Separations analysis fundamentals - Principles of Chemical Separations with Environmental Applications - page 46

PURE
SOLUTE ( A )

Conjugate line

Tie-line

Two-phase
envelope

PURE
DILUENT ( B )

PURE
SOLVENT ( S )

Figure 3.11 Construction of a tie-line from the conjugate line.

indicates a favorable separation. In these systems, the equilibrium solute concentration
in the extract is greater than that in equilibrium with the raffinate. Hence, less solvent is
needed to remove the solute from the diluent. Separation is still possible in systems in
which tie-lines slope up from the extract line to the raffinate line. However, more solvent
than in the prior case will be required to achieve the separation.
The right triangular diagram (Figure 3.11) is similar to the equilateral triangular
diagram; each corner represents one of the pure components.
There are two additional ways that equilibrium (tie-line) data can be shown on a trian-
gular diagram. The first, presented in Figure 3.11, is a conjugate line: a vertical line from
any point on the conjugate line gives one end of the tie-line (on the saturation line), and a
horizontal line from the same point will locate the other end of the tie-line. An equilibrium
curve may also be used to locate tie-lines on a triangular diagram.
Conjugate lines and equilibrium curves can avoid cluttering up the diagram by allowing
only the tie-lines of interest to be drawn. They can be used on equilateral triangle diagrams
as well as on right triangle diagrams, but care should be taken in transcribing equilibrium
data from an x - y diagram to an equilateral triangle diagram which will not have the same
axes.
Figure 3.12 illustrates an alternate method by which to generate a triangular diagram.
Regardless of the type of triangle diagram that is being used, remember that the weight
fractions of each phase must add up to one:

x A + x B + x S = y A + y B + y S = 1 .

This is a useful check to confirm that a triangle diagram is read correctly.
It is also important to know that as temperature increases, miscibility almost always
increases and the two-phase region shrinks, as shown in Figure 3.13. This dependence