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Chapter 7 Obtaining and Preparing Samples for Analysis 219

SOLUTION
(a) The fraction of solute remaining in the aqueous phase after two and three
extractions is
2
æ 50 .00 mL ö
)
(Q aq 2 = ç ÷ = . 0 160
è (5.00)(15.00 mL) + 50 .00 mLø
3
æ 50 .00 mL ö
)
(Q aq 3 = ç ÷ = . 0 064
.
50
0
1
è ( . )( .500 mL ) + 5000 mLø
Thus, the extraction efficiencies are 84.0% with two extractions and 93.6%
with three extractions.
(b) To determine the minimum number of extractions for an efficiency of
99.9%, we set (Q aq ) n to 0.001 and solve for n in equation 7.25
n
æ 50 00 mL ö
.
0 400)
.
0 001 = ç ÷ = (. n
.
è (5.00)(15.00 mL ) + 50 00 mL ø
Taking the log of both sides
log(0.001) = nlog(0.400)
and solving for n gives
n = 7.54 100
90
Thus, a minimum of eight extractions is necessary. 80
Extraction efficiency 60
70
50
An important observation from Examples 7.14 and 7.15 is that an extraction
efficiency of 99.9% can be obtained with less solvent when using multiple extrac- 40
30
tions. Obtaining this extraction efficiency with one extraction requires 9990 mL 20
of the organic solvent. Eight extractions using separate 15-mL portions of the or-
10
ganic solvent, however, requires only 120 mL. Although extraction efficiency in-
0
creases dramatically with the first few multiple extractions, the effect quickly di- 0 5 10
minishes as the number of extractions is increased (Figure 7.21). In most cases Number of extractions
there is little gain in extraction efficiency after five or six extractions. In Example
Figure 7.21
7.15 five extractions are needed to reach an extraction efficiency of 99%, and an
additional three extractions are required to obtain the extra 0.9% increase in ex- Plot of extraction efficiency versus number
of extractions for the liquid–liquid extraction
traction efficiency. scheme in Figure 7.20.
7 3 Liquid–Liquid Extractions Involving Acid–Base Equilibria
G.
In a simple liquid–liquid extraction the distribution ratio and the partition coeffi-
cient are identical. As a result, the distribution ratio is unaffected by any change in
the composition of the aqueous or organic phase. If the solute also partici-
HA
pates in a single-phase equilibrium reaction, then the distribution ratio and
the partition coefficient may not be the same. For example, Figure 7.22 Organic
shows the equilibria occurring when extracting an aqueous solution contain- K D Aqueous
ing a molecular weak acid, HA, with an organic phase in which ionic species K a
+
HA + H O H O + A –
are not soluble. In this case the partition coefficient and the distribution 2 3
ratio are Figure 7.22
[ HA org ] Scheme for the liquid–liquid extraction of a
K D = 7.26 molecular weak acid.
[ HA aq ]