the determination of the stability constants of some lanthanide-α-hydroxyisobutyrate complexes...

Bull. SOC. Chim. Belg., 73, pp. 597-614 (8 fig.), 1964 r THE DETERMINATION OF THE STABILITY CONSTANTS

OF SOME LANTHANIDE-a-HYDROXYISOBUTYRATE COMPLEXES USING CATION EXCHANGE METHODS

H. DEELSTRA AND F. V m ~ ~ ~ ( G h e n t )

The stabil ity constants of some lanthddea-hydroxyisobutyrate complex systems have been determined by cation exchange measurements. Fronaeus’ method was used to calculate the consecutive formation constants of the terbium and thulium complex systems in 0.2 M and 1 M ammonium perchlorate. The ps values of nine lanthanide complex systems have been derived by Schubert’s method. The formation constants determined by the cation exchange technique agree with the values found by potentiometric titration.

The stability constants of the complexes of the lanthanide elements with a-hydroxyisobutyrate and lactate were previously determined by potentiometric measurements (1). In this investigation some results obtained potentiometrically were checked by the cation exchange methods of Fronaeus(2) and Schubert(3.4). In addition to the fact that by cation exchangers it is simple to’ determine the distribution of the metal between the resin and aqueous phase by means of radionuclides, the use of low concentrations of tracers reduces the possibility of formation of polynuclear complexes.

Some lanthanide and actinide complex systems were already examined by Fronaeus’ cation exchange method, namely the cerium- acetate system by Fronaeus (9, the gadolinium-acetate and glycolate systems by Sonesson (6) and the americium-acetate, glycolate and thioglycolate systems by Grenthe (7).

(1) H. DEELSTRA and F. VERBEEK, Anal. Chim. Acta, in press. (a) S . FRONAEUS, Acru Chem. Scand., 5, 859 (1951); 6, 1200 (1952); 7,

(a) J. SCHUBERT, J. Phys. Colloid. Chem., 52, 340 (1948). (4) J. SCHUBERT and J.W. RICHTER, J. Phys. Colloid Chem., 52,350 (1948). (6) S. FRONAEUS, Suensk. Kem. Tidskr., 64, 317 (1952); 65, 19 (1953). (6) A. SONESSON, Actu Chem. Scand., 13, 1437 (1959). (7) I. GRENTHE, Actu Chem. Scand., 16, 1695 (1962).

21,469 (1953).

598 H. DEELSTRA AND F. VERBEEK

CALCULATION OF THE CONSTANTS

In the derivation of Fronaeus' method it is assumed that only mononuclear complexes are formed. The experimental measured distribution of the metal concentration in the resin, [ C ~ R and in the solution, CM is a function of the respective stability constants of the complexes between the metal M and the ligand L, and the concentration of the free ligand [L-] in solution.

where PI, P2, ..., Pn, are the over-all stability constants of the complexes ML, MLz, ..., MLn. The lanthanide ions M3+ and the a-hydroxyisobutyrate ligand L- form uninegative tetra-ligand complexes (1)

(n= 1, 2, 3, 4) [MLi-"] Pn = [M3+] [L-]n

If KD, is the distribution of the complex ions ML;-3 between resin and solution, then

where k5 is a function of the activity coefficients in resin and solution. In this case the activity coefficients in solution are kept constant

with ammonium perchlorate. The loading of the resin at [ C ~ R - 10-6M is very low compared with the ionic strength of both the exchanger and the liquid phase.

Combination of equations (l), (4) and (5 )

[CMIR = KD, [M3+l + KD, Pi [M3+l I&-I + KD,Pz [M3+1 IL-1' ( 5 )

gives

KD, + KD, PI [L-I + KD, P2 [L-12 (6)

KD = 1 + pi [L-I + pZ [L-12 + p3 [L-13 + p4 [L-I~

If one allows for the possible sorption of positively charged complexes by the cation exchange resin through a term h5 = Pj KDJKD,,,

THE DETERMINATION OF THE STABILITY CONSTANTS 5 99

the general formula is obtained

(7) 1 + hl [L-I + h2 &-I2

O 1 + p1 [L-I + p2 [L-12 + p3 [L-I3 + p4 [L-14 KD = KD

From equation (7) it is possible to evaluate the respective Pn-values by determining the distribution constants as a function of the [L-1- concentration at constant ionic strength and temperature.

