes on the CD-ROM.

(a)Graphical Solution

Figure E3-1.2(a) shows the semilog plots from which we can calculate the activation energy. From CD-ROM Appendix D, we show how to rearrange Equation (3-20) in the form

Rearranging

To use the decade method, choose 1/T_{1} and 1/T_{2} so that k_{2}= 0.1k_{1}. Then, log(k_{1}/k_{2})=1.

When k_{1} = 0.005: 1/T_{1} = 0.003025 and when k_{2}= 0.0005: 1/T_{2} = 0.00319

Therefore,

From Figure E3-1.2(b) and Equation (E3-1.3), we see

ln A = 37.12

taking the antilog

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