14–21
14–45 A rubber plate is exposed to nitrogen. The molar and mass density of nitrogen in the rubber at the interface is to be
determined.
Assumptions Rubber and nitrogen are in thermodynamic equilibrium at the interface.
3
kmol/m 0.0039=
bar) 5.2)(bar.kmol/m 00156.0(
)0(
3
side gas ,Nside solid ,N 22
=
= PC S
It corresponds to a mass density of
)0()0(
3
Nside solid ,Nside solid ,N 222 MC=
14-46 A rubber wall separates O2 and N2 gases. The molar concentrations of O2 and N2 in the wall are to be determined.
Assumptions The O2 and N2 gases are in phase equilibrium with the rubber wall.
Properties The molar mass of oxygen and nitrogen are 32.0 and 28.0 kg/kmol,
N2 = ?
N2
298 K
250 kPa
Rubber
14–22
14-47 Hydrogen gas is stored in a spherical nickel vessel that is in an atmospheric air surrounding. The concentrations of
hydrogen at the inner and outer surfaces are to be determined.
Assumptions 1 Hydrogen is in thermodynamic equilibrium with the nickel wall.
Properties The molar mass for H2 is 2.016 kg/kmol (Table A-1). The solubility of H2 in nickel at 358 K is S = 0.00901
14–23
14–24
14-49 A nickel wall separates H2 gas at different pressures. (a) The mass densities of H2 in the nickel wall and (b) outside the
0.00901 kmol/m3bar (Table 14-7).
Analysis (a) The mass density of H2 (for 5 atm) in the nickel at the interface is determined using
3
kg/m 0.0920=
=
=
)bar/atm 01325.1)(atm 5)(kg/kmol 016.2)(barkmol/m 00901.0(
)barkmol/m 00901.0(
3
side gas,H
3
side solid,H 22 MP
Then, the mass density of H2 (for 3 atm) in the nickel at the interface is
=
)barkmol/m 00901.0(
3
side gas,H
3
side solid,H 22 MP
14–25
14–26
14–51 A nickel vessel with specified dimensions is used to contain hydrogen. The rate gas loss from the vessel and the
fraction of the hydrogen lost after one year of storage are to be determined.
7).
3
3
1,1,
kg/m 05449.0
kmol 1
kg 016.2
)bar 3)(barkmol/m 00901.0(
=
=
=AA P
S
kg/year 101.65=
m 002.0
4
−−
=
kg/s 105.23 12
This corresponds to about 0.165 gram of H2 per year. The mass of H2 in the vessel is
)m 005.0)(kPa 300(3
P
14–27
14–52 A nickel wall separates H2 gas at different pressures. The molar diffusion rate per unit area through the nickel wall is to
be determined.
Assumptions 1 Mass diffusion is steady and one-dimensional. 2 There are no chemical reactions in the nickel wall that result
in the generation or depletion of hydrogen.
Properties The binary diffusion coefficient for hydrogen in the nickel at 85°C = 358 K is DAB = 1.2×10−12 m2/s (Table 14–
3
3
2,
3
2,
kmol/m0274.0
)bar/atm 01325.1)(atm 3)(barkmol/m 00901.0(
)barkmol/m 00901.0(
=
=
= AA PC
210 mkmol/s 102.18 =
−
m .00010
Discussion The molar mass of H2 is M = 2.016 kg/kmol (Table A-1). Hence, the mass diffusion rate per unit area of
hydrogen through the nickel wall is
210210
diff mkg/s 1040.4)kg/kmol 016.2)(mkmol/s 10182( == −−
.j
14–28
14–29
14–54C During one-dimensional mass diffusion of species A through a plane wall, the species A content of the wall will
remain constant during steady mass diffusion, but will change during transient mass diffusion.
14–55C The relations for steady one-dimensional heat conduction and mass diffusion through a plane wall
are expressed as follows:
Heat conduction:
L
TT
AkQcond
21 −
−=
ww
A,2A,1
−
−
14–30
14-57 A thin plastic membrane separates hydrogen from air. The diffusion rate of hydrogen by diffusion through the
membrane under steady conditions is to be determined.
5.310-10 m2/s. The molar mass of hydrogen is M = 2 kg/kmol (Table A-1).
