Chapter 14 Mass Transfer Notes | EduRev

: Chapter 14 Mass Transfer Notes | EduRev

 Page 1


Chapter 14 Mass Transfer 
 14-1 
Chapter 14 
MASS TRANSFER 
 
 
Mass Transfer and Analogy Between Heat and Mass Transfer 
 
14-1C Bulk fluid flow refers to the transportation of a fluid on a macroscopic level from one location to 
another in a flow section by a mover such as a fan or a pump. Mass flow requires the presence of two 
regions at different chemical compositions, and it refers to the movement of a chemical species from a high 
concentration region towards a lower concentration one relative to the other chemical species present in the 
medium.  Mass transfer cannot occur in a homogeneous medium. 
 
14-2C The concentration of a commodity is defined as the amount of that commodity per unit volume. The 
concentration gradient dC/dx is defined as the change in the concentration C of a commodity per unit 
length in the direction of flow x. The diffusion rate of the commodity is expressed as  
  
diff
?
Q k A
dC
dx
? ? 
where A is the area normal to the direction of flow and  k diff is the diffusion coefficient of the medium, 
which is a measure of how fast a commodity diffuses in the medium. 
 
14-3C Examples of different kinds of diffusion processes:   
(a)  Liquid-to-gas: A gallon of gasoline left in an open area will eventually evaporate and diffuse into air. 
(b)  Solid-to-liquid: A spoon of sugar in a cup of tea will eventually dissolve and move up. 
(c)  Solid-to gas: A moth ball left in a closet will sublimate and diffuse into the air. 
(d)  Gas-to-liquid: Air dissolves in water. 
 
14-4C Although heat and mass can be converted to each other, there is no such a thing as “mass radiation”, 
and mass transfer cannot be studied using the laws of radiation transfer. Mass transfer is analogous to 
conduction, but it is not analogous to radiation. 
 
14-5C (a) Temperature difference is the driving force for heat transfer, (b) voltage difference is the driving 
force for electric current flow, and (c) concentration difference is the driving force for mass transfer. 
 
14-6C (a) Homogenous reactions in mass transfer represent the generation of a species within the medium. 
Such reactions are analogous to internal heat generation in heat transfer. (b) Heterogeneous reactions in 
mass transfer represent the generation of a species at the surface as a result of chemical reactions occurring 
at the surface.  Such reactions are analogous to specified surface heat flux in heat transfer. 
Page 2


Chapter 14 Mass Transfer 
 14-1 
Chapter 14 
MASS TRANSFER 
 
 
Mass Transfer and Analogy Between Heat and Mass Transfer 
 
14-1C Bulk fluid flow refers to the transportation of a fluid on a macroscopic level from one location to 
another in a flow section by a mover such as a fan or a pump. Mass flow requires the presence of two 
regions at different chemical compositions, and it refers to the movement of a chemical species from a high 
concentration region towards a lower concentration one relative to the other chemical species present in the 
medium.  Mass transfer cannot occur in a homogeneous medium. 
 
14-2C The concentration of a commodity is defined as the amount of that commodity per unit volume. The 
concentration gradient dC/dx is defined as the change in the concentration C of a commodity per unit 
length in the direction of flow x. The diffusion rate of the commodity is expressed as  
  
diff
?
Q k A
dC
dx
? ? 
where A is the area normal to the direction of flow and  k diff is the diffusion coefficient of the medium, 
which is a measure of how fast a commodity diffuses in the medium. 
 
14-3C Examples of different kinds of diffusion processes:   
(a)  Liquid-to-gas: A gallon of gasoline left in an open area will eventually evaporate and diffuse into air. 
(b)  Solid-to-liquid: A spoon of sugar in a cup of tea will eventually dissolve and move up. 
(c)  Solid-to gas: A moth ball left in a closet will sublimate and diffuse into the air. 
(d)  Gas-to-liquid: Air dissolves in water. 
 
14-4C Although heat and mass can be converted to each other, there is no such a thing as “mass radiation”, 
and mass transfer cannot be studied using the laws of radiation transfer. Mass transfer is analogous to 
conduction, but it is not analogous to radiation. 
 
14-5C (a) Temperature difference is the driving force for heat transfer, (b) voltage difference is the driving 
force for electric current flow, and (c) concentration difference is the driving force for mass transfer. 
 