For this purpose two new parameters were introduced by Fronaeus

KDO

K D - -

L-I $1 =

and

Combining equations (7) and (8)

p1 - hl + [L-I (x2 - h2) 1 + hl I&-] + ha [L-12 $1 =

where

For [L-] = 0, in expressions (10) and (12) following limiting values are obtained

Combination of equations (71, (8) and (9) gives

f = p141 - x2 + h2 ($1 [L-I + 1)


In the same way equation (16) is deduced from equations (13), (14) and (15), where Af = f-foand A 9 1 = +I--$!

* 91

[L-I [L-I -- Af - p1- - ps - P4LL-I + h2$l

By plotting Aj/[L-] versus A+l/[L-], p1 is obtained as the slope. PI

In equations (15) and (16) the last terms vary with [L-1. At low

For the lanthanide ions M3f another new parameter was introduced

is also obtained from the slope of the curve off versus $1.

[L-]-concentrations they are however only small correction terms.

From equations (8), (15) and (17), it is obvious that

g = p2+1 - x3 = p291 - p3 - p 4 [L-I (18)

At low [L-]-concentration, g is a linear function of $1. The slope of the curve gives p2 and the intercept an approximate value of p3. When no complexes are bound in the resin (hl =ha =O), equation (7) becomes

For only one complex in solution, the Schubert equation (3’4) is obtained

Plotting of log (KD,/KD - 1) versus log [L-] yields n, the average number of ligands bound at the central metal ion.

THE DETERMINATION OF THE STABILITY CONSTANTS

EXPERIMENTAL

60 1

REAGENTS

Lanthanide tracers

A known amount of the Matthey “specpure” oxides were irradiated in the BR-1 reactor (Mol), at a neutron flux of lOl2 n. cm-2. sec-l. The oxides were dissolved in nitric acid. The solution was evaporated below 60oC to remove the excess nitric acid.

Resin

The cation exchanger Dowex 50-WX 8, 200-400 mesh, with a capacity of 5.2 meq. grammes, was washed several times with 6 N hydrochloric acid to remove iron, converted in the ammonium form and air dried at 50oC.

u-hydroxyisobutyrrc acid

Aqueous solutions of u-hydroxyisobutyric acid (Fluka) were standardized against sodium hydroxide. The acid was adjusted to the desired pH by adding concentrated ammonium hydroxide.

PROCEDURE

The procedure followed is described by Speecke and Haste(*). The equation used to determine the distribution coefficient is given by

activity/g resin S - E ml of solution - -- KD =

activity/ml liquid E g of resin

where S and E are the respective activities in solution before and after the equilibration with the resin. Distribution measurements were performed by mechanical shaking 10 ml of solution of the lanthanide complexes, prepared from stock lanthanide isotopes, a-hydroxyisobutyrate and ammonium perchlorate, with 100 mg portions of dried resin in 50 ml in Pyrex flasks fitted with ground glass stoppers. Mixing time was 15 hours in a constant temperature bath at 25.0 f 0.1oC. Separate experiments demonstrated that the equilibrium was obtained within approximately three hours. The activity was measured by y-ray scintillation counting of 5 ml of the aqueous phase in a NaI(T1)-well type crystal.

The pH of the solution was checked after equilibration. The solutions were kept at a constant ionic strength with ammonium perchlorate. The pL = - log [L] value was calculated from the concentration and the disso- ciation constant of the u-hydroxyisobutyric acid at the appropriate ionic strength (9. The determinations were at least duplicated.

A. SPEECKE and J. HOSTE, Tulanta, 2, 332 (1959). (9) H. DEEUTRA and F. VERBEEK, Bull. Soc. Chim. Belg., 72, 612 (1963).

602 H. DEELSTRA AND P. VERBEEK

RESULTS AND DISCUSSION

The [L-]-concentration was varied by changing the pH of a 0.1 M acid solution by adding perchloric acid or ammonium hydroxide.

As the experiments showed that the distribution coefficients are very sensitive to the addition of increasing amounts of indifferent electro- lyte (Fig. l), experiments were performed in 1 M and 0.2M ammonium perchlorate solutions.

