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Rationale of analytical separations by simple immiscible solvent extraction
ANALYTICA
504
RATIONALE
OF ANALYTICAL
CIIIMICA
ACTA
SEPARATIONS
SOLVENT
VOL.
4 (1950)
BY SITQPLE IMMISCIBLE
EXTRACTION bY
E. B. SRNDELL Uwivevsity
of Minnesota,
Mznnoapol~s,
Mzn~t.
( U.S. A .)
The general problem in separating A from B before determining A is to isolate a specified fraction of A, near unity, which may be designated as R, (the recovery factor), without isolating more than a certain absolute quantity of B, Q,,. such that QL7/QA does not exceed a specified value. The nature of the &termination decides the values of R,, and QU/Qh. I n other words, the original ratio of B to A, (Qn)o/(QJo, must be altered to the permissible ratio Qu/Q,, = Q,/R,(Q,), 2 Qa/(Q,l)o. The ratio (QJ/~(QIJo x QP/QA G QdQh will be ded the separation factor for B with respect to A. This means that the separation factor for the undesired constituent is for all practical purposes equal to its recovery factor. The smaller the separation factor the better will bc the separation. RECOVERY
AND
SEPARATION
IN
EXTRACTIONS
If the substances A and B arc to be separated by shaking their aqueous solution (usually after treating with a suitable reagent) with an immiscible organic solvent, a simple procedure can be applied if the respective extraction coefficients are widely different so that an insignificant amount of B is extracted. The aqueous solution is shaken in a separatory funnel with one or more portions of the immiscible solvent to provide the desired recovery of A. The following simple relation between the concentration of A (not necessarily present as the same species) in the two solvents holds at least approximately in many cases as will he shown later: - [Alo __ - = lz:n, [Alw where subscript w refers to the aqueous solution and o refers to the organic solvent, and E,, is the extraction coefficient. (Note that E, is an extmcliofl coefficient, which gives the concentration ratio of all species of the same substance in the respective phases; it is not necessarily a partition or distribution coefficient, which refers to the ratio of concentrations of the same species in the two immiscible solvents at equilibrium.)
VOL. 4
(1950)
IMMISCIBLE
SOLVENT
EXTRACTION
505
When this relation holds, the recovery factor for A as a function of the number of extractions (1~)is given by the following expression when the volumes of the two phases are equal: (RA)~
= (Q.-i)rt/(Q~)o
=
I
-(ET%): ,
(1)
If the volume of the aqueous phase is V,” and the volume of each portion of the organic solvent is V,, the preceding expression becomes : (RA)”
=
I -
n
VW EAVo
+
VW
>
(2)
.
In the followmg treatment it will be assumed for simplicity that the volumes of the two phases are always equal. When EA is large (e.g., greater than IO), as it usually will be in a quantitative procedure, and n is not too large, expression (I) becomes: (RA)”
Conversely,
22 E:,‘(E;
+
I).
(34
if RA is specified, EA can be found for given tt’s:
The fraction of B extracted under the conditions analogous to (I), which simplifies to (RII),, 52 nE:r,
when EB is small (<
is given by an expression
(3’3
0.1) and n is not too large. The separation factor then is:
When A and B arc present as compounds of the same reagent, there will usually be some fixed relation between EA and Ea. For example, if A and B are cations of the same valence (A+‘“, B+“) reacting with the reagent HC to give the extractable compounds AC, and BC,, EA and Es will differ by a constant factor. The values of EA and Es will depend on the concentration of reagent and the acidity (if HC is slightly dissociated), and the extraction coefficients can be varied by changing these, subject to the condition that E,/Es = constant. It is evident that EA should not be made larger than actually necessary for a satisfactory recovery of A. For a given recovery, slightly better separations can be achieved by decreasing EA and increasing n. However, in itself this device is practically inadequate and more powerful methods are needed.
506
E. B. SANDELL
VOL.
4 (1950)
The principle of such a method is illustrated in the adjoining diagram. The horizontal row I, I . . . n represents the extraction of aqueous solution containing A and 13, by n successive portions of immiscible organic solvent (each equal in volume to that of the aqueous phase), which are combined with each other. The combined extracts are now treated in some suitable way to remove A and B from the organic solvent and transfer them to an aqueous solution. (For example, certain metal dithizonates can be dissociated and the metals returned to the water phase by shaking with a solution of a strong acid). The resulting water solution (II, 0) is shaken with fl successive portions of organic solvent under the same conditions as before (same acidity, same reagent concentration). The sequence of operations is repeated as many times as may be required. PracticaIly, in the separation of inorganic constituents, N would rarely bc above 2 ancl n rarely greater than 2 or 3 when separatory funnels are used.
