The rate at which a substance passes through a semi permeable membrane is determined by the diffusivity D(cm²/s) of the gas. D varies with the membrane temperature T(K) according to the Arrhenius equation: D = D₀ exp (? E RT) where D₀ = the pre-exponential factor E = the activation energy for diffusion R = 1.987 cal/mol ?K). Diffusitivities of SO₂ in a fluorosilicone rubber tube are measured at several temperatures, with the following results:

(a) What are the units of D₀ and E?

(b) How should the data be plotted to obtain a straight line on rectangular coordinates?

(c) Plot the data in the manner indicated in part (b) and determine D₀ and E from the resulting line.

(d) Write a computer program or spreadsheet to read in the (T, D) data and to calculate D₀ and E using the method of least squares (Appendix A.1). Then run the program and print out the results.

Transcribed Image Text:

T(K) 347.0 374.2 396.2 420.7 447.7 471.2 D (cm²/s) x 10° 1.34 2.50 4.55 8.52 14.07 19.99 (so that D = 1.34 x 10-cm²/s)