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

  1. Oct 31, 2006 #1
    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.
     
  2. jcsd
  3. Oct 31, 2006 #2
    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.
     
  4. Oct 31, 2006 #3
    (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?
     
  5. Nov 1, 2006 #4
    Are you working with the correct units (e.g. [itex]^{\circ} C \rightarrow K[/itex])?
     
  6. Nov 1, 2006 #5
    So it needs to be Kelvin? Why's that?

    ln P1sat = A - B/(Temp(K) + C)
     
  7. Nov 1, 2006 #6
    BTW I copied the wrong table.. it should be constant temperature. Shouldnt make a difference though. I tried in Kelvin still dont 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
     
  8. Nov 2, 2006 #7

    siddharth

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    Homework Helper
    Gold Member

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

    (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: Nov 2, 2006
  9. Nov 2, 2006 #8
    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 whats the difference in using margules, van laar and wilson.. whichs one more accurate and if its marginal whats the point?
     
  10. Nov 2, 2006 #9

    siddharth

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    Homework Helper
    Gold Member

    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.

    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.
     
  11. Nov 3, 2006 #10
    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?
     
  12. Nov 3, 2006 #11
    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.
     
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