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216 Modern Analytical Chemistry

7G.1 Partition Coefficients and Distribution Ratios
Earlier we learned that the partitioning of a solute between two phases is described
by a partition coefficient. If the solute is initially in an aqueous phase and is ex-
tracted into an organic phase*

S aqt S org
the partition coefficient is
[ S org ]
K D =
[ S aq ]

A large value for K D indicates that the extraction of the solute into the organic phase
is favorable.
In evaluating the efficiency of an extraction, however, we must consider the
distribution ratio solute’s total concentration in each phase. We define the distribution ratio, D, to
A ratio expressing the total be the ratio of the solute’s total concentration in each phase.
concentration of solute in one phase
]
relative to a second phase; all forms of S [ org tot
the solute are considered in defining the D =
]
S [ aq tot
distribution ratio (D).
When the solute exists in only one form in each phase, then the partition coefficient
and the distribution ratio are identical. If, however, the solute exists in more than
one form in either phase, then K D and D usually have different values. For example,
if the solute exists in two forms in the aqueous phase, A and B, only one of which,
A, partitions itself between the two phases, then
]
]
S [ org A S [ org A
D = £ K D =
]
]
S [ aq A +[ aq S [ aq A
S ] B
This distinction between K D and D is important. The partition coefficient is an
equilibrium constant and has a fixed value for the solute’s partitioning between the
two phases. The value of the distribution ratio, however, changes with solution con-
ditions if the relative amounts of forms A and B change. If we know the equilibrium
reactions taking place within each phase and between the phases, we can derive an
algebraic relationship between K D and D.
7G.2 Liquid–Liquid Extraction with No Secondary Reactions
In the simplest form of liquid–liquid extraction, the only reaction affecting extrac-
S org
tion efficiency, is the partitioning of the solute between the two phases (Figure 7.20).
Organic
In this case the distribution ratio and the partition coefficient are equal.
Aqueous
]
S [ org tot S [ org ]
S aq D = = 7.19
]
S [ aq tot S [ aq ]
Figure 7.20
Scheme for a simple liquid–liquid extraction Conservation of mass requires that the moles of solute initially present in one
without any secondary reactions. phase equal the combined moles of solute in the aqueous and organic phases after
the extraction; thus
(Moles aq) 0 = (moles aq) 1 + (moles org) 1 7.20

*Although the following treatment assumes that the solute is initially present in the aqueous phase, the resulting
equations for the distribution of the solute between the two phases are independent of which phase originally contains
the solute.