Page 148 - Separation process principles 2

Exercises 113

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EXERCISES
Section 3.1 level was originally 0.5 in. below the top of the tube. The diffusiv-
ity of water in air at 25°C is 0.256 cm2/s.
3.1 A beaker filled with an equimolar liquid mixture of ethyl
alcohol and ethyl acetate evaporates at PC into still air at 101 kPa (a) How long will it take for the liquid level in the tube to drop 3 in.?
(1 atm) total pressure. Assuming Raoult's law applies, what will be (b) Make a plot of the liquid level in the tube as a function of time
the composition of the liquid remaining when half the original ethyl for this period.
alcohol has evaporated, assuming that each component evaporates 3.5 Two bulbs are connected by a tube, 0.002 m in diameter and
independently of the other? Also assume that the liquid is always 0.20 m in length. Initially bulb 1 contains argon, and bulb 2 con-
well mixed. The following data are available: tains xenon. The pressure and temperature are maintained at 1 atrn
and 105"C, at which the diffusivity is 0.180 cm2/s. At time t = 0,
Vapor Pressure, Diffusivity in Air diffusion is allowed to occur between the two bulbs. At a later time,
kPa at 0°C m2/s the argon mole fraction in the gas at end 1 of the tube is 0.75, and
0.20 at the other end. Determine at the later time:
Ethyl acetate (AC) 3.23 6.45 x
Ethyl alcohol (AL) 1.62 9.29 x (a) The rates and directions of mass transfer of argon and xenon
(b) The transport velocity of each species
3.2 An open tank, 10 ft in diameter and containing benzene at
(c) The molar average velocity of the mixture
25"C, is exposed to air in such a manner that the surface of the liq-
uid is covered with a stagnant air film estimated to be 0.2 in. thick. Section 3.2
If the total pressure is 1 atrn and the air temperature is 25"C, what 3.6 The diffusivity of toluene in air was determined experimen-
loss of material in pounds per day occurs from this tank? The spe- tally by allowing liquid toluene to vaporize isothermally into air
cific gravity of benzene at 60°F is 0.877. The concentration of ben- from a partially filled vertical tube 3 mm in diameter. At a temper-
zene at the outside of the film is so low that it may be neglected. For ature of 39.4"C, it took 96 x lo4 s for the level of the toluene to
benzene, the vapor pressure at 25OC is 100 torr, and the diffusivity drop from 1.9 cm below the top of the open tube to a level of 7.9 cm
in air is 0.08 cm2/s. below the top. The density of toluene is 0.852 g/cm3, and the vapor
3.3 An insulated glass tube and condenser are mounted on a pressure is 57.3 torr at 39.4"C. The barometer reading was 1 atm.
reboiler containing benzene and toluene. The condenser returns liq- Calculate the diffusivity and compare it with the value predicted
uid reflux so that it runs down the wall of the tube. At one point in from (3-36). Neglect the counterdiffusion of air.
the tube the temperature is 170°F, the vapor contains 30 mol% 3.7 An open tube, 1 rntn in diameter and 6 in. long, has pure hy-
toluene, and the liquid reflux contains 40 mol% toluene. The effec- drogen blowing across one end and pure nitrogen blowing across
tive thickness of the stagnant vapor film is estimated to be 0.1 in. the other. The temperature is 75°C.
The molar latent heats of benzene and toluene are equal. Calculate
(a) For equimolar counterdiffusion, what will be the rate of trans-
the rate at which toluene and benzene are being interchanged by
fer of hydrogen into the nitrogen stream (molls)? Estimate the dif-
equimolar countercurrent diffusion at this point in the tube in
fusivity from (3-36).
lbmovh-ft2.
(b) For part (a), plot the mole fraction of hydrogen against distance
Diffusivity of toluene in benzene = 0.2 ft2/h. from the end of the tube past which nitrogen is blown.
Pressure = 1 atrn total pressure (in the tube). 3.8 Some HC1 gas diffuses across a film of air 0.1 in. thick at
Vapor pressure of toluene at 170°F = 400 torr. 20°C. The partial pressure of HC1 on one side of the film is 0.08
atrn and it is zero on the other. Estimate the rate of diffusion, as mol
3.4 Air at 25°C with a dew-point temperature of 0°C flows past
~Clls-cm2, the total pressure is (a) 10 atm, (b) 1 atm, (c) 0.1 atm.
if
the open end of a vertical tube filled with liquid water maintained at
25°C. The tube has an inside diameter of 0.83 in., and the liquid The diffusivity of HCl in air at 20°C and 1 atrn is 0.145 cm2/s.