14-6C (a) Homogenous reactions in mass transfer represent the generation of a species within the medium. 
Such reactions are analogous to internal heat generation in heat transfer. (b) Heterogeneous reactions in 
mass transfer represent the generation of a species at the surface as a result of chemical reactions occurring 
at the surface.  Such reactions are analogous to specified surface heat flux in heat transfer. 
Chapter 14 Mass Transfer 
 14-2 
 
Mass Diffusion 
 
14-7C In the relation 
?
( / ) Q kA dT dx ? ? , the quantities 
?
Q , k, A, and T represent the following in heat 
conduction and mass diffusion: 
 
?
Q = Rate of heat transfer in heat conduction, and rate of mass transfer in mass diffusion. 
  k = Thermal conductivity in heat conduction, and mass diffusivity in mass diffusion. 
  A = Area normal to the direction of flow in both heat and mass transfer. 
  T = Temperature in heat conduction, and concentration in mass diffusion. 
 
14-8C  (a) T (b) F (c) F (d) T  (e) F   
 
14-9C  (a) T (b) F (c) F (d) T  (e) T   
 
14-10C In the Fick’s law of diffusion relations expressed as ? m AD
dw
dx
diff,A AB
A
? ? ? and 
?
N CAD
dy
dx
diff,A AB
A
? ? , the diffusion coefficients D AB   are the same. 
 
14-11C The mass diffusivity of a gas mixture (a) increases with increasing temperature and (a) decreases 
with increasing pressure. 
 
14-12C In a binary ideal gas mixture of species A and B, the diffusion coefficient of A in B is equal to the 
diffusion coefficient of B in A.  Therefore, the mass diffusivity of air in water vapor will be equal to the 
mass diffusivity of water vapor in air since the air and water vapor mixture can be treated as ideal gases. 
 
14-13C Solids, in general, have different diffusivities in each other. At a given temperature and pressure, 
the mass diffusivity of copper in aluminum will not be the equal to the mass diffusivity of aluminum in 
copper. 
 
14-14C We would carry out the hardening process of steel by carbon at high temperature since mass 
diffusivity increases with temperature, and thus the hardening process will be completed in a short time. 
 
14-15C The molecular weights of CO 2 and N 2O gases are the same (both are 44). Therefore, the mass and 
mole fractions of each of these two gases in a gas mixture will be the same.   
Page 3


Chapter 14 Mass Transfer 
 14-1 
Chapter 14 
MASS TRANSFER 
 
 
Mass Transfer and Analogy Between Heat and Mass Transfer 
 
14-1C Bulk fluid flow refers to the transportation of a fluid on a macroscopic level from one location to 
another in a flow section by a mover such as a fan or a pump. Mass flow requires the presence of two 
regions at different chemical compositions, and it refers to the movement of a chemical species from a high 
concentration region towards a lower concentration one relative to the other chemical species present in the 
medium.  Mass transfer cannot occur in a homogeneous medium. 
 
14-2C The concentration of a commodity is defined as the amount of that commodity per unit volume. The 
concentration gradient dC/dx is defined as the change in the concentration C of a commodity per unit 
length in the direction of flow x. The diffusion rate of the commodity is expressed as  
  
diff
?
Q k A
dC
dx
? ? 
where A is the area normal to the direction of flow and  k diff is the diffusion coefficient of the medium, 
which is a measure of how fast a commodity diffuses in the medium. 
 
14-3C Examples of different kinds of diffusion processes:   
(a)  Liquid-to-gas: A gallon of gasoline left in an open area will eventually evaporate and diffuse into air. 
(b)  Solid-to-liquid: A spoon of sugar in a cup of tea will eventually dissolve and move up. 
(c)  Solid-to gas: A moth ball left in a closet will sublimate and diffuse into the air. 
(d)  Gas-to-liquid: Air dissolves in water. 
 
14-4C Although heat and mass can be converted to each other, there is no such a thing as “mass radiation”, 
and mass transfer cannot be studied using the laws of radiation transfer. Mass transfer is analogous to 
conduction, but it is not analogous to radiation. 
 
14-5C (a) Temperature difference is the driving force for heat transfer, (b) voltage difference is the driving 
force for electric current flow, and (c) concentration difference is the driving force for mass transfer. 
 
