CHE425: Problem set #1
1. A beaker filled with an equimolar liquid mixture of ethyl alcohol and ethyl acetate
evaporates at 0oC 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:
Ethyl acetate (AC)
Ethyl alcohol (AL)
Vapor pressure (kPa) at 0oC
3.23
1.62
Diffusivity in air (m2/s)
6.45×10-6
9.29×10-6
Therefore, the mole fractions in the well-mixed liquid when 50% of the AL has evaporated
are,
25
 0.566
25  19.2
19.2

 0.434
25  19.2
xAL 
xAC
2. An open tank, 10 ft in diameter, containing benzene at 25oC 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
temperature is 25oC, what is the loss of benzene in lb/day? The specific gravity of benzene at
60oF is 0.877. The concentration of benzene outside the film is negligible. For benzene, the
vapor pressure at 25oC is 100 torr, and the diffusivity in air is 0.08 cm2/s.
Benzene loss rate = 9.14 x 10-7 (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
tube, the temperature ia 170oF, 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
lbmol/hft2, assuming that the rate is controlled by mass transfer in the vapor phase. Gas
diffusivity of toluene in benzene = 0.2 ft2/h. Pressure = 1 atm (in the tube). Vapor pressure of
toluene at 170oF = 400 torr.
NT 
cDT,B  yT  yTI 

 0.00217  0.2  0.300  0.211
z
= 0.00464 lbmol/h-ft 2
0.00833
Benzene diffuses at the same rate in the opposite direction.
Pure water
4.2 Air at 25oC and a dew-point temperature of 0oC flows past the
open end of a vertical tube filled with water at 25oC. The tube has
an inside diameter of 0.83 inch, and the liquid level is 0.5 inch
below the top of the tube. The diffusivity of water in air at 25oC is
0.256 cm2/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
0.5 in
cm
5.2 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
105oC. The diffusivity is 0.180 cm2/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),
nA 
cDA,X A  yA1  yA 2 
 5 10
9

 0.0000322  0.180  0.0314  0.75  0.20 
z
mol/s from bulb 1 to 2
20
nX  5  109 mol/s from bulb 2 to 1
(b)
Distance from
Bulb 1, cm
0 (Bulb 1)
5
10
15
20 (Bulb 2)
yA
yX
cm/s
cm/s
0.7500
0.6125
0.4750
0.3375
0.2000
0.2500
0.3875
0.5250
0.6625
0.8000
0.0066
0.0081
0.0104
0.0147
0.0248
0.7500
0.6111
0.4760
0.3367
0.1996
(c) Because we have equimolar, countercurrent diffusion, the molar average velocity of the
mixture is zero.
6.2 HCl gas diffuses through a film of air 0.1 in. thick at 20oC. 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
HCl/scm2, if the total pressure is (a) 10 atm, (b) 1 atm, (c) 0.1 atm. The diffusivity of HCl in
air at 20oC and 1 atm is 0.145 cm2/s.
 1  ( yH )2  (6.03 106 )  1  0 
7
2
NH 
ln 
ln 

  1.9110 mol HCl/s-cm
z
 0.254)   1  0.008 
 1  ( yH )1 
cDH,A
(b) NH = 1.98 x 10-6 mol/s-cm2
(c) NH =3.82 x 10-5 mol/s-cm2
7. Water in an open disk exposed to dry air at 25oC vaporizes at a constant rate of 0.04
g/hcm2. It the water surface is at the wet-bulb temperature of 11.0oC, 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
atm and 291 K is 0.24 cm2/s.
 1 0 
4.29 105  0.24  ln 

1  0.013 

z 
 0.218 cm
6.17 107
Note that the bulk flow has little effect here.
8. A polyisoprene membrane of 0.8 m thickness is used to separate methane from H2.
Estimate the mass transfer fluxes using the following data:
Methane
Hydrogen
Partial pressure, MPa
Solubility
Membrane side Membrane side S, mol/m3-Pa
1
2
2.5
0.05
1.14 x 10-4
2.0
0.20
0.17 x 10-4
Diffusivity
D, m2/s
8.0 x 10-11
109 x 10-11
Solution ---------------------------------------------------------------------------------------------Species
H, mol/m3-Pa
D, m2/s
Flux, N, mol/m2-s
p, Pa
Methane
2.45 x 106
1.14 x 10-4
8.0 x 10-11
0.028
6
-4
-11
Hydrogen 1.80 x 10
0.17 x 10
109 x 10
0.042