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CHE425: Problem set #1
1. The gas CO2 is diffusing at steady state through a tube 0.20 m long having a diameter of
0.01 m and containing N2 at 298oK. The total pressure is constant at 101.32 kPa. The partial
pressure of CO2 at one end is 456 mmHg and 76 mm Hg at the other end. The diffusivity DAB
is 1.67×10-5 m2/s at 298oK. Calculate the flux of CO2 in cgs and SI units for equimolar
counterdiffusion.
2. Helium and nitrogen gas are contained in a conduit 5 mm in diameter and 0.1 m long at
298oK and a uniform constant pressure of 1.0 atm abs. The partial pressure of He at one end
of the tube is 0.060 atm and 0.020 atm at the other end. The diffusivity of Helium in nitrogen
at 298oK is 6.87×10-5 m2/s. Calculate the following for steady-state equimolar
counterdiffusion.
a) Flux of he in kmol/s∙m2.
b) Flux of N2.
c) Partial pressure of He at a point of 0.05 from either end.
3. A long glass capillary tube, of diameter 0.01 cm, is in contact with water at one end and
dry air at the other. Water vapor evaporates at the wet end within the capillary, and the vapor
diffuses through the capillary toward the dry end. How long is required for one gram of water
to evaporate through this system? The vapor pressure of water is 17.5 mmHg at 20 oC, the
temperature at which the entire system is maintained. Take the diffusivity of water vapor in
air at 20oC to be 0.3 cm2/s, and assume that the dry air is at a pressure of 760 mmHg. Assume
that the distance from the wet interface within the capillary to the dry end is always 10 cm.
Gas constant R = 82.057 cm3atm/(molK)
4.2 Find the initial evaporation rate of water, in units of
centimeters per second of surface velocity, for the Arnold cell
operating at 1 atm and 25oC as shown. The inside diameter of the
tube is 1 mm. Dry air is blow over the top of the tube. The
saturated humidity of water in air at 25oC is 0.0189 lb H2O/lb dry
air. Diffusivity of water vapor in air at 25oC is 0.22 cm2/s.
10 cm
Pure water
5.2 A process is carried out under ultrahigh vacuum in a reactor whose walls are a glass tube
of inside diameter 10 cm and wall thickness 1 cm. We do not want H2 to “leak” across the
tube wall by diffusion and there by reduce the quality of the vacuum environment for the
process. The diffusivity of H2 in glass at the process temperature, 700oK, is 10-8 cm2/s. The
molar solubility ratio of H2 in glass is 0.2 (mol/cm3) H2 in glass/(mol/cm3) H2 in air. Suppose
the tube is one meter long, and the end plates and fittings of the tube are impermeable to
hydrogen. Suppose further that at some instant of time the vacuum pump had bought the
system to a pressure of 10-6 torr. The glass tube is surrounded by atmospheric air, and the
partial pressure of hydrogen in air is 3.810-4 torr. Estimate the partial pressure of H2 inside
the glass tube after 1 hour.
6.2 A liquid A evaporates at one end of a capillary tube and the vapor diffuses toward the
other end, which is open to a large gas space B that is essentially free of A.
Assume that the gas B is insoluble in liquid A, and work with the following conditions
and properties:
Total pressure
P = 1 atm
Vapor pressure of A
Pvap = 550 torr
Temperature
T = 25oC
Capillary length
L = 10 cm
Molecular weights
MwA = 100, MwB = 28
Binary diffusivity
DAB = 0.25 cm2/s
a) Find the magnitude of the molar average velocity vM.
b) What is the factor by which you would be in error if you assume that yA << 1?
c) Is vM constant along the capillary axis? Explain your answer.
d) Is vm (the mass average velocity) constant along the capillary axis? Explain your
answer.
7. A water droplet having a diameter of 0.16 mm is suspended in still air at 50oC, 1.0132×105
Pa (1 atm), and 30% relative humidity. The droplet temperature can be assumed to be at 50 oC
and its vapor pressure at 50oC is 7.38 kPa.
1) Calculate the initial rate of evaporation of water if DAB of water vapor in air is 0.288
cm2/s.
2) Determine the time for the water droplet to evaporate completely.
8. A lime (CaO) slurry droplet having a diameter Dd of 0.20 mm is suspended in a gas
containing SO2 at 50oC, 1.0132×105 Pa (1 atm). The mole fraction of SO2 in the gas phase is
10-4. Rate of diffusion of SO2 from the gas to the droplet surface is given by
Ns = kd(πDd2) c (yg,s − yd,s)
In this equation c is the total gas concentration and kd is the mass transfer coefficient for SO2
in the gas phase given by
kd =
2 DSO 2 gas
Dd
Rate of diffusion of SO2 from the droplet surface into the interior droplet is given by
Ns = kL  (πDd2) C*SO2
In this equation C*SO2 is the equilibrium SO2 concentration at the droplet surface kL  is the
mass transfer coefficient for SO2 in the liquid phase given by
*


DlimeClime
kL  = kL  1 
 , where
*

DSO2 CSO
2 

kL =
DSO 2

and the liquid film thickness δ at the surface is estimated to be 1 μm.

D C* 
 =  1  lime lime
 = the enhancement factor of the liquid film coefficient kL due
*

D
C
SO2 SO2 

to the very fast reaction of dissolved SO2 with dissolved lime in the bulk liquid.
The gas- and liquid-phase surface concentrations are related by Henry’law as follows:
c yd,s = HC*SO2
The Henry’law constant for the solubility of SO2 in water at 50oC is given by
H = 0.054
mol/cm3in gas phase
mol/cm3in liquid phase
Other data at 50oC: Equilibrium concentration of lime, C*lime = 1.35×10-5 mol/cm3.
Diffusivity of SO2 and lime in water: Dlime = DSO2 = 2×10-5 cm2/s. Diffusivity of SO2 in gas:
DSO2-gas = 0.20 cm2/s
Estimate the rate of diffusion of SO2, Ns.