1, THE TERBIUM-C~-HYDROXYISOBUTYRATE SYSTEM IN 1 M AMMONIUM

PERCHLORATE SOLUTION

The distribution coefficient KD as a function of the ligand concentration is given in figure 1, curve a. The slope varies as a function of the pL-values. The intrinsic distribution coefficient KD, of terbium in 1 M

PL 2 3 L

1 1

Fig. 1 - KD vs. pL = - log[L-] for the Tb3+ and Tm3+-a-hydroxyisobutyrate systems. Tb3+ in 0.1 M a-hydroxyisobutyric acid: 1 M NH4C104 (curve a); 0.2 M N&C104 (curve b); OM NHiClO4 (curve d). Tm3+ in 0.1 M a-hydroxyisobutyric acid: 0.2M N&C104 (curve c).

THE DETERMINATION OF THE STABILITY CONSTANTS 603

ammonium perchlorate was determined in the absence of the ligand and gives a value of 700. Extrapolation of log K ~ = l o g KD, for [L-]=0 gives the same value (Fig. 2).

0 10 20

Fig. 2 - Log KD vs. [L-] for the Tb3+-a-hydroxyisobutyrate system (1M NKcl04).

The various functions used for the computation of the stability constants are given in Table I. $1 andfwere plotted against [L-] (Fig. 3 and 4) and extrapolated to [L-] = 0 giving @ and ,fO.

Following values were obtained :

TA

BL

E I

C

atio

n ex

chan

ge m

easu

rem

ents

of t

he te

rbiu

m-a

-hyd

roxy

isob

utyr

ate c

ompl

ex s

yste

m in

I M

am

mon

ium

perc

hlor

ate

solu

tion

: f-fO)/

[L-]

. 10

-6

-

PH -

1.19

1.

41

1.65

1.

86

2.06

2.

24

2.34

2.

54

2.70

2.

90

3.20

3.

35 -

g. 1

0-8

L-1.

103

KD

1.63

5 1.

716

2.00

0 2.

473

3.41

5 5.

303

5.98

3 1 1

.290

18

.918

38

.888

1 1

6.64

17

0.73

0.31

5 0.

522

0.904

1.45

8 2.

291

3.42

8 4.

266

6.61

2 9.

288

13.9

56

lo0

0

2 01

6 13

71

1106

10

10

1 05

4 12

55

1168

15

56

1 92

9 2

715

4 73

8 5

411

700

428

408

350

283

205

132

117 62

37

18

322.

4 71

0.7

117.

2 7.0

23

.6

74.3

39

.3

84.1

10

0.0

122.

8 15

3.1

140.

6

f. 10

-6

9.105

1.

211

0.66

1 0.

988

1.00

3 1.

030

1.18

1 1.

129

1.47

2 1.

829

2.59

2 4.

585

5.27

1

I I-

-

-

97.3

5 70

.64

56.7

4 81

.97

53.6

8 86

.51

100.

00

121.

24

150.

96

139.

36

-

0.90

7 1.

684

1.38

5 1.

330

1.31

0 1.

580

1.92

9 2.

697

4.71

6 5.

400

x2.1

0-4

-

-

-

-

-

7.4

3.9

8.2

10.0

12

.3

15.3

14

.0


It was possible to extrapolate with rather good accuracy. As seen in figure 5 , Afl[L-] is approximately a linear function of A+l/[L-]. The slope of this function gives the stability constant 971. Plotting f against 91 in figure 6, gives a function with a slope pi=976.

Fig. 3 - 41 vs. [L-] for the Tba+-a-hydroxyisobutyrate system (1 M NaC104).

According to equation (14), p2 -h2= 105. The value of g is then computed by means of equation (17). The slope of g as a function of $1 gives p2 = 105 (Fig. 7). The extrapolation to [L-] = 0 yields the intercept on the y-axis PS G 107. The g-value is a linear function of


0

41 over the whole concentration range indicating that there is no evidence of the formation of anionic complexes.

[ijrnml I I 1 1


The experiment shows that hl = 0, indicating that no TbL2+-complexes are adsorbed i.e. the sorption of these ions is small compared with that of the central ion. It is assumed that the sorption of TbL2+ must be smaller than. for TbL2+, then hl = hz = 0, within the limits of the sen- sitivity of the method.

150-

100-

0

O ! I I 1

0 50 100 150

Fig. 5 - Af/[L-] vs. A 41/[L-] for the Tb3+-a-hydroxyisobutyrate system (1 M mC104).

