Page 235 - Modern Analytical Chemistry

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218 Modern Analytical Chemistry

(b) The moles of solute present in the aqueous phase before the extraction is
. 0 050 mol
(Moles aq) 0 = S ] ´V aq = . ´ 0 05000 L . = 0 0025 mol
[ aq 0
L
Since 40.0% of the solute remains in the aqueous phase, and 60.0% has
been extracted into the organic phase, the moles of solute in the two
phases after extraction are
(Moles aq) 1 = (moles aq) 0 ´(q aq ) 1 = 0.0025 mol ´(0.400) = 0.0010 mol

(Moles org) 1 = (moles aq) 0 – (moles aq) 1 = 0.0025 mol – 0.0010 mol = 0.0015 mol
The solute’s concentration in each phase is
(moles aq) 1 . 0 0010 mol
]
[S aq 1 = = = . 0 020 M
V aq . 0 05000 L
(moles org) 1 . 0 0015 mol
]
. M
[S org 1 = = = 01 0
V org . 0 01500 L
(c) To extract 99.9% of the solute (q aq ) 1 must be 0.001. Solving equation 7.24
for V org , and making appropriate substitutions for (q aq ) 1 and V aq gives
V aq -( q aq ) 1 V aq 50 .00 mL -( .001 )( .00 mL)
0
50
V org = = = 9990 mL
0
( q aq ) 1 D (.001 )( . )
0
0
5
Clearly, a single extraction is not reasonable under these conditions.
In Example 7.14 a single extraction results in an extraction efficiency of only
60%. If a second extraction is carried out, the fraction of solute remaining in the
aqueous phase, (q aq ) 2 , is given by
(moles aq) 2 V aq
)
(q aq 2 = =
(moles aq) 1 DV org + V aq
Colorplate 4 shows an example of a If the volumes of the aqueous and organic layers are the same for both extractions,
liquid–liquid extraction. then the cumulative fraction of solute remaining in the aqueous layer after two ex-
tractions, (Q aq ) 2 , is
2
(moles aq) 2 æ V aq ö
(Q aq 2 = = (q aq 1 ) ç ÷
)
) (q aq 2 =
(moles aq) 0 è DV org + V aq ø

In general, for a series of n identical extractions, the fraction of analyte remaining in
the aqueous phase after the last extraction is
n
æ V aq ö
) n =
(Q aq ç ÷ 7.25
è DV org + V aq ø
7 5
EXAMPLE .1
For the extraction described in Example 7.14, determine (a) the extrac-
tion efficiency for two extractions and for three extractions; and
(b) the number of extractions required to ensure that 99.9% of the solute is
extracted.