Page 234 - Modern Analytical Chemistry

1400-CH07 9/8/99 4:04 PM Page 217

Chapter 7 Obtaining and Preparing Samples for Analysis 217

where the subscript indicates the extraction number. The concentration of S in the
aqueous phase after the extraction is

(moles aq) 1
]
[S aq = 7.21
V aq
whereas the solute’s concentration in the organic phase is
(moles org) 1
]
[S org = 7.22
V org
where V aq and V org are the volumes of the aqueous and organic phases. Solving
equation 7.20 for (moles org) 1 and substituting into equation 7.22 leave us with

(moles aq) - (moles aq) 1
0
]
[S org = 7.23
V org
Substituting equations 7.21 and 7.23 into equation 7.19, we obtain
]/ V
[(moles aq) 0 -(moles aq) 1 V org (moles aq) 0aq -(moles aq) 1 V aq
D = =
(moles aq) 1 / V aq (moles aq) 1 V org
Rearranging and solving for the fraction of solute remaining in the aqueous phase
after one extraction, (q aq ) 1 , gives
(moles aq) 1 V aq
(q aq 1 = = 7.24
)
(moles aq) 0 DV org + V aq

The fraction present in the organic phase after one extraction, (q org ) 1 , is
(moles org) 1 DV org
)
(q org 1 = = 1 - (q aq 1 =
)
(moles org) 0 DV org + V aq

Example 7.14 shows how equation 7.24 is used to calculate the efficiency of a simple
liquid–liquid extraction.
7 4
EXAMPLE .1
A solute, S, has a K D between water and chloroform of 5.00. A 50.00-mL
sample of a 0.050 M aqueous solution of the solute is extracted with 15.00 mL
of chloroform. (a) What is the extraction efficiency for this separation?
(b) What is the solute’s final concentration in each phase? (c) What volume of
chloroform is needed to extract 99.9% of the solute?
SOLUTION
For a simple liquid–liquid extraction, the distribution ratio, D, and the
partition coefficient, K D , are identical.
(a) The fraction of solute remaining in the aqueous phase after the extraction
is given by equation 7.24
50 .00 mL
(q aq 1 = = . 0 400
)
(5.00)(15.00 mL) + 50 .00 mL
The fraction of solute present in the organic phase is, therefore, 0.600.
Extraction efficiency is the percentage of solute successfully transferred
from its initial phase to the extracting phase. The extraction efficiency is,
therefore, 60.0%.