-___ 1 -n
r-i
‘m-7-7
It is evident that in this sequence of operations, the only ones resulting in a separation of the desired constituent (A) from the other are I,I. 11,x . . . N,r. The others are made to obtain a satisfactory recovery of A. The former kind of extraction may be called mu&t!&, the latter kind consecutive The two types are necessarily antagonistic in greater or less degree. The amount of A in the combined extracts at stage N,n is: (QA)N,”
:.
(&)N,n
=
(QA)o
{ 1
-(gA1+ I)n)“- (Qn)o(ETt I)
%?
(Ru)“,u
EA
g
(nEu)N
and
$62
( I~~N)“n
En c/) =I- RLN n
(5)
(64
(6b)
VOL.
4 (1950)
The separation
IMMISCIBLE
SOLVENT
EXTRACTION
507
factor for this scheme is: SE/A
E
(nJWN
(7)
If the extraction reactions are reversible, a simpler and more rapid separation procedure may be applicable, namely relrograde extraction. After A has been brought into the organic solvent with more or less of B, this phase is shaken with successive portions of an aqueous solution. Under suitable conditions the concentration of B in the organic phase can be rapidly decreased in geometrical progression, whereas the concentration of A can be maintained substantially unchanged. By adjusting the PH of the aqueous phase and the excess of the reagent it may be possible to increase the value of E,, (if it is not already large enough) to the point where there will be no significant loss of A. As an example of the combination of direct and retrograde extraction, consider the case in which EJEe = 10~. Make EA equal to 30 (Ea then 3 x IO-~) and shake the aqueous phase with two portions of organic solvent (phases of equal volume). The recovery factor for A will then be 0.999, that for B 6 x IO-~ (from equations 6a and 6b, iV = I, rr = 2). Now alter the conditions so that EA becomes equal to IOOO and EB equal to 0.01, and shake the organic solvent phase with two portions of aqueous solution (each equal in volume to the organic phase). At the end of this operation RA = 0.997 and Re = 6 x 10’~ (equations 6a and b, N = 2, n = I). In practice the close adjustment of conditions implied in this ideal example could hardly be realized, but the general effectiveness of the method will be apparent. Some use has been made of this principle but it has not been applied in a systematic way. If the constituent to be eliminated has the greater extraction coefficient, it may be possible to remove it satisfactorily by extracting the aqueous solution and leaving the desired constituent in the latter. If EJEn = IO-~, three consecutive extractions with E1\ = 0.001: and Ea = IOO, will leave 0.997 of the original amount of A and x0-0 of the original amount of B in the aqueous phase. In practice this case may offer the difficulty that the solubility of the reagent or reaction product will be limited and large volumes of solvent may sometimes be required. The rate of attainment of equilibrium will of course be an important factor in the application of these principles.
EXTRACTION
COEFFICIENTS
AND
THE
DISTRIBUTION
EXPRESSION
In considering the distribution of a constituent between an aqueous phase and an immiscible organic solvent as a function of the reagent concentration and acidity, we will take the constituent to be a cation, A+“, which reacts with the monovalent anion C- of the reagent to give the product AC,, which distributes itself between the two liquids. (If the reagent anion has a valence greater than one and forms the product A&,, in which a and c are not the same, the extraction
508
E. B. SANDELL
VOL.
4 (1950)
coefficient will not be constant, but will vary with the concentration of A in than the one which is the two phases; this case is less frequently encountered discussed below.) The following equilibria will be assumed to exist in the system: A+”
+ aC’ ~2
C- +
H+
AC
;-3HCn
(AC,),
cc z=-c WC) W
(aqueous
phase)
(aqueous
phase)
(AC,), WC),
It will further be assumed that neither AC, nor HC is associated in solution and that other species containing A or C are not formed in significant amounts. The equilibrium constants for the above reactions are respectively: [A+a]w
[C-la [ACa]w
(H+]w [C-I.. [HC],. [ACa 10 .-[AC*],.
