Spreadsheet Assignment #11:  Linear Regression - Arrhenius Equation

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For first-order chemical reactions, the rate constant, k, is related to the activation energy, Ea, by the Arrhenius equation:

      ln k = ln A - (Ea / RT),       where R = the gas constant, 8.314 J/K.mole

A series of reactions are run at different temperatures and the rate constant at each temperature is determined.  By plotting the rate constant, k, vs. 1/T in Kelvins, a linear plot is obtained, with the slope of the line equal to -Ea/R.  The intercept is ln A, or the pre-exponential factor.  Usually, 1/T is multiplied by 1000 to help make the units on the x-axis more manageable.  (This also converts Joules into kilojoules when the slope of the line is determined.)

Calculate 1000/T and plot the resulting values on the x-axis.  Plot the natural log, ln, of the rate constant on the y-axis and determine the value of the activation energy, Ea.  Extend your best-fit line to the y-axis intercept (x=0) and report the value of the y-intercept.  Report values for both A and Ea on your spreadsheet.   Click to download data: 11-ArEqn

Spreadsheet Activity #11: Arrhenius Equation - Evaluation of Ea
Temperature	Rate Const.	1000/TEMP	ln (k)
Kelvins	k (mol/L.sec)	(1000/Kelvins)	(mol/L.sec)
400	0.011	.	.
430	0.035	.	.
460	0.105	.	.
490	0.343	.	.
510	0.789	.	.
540	2.17	.	.
610	20.0	.	.
700	145	.	.
.
.	Slope:	.	.
.	Gas Const. R=	8.314	J/K.mole
.	Ea:	.	kJ/mole

 

Excel Programming Tips:

If you do not want an axis to cut through the middle of your graph, you can move it.  To move the X axis, right click on the Y axis and select Format Axis and then click on the scale tab.  You can place the axis where you want by entering values on the “Value (X) axis Crosses at” option.