Chem 162 Spring 2005 Equilibrium V Page 1 of 4

Equilibrium V

Reading: Special Handout

K. Three Component Systems Reading a ternary phase diagram:

Ternary phase diagrams are taken at constant T and P. Points A, B and C represent pure components A, B and C respectively. The line BC represents 0Ax = (a binary B-C mixture), and likewise for the other edges. The composition coordinates for a point are determined by the normal distance to the edge that corresponds to 0ix = . In this example, 0.33Ax = , 0.33Bx = and

0.33Cx = . Not too exciting, yet

In this example, we begin at the coordinates 0.12Ax = , 0.23Bx = and

0.65Cx = . The line shows how the compositions in the mixture change as we add pure component A. In terms of the phase rule, 5F P= , so in a one phase region there are 4 degrees of freedom (T, P and the mole fractions of two components.)

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Partially miscible liquids: Consider the ternary phase diagram between water, acetic acid (AA) and chloroform.

Taken as three different two-component systems, we find that water and acetic acid are miscible in all proportions, as are chloroform and acetic acid. However, water and chloroform are only partially miscible. This is represented by the two phase region that lies on the chloroform/water base of the triangle. Note that the compositions on the base represent the compositions of water-rich and chloroform-rich phases in equilibrium at this T and P. Consider a starting solution consisting of 60 % water and 40% chloroform. We are in a 2 phase region along the base of the triangle. When a small amount of AA is added to the mixture, the composition moves along the line towards the AA apex. The compositions of the two phases in equilibrium change, and are defined by the ends of the tie line, which in this case is not horizontal (but the Lever Rule still applies!) As more AA is added, the solution eventually becomes one phase above the curve. The point P is called the Plait Point, and it is another example of a critical point, where the composition of the two phases is equal. At this point, the relative volumes of the two phases are equal and the boundary vanishes as the system becomes homogeneous.

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On the left is the phase prism of this mixture (C = AA, A = chloroform, B = water) with temperature as the new variable. Note that the ABT face of the prism is the 2-component phase diagram for chloroform and water, so point P is the UCST. This type of diagram shows how the miscibility in this three component system changes with temperature. Finally, the plait point varies with temperature from Q to P along the line shown.

Two partially miscible pairs: Consider the ternary phase diagram when there both A-B and B-C mixtures are not miscible.

At high temperatures, the two 2-phase regions are separated, as shown in (a). As the temperature is decreased, the curves may overlap, resulting in two different possibilities. In diagram (b), the two plait points merge and result in a 2-phase band. If the curves do not join at the plait points, the diagram takes the form of (c). In this diagram, there are three 2-phase regions. The points inside of the abc triangle correspond to a three phase liquid region where the liquid layers have compositions equal to a, b and c. In general, if there is a triangle within a ternary phase diagram, this corresponds to a three phase region! We will see this again in the next example.

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The Common Ion Effect: The analytical chemist says, The presence of a common ion tends to decrease the solubility of a salt.

In this diagram, point a represents a saturated solution (2 phase) of water and solid ammonium chloride (in the absence of ammonium sulfate). The points between a and C represent an unsaturated (1 phase) solution, while the lever rule between a and A represent the relative amounts of solid ammonium chloride in equilibrium with the saturated solution. (Likewise for the CB line with ammonium sulfate in the absence of ammonium chloride.) Now, the addition of ammonium sulfate to the ammonium chloride solution changes the solubility along line ac. (Likewise for the addition of ammonium chloride to ammonium sulfate along line bc2.) Note that in the 2-phase regions, the apex (pure component) is one end of the tie line, so the equilibrium phases consist of solid A or B with a saturated solution. The points in the triangle AcB correspond to a three phase region with solid ammonium chloride, solid ammonium sulfate and a saturated solution with composition c all in equilibrium. Now consider a solution at point P that is slowly evaporated isothermally. At point d, the solution becomes saturated with ammonium chloride, which crystallizes. With further evaporation, the composition of the saturated solution moves along the dc line. At point e, ammonium sulfate begins to crystallize, and the two solids are in equilibrium with a saturated solution at c. This continues until point f, when the solution disappears.