When hl = h2 = 0, it is easy to show that from equation (14)

f0 = p; - pz and from equation (15) for h2 = 0

p1+1 -f= xz = p2+ps [L-I + p4 K-I2 (25)

From a plot of Xz against [L-] the slope p3 = 3.7 x 106 (Fig. 8). The stability constants found are then

log pi = 2.99; log pz = 5.00; log p3 = 6.57


0

2. THE TERBIUM- AND THULIUM-a-HYDROXYISOBUTYRATE SYSTEMS IN

0.2 M AMMONIUM PERCHLORATE SOLUTION

#, .I@ I I I I I

The distribution coefficients of terbium and thulium as a function of pL L- - log [L-] are given in figure 1, curves b and c. The KD,-values were determined graphically and directly by batch experiments

KEr= 20 000 KrT,b = 36 000

Fig. 6 - f vs. $1 for the Tb3+-cr-hydroxyisobutyrate system (1 M NH4C104).

The experimental data are given in Tables I1 and 111.

TABLE

I1

Cat

ion-

exch

ange

mea

sure

men

ts of

the terbium-a-hydroxyisobutyrate co

mpl

ex s

yste

m in

0.2

M a

mm

oniu

m p

erch

lora

te s

olut

ion

PH

2.49

2.

67

2.76

2.

90

3.06

3.

29

3.55

3.

73

3.90

4.

09

4.30

4.

45

~~

[L-I.

103

4.77

1 7.

055

8.54

2 11

.43

16.3

2 24

.07

36.5

3 46

.55

56.3

3 66

62

76.3

9 82

.05

KD

36 0

00

3 87

5 2.

000

1 43

0 76

4 39

4 13

4 36.0

16

.8

9.08

4.

53

3.05

2.

11

KD

,/KD

9.29

18

.00

25.1

7 47

.12

91.3

7 26

8.6

1000

2

143

3 96

4 7

947

11 8

03

17 06

1

10-3

1.20

0 1.

737

2.41

0 2.

830

4.11

2 5.

540

11.1

2 27

.35

46.0

1 70

.35

119.

3 15

4.4

207.

9

112.

5 17

1.5

190.

8 25

4.7

265.

9 42

1.1

715.

8 96

2.6

1227

.5

1772

.3

2 01

9.6

2 53

2.3

f. 10

-6

0.90

0.

974

2.72

4 3.

207

4.68

1 6.

374

12.9

3 32

.11

54.2

3 83

.20

141.

3 18

3.4

247.

0

225

258

270

330

335

500

854

1 14

5 14

61

2 10

8 2

389

3000

g. 10

-9

0.94

9 1.

245

1.45

7 2.

098

2.79

6 5.

582

13.7

0 23

.03

35.5

3 54

.08

78.6

0 99

.78

TA

BL

E I

II

Cat

ion-

exch

ange

mea

sure

men

ts of

the thulium-a-hydroxyisobutyrate co

mpl

ex s

yste

m in

0.2

M ammonium

perc

hlor

ate

solu

tion

2.49

2.65

2.

74

2.88

3.07

3.

22

3.50

4.771

6.

755

8.18

4 10

.960

16

.008

21

.210

33

.901

20 O

OO

986

500

318

150 54

20 4.26

20.2

8 40.00

62.8

9 13

3.33

37

0.3

lo0

0

4 69

4

- 2.00

4.

04

5.77

7.

56

12.0

5 23

.07

47.1

13

8.4

427.

7 55

8.1

679.

3 91

6.9

1316

.2

2 12

6.3

4 02

3

f.10-

6 1 C

f-fV

rL-I

I 3.

0 7.

658

10.9

90

15.2

80

23.2

29

44.8

22

92.0

75

272.

90

97.6

11

8.0

150.

0 18

4.5

261.

2 4

199.

6 7

961.

4

g. 10

-9

3.78

5.29

6.

98

10.9

2 20

.81

42.4

4 12

4.70

THE DETERMINATION OF THE STABILITY CONSTANTS 61 1

+: andfO-values were obtained, by extrapolationofthe $1- and f-values to [L-] = 0.

6

5

I,

3

2

1

0.

Tm Tb

+:= 2000 $10 = 1200 fo = 300 800 fO = 90 000

Fig. 7 - g vs. 41 for the Tb3+-a-hydroxyisobutyrate system (1 M N&C104).

The stability constants were computed and determined as before. The values obtained are listed in Table IV, together with the values found potentiometrically in 0.2 M sodium perchlorate solution using


Computer

3 . 0 8 5 .80 7 . 7 2 9.47

Bjerrum’s half ii-method and calculation by means of the 1BM 1620 computer (1).

