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A new spectrophotometric method for differentiating mononuclear and polynuclear complexes and for determining their extraction constants
0039-9140/X0/0601 -0545502 00/O
A NEW SPECTROPHOTOMETRIC METHOD FOR DIFFERENTIATING MONONUCLEAR AND POLYNUCLEAR COMPLEXES AND FOR DETERMINING THEIR EXTRACTION CONSTANTS T. ROMANGALAN,A.ARREBOLARA~IIREZandh4. ROMAN CEBA Department of Analytical Chemistry. Faculty of Sciences. University of Extremadura, Badajoz, Spain
(Received
4 July
1919. Reaised 4 December
1979. Accepted
21 December
1979)
Summary-A new spectrophotometric method is proposed for differentiating mononuclear and polynuclear complexes as well as for determining the extraction constant K: of any complex A-B.. The method is based on the efiect of dilution on the degree of dissociation of the complex. The precision of log K: is kO.03 when the degree of extraction of the metal is between 20 and 60%. The highest values of log Kf determinable by this method are 7, 19, 12 and I8 for I : I, 2: 2, 2: I and 3 : 1 complexes, respectively.
In a previous work we proposed a graphical method for the differentiation of mononuclear and polynuclear complexes, and for determination of the stability constant of any complex A,B,.’ The method was based on the effect of dilution on the degree of dissociation of the complex, and we now use the same principle for differentiating mononuclear and polynuclear complexes and determining their extraction constants. The method is particularly useful in solvent extrao tion work because dimers and higher polymers are often formed in extractions. Also, although the method is developed for binary complexes, we think it could easily be extended to mixed-ligand complexes, which also frequently occur in extraction systems. THEORY Let us consider the formation and extraction of any complex by means of the equilibrium
where m, n 3 1. For a particular value of pH, the conditional extraction constant is:
given by the equations E, =
K'P,
E;‘
C&Alo
CAlo”CW
(2) w
(3) p _ CAJMo
‘--CA,B,3,
(4)
CA’IWis the conditional concentration in the aqueous phase of the ligand not bound to the central ion B, in all its possible forms, molecular and ionic. Similarly, [B’], is the concentration of free metal ion in the aqueous phase that has not reacted with the complexant A. Let a and b be the initial concentrations of ligand and cation in the organic phase. and aqueous phase, respectively. Let us consider a 1: 1 phase-volume ratio, and the condition a/b = m/n. Under these conditions, the degree of extraction of the metal, a,, is C&Alo
C&J&lo= ___ CAAlo = - A b/n aim Aow
a, = CA,B”lm,. = ___ Kf=--=
s
(5)
(1) where A is the absorbance of the complex and A,,, the absoibance when complexation and extraction are complete for cation concentration b, i.e., when a, = 1. By ma&al balance from equations (2), (4) and (5), the concentrations of complex and reagents in equi-
where E,, K’ and PC are respectively the extraction coefficient of the l&and, the conditional stability constant and the partition coefficient of the complex, 545
546
SHORT COMMUNlCATIONS
librium are
depend on the pH in the aqueous phase:
CAmBnlo= fi a,
where P, is the partition coefficient of the ligand, K, the acidity constant of the ligand and K the stability constant of the complex. Under these conditions, neglecting possible side-reactions of the cation, equation (6) is transformed into
Substituting these values in expression (1) gives
K;
=
KS = 1
n’“-“a,(E,
+
I)”
mmj+m+n-lb[1 - (1 + JJaC]‘m+“E;
which can be rearranged to give
Kf =
K,rE;t (E, + 1)”
n(M-llu
-=
mmhl”t”-tI[l
_ (t l $aC~+”
(6) By analogy with the previous work,’ the following equation may be written:
Kf =
K’P,
_
(4 + lIm
KP,K,” [K, + (1 + P,)CH+ll”
This equation describes the effect of pH on the conditional extraction constant. The method proposed provides for the differentiation of mononuclear and polynuclear complexes. Suppose that the stoichiometry of a complex corresponds to a molar ratio equal to unity. If a plot of @A)*/(ho//3)f vs. /IA does not give a straight line then @A)i/(ho//?)* can be plotted LX./?A and a straight line obtained in that case will confirm that the complex is 2:2 and not I: I. The fact that the straight line and the curve have the same limit, @A),,,,, aids in differentiating between them.
