# Using the equations Wilson’s, Margules’, and van Laar’s, plot the

• scott_for_the_game
In summary, the conversation discusses using the equations Wilson’s, Margules’, and van Laar’s to plot the predicted VLE for a system at a certain temperature, with and without the use of fugacity coefficients. The conversation also mentions using antoine constants and activity coefficients to solve the equations. The question of what goes on the x and y axis for the plot is brought up, as well as the confusion about whether to use the given x1 and y1 values or calculate new ones. It is suggested to use the given x1 and y1 values and plot them against the new P obtained with the equations. The concept of iteration for obtaining values is also briefly mentioned.
scott_for_the_game
Using the equations Wilson’s, Margules’, and van Laar’s, plot the predicted VLE for this system at this temperature, with and without the use of fugacity coefficients.

Anyone know how to do this or can explain to me how to do VLE. Or have a link for a worked example.

Cheers.

scott_for_the_game said:
Using the equations Wilson’s, Margules’, and van Laar’s, plot the predicted VLE for this system at this temperature, with and without the use of fugacity coefficients.

Anyone know how to do this or can explain to me how to do VLE. Or have a link for a worked example.

Cheers.
Presumably, you were to learn this in class or from a text. Do you have a specific question you're troubled by? If so, post the question along with what you've accomplished so far and where you're stuck.

(a) Find the dew temperature and composition for a mixture of y1 = 0.55 at 3.954 bar. (Answers. 371 K and x1 = 0.58)
(b) Find the bubble temperature and composition for a mixture of x1 = 0.50 at 3.954 bar.
(Answers. 371 K and y1 = 0.49)
(c) Using the Wilson equation and the constants listed, find the bubble pressure and vapour composition for a mixture of 30 mol% methyl acetate at 90C.
(Answers. 3.1 bar and y1 = 0.36)

Pc, bar Tc, K  Vc zc
Methyl acetate (1) 46.3 506.8 0.324 228.0 cc/mol 0.254
Methanol (2) 79.9 512.6 0.559 118.0 cc/mol 0.224

Antoine Constants (P is in torr)
A B C Range, C
Methyl acetate (1) 7.41791 1386.510 247.853 57 - 205
Methanol (2) 7.97010 1521.230 233.970 65 - 214

Constants A12 A21
Margules’ 0.8427 0.4043
Van Laar 0.8914 0.4718
Wilson 336.148 350.841

Vapour-Liquid Equilibrium Data at 3.954 bar Total Pressure,
Methyl acetate – Methanol
Temperature, C x1 y1
104.40 0.0000 0.0000
100.50 0.0880 0.1540
98.60 0.1980 0.2730
97.30 0.2960 0.3680
97.20 0.3980 0.4370
97.10 0.5150 05220
97.00 0.5380 0.5380
97.30 0.6260 0.5980
98.10 0.7320 0.6840
98.90 0.7970 0.7500
99.60 0.8340 0.7950
101.30 0.9130 0.8950
103.80 1.0000 1.0000

How would i solve each qu? Cause I don't get the right answer. I used Raoult's Law for the first two and didnt get close, is that right?

Are you working with the correct units (e.g. $^{\circ} C \rightarrow K$)?

So it needs to be Kelvin? Why's that?

ln P1sat = A - B/(Temp(K) + C)

BTW I copied the wrong table.. it should be constant temperature. Shouldnt make a difference though. I tried in Kelvin still don't get the correct answer.

1. Use the antoine eq to get the two Psat
2. Use P = P2sat + (P1sat - p2sat)xX1
3. Use y1 = (x1 x P1sat) / P

scott_for_the_game said:
BTW I copied the wrong table.. it should be constant temperature. Shouldnt make a difference though. I tried in Kelvin still don't get the correct answer.