= ‘*
PWo -p=]q
=
(8)
kA
(9)
= kc (partition coefficient
of AC*)
= PC
From (8), (g), (IO), and [A& 10
jS]l,
w
(10)
(11)
(II) the following
expression a -WC]: [H+];=K
=
is obtained:
WCI: [H+l-EA
(14
The preceding expression gives the extraction coefficient of metal A for speof A in cified values of [HC], and [H+]W, i.e., the ratio of the concentrations the two phases if [AC,], can be neglected (as is usually the case when the reagent is an organic compound forming an internal complex) and the metal exists entirely in simple cationic form in the aqueous phase. For simplicity, concentrations have been written, but it will be understood that they should be replaced by activities for greater accuracy. It will be realized that E:A can not attain an indefinitely large value because it approaches pA as the limit. If the concentration of molecular AC, in the aqueous phase is taken into account, the true extraction coefficient is :
EA = ?A/@ where r = complexes,
CAGJo/[A+%~
the
metal
will
$_ PAI8
In most cases involving-organic reagent - metal have been quantitatively extracted before the
VOL.
4 (1950)
IMMISCIBLE
SOLVENT
EXTRACTION
509
concentration of molecular AC, in the aqueous phase attains an appreciable value compared to the concentration of A+‘. The value of K in equation (x:2), which is the equilibrium constant for the net reaction (Afa),
+
(aHC)o 7*
(ACn)o + (aH+),,.,
is of primary importance to the analyst. It is usually obtained by direct experiment, but it can also be calculated if certain data are available. kc /pc is equal to
W+l [C-1~ and the value-of the latter is readily found experimentally. It is IHC]o’ of interest to note that when the value of this quotient has been obtained, and the solubility of the reagent in the organic solvent has been determined, the solubility product of the reagent in water can be calculated. If the concentration of the undissociated form of the reagent in water can be found, then the dissociation constant of HC can be obtained. If the solubility of AC, in the organic solvent and the value of its solubility product in water are known the value of p,JkA is also known and thus K can be found. To be generally useful in analytical work the extraction expression (12) must usually be modified to take account of the presence of metal forms other than the simple cation in the aqueous phase. Frequently an appreciable fraction of the metal will be present as a slightly dissociated complex or molecule. Since the analyst is interested in the fraction of total metal going into the organic solvent from the aqueous phase, the value of [AC,],/Z[A], is actually desired, where the denominator represents the sum of concentrations of all the metal species in the water solution. If the metal ion A+” combines with a univalent anion to form a series of complexes (e.g., with Cl- to give ACP’, ACltMa, etc.) it can be shown that ([AC,],/Z[AJ, will have a constant value, independent of the amount of metal present, if the concentration of the complex forming substance is large compared to that of the metal so that the concentration of the former remains substantially unchanged. The extraction expression then becomes [ACa - 10 -=
z:[Alw
K’-_WC]: [H+];
EA’
(13)
where the value of K’ depends on the concentration of the complex former and to a smaller extent on the ionic strength of the solution. This expression has been shown to hold for the extraction of ferric cupferrate by chloroform from aqueous solution of various chloride concentrations. If the complexing anion is not univalent, the metal complexes will in general contain more than one metal atom per species, and since this is equivalent to association of metal ions in the aqueous phase, [AC,],/C[A], will vary with the concentration of the metal in the aqueous phase and EA will not be constant. Expression (13) will of course be most easily applicable in practice when
0.
5x0
B.
VOL.
SANDELL
4 (rgso)
the amount of reagent is large compared to the amount of metal present so that the equilibrium concentration of the reagent is substantially the same as its original concentration and E ,+, thus remains constant. The extent of recovery and separation (when EB is known) can then readily be obtained from equations (6a) and (6b). An organic reagent forming an internal complex with a metal is frequently a weak acid, so that in a sufficiently acidic medium it may be considered to be present entirely in the unclissociated form. Because this form will generally have a partition coefficient greatly in favor of the organic solvent, the value of [HC], is usually easily found from the total amount added, allowance being made if necessary for that which has combined with the metal. Equation (12) or (13) can be suitably modified to apply to basic solutions in which the metal may be present in the form of an anion. SEPARABILITY
OF
A
AND
B
Suppose that the feasibility of separating the cation extracting AC.,, with a minimum amount of BC,,, into an solvent is to be investigated:
(B”-“), + WI=), t-
A+=’ from B+b by immiscible organic
(BC,), + (bH+)w.
At equilibrium the following relations hold: [ACn]o . --Z[ A],
I
[B&lo __.c[B]w
[“‘l,”
”
W+l:,,
K;
WCII: [H+]z
Ic#
=
c E:A
(14)
=
(15)
ER
The extraction coefficients EA and Eu are assumed to be independent of the metal concentration. When K’,, and K’n are known and [HCJo and [H3] are specified (and assumed to remain constant or approximately so), E,+ and Es can be calculated and the separation factor found for the particular conditions. The following relation can be derived from (14) and (IS): K’l3
If the cations are of the same valence: En
=
x E*
gp
A
4
VOL.
