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#### Gibbs Free Energy and Phase Separation: Interactive Simulations

These simulations were prepared using Mathematica. Download the free Wolfram player, and then download the simulation CDF file (link given below or click on figure to download). Try to predict the behavior when a parameter changes before using a slider to change that parameter. Screencasts below explain how to use these simulations.

##### Simulation: Partially-Miscible Liquids

A temperature-composition diagram is shown for two liquids (A, B) that are only partially miscible within the region enclosed by the orange/purple curve. Each phase in the two-phase region contains both A and B; the α phase (represented by the purple line, mole fraction = $$x_A^\alpha$$) is enriched in A and the β phase (orange line, $$x_A^\beta$$) is enriched in B. Outside the phase envelope, A and B are completely miscible. Sliders for “temperature” and “overall mole fraction of A” move the black dot around the diagram. The sizes of the rectangles at the top for pure A and pure B are proportional to the overall mole fraction of that component. The size(s) of the container(s) on the right is/are proportional to the amounts of the phase(s) (either α and β or a single miscible phase) in equilibrium, and the mole fractions are represented by the relative numbers of green (A) and blue (B) circles.

Try to answer these questions before determining the answer with the simulation. We suggest that you write down the reasons for your answers.

1. As the temperature increases for a binary liquid mixture that exhibits phase separation, do you expect the compositions of the two phases to be closer together or further apart? Why?
2. Suppose a binary liquid mixture separates into two phases ( $$x_1^\alpha$$ = 0.10, $$x_1^\beta$$ = 0.79). If the liquid contains 6 moles of component 1 and 4 moles of component 2, is more liquid in the α phase or β phase? Why?