An empirical correlation for diffusion coefficients was developed by Wilke and C

Question

An empirical correlation for diffusion coefficients was developed by Wilke and Chang. For water as the solvent this formula is: D = 5.06 Times 10^-16 T/mu_W m^2/s Where T is the absolute temperature, mu w is the viscosity of water, and V_s is the molar volume of the solute at its boiling point (m^3/kgmol). Determine values for the following compounds in water at infinite dilution: methanol, propane, oxygen, and helium. How do they compare with experiment? [Wilke, C.R. and P.C. Chang, AlChE J, 1, 264, (1955).]

Explanation / Answer

At standar conditions T = 0 °C = 273 K; uW = 1.787 Pa.s; P = 101325 Pa

We are going to assume that every compound behave like an ideal gass, so the molar volume at boiling point would be:

Methanol: boling point Tb= 64.7 °C = 337.7

Vs = RT / P = (8.314 J/mol K *337.7 K) / 101325 Pa = 0.0277 m3/mol = 27.7 m3/kgmol

D = 1.053*10-14 m2/s

Propane Tb = -42 °C = 231 K

Vs =  (8.314 J/mol K *231 K) / 101325 Pa = 0.019 m3/mol = 19 m3/kgmol

D = 1.321*10-14 m2/s

Oxygen: Tb = -183 °C = 90 K

Vs= 0.0074 m3/mol = 7.4 m3/kgmol

D = 2.33*10-14 m2/s

Helium: Tb= -268.9 °C = 4.1 K

Vs = 0.00034 m3/mol = 0.34 m3/kgmol

D = 1.48*10-13 m2/s

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