Solution9-10 - Chapter 9 Gas Mixtures and Psychometrics 9-1...

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Unformatted text preview: Chapter 9 Gas Mixtures and Psychometrics 9-1 Chapter 9 GAS MIXTURES AND PSYCHROMETRICS Composition of Gas Mixtures 9-1C It is the average or the equivalent gas constant of the gas mixture. No. 9-2C No. We can do this only when each gas has the same mole fraction. 9-3C It is the average or the equivalent molar mass of the gas mixture. No. 9-4C The mass fractions will be identical, but the mole fractions will not. 9-5C Yes. 9-6C 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 ). 9-7C From the definition of mass fraction, = = = m i i m m i i m i i M M y M N M N m m mf 9-8C Yes, because both CO 2 and N 2 O has the same molar mass, M = 44 kg/kmol. 9-9 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 mf M M y M N M N m m mf = = = = and 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 / 1 ( B A A B A M mf M M y +- = and 1 A B y y- = which are the desired relations. Chapter 9 Gas Mixtures and Psychometrics 9-2 9-10 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 M y M i i = = × + × + × = ∑ 0 78 28 0 0 20 32 0 0 02 18 28 6 . . . . . . kg /kmol Then the mass fractions of constituent gases are determined to be N : 2 N N N 2 2 2 w y M M = = = ( . ) . . 0 78 28 0 28 6 0.764 O : 2 O O O 2 2 2 w y M M = = = ( . ) . . 0 20 32 0 28 6 0.224 H O: 2 H O H O H O 2 2 2 w y M M = = = ( . ) . . 0 02 18 0 28 6 0.012 Therefore, the mass fractions of N 2 , O 2 , and H 2 O in the air are 76.4%, 22.4%, and 1.2%, respectively. 9-11 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 ( 29( 29 ( 29( 29 kg 1,760 kg/kmol 44 kmol 40 kmol 40 kg 1,680 kg/kmol 28 kmol 60 kmol 60 2 2 2 2 2 2 2 2 CO CO CO CO N N N N = = = → = = = = → = M N m N M N m N m m m m = + = + = N CO 2 2 kg 1,760 kg...
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Solution9-10 - Chapter 9 Gas Mixtures and Psychometrics 9-1...

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