Analysis (a) We can consider the total molar concentration to be constant (C = CA + CB CB = constant), and the plastic
membrane to be a stationary medium since there is no diffusion of plastic molecules (
0=
B
N
) and the concentration of the
hydrogen in the membrane is extremely low (CA << 1). Then the molar flow rate of hydrogen through the membrane by
diffusion per unit area is determined from
.skmol/m1014.1
m102
kmol/m)002.0045.0(
28
3
3
210
2,1,
diff
diff
−
−
−
=
−
−
== L
CC
D
A
N
jAA
AB
The mass flow rate is determined by multiplying the molar flow rate by
kmol/m)002.0045.0(
3
210
2,1,
diff
diff
−
−
−
CC
D
A
N
jAA
AB
Plastic
membrane
mdiff
H2
Air
14–31
14–32
14-59 Natural gas with 8% hydrogen content is transported in an above ground pipeline. The highest rate of hydrogen loss
through the pipe at steady conditions is to be determined.
steel is given as
5.0
H
4
H22 )/3950exp(1009.2 PTw −= −
. The density of steel pipe is 7854 kg/m3 (Table A-3).
bar4.0kPa 40)kPa500)(08.0(
2
2
2H
H
H===→= P
P
P
y
10
5.04
5.0
H
4
H
1085.1
)4.0)(293/3950exp(1009.2
)/3950exp(1009.2 22
−
−
−
=
−=
−= PTw
Natural gas
H2, 8%
500 kPa
H2 diffusion
14–33
14–60 Prob. 14-59 is reconsidered. The highest rate of hydrogen loss as a function of the mole fraction of hydrogen in
natural gas is to be plotted.
Analysis The problem is solved using EES, and the solution is given below.
“GIVEN”
thickness=0.01 [m]
14–34
14–35
14–61 Pure H2 gas is flowing through an iron pipe. The rate at which H2 leaks out by diffusion is to be determined for a
known concentration at the inner surface.
Assumptions 1 Mass diffusion is steady and one-dimensional since the hydrogen concentration in the pipe and thus at the
inner surface of the pipe is practically constant, and the hydrogen concentration in the atmosphere and thus at the outer
surface is practically zero. Also, there is symmetry about the centerline of the pipe. 2 There are no chemical reactions in the
kmol/s 10855.4
)25/35ln(
kmol/m )01.0(
)/sm106.2)(m 10(2
)/ln(
2
12
3
213
12
2,1,
diff
−
−
=
−
=
−
=
rr
CC
DLN AA
AB
14–36
14–37
14–63 Helium gas stored inside a cylindrical Pyrex tank, and a sensor detects a leakage of the gas at 1.8 × 10−6 g/h. The
concentration of helium at the inner surface of the Pyrex tank is to be determined.
Assumptions 1 Mass diffusion is steady and one-dimensional since the helium concentration in the tank and thus at the inner
surface of the tank is practically constant, and the helium concentration in the atmosphere and thus at the outer surface is
practically zero. Also, there is symmetry about the centerline. 2 There are no chemical reactions in the tank that results in the
stationary medium since there is no diffusion of Pyrex molecules (B = 0) and the concentration of the helium in the tank is
extremely low (CA << 1). Then the molar flow rate of helium through the pipe wall by diffusion can be determined to be
)/ln(
2
12
2,1,
diff
diff
rr
CC
DL
M
m
N
AA
AB
−
=
=
3
kmol/m 0.0902=
=
=
−
−
)/sm 105.4)(m 2(2
)12/5.12ln(
kg/kmol 003.4
kg/s 105
2
)/ln(
215
13
12
diff
1,
AB
ADL
rr
M
m
C
14–38
14–64 Pressurized helium gas is stored in a spherical container. The diffusion rate of helium through the container is to be
determined.
Assumptions 1 Mass diffusion is steady and one-dimensional since the helium concentration in the tank and thus at the inner
surface of the container is practically constant, and the helium concentration in the atmosphere and thus at the outer surface is
1). Then the molar flow rate of helium through the shell by diffusion
can readily be determined from Eq. 14-28 to be
kmol/m 0)(0.00069
4
3
215
12
A,2A,1
AB21diff
−
−
−
−
=
rr
CC
DrrN
He
diffusion
He gas
293 K
Air
14–39
14–40
14-66 Helium gas is stored in a spherical fused silica container. The diffusion rate of helium through the container and the
pressure drop in the tank in one week as a result of helium loss are to be determined.
Assumptions 1 Mass diffusion is steady and one-dimensional since the helium concentration in the tank and thus at the inner
surface of the container is practically constant, and the helium concentration in the atmosphere and thus at the outer surface is
practically zero. Also, there is symmetry about the midpoint of the container. 2 There are no chemical reactions in the fused
3333
He1 , kmol/m0.00225= kmol/m102.25=bar).bar)(5kmol/m00045.0( −
== PSC A
The helium concentration in the atmosphere and thus at the
outer surface is taken to be zero since the tank is well
ventilated. Then the molar flow rate of helium through the