PRECISION AND FIELD OF APPLICATION
A straight line is obtained by plotting the left-hand side of equation (7) against flA. When
that is, the intersection of this straight line with the abscissa provides the value of A,(b,)/(l + l/P,). The slope of the straight line
OF THE METHOD
The precision of log K: is f0.03 when 3, is between 20 and 60”:,. The highest values of log Kr determinable are 7. 19. 12 and 18. for I : 1, 2:2,2: 1 and 3 : 1 complexes, respectively. ’ The approximation (I + I/P,)K: - K: introduces a new source of error, but it is easily evaluated as a function of P,, with the following result: PC A log K:
10 +0.04
20 +0.02
30 +0.01
40
+0.01
50 +o.oot?
The error is practically negligible, even for quite small values of PC.
EXPERIMENTAL
Procedure
allows the calculation of (1 + l/P,)K:. Metal chelates normally have high values of P,, so (1 + l/P,)K: + K:.
If the method is to be used with ligands that have protolytic reactions, e.g., a monoprotic ligand HA, is evident that the extraction coefficient of the ligand and the conditional stability constant of the complex
Shake equal volumes of solutions of A and B (in immiscible solvents) at different concentrations, but in stoichiometric ratios so that in each the ratio a/b = m/n. Measure ttie absorbance of each extract against a reagent blank prepare with the same reagent concentration, but no cation. It is convenient to increase the cell path-length by a factor equal or proportional to the dilution factor. In this fashion, the value of /IA is obtained directly.
SHORT
547
COMMUNICATIONS
Table I.
I W8 CWUI,
A
10-5M
(550 nm)
BA
1.o 2.0 4.5 6.0 8.0
0.060 0.160 0.470 0.652 0.935
0.480 0.640 0.835 0.870 0.935
(PA)’ (ho/W
W4’ __
%
(bo/B)l
%
- 4800
- 4000
219 179 134 121 108
4670 2990 1740 1420 1160
34.8 46.4 60.5 63.0 67.7
- 3200
-2400
Reagenrs (1,2,4-trihydro.ry~~r~raquinone). A prepared by dtssolving 0.256g of the Merck product and diluting to 1 litre with methyl isobutyl ketone, A 2 x 10m4M solution was prepared by dilution. Ni(lf) solution. Prepared from Ni(NO& .6H,O and standardized with dimethylglyoxime. A 2 x 10e4M solution was prepared by dilution.
Purpurin solution ,lO-‘M solution was
02
06
04
Fia. 1. Curve 1, oH Ni(ll)-Purpurin
IO
12
f3A
6.28; 2, 7.32; 3, 8.05; 4, 8.48; 5, 9.05;
system
The stoichiometry of this complex was determined by the continuous variation method, maximal absorption being at 1:l molar ratio. The extraction constant was determined for different values of pH and a b. value of 8 x IO- jM. The results obtained at pH 8.48 are presented m Table 1. The values of (bA)*/(b&I)* with respect to PA (at several pH values) are presented graphically in Fig. 1, producing straight lines which intersect the abscissa to give a value of 1.38 for A,,,,)/(1 + l/P,), which leads to a molar absorptivity of 1.72 x 1041.mole-‘.cm-‘. The values of (/IA)‘/( (which would correspond to a 2:2 complex) are shown in the same figure, and give a curve. This clearly indicates that the complex is 1:l and not 2:2. By substitution of the values found for AOcbs,/(1 + l/P,) and
08
6, 8.48 (A2B2). the slopes of the straight lines into the expression for the slope, the following values for (1 + l/P,)K: z K: can be calculated: PH log K:
6.28 3.61
7.32 4.7 1
8.05 4.83
8.48 4.91
9.05 4.9 1
REFERENCE I. D. V. Gonzalez Garcia, A. Arrebola Ramirez and M. Roman Cuba, Talanto, 1979, Xi, 215.
