A gas mixture consists of 50 lbm H2, 200 lbm H2O, 100 lbm CO2/ and 300 lbm of N2

Question

A gas mixture consists of 50 lbm H2, 200 lbm H2O, 100 lbm CO2/ and 300 lbm of N2. Values of specific heat at constant pressure are: for H2, cp = 3.43 Btu/lbm-R; for H2O, cp = 0.445 Btu/lbm-R; for CO2, cp = 0.203 Btu/lbm-R and for N2, cp = 0.248 Btu/lbm-R. Molecular mass/weight is 2 lbm/lbmol for H2, 18 lbm/lbmol for H2O, 44 lbm/lbmol for CO2 and 28 lbm/lbmol for N2. Find: (a) mole fraction of H2O (b) Average mixture value of cp in Btu/lbm-R (c) average molecular weight in lbm/lbmol (d) pressure of the mixture if it is kept in a 1200 ft3 tank at a temperature of 80 degree F in psia. [(a) 22.6%, (b) 0.556 Btu/lbm-R, (c) 13.24 lbm/lbmol, (d) 237 psia]

Explanation / Answer

no of moles,n=given mass/molecular mass

no of mole of H2.n1=50/2=25

no of moles of water,n2=200/18=11.11

no of moles of CO2,n3=100/44=2.27

no of moles of N2,n4=300/28=10.71

a)mole fraction of H2O,X1=n2/(n1+n2+n3+n4)

=0.2263

=22.63%

b)Cp of mixture=Cp1*x1+Cp2*x2+Cp3*x3+Cp4*x4

=0.556Btu/lbm.R

c)av. molecular mass=?(MWi?xi) (where MWi is the molecular weight of each componenet and xi is the respective mole fraction)

=13.246lbm/lbmol

d)for pressure applying dalton's law,

PT=p1+p2+p3+p4

where partial pressure are calculated by,

PV=nRT

Hence,PT=236.8psia

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