Acetone is to be removed from a nitrogen stream by cooling the gas in a condense
ID: 1057214 • Letter: A
Question
Acetone is to be removed from a nitrogen stream by cooling the gas in a condenser. The gas enters the condenser at 80 degree C and 2 atm at 75% relative saturation at a rate of 100 mol/s. The gas stream is to be cooled to 40 degree C at 2 atm pressure. Some of the acetone in the gas condenses in the condenser und leaves as a liquid at 40 degree C. Cooling water is used to cool the gas in the condenser. The cooling water enters at 30 degree C and leaves at 45 degree C. Calculate the mole fraction of acetone in the gas entering and leaving the condenser. Calculate the rate at which liquid acetone leaves the condenser in mol/s. Calculate eth fraction of acetone that enters with the gas that leaves the condenser as liquid condensate. Calculate the rate at which cooling water is fed to the condenser in kg/s. Construct an enthalpy table to do the energy balance. Make sure you state the reference states for your enthalpy calculations.Explanation / Answer
Relative saturation =100* partial pressure of acetone vapor/ vapor pressure of acetone liquid
Partial pressure of acetone vapor = 0.8* vapor pressure of acetone liquid
Vapor pressure of acetone at 80 deg.c = 1579mm Hg
Partial pressure of acetone vapor = 1579*0.8=1263 mm Hg
Partial presusre of nitrogen = 2*760-1263=257 mm Hg
Flow rate of gas = 100 mol/s
Moles of acetone vapor/total moles = partial pressure of acetone/ total pressure
Moles of acetone/100 = 1263/1520=0.83
Moles of acetone = 83 mol/s
Moles of nitrogen= 100-83= 17 mol/s
Mole fraction of acetone enterign = 83/100 =0.83
During condensation to 40 deg.c, moles of nitrogen rermaint the same
Vapor pressure of acetone at 40 deg.c =422 mm Hg
Acetone is assumed to be leaving under saturated conditions at 40 deg.c
Partial pressure of acetnoe = vapor pressure = 422 mm Hg
Partial pressue of nitrogen = total pressure – partial pressure of nitrogen = 1520-422
Partial pressure of acetone/ partial pressure of nitrogen = moles of acetone /moles of nitrogen
Moles of acetone/ 17= 422/(1520-422)
Moles of acetone = 0.533 moles/ s at 40 deg.c
Moles of acetone condensed = 83-0.533 =82.467 mol/s
Fraction of acetone condensed = 82.467/83= 0.9935
Vapor phase leaving contains 0.533 mol/s acetone and 17 mol/s nitrogen
Mole fraction of acetone leaving = 0.533/(17+0.533)=0.0189
Exit conditions of acetone at 40 deg.c is taken as the reference.
So moles of acetone condensed = 82.467
Latent heat of vaporization of acetone =518 j/g and assumed to be independent of pressure
Heat need to be removed to condense acetone = 82.467*518 =42718 joules/s
Heat need to be removed from nitrogen = moles of nitrogen * molar mass* specific heat* (80-40)
= 17*28*1.039J*40 = 19783 joules/s
Total heat that needs to be removed = 42718+19783 = 62501 j/s
This heat has to be supplied by water
Hecne 62501= mass flow rate of of water * specific heat of water (4.184)*(45-30)=996 kg/s