A NEW SPECTROPHOTOMETRIC METHOD FOR DIFFERENTIATING MONONUCLEAR AND POLYNUCLEAR COMPLEXES AND FOR DETERMINING THEIR EXTRACTION CONSTANTS T. ROMANGALAN,A.ARREBOLARA~IIREZandh4. ROMAN CEBA Department of Analytical Chemistry. Faculty of Sciences. University of Extremadura, Badajoz, Spain
(Received
4 July
1919. Reaised 4 December
1979. Accepted
21 December
1979)
Summary-A new spectrophotometric method is proposed for differentiating mononuclear and polynuclear complexes as well as for determining the extraction constant K: of any complex A-B.. The method is based on the efiect of dilution on the degree of dissociation of the complex. The precision of log K: is kO.03 when the degree of extraction of the metal is between 20 and 60%. The highest values of log Kf determinable by this method are 7, 19, 12 and I8 for I : I, 2: 2, 2: I and 3 : 1 complexes, respectively.
In a previous work we proposed a graphical method for the differentiation of mononuclear and polynuclear complexes, and for determination of the stability constant of any complex A,B,.’ The method was based on the effect of dilution on the degree of dissociation of the complex, and we now use the same principle for differentiating mononuclear and polynuclear complexes and determining their extraction constants. The method is particularly useful in solvent extrao tion work because dimers and higher polymers are often formed in extractions. Also, although the method is developed for binary complexes, we think it could easily be extended to mixed-ligand complexes, which also frequently occur in extraction systems. THEORY Let us consider the formation and extraction of any complex by means of the equilibrium
where m, n 3 1. For a particular value of pH, the conditional extraction constant is:
given by the equations E, =
K'P,
E;‘
C&Alo
CAlo”CW
(2) w
(3) p _ CAJMo
‘--CA,B,3,
(4)
CA’IWis the conditional concentration in the aqueous phase of the ligand not bound to the central ion B, in all its possible forms, molecular and ionic. Similarly, [B’], is the concentration of free metal ion in the aqueous phase that has not reacted with the complexant A. Let a and b be the initial concentrations of ligand and cation in the organic phase. and aqueous phase, respectively. Let us consider a 1: 1 phase-volume ratio, and the condition a/b = m/n. Under these conditions, the degree of extraction of the metal, a,, is C&Alo
C&J&lo= ___ CAAlo = - A b/n aim Aow
a, = CA,B”lm,. = ___ Kf=--=
s
(5)
(1) where A is the absorbance of the complex and A,,, the absoibance when complexation and extraction are complete for cation concentration b, i.e., when a, = 1. By ma&al balance from equations (2), (4) and (5), the concentrations of complex and reagents in equi-
where E,, K’ and PC are respectively the extraction coefficient of the l&and, the conditional stability constant and the partition coefficient of the complex, 545
546
SHORT COMMUNlCATIONS
librium are
depend on the pH in the aqueous phase:
CAmBnlo= fi a,
where P, is the partition coefficient of the ligand, K, the acidity constant of the ligand and K the stability constant of the complex. Under these conditions, neglecting possible side-reactions of the cation, equation (6) is transformed into
Substituting these values in expression (1) gives
K;
=
KS = 1
n’“-“a,(E,
+
I)”
mmj+m+n-lb[1 - (1 + JJaC]‘m+“E;
which can be rearranged to give
Kf =
K,rE;t (E, + 1)”
n(M-llu
-=
mmhl”t”-tI[l
_ (t l $aC~+”
(6) By analogy with the previous work,’ the following equation may be written:
Kf =
K’P,
_
(4 + lIm
KP,K,” [K, + (1 + P,)CH+ll”
This equation describes the effect of pH on the conditional extraction constant. The method proposed provides for the differentiation of mononuclear and polynuclear complexes. Suppose that the stoichiometry of a complex corresponds to a molar ratio equal to unity. If a plot of @A)*/(ho//3)f vs. /IA does not give a straight line then @A)i/(ho//?)* can be plotted LX./?A and a straight line obtained in that case will confirm that the complex is 2:2 and not I: I. The fact that the straight line and the curve have the same limit, @A),,,,, aids in differentiating between them.
