CHE 31301
MASS TRANSFER
________________________
LAST NAME, FIRST
QUIZ #1
I. A coal particle burns in air at 1145oK, 1 atm. The process is limited by diffusion of the oxygen
counterflow to the CO2 and CO that are formed at the particle surface where
3C + 2.5O2 --> CO + 2CO2
Assume that the coal is pure carbon with a density of 1280 kg/m3 and that the particle is spherical
with an initial diameter of 0.015 cm. Air (21 mol% oxygen, 79 mol% nitrogen) exists several
diameters away from the sphere.
1. NCO = ___NOxyen
2. The mole fraction of oxygen at the particle surface in the gas phase is ___
3. The mole fraction of carbon at the particle surface in the solid phase is ___
II.
1 ft
A tank containing water has its top open to air. The tank is cylindrical
with a diamter of 2 ft. The liquid level is maintained at a level of 3 ft
below the top of the tank as shown in sketch. The surrounding air is at
o
310 K, 1 bar, and 40 percent relative humidity.
z
3 ft
1. The molar concentration of H2O at the top of the tank
(z = 0) is ____________
2. The molar concentration of H2O at the air-water interface
in the gas phase is ___________
2 ft
Note: Gas constant = 8314 Pa.m3/kmol.K, at 40 % relative humidity, partial pressure of water =
0.4*water vapor pressure
Molecular weight of air = 28.9
Molecular weight of water = 18.0 , density of water at 310oK = 997 kg/m3
Vapor pressure of water at 310oK = 0.06221 bar, 1 bar = 105 Pa.
III. (10 pts) In a hot combustion chamber, oxygen diffuses through air to the carbon surface where
it reacts to make CO and CO2. The mole fraction of oxygen at z = L is 0.21. The reaction may be
assumed to be instantaneous. No reaction occurs in the gas film. The chamber is at 1 atm, 1000oK,
and L = 0.1 m. The diffusivity of oxygen at these conditions is 0.35 cm2/sec. Determine the molar
flux of oxygen if the following reaction occurs at the carbon surface:
4C + 3O2 --> 2CO + 2CO2
Data: Gas constant = 0.08205 atm.m3/kmol.K
CHE31301
1 ft
MASS TRANSFER
z
3 ft
QUIZ #2
A tank containing water has its top open to air. The
tank is cylindrical with a diameter of 2 ft. The liquid
surface is maintained at a level 3 ft below the top of
the tank as shown in the sketch. The surrounding air is
o
at 310 K, 1bar, and 40 percent relative humidity.
2 ft
1. If R is the radius of the tank in the range 0  z  3 ft, then an expression for R as a function of
z is ___________
2.
A. The molar flux of water vapor is independent of z.
B. If air is insoluble in water the molar flux of air is independent of z.
I. A and B are true
II. Only A is true
III. Only B is true
IV. A and B are false
3.
A. The molar concentration of water vapor is independent of z.
B. The total molar concentration is independent of z.
I. A and B are true
II. Only A is true
III. Only B is true
IV. A and B are false
4.
A. If the surrounding air is saturated with water vapor then the molar flux of H2O is zero.
B. If air is insoluble in water then the molar flux of air is zero.
I. A and B are true
II. Only A is true
III. Only B is true
IV. A and B are false
5. If the mole fraction of H2O is 0.1 then the mass fraction of H2O is ____________
Data: Gas constant = 8314 Pa.m3/kmol.K
Molecular weight of air = 28.9
Molecular weight of water = 18.0 , density of water at 310oK = 997 kg/m3
Vapor pressure of water at 310oK = 0.06221 bar, 1 bar = 105 Pa.
2. (10 pts) In the high-temperature combustion of coal in a power plant (1145oK), the average size
(diameter) of the coal particle is 0.02 cm. For complete combustion, the reaction at the surface of
the coal particle is 3C + 2O2 --> 2CO + CO2. Assuming that the combustion reaction is controlled
by the diffusion of oxygen to the coal particle surface, estimate the instantaneous consumption rate
of oxygen (mol/s) by the average size coal particle. Do not neglect the convection term. Assume
the diffusion coefficient of O2 at this temperature is 1.4 cm2/s and that far away from the particle
the partial pressure of O2 is 0.21 atm. Gas constant R = 82.06 atm.cm3/mol.oK.
CHE31301
MASS TRANSFER
QUIZ #3
I. Consider a spherical porous catalyst in which species A diffuses into the catalyst and undergoes
an irreversible reaction A --> B. The reaction is distributed homogeneously throughout the particle
and the conversion of A to B can be expressed by first-order kinetics. The system is steady at
constant T and P.
1. A. The rate of A diffuses into the catalyst will be the rate of A reacted within the catalyst
only if the reaction is very fast compared to the rate of diffusion.
B. The concentration of B is highest at the surface of the spherical catalyst.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
2. A. The concentration of A is a constant at r = 0.5R where R is the radius of the catalyst.
B. The concentration of B is a minimum at the center.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
3. A. Concentration of species A must be known at time t = 0 to solve for the amount of A
reacted within the catalyst.
B. The concentration profile can not be solved if the concentration of A is given at some
other positon and not at the surface.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
4. A. NA = NB
B. The total concentration within the catalyst is a constant.
a. A and B are true b. Only A is true c. Only B is true
d. A and B are false
5. The catalyst is 8.010-3 m in diameter and the first order reaction rate constant is 1.510-7
m/s. Concentration of A at the catalyst surface (r = R) is 18 kgmol/m 3. If the diffusion rate is much
faster than the reaction rate, determine the consumption rate of species A within the catalyst
particle.
II. (10 pts) Species A diffuses into a spherical particle where it is consumed by zero order reaction
rA = - ko where ko = 1.5x10-5 mol/cm3.s. The particle diameter is 0.1 cm and the diffusivity of A in
the particle is 1.26x10-5 cm2/s. Determine the concentration of A at the center of the particle if the
concentration of A at the particle surface is 0.025 mol/cm3.
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QUIZ #4
I. A homogeneous reaction A  P takes place inside a porous spherical catalyst with radius R.
The effective diffusivity, De, of A within the catalyst is 1.210-7 m2/s. The concentration of A
within the catalyst is given by
2