(1950)
IMMISCIBLE
SOLVENT
EXTRACTION
5x1
When b < a, less careful adjustment of acidity and reagent concentration is required for satisfactory recovery of A and minimum recovery of B than when b > a. Thus when b = z and a = 3 a ten-fold increase in EA results in an approximately five-fold increase in Ea, whereas when b = 3 and a = 2, a ten-fold increase in EA means an approximately thirty-fold increase in Eg. Table I illustrates the separations and recoveries that can be obtained for various values of Es/E,,, according to the extraction scheme outlined above, when E,+ is taken equal to IO. This particular value is chosen as an example because of its applicability in trace analysis. When, in such analysis, the effective separation of A from interfering elements is important, the value of EA would be adjusted (so far as this may be practicable) to IO or a little greater to obtain the most effective separation consistent with satisfactory recovery, such as can be achieved with 2 or 3 consecutive extractions. TABLE R,,
RB FOR
AND
VARIOUS
(Volumes
&,/E,,
of the two
phases
n
NI
N, AND n, WHISN EA =
I
I
RI\ TRu __-~--_____
/RAioejnl
/ 0.9
2
1 0.99
/
o.gg
0.02
j
0.002
0.9
. I
I
/ :.:,
/ 2
o-99
Ip,..
-
--___-----
-o.ggrJ/o.oo3
I I
I
3 x x0-4
1 o.g98/
Y-1
1
0.98
10-a
F.-I[
0.8 ---
10-M
0.98
1 4 x IO-~
( 4 x
1
3
1 0.9981
g:,,-I
-
0.7
1 I
x ,,I]
0.998/
g
x
2
) 0.97
x 10-o
-L
0.7
,-/-Eo-q
(I
x
,1
I 1
3
1 8 x x0-O
I I 1 o.ggS’3,
x0-6
x
4 x x0-10
a
0.97
/ 8 x IO+ 1 0.97
)8 x
IO-' 2
I I IO-“ 1 0.998 1 3 x
g x x0-1” I
o-7
I
x
10'~~
s
x
xo-~~
I3
x
10-14
I
-
-
3
x
1o-l0
I
0.998
10-8
-
T_i
TO-s
I 0.9981 g
-
T1T-j
X
-
3
0.98
IO+-+::
_-
2
2
I
o.ggg
-. --_ 2
10-n
I
_‘_
<;-
_--_ 1
Ru
RA ---
0.00 I
0.9
0.01
i;rR~
/
IO
in each extraction)
-.
---_
_y-'--
2
equal
x0-a _
_+yj
I ED/EA,
OF
3
-
I
VALUES
0.97
-
I
10-8
I
1 o*gP8/ 3 X 10-l
1 -
0.997
I
512
E.
B.
SANDELL
VOL.
4 (1950)
When EA and EB arc not sufficiently different for good separation in a simple solution, differential complex formation can often be applied to great advantage It is generally desirable that A be complexed in producing a change in E,J&. to the smaller extent so that it can be extracted into the organic solvent, while the other elements are left in the aqueous solution, although the converse case can also be of use. Alteration in the valence of A or B is scmetimes applicable as an effective means of changing the ratio of the extraction coefficients.
SUMMARY Expressions are given for the calculation of recovery and separation factors from extraction coefficients in immiscible solvent separations. Extraction coefficients of separation forms in inorganic analysis arc usually variables which arc a function of reagent concentration and acidity, and whose value can be derived from the equilibrium constant of the extraction reaction. RESUME Des formules sont donndes pour le calcul des facteurs de recuperation et de sdpnration, ir partir des coefficients d’cxtraction, en dissolvants non miscibles. Lcs coefficients d’extraction en analyse inorganique sont generalcmcnt variables, &ant fonction de la concentration du reactif et de l’acidrte, et ces valeurs ddpendent de l’dquilibre dc la reaction d’extraction. ZUSAMMENFASSUNG und Trennungsfaktoren aus Formeln zur Bercchnung der Zurtickgewinnungsden Extraktionskoeffizicnten bei Trennungcn in mcht rmschbaren Losungsmitteln wcrdcn angegeben. Extraktionskoeffizienten in der anorganischen Analyse sind meist variabel, und zwar sind sic Funktion der Reagenskonzentration und der Aziditgt und klinnen von der Gleichgewichtskonstante der Extraktionsrcaktion abgeleitct wcrdcn.
