Dr. Mohamed Helmy Page 1 Kingdom of Saudi Arabia
Ministry of Higher Education King Abdulaziz University Faculty of Engineering (Rabigh)
Department of Chemical and Materials Engineering
ةيلك ةسدنهلا غبارب
مسق هسدنهلا ةيئايميكلا
ةسدنهو لا داوم
Mass Transfer CHEN 331 Tutorial # 4
Answer the following questions:
Question: 1
Diffusion of A through non-diffusing B
There is a 2 mm thick layer of water on the floor of a room. The water vaporizes and diffuses through a stagnant film of air of estimated thickness 2.5 mm on the water surface. Under the conditions of evaporation, the water temperature is 22 ˚C and the ambient air temperature is 28
˚C. Calculate the time required for the water layer to disappear completely for the following cases:
a) The ambient air has a relative humidity of 60%.
b) The floor has micropores and water penetrates the floor at a constant rate of 0.1 kg/m2. Given:
The diffusivity of water vapor in air is 0.853 ft2/h at 1 atm and 0 ˚C.
Vapor pressure of water (in bar) is given by: 𝑙𝑛𝑝𝑣 = 13.8573 − 5160.2/𝑇, where T is the temperature in K.
Question: 2
Diffusion of A through non-diffusing B
Ammonia (A) diffuses through a stagnant layer of air (B), 1 cm thick, at 25 ˚C and 1 atm total pressure. The partial pressure of NH3 on the two sides of the air layer are 𝑝𝐴1 = 0.9 atm and 𝑝𝐴2 = 0.1 atm respectively. Air is non-diffusing and 𝐷𝐴𝐵 = 0.214 𝑐𝑚2/𝑠. Calculate;
a) the molar flux of NH3,
b) the velocities of the individual components with respect to a stationary observer, c) the molar and the mass average velocities of the components, and
d) the molar flux of NH3 with respect to an observer moving with the mass average velocity.
Prepare the plots for the partial pressure distribution of ammonia and air along the diffusion path.
Question: 3
A test tube, 1.5 cm in diameter and 12 cm height, is partially filled with a solution of alkaline pyrogallate. The depth of the empty space above the solution is 5 cm. The temperature is 25 ˚C and the total pressure is 1 atmosphere. Air composition is 21% O2 and 79% N2. The diffusivity of O2 in N2 at given conditions is 0.21 cm2/s.
Dr. Mohamed Helmy Page 2 a) Calculate the rate of absorption of oxygen from air in the solution at steady state if air
flows gently over the open end of the test tube. Make plots of the distribution of partial pressures of the gases along the diffusion path.
b) Calculate the partial pressure gradient of oxygen midway in the diffusion path.
c) Calculate the molar average velocity of the mixture and the diffusion velocity of the two components oxygen and nitrogen at the top end, at the middle, and at the liquid surface.
d) Calculate the flux of the components midway of the diffusion path with respect to an observer moving with twice the molar average velocity at the location in the direction away from the liquid surface.
Question: 4
Equimolar counter diffusion.
Two large vessels are connected by a tube of 5 cm in diameter and 15 cm in length. Vessel 1 contains 80% N2 (A) and 20% O2 (B); vessel 2 contains 20% N2 and 80% O2. The temperature is 20 ˚C and the pressure is 2 atmosphere. Calculate:
(a) The stead state flux and rate of transport of N2 from vessel 1 to vessel 2, (b) The same quantities for O2,
(c) The partial pressure of N2 and its gradient in the tube 0.05 m from vessel 1, (d) The net flux with respect to a stationary observer.
Given: The diffusivity of N2-O2 pair is 0.23 cm2/s at 316 K and 1 atm.
Question: 5
Ethanol is diffusing through a 4-mm stagnant film of water. The ethanol concentrations of the entrance and the existing planes are maintained at 0.1 and 0.02 mol/m3, respectively. If the water film temperature is 283 K, determine the steady-state molar flux of the ethanol and the concentration profile as a function of the position z within the liquid film.
Compare these results with a 4-mm stagnant film of air at 283 K and 1 atm at the same entrance and exit ethanol concentrations.
Question: 6
A spherical ball of solid, nonporous naphthalene, a ‘‘moth ball’’, is suspended in still air. The naphthalene ball slowly sublimes, releasing the naphthalene into the surrounding air by molecular diffusion-limited process. Estimate the time required to reduce the diameter from 2 to 0.5 cm when the surrounding air is at 347 K and 1.013×105 Pa. Naphthalene has a molecular weight of 128 g/mol, a solid density of 1.145 g/cm3, a diffusivity in air of 8.19×106 m2/s, and exerts a vapor pressure of 5 Torr (666 Pa) at 347 K.
