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1. Obtain the equilibrium mole fractions (liquid and vapor) of a mixture of water, methanol and...

1. Obtain the equilibrium mole fractions (liquid and vapor) of a mixture of water, methanol and ethanol at 100 kPa and 70°C. You can assume the mixture is ideal.
2. Create one plot where the equilibrium mole fraction of benzene in the vapor phase is plotted against the equilibrium mole fraction of benzene in the liquid phase for three different pressures (0.2 bar, 0.6 bar and 1 bar). Comment on the effect of pressure on the relative volatility

Solutions

Expert Solution

1. to obtain the equilibrium mole fractions of mixture of water ,methanol & ethanol at 100 kPa & 70oC

assuming ideal mixture

using antoine equation

ln Psat = A-B/(T+C)

component A B C
water 16.2620 3799.89 -46.80
methanol 16.5938 3644.30 -33.39
ethanol 16.6758 3674.49 -46.70

therefore

by solving equations at 70o(343.15K)

ln Psatwater=16.2620-3799.89/(343.15-46.80)

lnPsatwater=3.43969529

Psatwater=31.1774566 kPa

similarly for methanol

Psatmethanol=125.071kPa

for ethanol

Psatethanol=72.3001454 kPa

now by using Raoults law

yiP=xiPisat

as            &         

100 = xw*31.1774566 +xM*125.071+xE*72.3001454     we can put xw=1-xM-xE

100 =(1-xM-xE)*31.1774566 +xM*125.071+xE*72.3001454

68.82=93.89*xM+41.12*xE

by trial & error we get xM=0.6 & xE=0.3   so

xw=0.1

yM=1.25*0.6=0.75

yw=0.3117xw=0.031

yE=0.723xE=0.216

checking answer

yw+yM+yE=0.75+0.031+0.216=0.9971

hence solution is appropriate

Q.2

to create plot where equilibrium mole fraction of benzene in the vapor is plotted against the equilibrium mole fraction of benzene in liquid phase .

yP=xPsat

for 3 different P=0.2,0.6,1 bar

for P=0.2 bar

we can plot on graph at different P

& to comment on effect of pressure on relative volatility

volatility of component is defined as partial pressure of component i to its mole fraction in liquid phase.

as the partial pressure is higher volatility increases

but the relative volatility is independant of total pressure. total pressure doesnt affect relative volatility.


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