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CHE425: Problem set #1

1. A beaker filled with an equimolar liquid mixture of ethyl alcohol and ethyl acetate oevaporates at 0C into still air at 101 kPa. All of the mass-transfer resistance is in the still air layer in the beaker. If each component evaporates independently determine the liquid composition when half the ethyl alcohol has evaporated. You can assume well-mixed liquid, ne negligible bulk flow effect, and Raoult’s law. The following data are available:

o2 Vapor pressure (kPa) at 0C Diffusivity in air (m/s) -6 Ethyl acetate (AC) 3.23 6.45×10-6 Ethyl alcohol (AL) 1.62 9.29×10

Therefore, the mole fractions in the well-mixed liquid when 50% of the AL has evaporated are,

25x0.566AL2519.2 19.2x0.434AC2519.2

o2. An open tank, 10 ft in diameter, containing benzene at 25C is exposed to air. Above the

liquid surface is a stagnant air film 0.2 in. thick. If the pressure is 1 atm and the air otemperature is 25C, what is the loss of benzene in lb/day? The specific gravity of benzene at o60F is 0.877. The concentration of benzene outside the film is negligible. For benzene, the o2vapor pressure at 25C is 100 torr, and the diffusivity in air is 0.08 cm/s.

-7Benzene loss rate = 9.14 x 10 (78.11)(72,930)(3600)(24)/454 = 991 lb/day

3) An insulated glass tube and condenser are mounted on a reboiler containing benzene and toluene. The condenser returns liquid reflux down the wall of the tube. At one point in the otube, the temperature ia 170F, the vapor contains 30 mol% toluene, and the reflux contains 40 mol% toluene. The thickness of the stagnant vapor film is estimated to be 0.1 in. The molar latent heats of benzene and toluene are equal. Calculate the rate at which toluene and benzene are being interchanged by equimolar counter diffusion at this point in the tube in 2lbmol/h?ft, assuming that the rate is controlled by mass transfer in the vapor phase. Gas 2diffusivity of toluene in benzene = 0.2 ft/h. Pressure = 1 atm (in the tube). Vapor pressure of otoluene at 170F = 400 torr.

cDyy；？0.002170.20.3000.211；？；？；？T,BTTIN，，T z0.00833

2 = 0.00464 lbmol/h-ft

Benzene diffuses at the same rate in the opposite direction.

Pure water

2oo4. Air at 25C and a dew-point temperature of 0C flows past the oopen end of a vertical tube filled with water at 25C. The tube has 0.5 in an inside diameter of 0.83 inch, and the liquid level is 0.5 inch cm obelow the top of the tube. The diffusivity of water in air at 25C is 20.256 cm/s. (a) How long will it take for the liquid level in the tube to drop 3 inches? (b) Use Matlab to plot the tube liquid level as a function of time for this period. Label the graph with your name using the Title command.

t = 2,260 h

25. Two bulbs are connected by a tube, 0.002 m in diameter and 0.20 m long. Bulb 1 contains argon, and bulb 2 contains xenon. The pressure and temperature are maintained at 1 atm and o2105C. The diffusivity is 0.180 cm/s. At a time when the argon mole fraction at end 1 of the tube is 0.75, and 0.20 at the other end, determine the: (a) Rates and directions of mass transfer of argon and xenon; (b) Transport velocity of each species; (c) Molar average velocity of the mixture.

Solution

(a) From form of Eq. (3-18),

cDAyy0.00003220.1800.03140.750.20；？；？；？；？；？A,XAA12nAz20

9 510 mol/s from bulb 1 to 2~

9n510 mol/s from bulb 2 to 1，~X

(b)

Distance from y y ，;cm/s ，;cm/s AX(

Bulb 1, cm

0 (Bulb 1) 0.7500 0.2500 0.0066 0.7500

5 0.6125 0.3875 0.0081 0.6111

10 0.4750 0.5250 0.0104 0.4760

15 0.3375 0.6625 0.0147 0.3367

20 (Bulb 2) 0.2000 0.8000 0.0248 0.1996

(c) Because we have equimolar, countercurrent diffusion, the molar average velocity of the mixture is zero.

2o6. HCl gas diffuses through a film of air 0.1 in. thick at 20C. The partial pressure of HCl on

one side of the film is 0.08 atm and zero on the other. Estimate the rate of diffusion in mol 2HCl/s?cm, if the total pressure is (a) 10 atm, (b) 1 atm, (c) 0.1 atm. The diffusivity of HCl in o2air at 20C and 1 atm is 0.145 cm/s.

6cD?(1()(6.0310)10！~！y?(H,A72H2N，，lnln，~1.9110 mol HCl/s-cm?)H?)z1()0.254)10.00y8；！！；？??H1??

-62(b) N = 1.98 x 10 mol/s-cm H

-52 (c) N =3.82 x 10 mol/s-cm H

o7. Water in an open disk exposed to dry air at 25C vaporizes at a constant rate of 0.04 2og/h?cm. It the water surface is at the wet-bulb temperature of 11.0C, calculate the effective

gas-film thickness (i.e., the thickness of a stagnant air film that would offer the same

resistance to vapor diffusion as is actually encountered). Diffusivity of water vapor in air at 1 2atm and 291 K is 0.24 cm/s.

10?(54.29100.24ln~；？?)10.013??；，z0.218 cm 76.17~10

Note that the bulk flow has little effect here.

8. A polyisoprene membrane of 0.8 m thickness is used to separate methane from H. 2

Estimate the mass transfer fluxes using the following data:

Partial pressure, MPa Solubility Diffusivity 32 Membrane side Membrane side S, mol/m-Pa D, m/s

1 2 -4-11Methane 2.5 0.05 1.14 x 10 8.0 x 10 -4-11Hydrogen 2.0 0.20 0.17 x 10 109 x 10

Solution ---------------------------------------------------------------------------------------------- 322Species H, mol/m-Pa D, m/s Flux, N, mol/m-s p, Pa 6-4-11Methane 2.45 x 10 1.14 x 10 8.0 x 10 0.028 6-4-11Hydrogen 1.80 x 10 0.17 x 10 109 x 10 0.042

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