Table IV shows that the results from cation exchange experiments confirm the potentiometrically obtained values for the first three stability constants.

Ion exchange

3.07 5.70 7 .00 -

TABLE IV Stability constants of the u-hydroxyisobutyrate complex terbium and thyliurn-y systems determined by cation exchange and potentiometric titration in 0.2 M

perchlorate solution

I Thulium _____

Constants 1 Ion

I exchange

_ _

Bjerrum

3.25 5 .90 7 . 9 4 9.37

I Terbium

Bjerrum

3.10 5 .40 7 .08 8.08

Computer

____

2.92 5.24 6 .86 8 .09

3. METHOD OF SCHUBERT

Schubert’s cation exchange method was applied to determine the stability constants of some MLs complexes using equation (22). This equation is only accurate when no complexes are adsorbed on the resin and only one complex is in solution. As shown, the adsorption of positively charged complexes (ML2f and M L h can be neglected, especially at pL-values where mainly neutral complexes are formed.

When the average number of ligand bound per metal ion A-3, mainly ML3 complexes are in solution, but also ML;, MLi and even ML2f complexes. This can be seen from the distribution curves calculated by means of the stability constants obtained from potentiometric data (l).

As in general for the lanthanides at ti = 3, [MLgf] + [ML;] [ML;], the constants P3 calculated from ion exchange data give good approximate values.


The results of tbe measurements at 25.0&0.1°C and in presence of 0.2M ammonium perchlorate are summarized in Table V. The KD- values were determined by batch and column experiments at pL-values where A 3. These pL-values can be read from the formation curves obtained by potentiometric titration (I) and also from the elution curves for a slope d log K ~ l d l o g [L-] = - 3.

TABLE V

determined by Schubert’s method Stability constants of lanthanide-a-hydroxyisobutyrate complexes

CHL Moll1

0.6 0.1

0.6 0.1

0 .6 0.1

1 .o 0.1

1 .o 0.1

1.777

1.777 1.422 0.1

1.777 1.422 0.1

1.777 0.1

1.777 0.1

2.22 2.96

2.22 3.04

2.22 3.17

2.21 3.30

2.22 3.41

2.33

2.255 2.30 3.69

2.255 2.30 3.74

2.25s 3.78

2.255 3.86

PL A g 3

1.81 1.90

1.81 1.83

1.81 1.72

1.60 1.62

1.61 1.54

1.235

1.30 1.36 1.36

1.30 1.36 1.33

1.30 1.31

1.30 1.27

KD

22.5 42.0

29.1 36.0

48.1 27.0

19.7 23.5

30.5 20.5

5.27

12.1 19.0 19.7

28.7 42.8 36.5

41.2 46.0

70.3 56.0

KDo

18 OOO

19 5 0 0

20 OOO

25 OOO

29 OOO

34 OOO

36 OOO

37 OOO

39 OOO

44 000

~~ ~

log p3

8.33 8.33

8.25 8.28

8.05 8.03

7.90 7.89

7.80 7.77

7.51

7.38 7.36 7.34

7.01 7.02 7.00

6.88 6.86

6.70 6.70

log Fa Bjerrum

8.39

8.20

7.94

7.71

7.59

7.42

7.08

6.79

6.60

6.44

(1) batch experiments (2) column experiments


For comparison the constants found by Bjerrum’s half ii-method (1) are also given in Table V. Considering the difference in the methods used, there is generally good agreement between the log pa-values determined by cation exchange and those by potentiometric titration.

”1

0

Fig. 8 - XZ vs. [L-] for the Tb3+-a-hydroxyisobutyrate system (1 M N&c104)

ACKNOWLEDGEMENTS

The authors wish to express their thanks to Prof. Dr. J. Hoste for his kind interest in this work, and to Mrs J. Gorlee and Mrs F. Van den Abeele for technical assistance.

This investigation has partly been sponsored by the “Interuniversi- tair Instituut voor Kernwetenschappen *’.

Laboratorium voor Analytische Cheniie RIJKSUNIVERSITIET GENT

Directeur : Prof. Dr. J. HOSTE

Medegedeeld aan de Vlaamse Chemische Vereniging op 27,februari 1964

the determination of the stability constants of some lanthanide-α-hydroxyisobutyrate complexes...

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