Question

Given:

Vapor–liquid equilibrium data in mole fractions for the system
acetone–air–water at 1 atm (101.3 kPa) are as follows:

y acetone in air	0.004	0.008	0.014	0.017	0.019	0.020
x acetone in water	0.002	0.004	0.006	0.008	0.010	0.012

Find:

(a) Plot the data as (1) moles acetone per mole air versus moles
acetone per mole water, (2) partial pressure of acetone versus g acetone
per g water, and (3) y versus x. (b) If 20 moles of gas containing
0.015 mole-fraction acetone is contacted with 15 moles of water,
what are the stream compositions? Solve graphically. Neglect water/
air partitioning.

Answer 1

(a) 1. Here data is given between mole fractions so first we convert in the form of mole ratio

Where Y is the mole ratio that is

similarly

X	Y
0.002004	0.00401
0.004016	0.00806
0.006036	0.0142
0.008064	0.0173
0.01010	0.0194
0.01214	0.0204

2. now we have to plot partial pressure of acetone verses g acetone per gram of water

Partial Pressure

Where P_T is the total pressure = 101.3 kPa

To calculate the g acetone per g of water we multiply by molecular weight of acetone and divide by molecular weight of water

(g acetone /g water) X'=

P acetone (kPa)	X'
0.4052	0.00645
0.8104	0.0129
1.4182	0.01936
1.722	0.0258
1.9247	0.032
2.026	0.03872

(3) For y verses x we can directly plot from the given data

(b)

20 mole of gas containing 0.015 mole fraction of acetone

Water = 15 moles

Let G = Moles of gas free from acetone = 20 - 20 0.015

G= 19.7 moles of acetone free gas

Pure water L = 15 moles

Let the counter current contact and

Y1 = moles ratio for gas at inlet = 0.0152

X1 = mole ratio for water outlet

Y2 = Mole ratio for Gas outlet

X2 mole ratio for water inlet = 0 (Water is pure initially)

We apply acetone mole balance

X1 and Y2 are in euillibrium

GY1+ LX2 =GY2 + LX1

G(Y1-Y2)=LX1

We put Y2 =Y

X1=X

Therfore Y=Y1-(L/G)X

When we draw this line in Graph A1 . Where this line intersect with the equillibrium line it gives us stram composition

Y= -(0.76)X + 0.0152

The Red line provides the by the equation of line

The stream composition

X= 0.005 (moles of acetone / mole of air)

Y= 0.012 (mole of acetone/ moles of water)