r 
CA = CAo 0.20     , where CAo = 0.160 kmol/m3 and R = 1.00 mm
 R  

1. The concentration of A at the surface of the catalyst is
__________
2. The molar flux of A at r = R/2 is
__________
3. The moles of A within the spherical catalyst is
__________
4. The consumption rate of A within the catalyst is
__________
5. If the reaction rate can be expressed by RA = kCA where RA is reaction rate per unit volume and
the molar flux of A at r = R is 4.810-4 kmol/(m2.s),
the reaction rate constant k is
IV. (10 pts) A common procedure for increasing the moisture content of air is to bubble it through
a column of water. Assume the air bubbles to be spheres of radius 1.2 mm and to be in thermal
equilibrium with the water at 300oK. How long should the bubbles remain in the water to achieve a
vapor concentration at r = 0.2 mm that is 99% of the maximum possible concentration. The air is at
10% relative humidity when it enters the water. Diffusivity of water in air at this temperature is
0.26 cm2/s.
CHE31301
MASS TRANSFER
QUIZ #5
Spring ‘99
I. A homogeneous reaction A  P takes place inside a porous spherical catalyst with radius R.
The effective diffusivity, De, of A within the catalyst is 1.210-7 m2/s. The concentration of A
within the catalyst is given by
2

r 
CA = CAo 0.20     , where CAo = 0.160 kmol/m3 and R = 1.00 mm
 R  

1. The concentration of A at the surface of the catalyst is
__________
2. The molar flux of A at r = R/2 is
__________
3. The moles of A within the spherical catalyst is
__________
4. The consumption rate of A within the catalyst is
__________
5. If the reaction rate can be expressed by RA = kCA where RA is reaction rate per unit volume and
the molar flux of A at r = R is 4.810-4 kmol/(m2.s),
the reaction rate constant k is
__________
II. (10 pts) A solar pond operates on the principle that heat losses from a shallow layer of water,
which acts as a solar absorber, may be minimized by establishing a stable vertical salinity gradient
in the water. In practice such condition may be achieved by applying a layer of pure salt to the
bottom and adding an overlying layer of pure water. As a first approximation, the total mass
density  and the diffusion coefficient for salt in water (DAB) may be assumed to be constant, with
DAB = 1.210-9 m2/s. A saturated density As = 380 kg/m3 is maintained for salt in solution at the
bottom of the water layer of thickness L = 0.5 m. If the bottom is depleted of salt at the time that
the salt density reaches 40% of saturation at the top, what is the final (steady-state) density of the
salt at the bottom?