## Phase Diagrams (con't)

### Deviations for Raulot's Law

Deviations from Rauolt's Law are often found. They can be positive or negative. For positive deviations we find something similar to that below where an azeotrope is found. An azetrope is where the composition of the liquid and vapor are the same. In this case, the azeotrope formed is a minimum boiling azeotrope. If we follow the red line from the liquid, we enter the two phase region and the vapor has a relatively more of B in it than it had in the liquid. The composition and the amounts of the two phases are given by the horizontal tie lines. For a closed system, the composition of both the vapor and liquid phase change continuously.

Negative deviations from Rauolt's Law yield phase diagrams similar to that below. These have a maximum boiling azeotrope.

Remember open and closed systems can behave differently. If we were to conduct a distillation (the system would be open). The first would initially have vapor composition closer to the azeotrope than the original liquid. As the distillation proceeds, the liquid and vapor composition move more toward the pure component. In contrast, for the negative deviations, the vapor composition is initially more like the pure component, and later both the liquid and vapor move toward the composition of the azeotrope. The blue arrows indicate the direction of composition drift.

### C. Immiscible Liquid Phases

In many systems, the two liquid phases separate at lower temperatures into a two phase system. As we noted before, regular solution theory provided us with a method of qualitatively determining the phase boundries. The diagram below is like the first one above with the 2 phase liquid region added.

The critical temperature, Tc, is the temperature above which the two liquids are miscible in all proportions. When the Tc gets higher, the two regions approach each other and the following diagram results.

On the above diagram, A (liquid heavy in A), B (solution of A and B), and C (liquid heavy in B) can all be in equilibrium at one temperature (within a certain overall composition range). In other words, a 3 phase region separates the two two-phase regions.

### D. Solids

For solids, diagrams like the followings are found for simple systems. A eutectic is a minimum melting point for a solid. In this case both species freeze out as pure solids. Note that there is a 3 phase region where the line is. The 3 phases are solid A and B plus the eutectic liquid.

Sometimes compounds are formed in the mixture, such as MgZn(2). This has a fixed stoichiometric ratio. A typical phase diagram might be:

Note that this is almost like two separate diagrams with the compound, C in between. Thus on each side the pure A or B is in equilibrium with the compound. There are two different eutectics in this diagram.

Think about what would happen to the liquid in each of the different regions of the phase diagram as it was cooled. What would be in equilibrium with what?

Sorry, but haven't yet had the ambition to draw in solid solutions or phase diagrams with incongruent melting points.