Calculation of the Rate Constant


If you've ever left something in your refrigerator too long, you know that once bacteria starts growing, it usually spreads fast. The following example is not specific to any type of yeast or bacteria.

Let's use a pre-exponential factor of 1 x 1010 s-1. The ideal gas constant is 8.3145 J/mol K. Assume an activation energy of 50 kJ/mol and a temperature of 40 ° C. Find the rate constant from the given information.

Solution:

Arrhenius' equation requires temperatures to be in the Kelvin scale. Therefore, we must convert the temperature we are given into Kelvin. This can be done easily by adding 273.15 to the temperature in degrees Celsius. You could also use the automatic unit converter.

Temperature in Kelvin = Temperature in Celsius + 273.15
Kelvin = 40 + 273.15 = 313.15 K

Now that we have the temperature in the correct scale, we can put the given numbers directly into the Arrhenius equation:

k = A*exp(-E/(RT))
k = 1 x 1010*exp(-50,000/(8.3145*313.15)) = 45.7 s-1

If these numbers were for a specific yeast or bacteria, this would represent 45.7 cells growing per second. Time to clean that refrigerator!

Return to the Bread Making page
Return to Kinetics

[Introduction | Kinetics | Heat Transfer | Mass Transfer | Bibliography]

This project was funded in part by the National Science Foundation and is advised by Dr. Masel and Dr. Blowers at the University of Illinois.

© 2007 Arizona Board of Regents for The University of Arizona