13-12 The masses of the constituents of a gas mixture are given. The mass fractions, the
mole fractions, the average molar mass, and gas constant are to be determined.
Properties The molar masses of O2, N2, and CO2 are 32.0, 28.0 and 44.0 kg/kmol,
respectively (Table A-1)
Analysis (a) The total mass of the mixture is
mm  mO2  mN2  mCO2  5 kg  8 kg  10 kg  23 kg
Then the mass fraction of each component becomes
mf O 2 
mf N 2 
mf CO 2 
mO 2
mm

5 kg
 0.217
23 kg

8 kg
 0.348
23 kg
mN2
mm
m CO 2

mm
5 kg O2
8 kg N2
10 kg CO2
10 kg
 0.435
23 kg
(b) To find the mole fractions, we need to determine the mole numbers of each
component first,
N O2 
N N2 
N CO 2 
mO2
M O2
mN2
M N2

5 kg
 0.156 kmol
32 kg/kmol

8 kg
 0.286 kmol
28 kg/kmol
m CO 2

M CO 2
10 kg
 0.227 kmol
44 kg/kmol
Thus,
N m  N O2  N N2  N CO2  0.156 kmol  0.286kmol  0.227 kmol  0.669kmol
and
y O2 
y N2 
y CO 2 
N O2
Nm
N N2
Nm
N CO 2
Nm

0.156 kmol
 0.233
0.699 kmol

0.286 kmol
 0.428
0.669 kmol

0.227 kmol
 0.339
0.669 kmol
(c) The average molar mass and gas constant of the mixture are determined from their
definitions:
Mm 
mm
23 kg

 34.4 kg/kmol
N m 0.669 kmol
and
Rm 
Ru
8.314 kJ/kmol  K

 0.242 kJ/kg K
Mm
34.4 kg/kmol
13-15E The mole numbers of the constituents of a gas mixture are given. The mass of
each gas and the apparent gas constant are to be determined.
Properties The molar masses of H2, and N2 are 2.0 and 28.0 lbm/lbmol, respectively
(Table A-1E).
Analysis The mass of each component is determined from
N H 2  5 lbmol 
 mH 2  N H 2 M H 2  5 lbmol 2.0 lbm/lbmol   10 lbm
N N 2  4 lbmol 
 m N 2  N N 2 M N 2  4 lbmol 28 lbm/lbmol   112 lbm
The total mass and the total number of moles are
5 lbmol H2
4 lbmol N2
m m  m H 2  m N 2  10 lbm  112 lbm  122 lbm
N m  N H 2  N N 2  5 lbmol  4 lbmol  9 lbmol
The molar mass and the gas constant of the mixture are determined from their definitions,
Mm 
m m 122 lbm

 13. 56 lbm/lbmol
N m 9 lbmol
and
Rm 
Ru
1.986 Btu/lbmol  R

 0.1465 Btu/lbm  R
Mm
13.56 lbm/lbmol
13-31 The masses of the constituents of a gas mixture at a specified pressure and
temperature are given. The partial pressure of each gas and the apparent molar mass of
the gas mixture are to be determined.
Assumptions Under specified conditions both CO2 and CH4 can be treated as ideal gases,
and the mixture as an ideal gas mixture.
Properties The molar masses of CO2 and CH4 are 44.0 and 16.0 kg/kmol, respectively
(Table A-1)
Analysis The mole numbers of the constituents are
mCO 2  1 kg


mCH 4  3 kg


N CO 2 
N CH 4 
mCO 2
MCO 2
mCH 4
MCH 4


1 kg
 0.0227 kmol
44 kg / kmol
3 kg
 0.1875 kmol
16 kg / kmol
Nm  NCO2  NCH 4  0.0227 kmol  0.1875 kmol  0.2102 kmol
yCO 2 
yCH 4 
N CO 2
Nm
N CH 4
Nm

