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ThermoSolutions-CHAPTER13

# ThermoSolutions-CHAPTER13 - 13-1 Chapter 13 GAS MIXTURES...

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13-1 Chapter 13 GAS MIXTURES Composition of Gas Mixtures 13-1C It is the average or the equivalent gas constant of the gas mixture. No. 13-2C No. We can do this only when each gas has the same mole fraction. 13-3C It is the average or the equivalent molar mass of the gas mixture. No. 13-4C The mass fractions will be identical, but the mole fractions will not. 13-5C Yes. 13-6C The ratio of the mass of a component to the mass of the mixture is called the mass fraction ( mf ), and the ratio of the mole number of a component to the mole number of the mixture is called the mole fraction ( y ). 13-7C From the definition of mass fraction, ¸ ¸ ¹ · ¨ ¨ © § m i i m m i i m i i M M y M N M N m m mf 13-8C Yes, because both CO 2 and N 2 O has the same molar mass, M = 44 kg/kmol. 13-9 A mixture consists of two gases. Relations for mole fractions when mass fractions are known are to be obtained . Analysis The mass fractions of A and B are expressed as m B B B m A A m m A A m A A M M y M M y M N M N m m mf and mf Where m is mass, M is the molar mass, N is the number of moles, and y is the mole fraction. The apparent molar mass of the mixture is B B A A m B B A A m m m M y M y N M N M N N m M . . Combining the two equation above and noting that 1 . B A y y gives the following convenient relations for converting mass fractions to mole fractions, ) 1 mf / 1 ( B A A B A M M M y . 0 and 1 A B y y 0 which are the desired relations.

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13-2 13-10 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 2 O are 28.0, 32.0, and 18.0 kg/kmol, respectively (Table A- 1). Analysis The molar mass of moist air is My M ii u.u.u ¦ 078 280 020 320 002 18 286 .. . . k g / k m Moist air 78% N 2 20% O 2 2% H 2 O (Mole fractions) ol Then the mass fractions of constituent gases are determined to be 0.764 6 . 28 0 . 28 ) 78 . 0 ( mf : N 2 2 2 N N N 2 M M y 0.224 6 . 28 0 . 32 ) 20 . 0 ( mf : O 2 2 2 O O O 2 M M y 0.013 6 . 28 0 . 18 ) 02 . 0 ( mf : O H O H O H O H 2 2 2 2 M M y Therefore, the mass fractions of N 2 , O 2 , and H 2 O in the air are 76.4%, 22.4%, and 1.3%, respectively. 13-11 The molar fractions of the constituents of a gas mixture are given. The gravimetric analysis of the mixture, its molar mass, and gas constant are to be determined. Properties The molar masses of N 2 , and CO 2 are 28.0 and 44.0 kg/kmol, respectively (Table A-1) Analysis Consider 100 kmol of mixture. Then the mass of each component and the total mass are +, + , + , kg 1760 kg/kmol 44 kmol 40 kmol 40 kg 1680 kg/kmol 28 kmol 60 kmol 60 2 2 2 2 2 2 2 2 CO CO CO CO N N N N ¡o ¡ ¡ M N m N M N m N kg 3440 kg 1760 kg 1680 2 2 CO N . . m m m m mole 60% N 2 40% CO 2 Then the mass fraction of each component (gravimetric analysis) becomes 51.2% 48.8% or 0.512 kg 3440 kg 1760 mf or 0.488 kg 3440 kg 1680 mf 2 2 2 2 CO CO N N m m m m m m The molar mass and the gas constant of the mixture are determined from their definitions, and M m N R R M m m m m u m ¢ ¢ 3,440 kg 100 kmol 8.314 kJ /kmol K 34.4 kg /kmol 34.40 kg / kmol 0.242 kJ / kg K
13-3 13-12 The molar fractions of the constituents of a gas mixture are given. The gravimetric analysis of the

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ThermoSolutions-CHAPTER13 - 13-1 Chapter 13 GAS MIXTURES...

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