14-6C (a) Homogenous reactions in mass transfer represent the generation of a species within the medium. 
Such reactions are analogous to internal heat generation in heat transfer. (b) Heterogeneous reactions in 
mass transfer represent the generation of a species at the surface as a result of chemical reactions occurring 
at the surface.  Such reactions are analogous to specified surface heat flux in heat transfer. 
Chapter 14 Mass Transfer 
 14-2 
 
Mass Diffusion 
 
14-7C In the relation 
?
( / ) Q kA dT dx ? ? , the quantities 
?
Q , k, A, and T represent the following in heat 
conduction and mass diffusion: 
 
?
Q = Rate of heat transfer in heat conduction, and rate of mass transfer in mass diffusion. 
  k = Thermal conductivity in heat conduction, and mass diffusivity in mass diffusion. 
  A = Area normal to the direction of flow in both heat and mass transfer. 
  T = Temperature in heat conduction, and concentration in mass diffusion. 
 
14-8C  (a) T (b) F (c) F (d) T  (e) F   
 
14-9C  (a) T (b) F (c) F (d) T  (e) T   
 
14-10C In the Fick’s law of diffusion relations expressed as ? m AD
dw
dx
diff,A AB
A
? ? ? and 
?
N CAD
dy
dx
diff,A AB
A
? ? , the diffusion coefficients D AB   are the same. 
 
14-11C The mass diffusivity of a gas mixture (a) increases with increasing temperature and (a) decreases 
with increasing pressure. 
 
14-12C In a binary ideal gas mixture of species A and B, the diffusion coefficient of A in B is equal to the 
diffusion coefficient of B in A.  Therefore, the mass diffusivity of air in water vapor will be equal to the 
mass diffusivity of water vapor in air since the air and water vapor mixture can be treated as ideal gases. 
 
14-13C Solids, in general, have different diffusivities in each other. At a given temperature and pressure, 
the mass diffusivity of copper in aluminum will not be the equal to the mass diffusivity of aluminum in 
copper. 
 
14-14C We would carry out the hardening process of steel by carbon at high temperature since mass 
diffusivity increases with temperature, and thus the hardening process will be completed in a short time. 
 
14-15C The molecular weights of CO 2 and N 2O gases are the same (both are 44). Therefore, the mass and 
mole fractions of each of these two gases in a gas mixture will be the same.   
Chapter 14 Mass Transfer 
 14-3 
14-16 The molar fractions of the constituents of moist air are given. The mass fractions of the constituents 
are to be determined.  
Assumptions The small amounts of gases in air are ignored, and dry air is assumed to consist of N 2 and O 2 
only.   
Properties The molar masses of N 2, O 2, and H 2O are 28.0, 32.0, and 18.0 kg/kmol, respectively (Table A-1) 
Analysis The molar mass of moist air is determined to be 
 M y M
i i
? ? ? ? ? ? ? ?
?
0 78 280 0 20 32 0 0 02 18 286 . . . . . . kg / kmol 
Then the mass fractions of constituent gases are 
determined from Eq. 14-10 to be 
 N :         
2 N N
N
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 78
280
286
0.764 
 O :         
2 O O
O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 20
32 0
286
0.224 
 H O:         
2 H O H O
H O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 02
180
286
0.012 
Therefore, the mass fractions of N 2, O 2, and H 2O in dry air are 76.4%, 22.4%, and 1.2%, respectively. 
Moist air 
78% N 2 
20% O 2 
2% H 2 O 
(Mole fractions) 
Page 4


Chapter 14 Mass Transfer 
 14-1 
Chapter 14 
MASS TRANSFER 
 
 
Mass Transfer and Analogy Between Heat and Mass Transfer 
 
14-1C Bulk fluid flow refers to the transportation of a fluid on a macroscopic level from one location to 
another in a flow section by a mover such as a fan or a pump. Mass flow requires the presence of two 
regions at different chemical compositions, and it refers to the movement of a chemical species from a high 
concentration region towards a lower concentration one relative to the other chemical species present in the 
medium.  Mass transfer cannot occur in a homogeneous medium. 
 
14-2C The concentration of a commodity is defined as the amount of that commodity per unit volume. The 
concentration gradient dC/dx is defined as the change in the concentration C of a commodity per unit 
length in the direction of flow x. The diffusion rate of the commodity is expressed as  
  
diff
?
Q k A
dC
dx
? ? 
where A is the area normal to the direction of flow and  k diff is the diffusion coefficient of the medium, 
which is a measure of how fast a commodity diffuses in the medium. 
 