1. Use the antoine eq to get the two Psat

(i) In the antoine eq, it should be specified whether you need to use celcius or kelvin. Use the correct one to find Psat

3. Use y1 = (x1 x P1sat) / P

(ii) The solution is non-ideal. So, you cannot use Raoult's law. You need to equate the fugacities and calculate the activity coefficients from the models

You may want to visit this website for an introduction to VLE
http://www.et.byu.edu:8080/~rowley/VLEfinal/VLE_home.htm

I found Chemical Engineering Thermodynamics by Smith & Van Ness very useful in understanding VLE. You might want to use that as a reference book.

Last edited by a moderator:
Yeh I got that book, not impressed. Whats the deal with fugacity.. I hear you have to iterate to get the value? How do u do this?

Also what's the difference in using margules, van laar and wilson.. whichs one more accurate and if its marginal what's the point?

scott_for_the_game said:
Yeh I got that book, not impressed. Whats the deal with fugacity.. I hear you have to iterate to get the value? How do u do this?

I don't understand. Iterate to get what value?

Have you read the chapter on Solution thermodynamics? That introduces the concept of fugacity of a species very clearly, IMO. If you're stuck somewhere and don't understand, post the specific question here.

Also what's the difference in using margules, van laar and wilson.. whichs one more accurate and if its marginal what's the point?

The difference between the various models is explained pretty clearly in the text.

If you're stuck in a specific concept, then post your question here.

Listed below are the constants in three activity-coefficient equations - Wilson’s, Margules', and van Laar’s - for the system methyl acetate-methanol. In addition, the vapour liquid equilibria at one temperature are tabulated. Using the three equations, plot the predicted VLE for this system at this pressure, with and without the use of fugacity coefficients.

My question is what goes on the x and y axis.

Is it just the x1 and y1 composition on the x-axis and the P on the y-axis?

I'm confused on whether I use the x1 and y1 values given and graph is against the new P I obtain with the equations. Or do I need to calculate new values for x1 and y1?

Basically what I'm trying to ask is if your just calculating P with the 3 equations and plotting against the the x1 and y1 in the given data table.

I've got a feeling you have to calculate new x1 and y1 values.. but for instance with the margules eq you can calculate a new y1 but u have to use the given x1 to calculate gamma and P. So how would you get a new x1 value.

Or maybe I've got it all wrong.

Theres qu's such as:

Find the dew temperature and composition for a mixture of y1 = 0.55 at 3.954 bar.

Where you need to iterate to obtain values. Does something as such need to be done for the plots?

Cheers.

JamesFinHuman

## 1. What are the equations used for Wilson's, Margules', and van Laar's plots?

The equations used for Wilson's, Margules', and van Laar's plots are used to model the behavior of binary liquid mixtures. These equations take into account the interactions between the two components of the mixture and can be used to predict properties such as vapor-liquid equilibrium, activity coefficients, and excess enthalpies.

## 2. How do you use Wilson's equation to plot a liquid-liquid equilibrium curve?

To plot a liquid-liquid equilibrium curve using Wilson's equation, you will need to know the values of the Wilson parameters for the two components in the mixture. These parameters can be obtained from experimental data or calculated using thermodynamic models. Once you have the parameters, you can use them to solve the Wilson equation and plot the equilibrium curve.

## 3. What is the purpose of using Margules' equation in binary liquid mixtures?

The purpose of using Margules' equation in binary liquid mixtures is to calculate the activity coefficients of the components in the mixture. This equation takes into account the non-ideal behavior of the mixture and can be used to predict the deviation from ideal behavior. It is particularly useful in systems with large deviations from ideality.

## 4. How is van Laar's equation used to predict excess enthalpies in binary liquid mixtures?

Van Laar's equation is used to predict excess enthalpies in binary liquid mixtures by taking into account the interactions between the components in the mixture. This equation can be used to calculate the deviation from ideal behavior and predict the heat of mixing in the system. It is often used in the design and optimization of industrial processes.

## 5. Can these equations be used for ternary or multicomponent mixtures?

No, these equations are only applicable to binary liquid mixtures. For ternary or multicomponent mixtures, more complex equations, such as NRTL or UNIQUAC, are needed to take into account the interactions between three or more components. However, some of the parameters used in Wilson's, Margules', and van Laar's equations can be modified to make them applicable to ternary or multicomponent systems.

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