PRECISION AND FIELD OF APPLICATION
A straight line is obtained by plotting the left-hand side of equation (7) against flA. When
that is, the intersection of this straight line with the abscissa provides the value of A,(b,)/(l + l/P,). The slope of the straight line
OF THE METHOD
The precision of log K: is f0.03 when 3, is between 20 and 60”:,. The highest values of log Kr determinable are 7. 19. 12 and 18. for I : 1, 2:2,2: 1 and 3 : 1 complexes, respectively. ’ The approximation (I + I/P,)K: - K: introduces a new source of error, but it is easily evaluated as a function of P,, with the following result: PC A log K:
10 +0.04
20 +0.02
30 +0.01
40
+0.01
50 +o.oot?
The error is practically negligible, even for quite small values of PC.
EXPERIMENTAL
Procedure
allows the calculation of (1 + l/P,)K:. Metal chelates normally have high values of P,, so (1 + l/P,)K: + K:.
If the method is to be used with ligands that have protolytic reactions, e.g., a monoprotic ligand HA, is evident that the extraction coefficient of the ligand and the conditional stability constant of the complex
Shake equal volumes of solutions of A and B (in immiscible solvents) at different concentrations, but in stoichiometric ratios so that in each the ratio a/b = m/n. Measure ttie absorbance of each extract against a reagent blank prepare with the same reagent concentration, but no cation. It is convenient to increase the cell path-length by a factor equal or proportional to the dilution factor. In this fashion, the value of /IA is obtained directly.
SHORT
547
COMMUNICATIONS
Table I.
I W8 CWUI,
A
10-5M
(550 nm)
BA
1.o 2.0 4.5 6.0 8.0
0.060 0.160 0.470 0.652 0.935
0.480 0.640 0.835 0.870 0.935
(PA)’ (ho/W
W4’ __
%
(bo/B)l
%
- 4800
- 4000
219 179 134 121 108
4670 2990 1740 1420 1160
34.8 46.4 60.5 63.0 67.7
- 3200
-2400
Reagenrs (1,2,4-trihydro.ry~~r~raquinone). A prepared by dtssolving 0.256g of the Merck product and diluting to 1 litre with methyl isobutyl ketone, A 2 x 10m4M solution was prepared by dilution. Ni(lf) solution. Prepared from Ni(NO& .6H,O and standardized with dimethylglyoxime. A 2 x 10e4M solution was prepared by dilution.
Purpurin solution ,lO-‘M solution was
02
06
04
Fia. 1. Curve 1, oH Ni(ll)-Purpurin
IO
12
f3A
6.28; 2, 7.32; 3, 8.05; 4, 8.48; 5, 9.05;
system
The stoichiometry of this complex was determined by the continuous variation method, maximal absorption being at 1:l molar ratio. The extraction constant was determined for different values of pH and a b. value of 8 x IO- jM. The results obtained at pH 8.48 are presented m Table 1. The values of (bA)*/(b&I)* with respect to PA (at several pH values) are presented graphically in Fig. 1, producing straight lines which intersect the abscissa to give a value of 1.38 for A,,,,)/(1 + l/P,), which leads to a molar absorptivity of 1.72 x 1041.mole-‘.cm-‘. The values of (/IA)‘/( (which would correspond to a 2:2 complex) are shown in the same figure, and give a curve. This clearly indicates that the complex is 1:l and not 2:2. By substitution of the values found for AOcbs,/(1 + l/P,) and
08
6, 8.48 (A2B2). the slopes of the straight lines into the expression for the slope, the following values for (1 + l/P,)K: z K: can be calculated: PH log K:
6.28 3.61
7.32 4.7 1
8.05 4.83
8.48 4.91
9.05 4.9 1
REFERENCE I. D. V. Gonzalez Garcia, A. Arrebola Ramirez and M. Roman Cuba, Talanto, 1979, Xi, 215.