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# mole fractions, partial P and V

By Erica Reed,2014-05-06 12:27
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mole fractions, partial P and V

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 O, N, and CO are 32.0, 28.0 and 44.0 kg/kmol, 222

respectively (Table A-1)

Analysis (a) The total mass of the mixture is

m?m?m?m?5 kg?8 kg?10 kg?23 kg mONCO222

Then the mass fraction of each component becomes

m25 kgOmf???0.2172O8 kg N 223 kgm2m 10 kg CO 2m8 kgN5 kg O 2mf???0.348N223 kgmm

mCO10 kg2mf???0.435CO223 kgmm

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

component first,

m5 kgO2N???0.156 kmolO2M32 kg/kmolO2

m8 kgN2 N???0.286 kmolN2M28 kg/kmolN2

m10 kgCO2N???0.227 kmolCO2M44 kg/kmolCO2

Thus,

N?N?N?N?0.156 kmol?0.286 kmol?0.227 kmol?0.669 kmol mONCO222

and

N0.156 kmolO???0.233y2O0.699 kmolN2m N0.286 kmolN 2???0.428yN20.669 kmolNm

NCO0.227 kmol2???0.339yCO20.669 kmolNm

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

definitions:

m23 kgm???34.4 kg/kmolMmN0.669 kmolmand

R8.314 kJ/kmol?Ku???0.242 kJ/kg?KRm34.4 kg/kmolMm

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. , and N are 2.0 and 28.0 lbm/lbmol, respectively 22Properties The molar masses of H(Table A-1E).

Analysis The mass of each component is determined from

N?5 lbmol???m?NM?????5 lbmol2.0 lbm/lbmol?10 lbmHHHH2222 ????N?4 lbmol???m?NM?4 lbmol28 lbm/lbmol?112 lbm NNNN222224 lbmol N 2The total mass and the total number of moles are

m?m?m?10 lbm?112 lbm?122 lbm5 lbmol HmHN22 N?N?N?5 lbmol?4 lbmol?9 lbmolmHN22

The molar mass and the gas constant of the mixture are determined from their definitions,

m122 lbmm ???13.56 lbm/lbmolMmN9 lbmolm

and

R1.986 Btu/lbmol?Ru ???0.1465 Btu/lbm?RRmM13.56 lbm/lbmolm

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 CO and CH can be treated as ideal gases, 24

and the mixture as an ideal gas mixture.

Properties The molar masses of CO and CH are 44.0 and 16.0 kg/kmol, respectively 24(Table A-1)

Analysis The mole numbers of the constituents are

1 kg COm1kgCO2mN???1kg????0.0227kmolCOCO22M44kg/kmolCO 2 2 m3 kg CH 3kgCH44mN???3kg????0.1875kmolCHCH44 M16kg/kmolCH4300 K NNN?????00227.kmol0.1875kmol0.2102kmol mCOCH200 kPa 24

N0.0227kmolCO2y???0108.CO2N0.2102kmolm N0.1875kmolCH4y???0892.CH4N0.2102kmolm

Then the partial pressures become

P?yP?????0.108200 kPa?21.6 kPaCOCOm22 ????P?yP?0.892200 kPa?178.4 kPaCHCHm44

The apparent molar mass of the mixture is

m4kgm M???19.03kg/kmolmN0.2102kmolm

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 CO and CH can be treated as ideal gases, 24

and the mixture as an ideal gas mixture.

Properties The molar masses of CO and CH are 44.0 and 16.0 kg/kmol, respectively 24(Table A-1)

Analysis The mole numbers of the constituents are

m1kgCO2mN???1kg????0.0227kmolCOCO22M44kg/kmolCO 2 2 m3 kg CH 3kgCH44mN???3kg????0.1875kmolCHCH441 kg CO M16kg/kmolCH4300 K NNN?????00227.kmol0.1875kmol0.2102kmol mCOCH200 kPa 24

N0.0227kmolCO2y???0108.CO2N0.2102kmolm N0.1875kmolCH4y???0892.CH4N0.2102kmolm

Then the partial pressures become

P?yP?????0.108200 kPa?21.6 kPaCOCOm22 ????P?yP?0.892200 kPa?178.4 kPaCHCHm44

The apparent molar mass of the mixture is

m4kgm M???19.03kg/kmolmN0.2102kmolm

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 N and O can be treated as ideal gases, 22

and the mixture as an ideal gas mixture Properties The molar masses of N and O are 28.0 and 32.0 kg/kmol, respectively 22(Table A-1)

Analysis The volumes of the tanks are

3(1 kg)(0.2968 kPa?m/kg?K)(298 K)mRT??3V???0.295 m??N2300 kPaP 3 kg O ??22N2 325?C 25?C (3 kg)(0.2598 kPa?m/kg?K)(298 K)mRT??3V???0.465 m??O300 kPa 2500 kPa P500 kPa1 kg N??O2

333VV?V??0.295 m?0.465 m?0.76 m totalNO22

Also,

m1 kgN2m?1 kg???N???0.03571 kmolNN22M28 kg/kmolN 2 m3 kgO2m?3 kg???N???0.09375 kmolOO22M32 kg/kmolO2

N?N?N?0.03571 kmol?0.09375 kmol?0.1295 kmol mNO22

Thus,

3NRT(0.1295 kmol)(8.314 kPam/kmolK)(298 K)????u P?????422.2 kPa m??3V0.76 m??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

m1 lbm3A ???1000 ftVA31 lbm gas A ?0.001 lbm/ftA and the volume of constituent gas B is 2 lbm gas B

m2 lbm3B ???1000 ftVB3?0.002 lbm/ftB

Hence, the volume of the mixture is

3 V?V?V?1000?1000?2000 ft AB

The specific volume of the mixture will then be

3V2000 ft3 v???666.7 ft/lbm m(1?2) lbm

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