14-3C Examples of different kinds of diffusion processes:   
(a)  Liquid-to-gas: A gallon of gasoline left in an open area will eventually evaporate and diffuse into air. 
(b)  Solid-to-liquid: A spoon of sugar in a cup of tea will eventually dissolve and move up. 
(c)  Solid-to gas: A moth ball left in a closet will sublimate and diffuse into the air. 
(d)  Gas-to-liquid: Air dissolves in water. 
 
14-4C Although heat and mass can be converted to each other, there is no such a thing as “mass radiation”, 
and mass transfer cannot be studied using the laws of radiation transfer. Mass transfer is analogous to 
conduction, but it is not analogous to radiation. 
 
14-5C (a) Temperature difference is the driving force for heat transfer, (b) voltage difference is the driving 
force for electric current flow, and (c) concentration difference is the driving force for mass transfer. 
 
14-6C (a) Homogenous reactions in mass transfer represent the generation of a species within the medium. 
Such reactions are analogous to internal heat generation in heat transfer. (b) Heterogeneous reactions in 
mass transfer represent the generation of a species at the surface as a result of chemical reactions occurring 
at the surface.  Such reactions are analogous to specified surface heat flux in heat transfer. 
Chapter 14 Mass Transfer 
 14-2 
 
Mass Diffusion 
 
14-7C In the relation 
?
( / ) Q kA dT dx ? ? , the quantities 
?
Q , k, A, and T represent the following in heat 
conduction and mass diffusion: 
 
?
Q = Rate of heat transfer in heat conduction, and rate of mass transfer in mass diffusion. 
  k = Thermal conductivity in heat conduction, and mass diffusivity in mass diffusion. 
  A = Area normal to the direction of flow in both heat and mass transfer. 
  T = Temperature in heat conduction, and concentration in mass diffusion. 
 
14-8C  (a) T (b) F (c) F (d) T  (e) F   
 
14-9C  (a) T (b) F (c) F (d) T  (e) T   
 
14-10C In the Fick’s law of diffusion relations expressed as ? m AD
dw
dx
diff,A AB
A
? ? ? and 
?
N CAD
dy
dx
diff,A AB
A
? ? , the diffusion coefficients D AB   are the same. 
 
14-11C The mass diffusivity of a gas mixture (a) increases with increasing temperature and (a) decreases 
with increasing pressure. 
 
14-12C In a binary ideal gas mixture of species A and B, the diffusion coefficient of A in B is equal to the 
diffusion coefficient of B in A.  Therefore, the mass diffusivity of air in water vapor will be equal to the 
mass diffusivity of water vapor in air since the air and water vapor mixture can be treated as ideal gases. 
 
14-13C Solids, in general, have different diffusivities in each other. At a given temperature and pressure, 
the mass diffusivity of copper in aluminum will not be the equal to the mass diffusivity of aluminum in 
copper. 
 
14-14C We would carry out the hardening process of steel by carbon at high temperature since mass 
diffusivity increases with temperature, and thus the hardening process will be completed in a short time. 
 
