9716

Vapor-Liquid Equilibrium Data Using Arc Length Continuation

Consider two binary mixtures: (1) ethanol and water and (2) ethanol and ethyl acetate. This Demonstration computes the isobaric vapor-liquid diagram as well as the equilibrium curve at user-set values of the total pressure (expressed in ). The modified Raoult's law is used along with the van Laar model and Antoine equation. Both systems present a positive pressure-sensitive azeotrope. When present, this azeotrope is indicated on the equilibrium curve by a red dot. The loci of the azeotrope versus pressure is given in a separate plot. In both cases, the azeotrope disappears at a low enough total pressure. One particular feature of the present calculation is that it uses the arc length continuation method (see the Details section) to find the bubble/dew point temperatures versus liquid/vapor phase compositions. This takes advantage of a new function as of Mathematica 9.0, WhenEvent, which determines the loci of the azeotropes; indeed they verify , where is the arc length parameter.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

For vapor-liquid equilibrium data computations, the nonlinear equation , where is the liquid mole fraction and is the bubble temperature, is the bubble point equation derived from Dalton's law and the modified Raoult's law. Introduce an arc length parameter . The nonlinear algebraic equation becomes . We use the built-in Mathematica function NDSolve to solve this equation together with the differential equation (called the arc length constraint) in order to find and . A simple initial condition is found by taking and equal to the boiling temperature of pure ethanol at .
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in Step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2014 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+