Example 3: Two phases, phase loop with minimum coincidence

When two phases coexist at some P and T with equal composition, the constraint of equal composition modifies the phase rule and yields a variance of one in a system of any number of components. This univariant reaction is called a coincidence or an azeotrope. It can be shown that the tangent to a coincidence point on a T-X diagram must be horizontal; hence it must form either a minimum or a maximum in temeprature. On this page the applet is set up to show a minimum.

The formation of a coincidence point is illustrated first using the static -X diagrams at three different temperatures and the section of a T-X diagram that results from extracting the stable sequences across the X axes. An example of a coincidence is a congruently melting compound, i.e. one that coexists with a liquid of its own composition along its melting curve. Figure 6

Now look at the applet below, which is initialized to Example 3. The P-T panel shows three curves. Two are the degenerate coincidences formed by the bounding one-component systems. The third is the binary coincidence curve formed by the meeting of the free-energy curves in the middle of the composition axis. Try the exercise of clicking three points at equal pressure that are below, on, and above the lowest coincidence curve as you change temperature. Do the resulting -X diagrams remind you of the static figure? The curvature is much lower here and the static figure shows a coincidence that forms a maximum rather than a minimum in temperature, but the topology is the same.

Since this applet was written, browers have stopped supporting applets for security reasons. You can download a standalone executable that runs all the functionality of the applet on your own platform here. When you run it, select "Example 3" to get this page's content.

Return to the curriculum.
by Paul Asimow and Nizar Almoussa