14-15C The molecular weights of CO 2 and N 2O gases are the same (both are 44). Therefore, the mass and 
mole fractions of each of these two gases in a gas mixture will be the same.   
Chapter 14 Mass Transfer 
 14-3 
14-16 The molar fractions of the constituents of moist air are given. The mass fractions of the constituents 
are to be determined.  
Assumptions The small amounts of gases in air are ignored, and dry air is assumed to consist of N 2 and O 2 
only.   
Properties The molar masses of N 2, O 2, and H 2O are 28.0, 32.0, and 18.0 kg/kmol, respectively (Table A-1) 
Analysis The molar mass of moist air is determined to be 
 M y M
i i
? ? ? ? ? ? ? ?
?
0 78 280 0 20 32 0 0 02 18 286 . . . . . . kg / kmol 
Then the mass fractions of constituent gases are 
determined from Eq. 14-10 to be 
 N :         
2 N N
N
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 78
280
286
0.764 
 O :         
2 O O
O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 20
32 0
286
0.224 
 H O:         
2 H O H O
H O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 02
180
286
0.012 
Therefore, the mass fractions of N 2, O 2, and H 2O in dry air are 76.4%, 22.4%, and 1.2%, respectively. 
Moist air 
78% N 2 
20% O 2 
2% H 2 O 
(Mole fractions) 
Chapter 14 Mass Transfer 
 14-4 
14-17E The masses of the constituents of a gas mixture are given. The mass fractions, mole fractions, and 
the molar mass of the mixture are to be determined.   
Assumptions None. 
Properties The molar masses of N 2, O 2, and CO 2 are 28, 32, and 44 lbm/lbmol, respectively (Table A-1) 
Analysis (a) The total mass of the gas mixture is determined to be  
 m m m m m
i
? ? ? ? ? ? ? ?
? O N CO
2 2 2
lbm 5 8 10 23 
Then the mass fractions of constituent gases are determined to be 
 N :         
2 N
N
2
2
w
m
m
? ? ?
8
23
0.348 
 O :         
2 O
O
2
2
w
m
m
? ? ?
5
23
0.217 
 CO
2 CO
CO
2
2
: w
m
m
? ? ?
10
23
0.435 
(b) To find the mole fractions, we need to determine the mole numbers of each component first,  
  N :         
 lbm
 lbm / lbmol
2 N
N
N
2
2
2
N
m
M
? ? ?
8
28
0.286 lbmol 
 O :         
 lbm
 lbm / lbmol
2 O
O
O
2
2
2
N
m
M
? ? ?
5
32
0.156 lbmol 
 CO
 lbm
 lbm / lbmol
2 CO
CO
CO
2
2
2
: N
m
M
? ? ?
10
44
0.227 lbmol 
Thus, 
 N N N N N
m i
? ? ? ? ? ? ? ?
? N O CO
2 2 2
 lbmol 0 286 0156 0 227 0 669 . . . . 
Then the mole fraction of gases are determined to be 
 N
2 N
N
2
2
:
.
.
y
N
N
m
? ? ?
0 2868
0 669
0.428 
 O
2 O
O
2
2
:
.
.
y
N
N
m
? ? ?
0156
0 669
0.233 
 CO
2 CO
CO
2
2
:
.
.
y
N
N
m
? ? ?
0 227
0 669
0.339 
(c) The molar mass of the mixture is determined from 
 M
m
N
m
m
? ? ?
23 lbm
0.669 lbmol
34.4 lbm / lbmol 
 
5 lbm O 2 
8 lbm N 2 
10 lbm CO 2 
 
 
Page 5


Chapter 14 Mass Transfer 
 14-1 
Chapter 14 
MASS TRANSFER 
 
 
Mass Transfer and Analogy Between Heat and Mass Transfer 
 
14-1C Bulk fluid flow refers to the transportation of a fluid on a macroscopic level from one location to 
another in a flow section by a mover such as a fan or a pump. Mass flow requires the presence of two 
regions at different chemical compositions, and it refers to the movement of a chemical species from a high 
concentration region towards a lower concentration one relative to the other chemical species present in the 
medium.  Mass transfer cannot occur in a homogeneous medium. 
 
14-2C The concentration of a commodity is defined as the amount of that commodity per unit volume. The 
concentration gradient dC/dx is defined as the change in the concentration C of a commodity per unit 
length in the direction of flow x. The diffusion rate of the commodity is expressed as  
  
diff
?
Q k A
dC
dx
? ? 
where A is the area normal to the direction of flow and  k diff is the diffusion coefficient of the medium, 
which is a measure of how fast a commodity diffuses in the medium. 
 
14-3C Examples of different kinds of diffusion processes:   
(a)  Liquid-to-gas: A gallon of gasoline left in an open area will eventually evaporate and diffuse into air. 
(b)  Solid-to-liquid: A spoon of sugar in a cup of tea will eventually dissolve and move up. 
(c)  Solid-to gas: A moth ball left in a closet will sublimate and diffuse into the air. 
(d)  Gas-to-liquid: Air dissolves in water. 
 
14-4C Although heat and mass can be converted to each other, there is no such a thing as “mass radiation”, 
and mass transfer cannot be studied using the laws of radiation transfer. Mass transfer is analogous to 
conduction, but it is not analogous to radiation. 
 
14-5C (a) Temperature difference is the driving force for heat transfer, (b) voltage difference is the driving 
force for electric current flow, and (c) concentration difference is the driving force for mass transfer. 
 