0.0227 kmol
 0108
.
0.2102 kmol

0.1875 kmol
 0.892
0.2102 kmol
Then the partial pressures become
PCO 2  y CO 2 Pm  0.108 200 kPa   21.6 kPa
PCH 4  y CH 4 Pm  0.892 200 kPa   178.4 kPa
The apparent molar mass of the mixture is
1 kg CO2
3 kg CH4
300 K
200 kPa
Mm 
mm
4 kg

 19.03 kg / kmol
N m 0.2102 kmol
13-31 The masses of the constituents of a gas mixture at a specified pressure and
temperature are given. The partial pressure of each gas and the apparent molar mass of
the gas mixture are to be determined.
Assumptions Under specified conditions both CO2 and CH4 can be treated as ideal gases,
and the mixture as an ideal gas mixture.
Properties The molar masses of CO2 and CH4 are 44.0 and 16.0 kg/kmol, respectively
(Table A-1)
Analysis The mole numbers of the constituents are
mCO 2  1 kg


mCH 4  3 kg


N CO 2 
N CH 4 
mCO 2
MCO 2
mCH 4
MCH 4


1 kg
 0.0227 kmol
44 kg / kmol
3 kg
 0.1875 kmol
16 kg / kmol
Nm  NCO2  NCH 4  0.0227 kmol  0.1875 kmol  0.2102 kmol
yCO 2 
yCH 4 
N CO 2
Nm
N CH 4
Nm

0.0227 kmol
 0108
.
0.2102 kmol

0.1875 kmol
 0.892
0.2102 kmol
1 kg CO2
3 kg CH4
300 K
200 kPa
Then the partial pressures become
PCO 2  y CO 2 Pm  0.108 200 kPa   21.6 kPa
PCH 4  y CH 4 Pm  0.892 200 kPa   178.4 kPa
The apparent molar mass of the mixture is
Mm 
mm
4 kg

 19.03 kg / kmol
N m 0.2102 kmol
13-33 The masses, temperatures, and pressures of two gases contained in two tanks
connected to each other are given. The valve connecting the tanks is opened and the final
temperature is measured. The volume of each tank and the final pressure are to be
determined.
Assumptions Under specified conditions both N2 and O2 can be treated as ideal gases,
and the mixture as an ideal gas mixture
Properties The molar masses of N2 and O2 are 28.0 and 32.0 kg/kmol, respectively
(Table A-1)
Analysis The volumes of the tanks are
(1 kg)(0.2968 kPa  m 3 /kg  K)(298 K)
 mRT 
 0.295 m 3
 
300 kPa
 P  N2
V N2  
(3 kg)(0.2598 kPa  m 3 /kg  K)(298 K)
 mRT 
 0.465 m 3
 
P
500
kPa

 O2
V O2  
1 kg N2
25C
300 kPa
3 kg O2
25C
500 kPa
V total  V N 2 V O 2  0.295 m 3  0.465 m 3  0.76 m 3
Also,
m N 2  1 kg 
 N N 2 
m O 2  3 kg 
 N O 2 
mN2
M N2
mO2
M O2

1 kg
 0.03571 kmol
28 kg/kmol

3 kg
 0.09375 kmol
32 kg/kmol
N m  N N2  N O2  0.03571 kmol  0.09375 kmol  0.1295 kmol
Thus,
(0.1295 kmol)(8.31 4 kPa  m 3 /kmol  K)(298 K)
 NRu T 
Pm  
 
 422.2 kPa
0.76 m 3
 V m
13-35E A mixture is obtained by mixing two gases at constant pressure and temperature.
The volume and specific volume of the mixture are to be determined.
Properties The densities of two gases are given in the problem statement.
Analysis The volume of constituent gas A is
VA 
mA
A

1 lbm
0.001 lbm/ft 3
 1000 ft 3
and the volume of constituent gas B is
VB 
mB
B

2 lbm
0.002 lbm/ft 3
 1000 ft
1 lbm gas A
3
Hence, the volume of the mixture is
V  V A V B  1000  1000  2000 ft 3
The specific volume of the mixture will then be
v
V
m

2000 ft 3
 666.7 ft 3 /lbm
(1  2) lbm
2 lbm gas B