Received
February
asrd,
r g5o
504
RATIONALE
OF ANALYTICAL
CIIIMICA
ACTA
SEPARATIONS
SOLVENT
VOL.
4 (1950)
BY SITQPLE IMMISCIBLE
EXTRACTION bY
E. B. SRNDELL Uwivevsity
of Minnesota,
Mznnoapol~s,
Mzn~t.
( U.S. A .)
The general problem in separating A from B before determining A is to isolate a specified fraction of A, near unity, which may be designated as R, (the recovery factor), without isolating more than a certain absolute quantity of B, Q,,. such that QL7/QA does not exceed a specified value. The nature of the &termination decides the values of R,, and QU/Qh. I n other words, the original ratio of B to A, (Qn)o/(QJo, must be altered to the permissible ratio Qu/Q,, = Q,/R,(Q,), 2 Qa/(Q,l)o. The ratio (QJ/~(QIJo x QP/QA G QdQh will be ded the separation factor for B with respect to A. This means that the separation factor for the undesired constituent is for all practical purposes equal to its recovery factor. The smaller the separation factor the better will bc the separation. RECOVERY
AND
SEPARATION
IN
EXTRACTIONS
If the substances A and B arc to be separated by shaking their aqueous solution (usually after treating with a suitable reagent) with an immiscible organic solvent, a simple procedure can be applied if the respective extraction coefficients are widely different so that an insignificant amount of B is extracted. The aqueous solution is shaken in a separatory funnel with one or more portions of the immiscible solvent to provide the desired recovery of A. The following simple relation between the concentration of A (not necessarily present as the same species) in the two solvents holds at least approximately in many cases as will he shown later: - [Alo __ - = lz:n, [Alw where subscript w refers to the aqueous solution and o refers to the organic solvent, and E,, is the extraction coefficient. (Note that E, is an extmcliofl coefficient, which gives the concentration ratio of all species of the same substance in the respective phases; it is not necessarily a partition or distribution coefficient, which refers to the ratio of concentrations of the same species in the two immiscible solvents at equilibrium.)
VOL. 4
(1950)
IMMISCIBLE
SOLVENT
EXTRACTION
505
When this relation holds, the recovery factor for A as a function of the number of extractions (1~)is given by the following expression when the volumes of the two phases are equal: (RA)~
= (Q.-i)rt/(Q~)o
=
I
-(ET%): ,
(1)
If the volume of the aqueous phase is V,” and the volume of each portion of the organic solvent is V,, the preceding expression becomes : (RA)”
=
I -
n
VW EAVo
+
VW
>
(2)
.
In the followmg treatment it will be assumed for simplicity that the volumes of the two phases are always equal. When EA is large (e.g., greater than IO), as it usually will be in a quantitative procedure, and n is not too large, expression (I) becomes: (RA)”
Conversely,
22 E:,‘(E;
+
I).
(34
if RA is specified, EA can be found for given tt’s:
The fraction of B extracted under the conditions analogous to (I), which simplifies to (RII),, 52 nE:r,
when EB is small (<
is given by an expression
(3’3
0.1) and n is not too large. The separation factor then is:
When A and B arc present as compounds of the same reagent, there will usually be some fixed relation between EA and Ea. For example, if A and B are cations of the same valence (A+‘“, B+“) reacting with the reagent HC to give the extractable compounds AC, and BC,, EA and Es will differ by a constant factor. The values of EA and Es will depend on the concentration of reagent and the acidity (if HC is slightly dissociated), and the extraction coefficients can be varied by changing these, subject to the condition that E,/Es = constant. It is evident that EA should not be made larger than actually necessary for a satisfactory recovery of A. For a given recovery, slightly better separations can be achieved by decreasing EA and increasing n. However, in itself this device is practically inadequate and more powerful methods are needed.
506
E. B. SANDELL
VOL.
4 (1950)
The principle of such a method is illustrated in the adjoining diagram. The horizontal row I, I . . . n represents the extraction of aqueous solution containing A and 13, by n successive portions of immiscible organic solvent (each equal in volume to that of the aqueous phase), which are combined with each other. The combined extracts are now treated in some suitable way to remove A and B from the organic solvent and transfer them to an aqueous solution. (For example, certain metal dithizonates can be dissociated and the metals returned to the water phase by shaking with a solution of a strong acid). The resulting water solution (II, 0) is shaken with fl successive portions of organic solvent under the same conditions as before (same acidity, same reagent concentration). The sequence of operations is repeated as many times as may be required. PracticaIly, in the separation of inorganic constituents, N would rarely bc above 2 ancl n rarely greater than 2 or 3 when separatory funnels are used.