14-6C (a) Homogenous reactions in mass transfer represent the generation of a species within the medium. 
Such reactions are analogous to internal heat generation in heat transfer. (b) Heterogeneous reactions in 
mass transfer represent the generation of a species at the surface as a result of chemical reactions occurring 
at the surface.  Such reactions are analogous to specified surface heat flux in heat transfer. 
Chapter 14 Mass Transfer 
 14-2 
 
Mass Diffusion 
 
14-7C In the relation 
?
( / ) Q kA dT dx ? ? , the quantities 
?
Q , k, A, and T represent the following in heat 
conduction and mass diffusion: 
 
?
Q = Rate of heat transfer in heat conduction, and rate of mass transfer in mass diffusion. 
  k = Thermal conductivity in heat conduction, and mass diffusivity in mass diffusion. 
  A = Area normal to the direction of flow in both heat and mass transfer. 
  T = Temperature in heat conduction, and concentration in mass diffusion. 
 
14-8C  (a) T (b) F (c) F (d) T  (e) F   
 
14-9C  (a) T (b) F (c) F (d) T  (e) T   
 
14-10C In the Fick’s law of diffusion relations expressed as ? m AD
dw
dx
diff,A AB
A
? ? ? and 
?
N CAD
dy
dx
diff,A AB
A
? ? , the diffusion coefficients D AB   are the same. 
 
14-11C The mass diffusivity of a gas mixture (a) increases with increasing temperature and (a) decreases 
with increasing pressure. 
 
14-12C In a binary ideal gas mixture of species A and B, the diffusion coefficient of A in B is equal to the 
diffusion coefficient of B in A.  Therefore, the mass diffusivity of air in water vapor will be equal to the 
mass diffusivity of water vapor in air since the air and water vapor mixture can be treated as ideal gases. 
 
14-13C Solids, in general, have different diffusivities in each other. At a given temperature and pressure, 
the mass diffusivity of copper in aluminum will not be the equal to the mass diffusivity of aluminum in 
copper. 
 
14-14C We would carry out the hardening process of steel by carbon at high temperature since mass 
diffusivity increases with temperature, and thus the hardening process will be completed in a short time. 
 
14-15C The molecular weights of CO 2 and N 2O gases are the same (both are 44). Therefore, the mass and 
mole fractions of each of these two gases in a gas mixture will be the same.   
Chapter 14 Mass Transfer 
 14-3 
14-16 The molar fractions of the constituents of moist air are given. The mass fractions of the constituents 
are to be determined.  
Assumptions The small amounts of gases in air are ignored, and dry air is assumed to consist of N 2 and O 2 
only.   
Properties The molar masses of N 2, O 2, and H 2O are 28.0, 32.0, and 18.0 kg/kmol, respectively (Table A-1) 
Analysis The molar mass of moist air is determined to be 
 M y M
i i
? ? ? ? ? ? ? ?
?
0 78 280 0 20 32 0 0 02 18 286 . . . . . . kg / kmol 
Then the mass fractions of constituent gases are 
determined from Eq. 14-10 to be 
 N :         
2 N N
N
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 78
280
286
0.764 
 O :         
2 O O
O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 20
32 0
286
0.224 
 H O:         
2 H O H O
H O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 02
180
286
0.012 
Therefore, the mass fractions of N 2, O 2, and H 2O in dry air are 76.4%, 22.4%, and 1.2%, respectively. 
Moist air 
78% N 2 
20% O 2 
2% H 2 O 
(Mole fractions) 
Chapter 14 Mass Transfer 
 14-4 
14-17E The masses of the constituents of a gas mixture are given. The mass fractions, mole fractions, and 
the molar mass of the mixture are to be determined.   
Assumptions None. 
Properties The molar masses of N 2, O 2, and CO 2 are 28, 32, and 44 lbm/lbmol, respectively (Table A-1) 
Analysis (a) The total mass of the gas mixture is determined to be  
 m m m m m
i
? ? ? ? ? ? ? ?
? O N CO
2 2 2
lbm 5 8 10 23 
Then the mass fractions of constituent gases are determined to be 
 N :         
2 N
N
2
2
w
m
m
? ? ?
8
23
0.348 
 O :         
2 O
O
2
2
w
m
m
? ? ?
5
23
0.217 
 CO
2 CO
CO
2
2
: w
m
m
? ? ?
10
23
0.435 
(b) To find the mole fractions, we need to determine the mole numbers of each component first,  
  N :         
 lbm
 lbm / lbmol
2 N
N
N
2
2
2
N
m
M
? ? ?
8
28
0.286 lbmol 
 O :         
 lbm
 lbm / lbmol
2 O
O
O
2
2
2
N
m
M
? ? ?
5
32
0.156 lbmol 
 CO
 lbm
 lbm / lbmol
2 CO
CO
CO
2
2
2
: N
m
M
? ? ?
10
44
0.227 lbmol 
Thus, 
 N N N N N
m i
? ? ? ? ? ? ? ?
? N O CO
2 2 2
 lbmol 0 286 0156 0 227 0 669 . . . . 
Then the mole fraction of gases are determined to be 
 N
2 N
N
2
2
:
.
.
y
N
N
m
? ? ?
0 2868
0 669
0.428 
 O
2 O
O
2
2
:
.
.
y
N
N
m
? ? ?
0156
0 669
0.233 
 CO
2 CO
CO
2
2
:
.
.
y
N
N
m
? ? ?
0 227
0 669
0.339 
(c) The molar mass of the mixture is determined from 
 M
m
N
m
m
? ? ?
23 lbm
0.669 lbmol
34.4 lbm / lbmol 
 
