Microsoft Word - Cengel and Boles TOC _2-03-05_.doc

Chapter 13 | 683

EXAMPLE 13–1 Mass and Mole Fractions of a Gas Mixture

Consider a gas mixture that consists of 3 kg of O 2 , 5 kg of N 2 , and 12 kg of

CH 4 , as shown in Fig. 13–4. Determine (a) the mass fraction of each compo-

nent, (b) the mole fraction of each component, and (c) the average molar

mass and gas constant of the mixture.

Solution The masses of components of a gas mixture are given. The mass

fractions, the mole fractions, the molar mass, and the gas constant of the

mixture are to be determined.

Analysis (a) The total mass of the mixture is

Then the mass fraction of each component becomes

(b) To find the mole fractions, we need to determine the mole numbers of

each component first:

Thus,

and

(c) The average molar mass and gas constant of the mixture are determined

from their definitions,

Mm

mm

Nm

20 kg

1.023 kmol

19.6 kg/kmol

yCH 4 

NCH 4

Nm

0.750 kmol

1.023 kmol

0.733

yN 2 

NN 2

Nm

0.179 kmol

1.023 kmol

0.175

yO 2 

NO 2

Nm

0.094 kmol

1.023 kmol

0.092

Nm
NO 2 NN 2 NCH 4 
0.0940.1790.750
1.023 kmol

NCH 4 

mCH 4

MCH 4

12 kg

16 kg>kmol

0.750 kmol

NN 2 

mN 2

MN 2

5 kg

28 kg>kmol

0.179 kmol

NO 2 

mO 2

MO 2

3 kg

32 kg>kmol

0.094 kmol

mfCH 4 

mCH 4

mm

12 kg

20 kg

0.60

mfN 2 

mN 2

mm

5 kg

20 kg

0.25

mfO 2 

mO 2

mm

3 kg

20 kg

0.15

mm
mO 2 mN 2 mCH 4 
 3  5  12 
20 kg

3 kg O 2

5 kg N 2

12 kg CH 4

FIGURE 13–4

Schematic for Example 13–1.

cen84959_ch13.qxd 4/6/05 9:35 AM Page 683