-___ 1 -n
r-i
‘m-7-7
It is evident that in this sequence of operations, the only ones resulting in a separation of the desired constituent (A) from the other are I,I. 11,x . . . N,r. The others are made to obtain a satisfactory recovery of A. The former kind of extraction may be called mu&t!&, the latter kind consecutive The two types are necessarily antagonistic in greater or less degree. The amount of A in the combined extracts at stage N,n is: (QA)N,”
:.
(&)N,n
=
(QA)o
{ 1
-(gA1+ I)n)“- (Qn)o(ETt I)
%?
(Ru)“,u
EA
g
(nEu)N
and
$62
( I~~N)“n
En c/) =I- RLN n
(5)
(64
(6b)
VOL.
4 (1950)
The separation
IMMISCIBLE
SOLVENT
EXTRACTION
507
factor for this scheme is: SE/A
E
(nJWN
(7)
If the extraction reactions are reversible, a simpler and more rapid separation procedure may be applicable, namely relrograde extraction. After A has been brought into the organic solvent with more or less of B, this phase is shaken with successive portions of an aqueous solution. Under suitable conditions the concentration of B in the organic phase can be rapidly decreased in geometrical progression, whereas the concentration of A can be maintained substantially unchanged. By adjusting the PH of the aqueous phase and the excess of the reagent it may be possible to increase the value of E,, (if it is not already large enough) to the point where there will be no significant loss of A. As an example of the combination of direct and retrograde extraction, consider the case in which EJEe = 10~. Make EA equal to 30 (Ea then 3 x IO-~) and shake the aqueous phase with two portions of organic solvent (phases of equal volume). The recovery factor for A will then be 0.999, that for B 6 x IO-~ (from equations 6a and 6b, iV = I, rr = 2). Now alter the conditions so that EA becomes equal to IOOO and EB equal to 0.01, and shake the organic solvent phase with two portions of aqueous solution (each equal in volume to the organic phase). At the end of this operation RA = 0.997 and Re = 6 x 10’~ (equations 6a and b, N = 2, n = I). In practice the close adjustment of conditions implied in this ideal example could hardly be realized, but the general effectiveness of the method will be apparent. Some use has been made of this principle but it has not been applied in a systematic way. If the constituent to be eliminated has the greater extraction coefficient, it may be possible to remove it satisfactorily by extracting the aqueous solution and leaving the desired constituent in the latter. If EJEn = IO-~, three consecutive extractions with E1\ = 0.001: and Ea = IOO, will leave 0.997 of the original amount of A and x0-0 of the original amount of B in the aqueous phase. In practice this case may offer the difficulty that the solubility of the reagent or reaction product will be limited and large volumes of solvent may sometimes be required. The rate of attainment of equilibrium will of course be an important factor in the application of these principles.
EXTRACTION
COEFFICIENTS
AND
THE
DISTRIBUTION
EXPRESSION
In considering the distribution of a constituent between an aqueous phase and an immiscible organic solvent as a function of the reagent concentration and acidity, we will take the constituent to be a cation, A+“, which reacts with the monovalent anion C- of the reagent to give the product AC,, which distributes itself between the two liquids. (If the reagent anion has a valence greater than one and forms the product A&,, in which a and c are not the same, the extraction
508
E. B. SANDELL
VOL.
4 (1950)
coefficient will not be constant, but will vary with the concentration of A in than the one which is the two phases; this case is less frequently encountered discussed below.) The following equilibria will be assumed to exist in the system: A+”
+ aC’ ~2
C- +
H+
AC
;-3HCn
(AC,),
cc z=-c WC) W
(aqueous
phase)
(aqueous
phase)
(AC,), WC),
It will further be assumed that neither AC, nor HC is associated in solution and that other species containing A or C are not formed in significant amounts. The equilibrium constants for the above reactions are respectively: [A+a]w
[C-la [ACa]w
(H+]w [C-I.. [HC],. [ACa 10 .-[AC*],.
