Toluene(l) and water(2) are essentially immiscible as liquids.

ALEX PEPSEGA INDRA PUTRA 

Toluene(l) and water(2) are essentially immiscible as liquids. Determine the dew-point temperatures and the compositions of the first drops of liquid formed when vapor mixtures of these species with mole fractions z₁ = 0.2 and z₁ = 0.7 are cooled at a constant pressure of 101.33 kPa. What is the bubblepoint temperature and the composition of the last drop of vapor in each case? See Table B.2 for vapor-pressure equations.

Table B.2: Constants for the Antoine Equation for Vapor Pressures of Pure Species

Latent heat of vaporization at the normal boiling point (ΔHn), and normal boiling point (tn)

Vapor pressure of a species as a function of temperature is given by the Antoine equation.

Where are parameters which vary as per the chemical species.

A three-phase vapor/liquid/liquid equilibrium (VLLE) is a binary system which consists of two liquid phases and one vapor phase in equilibrium. For a given pressure, the temperature and compositions of all three phases are fixed.

The three phases are in equilibrium at a temperature.

The three-phase-equilibrium pressure is given by.

The three-phase-equilibrium vapor composition as.

For immiscible systems the composition of the species in liquid phase is unity and also their activities approach unity.

Given two species toluene and water,

From table C.2 page 654 of the text, get the parameters of the Antoine equation for the calculation of saturation pressure for toluene and water.

 for toluene.

 for water.

Pressure, 

The three-phase equilibrium pressure for immiscible liquids is given by,

Three-phase vapor composition is given by,

Now calculate  and 

Assume a set of temperature, values with an interval of 10 ?, starting from 30? or and then calculate values of  and  from the Antoine equation given above, till .

Similarly calculate the other values and then tabulate the values in a Table as follows.

As,  is between the temperatures 80 ? and 90 ?.

Now plot a XY scatter graph between the 3-phase equilibrium and temperature.

Now, add a trendline and in the options select a trendline which suits the curve in the graph, add the equation for the corresponding trendline.

Which is, . Here .

So, for a  value of 101.33 .

The value of temperature is as follows,

Therefore, =83.27 ?.

Now, again by graphical interpolation between the values of  and .

calculate the value of  at =83.27 ?.

The equation for trendline is .

Here 

Now calculate the three-phase equilibrium vapor composition, which is as follows:

Consider the possible cases,

For , the first drop of liquid consists of pure liquid species 2.

So here,  , here the  is the dew point temperature.

From the equation for vapor in equilibrium with pure liquid 2,

Now, by graphical interpolation between the values  and , calculate the value of 

The trendline equation is .

Here .

So, for a  value of 81.064 , is calculated as follows,

The value of temperature is as follows,

Therefore, the dew point for the above case is 

For , the first liquid consists of pure liquid species 1.

So here  , here let  is the dew point temperature.

From the equation for vapor in equilibrium with pure liquid 1,

Now, by graphical interpolation between the values  and , calculate the value of 

The trendline equation is .

Here .

So, for a  value of 30.4 , is calculated as follows,

The value of temperature is as follows,

Therefore, the dew point for the above case is 

From the above calculations, the bubble point temperature for both the cases is , and the mole fraction of the last vapor is .