Question

In a factory in which metal parts are degreased with organic solvents, the intern breaks a bottle containing a mixture of 5 liters of tetrachloroethylene (PER, MW = 166 g/mol, ρ = 1.62 g/cm3 , Pv = 18 mm Hg) and 10 liters of trichloroethene (TCE, MW = 131 g/mol, ρ = 1.46 g/cm3 , Pv = 54 mm Hg) in a closed room at 20oC. The room has a total volume of 50 m3 . Assume PER and TCE form an ideal mixture in the liquid phase.

a. What is the composition (in mole fractions) of the liquid mixture in the bottle?

b. What are the equilibrium concentrations of PER and TCE in the air of the room in mg/L? Note: Make sure to use Raoult’s Law. [PER] = 49.9 mg/L

c. What is the composition (in mole fractions) of the remaining liquid on the floor after equilibrium? XPER = 0.790

Answer 1

volume of PER= 5 L, =5000cc, density= 1.46 g/cc

Mass of tetrachloroethene= 5000*1.62 g=8100 gm, moles = mass/Molecular weight=8100/166=48.79

similarly moles ofTCE= 10*1000*1.46/131=111.45, mass of PER= 14600 gm

total moles= 111.45+48.79=160.24 moles

mole fractions in the liquid phase ,   PER =48.79/160.24=0.3044,TCE=0.6956

From raoults law

Partial pressure of PER in the vapor phase = mole fraction in the liqud phase* pure component vapor pressure= 0.3044*18=5.48 mm Hg

partial pressure of TEC = 0.6956*54=37.56 mm Hg

partial pressure of air = 760-5.48- 37.56=716.96 mm Hg

Gas law equation PV=nRT

n= mass/ Molecular weoght PV= (mass/ Moelcular weight)*RT

P*Molecular weight= (mass/Volume)*RT

for PER

Mass/ Volume = P*molecular weight/RT= (5.48/760)*166/(0.08206*293.15)=0.0497 g/L= 49.75 mg/L

TCE= (37.56/760)*131/(0.08206*293.15)=0.269 g/L= 269 mg/L

mass of TCE in vapor phase = 49.75*10^-3*50*1000=2487.5 gm

remaining mass in the liquid phase = 8100-2487.5=5612.5 gm moles of TCE as liquid =5612.5/166=33.81

mass of PER in the vapor phase= 269*10^-3*50*1000=13450 gm

Mass of TCE in liqiud phase = 14600- 13450= 1150gm moles of PER= 1150./131=8.778

total moles after equiliberium is establsihed= 33.81+8.778=42.588

mole fraction in the liquid phase , PER = 33.81/42.588=0.7938   and TCE= 1-0.7938=0.2062