= ‘*
PWo -p=]q
=
(8)
kA
(9)
= kc (partition coefficient
of AC*)
= PC
From (8), (g), (IO), and [A& 10
jS]l,
w
(10)
(11)
(II) the following
expression a -WC]: [H+];=K
=
is obtained:
WCI: [H+l-EA
(14
The preceding expression gives the extraction coefficient of metal A for speof A in cified values of [HC], and [H+]W, i.e., the ratio of the concentrations the two phases if [AC,], can be neglected (as is usually the case when the reagent is an organic compound forming an internal complex) and the metal exists entirely in simple cationic form in the aqueous phase. For simplicity, concentrations have been written, but it will be understood that they should be replaced by activities for greater accuracy. It will be realized that E:A can not attain an indefinitely large value because it approaches pA as the limit. If the concentration of molecular AC, in the aqueous phase is taken into account, the true extraction coefficient is :
EA = ?A/@ where r = complexes,
CAGJo/[A+%~
the
metal
will
$_ PAI8
In most cases involving-organic reagent - metal have been quantitatively extracted before the
VOL.
4 (1950)
IMMISCIBLE
SOLVENT
EXTRACTION
509
concentration of molecular AC, in the aqueous phase attains an appreciable value compared to the concentration of A+‘. The value of K in equation (x:2), which is the equilibrium constant for the net reaction (Afa),
+
(aHC)o 7*
(ACn)o + (aH+),,.,
is of primary importance to the analyst. It is usually obtained by direct experiment, but it can also be calculated if certain data are available. kc /pc is equal to
W+l [C-1~ and the value-of the latter is readily found experimentally. It is IHC]o’ of interest to note that when the value of this quotient has been obtained, and the solubility of the reagent in the organic solvent has been determined, the solubility product of the reagent in water can be calculated. If the concentration of the undissociated form of the reagent in water can be found, then the dissociation constant of HC can be obtained. If the solubility of AC, in the organic solvent and the value of its solubility product in water are known the value of p,JkA is also known and thus K can be found. To be generally useful in analytical work the extraction expression (12) must usually be modified to take account of the presence of metal forms other than the simple cation in the aqueous phase. Frequently an appreciable fraction of the metal will be present as a slightly dissociated complex or molecule. Since the analyst is interested in the fraction of total metal going into the organic solvent from the aqueous phase, the value of [AC,],/Z[A], is actually desired, where the denominator represents the sum of concentrations of all the metal species in the water solution. If the metal ion A+” combines with a univalent anion to form a series of complexes (e.g., with Cl- to give ACP’, ACltMa, etc.) it can be shown that ([AC,],/Z[AJ, will have a constant value, independent of the amount of metal present, if the concentration of the complex forming substance is large compared to that of the metal so that the concentration of the former remains substantially unchanged. The extraction expression then becomes [ACa - 10 -=
z:[Alw
K’-_WC]: [H+];
EA’
(13)
where the value of K’ depends on the concentration of the complex former and to a smaller extent on the ionic strength of the solution. This expression has been shown to hold for the extraction of ferric cupferrate by chloroform from aqueous solution of various chloride concentrations. If the complexing anion is not univalent, the metal complexes will in general contain more than one metal atom per species, and since this is equivalent to association of metal ions in the aqueous phase, [AC,],/C[A], will vary with the concentration of the metal in the aqueous phase and EA will not be constant. Expression (13) will of course be most easily applicable in practice when
0.
5x0
B.
VOL.
SANDELL
4 (rgso)
the amount of reagent is large compared to the amount of metal present so that the equilibrium concentration of the reagent is substantially the same as its original concentration and E ,+, thus remains constant. The extent of recovery and separation (when EB is known) can then readily be obtained from equations (6a) and (6b). An organic reagent forming an internal complex with a metal is frequently a weak acid, so that in a sufficiently acidic medium it may be considered to be present entirely in the unclissociated form. Because this form will generally have a partition coefficient greatly in favor of the organic solvent, the value of [HC], is usually easily found from the total amount added, allowance being made if necessary for that which has combined with the metal. Equation (12) or (13) can be suitably modified to apply to basic solutions in which the metal may be present in the form of an anion. SEPARABILITY
OF
A
AND
B
Suppose that the feasibility of separating the cation extracting AC.,, with a minimum amount of BC,,, into an solvent is to be investigated:
(B”-“), + WI=), t-
A+=’ from B+b by immiscible organic
(BC,), + (bH+)w.
At equilibrium the following relations hold: [ACn]o . --Z[ A],
I
[B&lo __.c[B]w
[“‘l,”
”
W+l:,,
K;
WCII: [H+]z
Ic#
=
c E:A
(14)
=
(15)
ER
The extraction coefficients EA and Eu are assumed to be independent of the metal concentration. When K’,, and K’n are known and [HCJo and [H3] are specified (and assumed to remain constant or approximately so), E,+ and Es can be calculated and the separation factor found for the particular conditions. The following relation can be derived from (14) and (IS): K’l3
If the cations are of the same valence: En
=
x E*
gp
A
4
VOL.
