1.28c. Steady-state molecular diffusion in gases.
A mixture of ethanol and water vapor is being rectified in an adiabatic distillation column. The alcohol is vaporized and transferred from the liquid to the vapor phase. Water vapor condenses (enough to suply the latent heat of vaporization needed by the alcohol being evaporated) and is transferred from the vapor to the liquid phase. Both components diffuse through a gas film 0.1 mm thick. The temperature is 368 K and the pressure is 1 atm. The mole fraction of ethanol is 0.8 on one side of the film and 0.2 on the other side of the film. Calculate the rate of diffusion of ethanol and of water, in kg/m2-s. The latent heat of vaporization of the alcohol and water at 368 K can be estimated by the Pitzer acentric factor correlation (Reid, et al., 1987)
where w is the acentric factor.
Solution
A = ethanol B = water
Calculate ethanol heat of vaporization
Calculate water heat of vaporization
Estimate diffusivity from Wilke-Lee
1.29a, d. Analogy among molecular heat and mass transfer.
It has been observed that for the system air-water vapor at near ambient conditions, Le = 1.0 (Treybal, 1980). This observation, called the Lewis relation, has profound implications in humidification operations, as will be seen later. Based on the Lewis relation, estimate the diffusivity of water vapor in air at 300 K and 1 atm. Compare your result with the value predicted by the Wilke-Lee equation. For air at 300 K and 1 atm:Cp = 1.01 kJ/kg-K, k = 0.0262 W/m-K, m = 1.846 ´ 10-5 kg/m-s, and r = 1.18 kg/m3.
Solution
Estimate diffusivity from the Wilke-Lee equation