Problem #7 The diffusivity coefficient of a substance can be calculated from Fic

Question

Problem #7 The diffusivity coefficient of a substance can be calculated from Fick's Law and is represented in the following equation: D = Doe-E/1987T Where D : diffusion coefficient, [cm2/s] Do = maximum diffusion coefficient E activation energy of diffusion, [cal/g-mole] T = absolute temperature, [K] Please answer the following: 1) What are the units of Do and the constant 1.987? Justify your answer 2) Derive an equation for D [in2/s] where T and E can be entered in 'R and Btu/lb-mole, respectively 3) What is the maximum diffusion coefficient DO for a D 2 in2/s, E 1,000 Btu/lb-mole, and T 180 'R.

Explanation / Answer

Part 1

Units of Do = units of D = cm2/s

Exp (-E/1.987T) = unitless

Units of 1.987 x T = units of E = cal/gmol

Units of 1.987 = cal/gmol-K

Part 2

D cm2/s x (1in/2.54cm)2 = Do cm2/s x (1in/2.54cm)2 x exp (-E/1.987T)

D = Do x exp (-E/1.987T)

Where D = in2/s

E = BTU/lbmol

T = °R

Part 3

Do = D/exp(-E/1.987T)

= 2/exp(-1000/1.987*180)

= 32.75 in2/s

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