(1950)
IMMISCIBLE
SOLVENT
EXTRACTION
5x1
When b < a, less careful adjustment of acidity and reagent concentration is required for satisfactory recovery of A and minimum recovery of B than when b > a. Thus when b = z and a = 3 a ten-fold increase in EA results in an approximately five-fold increase in Ea, whereas when b = 3 and a = 2, a ten-fold increase in EA means an approximately thirty-fold increase in Eg. Table I illustrates the separations and recoveries that can be obtained for various values of Es/E,,, according to the extraction scheme outlined above, when E,+ is taken equal to IO. This particular value is chosen as an example because of its applicability in trace analysis. When, in such analysis, the effective separation of A from interfering elements is important, the value of EA would be adjusted (so far as this may be practicable) to IO or a little greater to obtain the most effective separation consistent with satisfactory recovery, such as can be achieved with 2 or 3 consecutive extractions. TABLE R,,
RB FOR
AND
VARIOUS
(Volumes
&,/E,,
of the two
phases
n
NI
N, AND n, WHISN EA =
I
I
RI\ TRu __-~--_____
/RAioejnl
/ 0.9
2
1 0.99
/
o.gg
0.02
j
0.002
0.9
. I
I
/ :.:,
/ 2
o-99
Ip,..
-
--___-----
-o.ggrJ/o.oo3
I I
I
3 x x0-4
1 o.g98/
Y-1
1
0.98
10-a
F.-I[
0.8 ---
10-M
0.98
1 4 x IO-~
( 4 x
1
3
1 0.9981
g:,,-I
-
0.7
1 I
x ,,I]
0.998/
g
x
2
) 0.97
x 10-o
-L
0.7
,-/-Eo-q
(I
x
,1
I 1
3
1 8 x x0-O
I I 1 o.ggS’3,
x0-6
x
4 x x0-10
a
0.97
/ 8 x IO+ 1 0.97
)8 x
IO-' 2
I I IO-“ 1 0.998 1 3 x
g x x0-1” I
o-7
I
x
10'~~
s
x
xo-~~
I3
x
10-14
I
-
-
3
x
1o-l0
I
0.998
10-8
-
T_i
TO-s
I 0.9981 g
-
T1T-j
X
-
3
0.98
IO+-+::
_-
2
2
I
o.ggg
-. --_ 2
10-n
I
_‘_
<;-
_--_ 1
Ru
RA ---
0.00 I
0.9
0.01
i;rR~
/
IO
in each extraction)
-.
---_
_y-'--
2
equal
x0-a _
_+yj
I ED/EA,
OF
3
-
I
VALUES
0.97
-
I
10-8
I
1 o*gP8/ 3 X 10-l
1 -
0.997
I
512
E.
B.
SANDELL
VOL.
4 (1950)
When EA and EB arc not sufficiently different for good separation in a simple solution, differential complex formation can often be applied to great advantage It is generally desirable that A be complexed in producing a change in E,J&. to the smaller extent so that it can be extracted into the organic solvent, while the other elements are left in the aqueous solution, although the converse case can also be of use. Alteration in the valence of A or B is scmetimes applicable as an effective means of changing the ratio of the extraction coefficients.
SUMMARY Expressions are given for the calculation of recovery and separation factors from extraction coefficients in immiscible solvent separations. Extraction coefficients of separation forms in inorganic analysis arc usually variables which arc a function of reagent concentration and acidity, and whose value can be derived from the equilibrium constant of the extraction reaction. RESUME Des formules sont donndes pour le calcul des facteurs de recuperation et de sdpnration, ir partir des coefficients d’cxtraction, en dissolvants non miscibles. Lcs coefficients d’extraction en analyse inorganique sont generalcmcnt variables, &ant fonction de la concentration du reactif et de l’acidrte, et ces valeurs ddpendent de l’dquilibre dc la reaction d’extraction. ZUSAMMENFASSUNG und Trennungsfaktoren aus Formeln zur Bercchnung der Zurtickgewinnungsden Extraktionskoeffizicnten bei Trennungcn in mcht rmschbaren Losungsmitteln wcrdcn angegeben. Extraktionskoeffizienten in der anorganischen Analyse sind meist variabel, und zwar sind sic Funktion der Reagenskonzentration und der Aziditgt und klinnen von der Gleichgewichtskonstante der Extraktionsrcaktion abgeleitct wcrdcn.
Received
February
asrd,
r g5o