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D = D_0exp [-E/RT] Where: D_0 is the pre-exponential factor E is the activation

ID: 1842950 • Letter: D

Question

D = D_0exp [-E/RT] Where: D_0 is the pre-exponential factor E is the activation energy for diffusion R = universal gas constant The whitening of teeth is a rapidly expanding cosmetic industry, but little is known, quantitatively, about the rate at which hydrogen peroxide permeates the enamel of teeth. A biomedical engineering student is studying this phenomenon and wants to see if the Arrhenius equation shown above works well as a model of hydrogen peroxide transport into teeth. She measures the diffusivities of hydrogen peroxide in tooth enamel at several temperatures with the following results: What are the units of D_0 and E? How should the data be plotted to obtain a straight line on rectangular coordinate paper? Plot the data in the manner indicated in part b and determine D_0 and E from the resulting line. Use excel to calculate D0 and E using the method of least squares. Print a screen shot of your results and staple it to your homework before you turn it in.

Explanation / Answer

a) The unit of Do is cm^2/s which is same as that of D

The of E is Joules which is the unit of energy

b)

By taking natural logarithm on both sides if the equation we get

ln(D)= ln(Do) -E/(RT)

Let ln(D) = y

Ln(Do)= b

-E/R= m

and 1/T = x

the equation becomes y = mx+b which is a straight line