VLE Virtual Laboratory

To complete this virtual laboratory, one must have knowledge of:

Modified Raoult's law
- View Raoult's law screencast
- View Raoult's law self-study module
Nonlinear regression
- View "Iterative Solutions of Nonlinear Equations Using Excel Solver" self-study module

This virtual laboratory measures the vapor composition in equilibrium with a liquid composition for a binary mixture. Initially 1,000 mL each of liquids A and B are available. Use the slider at the top of the page to select the volume of component A added to the boiling flask. An amount of component B is then added so the total volume in the flask is 100 mL. Click the "collect sample" button to obtain a sample of the condensed vapor and analyze it to determine the vapor mole fraction. Because the amount of condensate is small, the experiment assumes the liquid composition to be essentially the same as the starting composition. The virtual laboratory stores your data in a spreadsheet that is accessed by clicking the "download measurements" button.

Plan your experiments to obtain a wide range of liquid mole fractions. After sufficient vapor-liquid equilibrium measurements are made, the objective is to fit the data to the two-parameter Margules equation using nonlinear regression. Once you have determined the values of the Margules parameters, enter the Margules parameters, their 95% confidence intervals, and your name (or the names of members of your group) by pressing the "submit answers" button. Select the "view results" button on the submit answers page to end the experiment and see the correct values of the Margules parameters. This page can be screenshotted and submitted to an instructor as part of a laboratory report or an assignment.

When first opening the laboratory or when selecting the "reset laboratory" button, the laboratory creates new, randomized Margules parameters and liquid properties. To allow students to have extended time for measurements and analysis, the virtual laboratory stores your data, the component properties, and the correct Margules parameters in your web browser. Thus, if you close the web page and come back, you can access your stored data and continue to make measurements or submit your answer. Note that you must use the same web browser and computer for this to work; for example, if you use Google Chrome to make measurements then revisit the virtual laboratory in Firefox, you will not have the same liquid properties, Margules parameters, and your previous measurements will not be saved. Therefore, if you are doing this virtual laboratory in a group, only one group member should take measurements, as the virtual laboratory will generate different Margules parameters and liquid properties on different computers. A video that demonstrates how to use this virtual laboratory is available on the "video instructions" tab.

After completing this laboratory, you should be able to:

More effectively choose conditions for measurements in order to obtain accurate parameters for vapor-liquid equilibrium (VLE)
Apply nonlinear regression to determine parameters and their 95% confidence limits for VLE measurements
Explain why the boiling temperature changes as the liquid composition changes

This video demonstrates how to use this virtual laboratory. Try watching this video in full screen mode if the cursor is difficult to see.

The saturation pressure of component $ i = (A, B) $ is calculated using the Antoine equation:

$$ [1] \qquad P_{i}^{sat} = 10^{ ( A_{i} - \frac{ B_{i} }{ T + C_{i} } ) } $$

where $ P_{i}^{sat} $ is saturation pressure of component $ i $ (mmHg), $ A_{i} $, $ B_{i} $, and $ C_{i} $ are Antoine constants of component $ i $, and $ T $ is temperature (°C). The two-parameter Margules model is used to calculate the activity coefficients for a non-ideal liquid mixture of components A and B. This model fits the excess Gibbs free energy:

$$ [2] \qquad \frac{G^{E}}{RT} = x_{A} x_{B} (A_{21} x_{A} + A_{12} x_{B}) $$

where $ G_{E} $ is excess Gibbs energy, and $ R $ is the ideal gas constant. The activity coefficients $ \gamma_{A} $ and $ \gamma_{B} $ are given by:

$$ [3] \qquad \mathrm{ln} \, \gamma_{A} = x_{B}^{2} (A_{12} + 2 ( A_{21} - A_{12} ) x_{A} ) $$ $$ [4] \qquad \mathrm{ln} \, \gamma_{B} = x_{A}^{2} (A_{21} + 2 ( A_{12} - A_{21} ) x_{B} ) $$

where $ x_{A} $ and $ x_{B} $ are the liquid mole fractions of components and A and B, and $ x_{A} + x_{B} = 1 $, and $ A_{12} $ and $ A_{21} $ are the Margules parameters, which are independent of temperature. The modified Raoult's law is used to calculate the bubble-point and dew-point pressures using the $ K $ factors:

$$ [5] \qquad K_{i} = \frac{y_{i}}{x_{i}} = \frac{\gamma_{i} P_{i}^{sat}}{P} $$

where $ y_{i} $ is the vapor mole fraction, $ y_{A} + y_{B} = 1 $, and $ P $ is the total pressure (mmHg). Bubble-point pressure calculation:

$$ [6] \qquad P = x_{A} \gamma_{A} P_{A}^{sat} + x_{B} \gamma_{B} P_{B}^{sat} $$

The mole fractions of components A and B in the liquid in the boiling flask ($x_{A}$ and $x_{B}$) can be determined using the volumes $ V_{i} $ (mL), molecular weights $ MW_{i} $ (g/mol), and densities $ \rho_{i} $ (g/mL) of components A and B. First, molar density $ C_{i} $ (mol/mL) must be determined:

$$ [7] \qquad C_{i} = \frac{ \rho_{i} }{ MW_{i} } $$

The mole fractions of components A and B can then be determined from the molar densities and volumes of each component:

$$ [8] \qquad x_{A} = \frac{ V_{A} C_{A} }{ V_{A} C_{A} + V_{B} C_{B} } $$

$$ [9] \qquad x_{B} = 1 - x_{A} $$

Nonlinear regression (NLR) should be used to obtain the Margules parameters and the 95% confidence limits. Assume the values of the liquid mole fractions and the temperature are accurate and apply NLR to the vapor mole fractions.

What do the signs of your Margules parameters indicate about the interactions between molecules A and B?
What do the magnitudes of your activity coefficients indicate about the interactions between molecules A and B?
As the mole fraction of component A in the liquid phase increases, does the boiling temperature increase or decrease? Why?
How could you obtain more accurate measurements of the Margules parameters using the experiment equipment used in this laboratory?
In this lab, when a new mixture is added to the boiling flask, the vapor mole fraction is measured in a few seconds. How would this be different in a physical laboratory and why?