5 lbm O 2 
8 lbm N 2 
10 lbm CO 2 
 
 
Chapter 14 Mass Transfer 
 14-5 
14-18 The mole fractions of the constituents of a gas mixture are given. The mass of each gas and the molar 
mass of the mixture are to be determined.   
Assumptions None. 
Properties The molar masses of H 2 and N 2 are 2.0 and 28.0 kg/kmol, respectively (Table A-1) 
Analysis The mass of each gas is 
H kmol) kg / kmol
2 H H H
2 2 2
: ( ( ) m N M ? ? ? ? 8 2 16 kg 
N kmol) kg / kmol
2 N N N
2 2 2
: ( ) m N M ? ? ? ? 2 28 56 kg 
The molar mass of the mixture and its apparent gas constant are determined to be  
 M
m
N
m
m
? ?
?
?
?
16 56
8 2
 kg
 kmol
7.2 kg / kmol 
  R
R
M
u
? ?
?
? ?
8 314
7 2
.
.
kJ / kmol K
kg / kmol
1.15 kJ / kg K 
 
 
14-19 The mole numbers of the constituents of a gas mixture at a specified pressure and temperature are 
given. The mass fractions and the partial pressures of the constituents are to be determined.   
Assumptions The gases behave as ideal gases. 
Properties The molar masses of N 2, O 2 and CO 2 are 28, 32, and 44 kg/kmol, respectively (Table A-1) 
Analysis When the mole fractions of a gas mixture are known, the mass fractions can be determined from 
 w
m
m
N M
N M
y
M
M
i
i
m
i i
m m
i
i
m
? ? ? 
The apparent molar mass of the mixture is 
      M y M
i i
? ? ? ? ? ? ? ?
?
0 65 280 0 20 32 0 015 44 0 312 . . . . . . . kg / kmol 
Then the mass fractions of the gases are determined from 
N :         (or 58.3%)
2 N N
N
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 65
280
312
0.583    
O :         (or 20.5%)
2 O O
O
2 2
2
w y
M
M
? ? ? ( . )
.
.
0 20
32 0
312
0.205   
CO :       (or 21.2%)
2 CO CO
CO
2 2
2
w y
M
M
m
? ? ? ( . )
.
015
44
312
0.212   
Noting that the total pressure of the mixture is 250 kPa and the pressure fractions in an ideal gas mixture 
are equal to the mole fractions, the partial pressures of the individual gases become 
 P y P
N N
2 2
kPa ? ? ? ( . )( ) 0 65 250 162.5 kPa 
 P y P
O O
2 2
kPa ? ? ? ( . )( ) 0 20 250 50 kPa 
 P y P
CO CO
2 2
kPa ? ? ? ( . )( ) 015 250 37.5 kPa 
 
8 kmol H 2 
2 kmol N 2 
 
 
65%  N2 
20%  O2 
15%  CO2 
290 K 
250 kPa 
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