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Aluminum complexes with diglycolic and thiodiglycolic acids
J, inorg, nucl. Chem., 1972, Vol. 34, pp. 1225-1231.
ALUMINUM
Pergamon Press. Printed in Great Britain
COMPLEXES WITH DIGLYCOLIC THIODIGLYCOLIC ACIDS*
AND
ALDO NAPOLI Istituto di C h i m i c a Analitica, Universith di R o m a (Received 9 August 1971 )
A b s t r a c t - C o m p l e x e s formation b e t w e e n a l u m i n u m ions and diglycolic and thiodiglycolic acids was studied at 25°C in 0"5 M N a C I O , by potentiometric m e a s u r e m e n t s . In the investigated concentration ranges (--log IH+I < 3-5; 2.55 m M ~< CM ~< 7"66 m M ; 2-0 m M ~< CL ~< 12'5 m M ) experimental data can be explained for the a l u m i n u m diglycolate ( D G 2-) with the formation of two m o n o n u c l e a r complexes and for the a l u m i n u m thiodiglycolate ( T D G 2-) with the formation of a I :1 c o m p l e x and a mixed c o m p l e x with O H - , according to the equilibria: A I 3 + + D G 2- ~ A I D G + AI 3+ + 2 D G 2- ~ AI(DG)2AI a+ + T D G z- ~ A I T D G + AI3++OH-+TDG2~ AIOHTDG
log/3~ = 3.16_+0.012 log/3z = 5'25 -+ 0.02 log 131 = 1.93 -+ 0.08 Iog/3n -- 12"34-+0'05.
SYMBOLS CM~-~
C H -~ C L -~
K n -~
total concentration of aluminum ions total concentration of hydrogen ion total concentration of ligand over-all stability constant of the complex species AIL~ over-all stability constant of the species AI(OH)nLi stepwise protonation constant of the acid species HnL.
Tins report deals with the species formed in aqueous solutions containing aluminum ions and diglycolic and thiodiglycolic acids (H2DG and H~TDG) and with the calculation of the stability constants of the complexes found. Investigation was carried out at 25°C in a 0.5 M medium (using sodium perchlorate as neutral salt). Measurements were performed by a potentiometric method measuring the hydrogen ion concentration with a glass electrode. EXPERIMENTAL Materials
Acids were recrystallized from water, dried at i 15°C and c h e c k e d by potentiometric titrations. T h e solutions of the titrant had the following composition: [Na +] = 0"5 M
[L 2-] = 0"050 M L 2- = acid anion.
O t h e r solutions were prepared as previously described [ 1]. I. A, Napoli, Talanta 5, 189 (1968). *Work carried out with the C N R aid. 1225
[ClO4-] = 0.4 M
1226
A. N A P O L I
Apparatus All emf measurements were performed at 25.0---0-I°(2 with a Radiometer valve potentiometer PHM4, a Thalamid glass electrode being used. The Wilhelm type half-cell, similar to that described by Forsling, Hietanen and Sill/m [2l was used: Ag, AgCI{NaCI 0.01 M, NaCIO4 0.49 M INaC104 0.50 M. The Ag,AgCl electrode was prepared as recommended by Brown [3]. According to Biedermann and Sill~n [4] the e m f o f the cell at 25°(2, in mV units, may be written as: E = E°+59-16 log [H +] + Es
(i)
where E ° is a constant and E j is the liquid junction potential given by J [ H ÷] ( = - 100[H +] mV under our experimental conditions). E ° was determined before and after each titration and later, from emf measurements, [H +] was derived from Equation (1), while [OH-] was calculated from: - log [H +] - log [OH-] = p ( Kw )c
(2)
where p (Kw)c is 13.73 at 25°C in 0"5 M NaCIO4 [5]. The emf measurements were repeated until two successive values agreed to within 0.1 mV. Titrations were performed by the Leden procedure [6]; the total concentrations of the metal and hydrogen ions were kept constant, while the ligand concentration was progressively increased from 2-0 to 12'5 mM. Air in the titration vessel was replaced by nitrogen, free from carbon dioxide, passed through 0'5 M NaCIO4. Calculations were carried out on a U N I V A C 1108 computer. RESULTS
Investigation was carried out at various total concentrations of metal and hydrogen ions in order to check the presence of polynuclear or mixed complexes. Measurements were carried out in a medium sufficiently acidic to minimize the hydrolysis of aluminum ions [7]. The concentration of the free ligand and the average number of ligands can be calculated from the relationships:
[L z-] = (Cu - [H +1) / (K1 [H +] + 2K1Kz [H +]2 )
(3)
t / = (CL -- [L 2-1 -- K1 [L2-][H +1 -- K~K2[L2-I[H+] z )/Cu.
(4)
If the formation function is found to be independent of C , no hydrolytic equilibria occur in solution. If ~ is independent of Cu polynuclear reactions can be ignored and only mononuclear complexes should exist in solution.
.4 luminum-diglycolic acid system Formation function for aluminum diglycolic acid system, h vs --log [DG2-], is plotted in Fig. I. The experimental points fall on the same curve for all C , and Cu values. This means that in the chosen concentration ranges (2.55 mM ~< C~ ~< 7.66 mM; 5.15 mM ~ Cn ~ 12.87 mM) polynuclear and mixed complexes are negligible. 2. 3. 4. 5. 6. 7.
W, Forsling, S. Hietanen and L. G. Sill~n, Acta chem. scand. 6, 901 (1952). A. S. Brown, J. Am. chem. Soc. 56, 646 (i 934). G. Biedermann and L. G. Sill~n, Ark. K e m i 5 , 425 (1953). G. Lagestrom, Acta chem. scand. 13, 722 (1959). I. Leden, Thesis, Lund (1943). J. Aveston, J. chem. Soc. 4438 (1965).
Aluminum complexes
1227
7'5 CM •
o a
CH (raM) 5.11 5'15 5.11 12"87 7"66 7"72
.~/
/
1"0_
05
00
----~'~1
50
I
~0
3O og ~D5~7 2"0
Fig. 1. Formation function of aluminum diglycolic acid system. Full curve calculated from the equilibrium constants obtained in this work: log/3, = 3.16; log/3..,= 5.25. By applying the graphical method described by Sill~n[8], the values of the formation constants can be obtained. Such values, refined by a computing minimization method [9], are: log/3, = 3.16___0.012
log fl,, = 5-25 ___0.02.
Aluminum thiodiglycolic acid system In Fig. 2 is shown the formation function of the aluminum thiodiglycolic acid system. By varying Cn the experimental points fall on different curves and, since t~ decreases on increasing CH, mixed complexes with O H - are certainly present in solution. Also, since the formation function is independent on CM, polynuclear complexes are negligible. The maximum value of t~ is less than 0-5, so probably only 1:1 complexes exist in solution. According to this hypothesis, a plot of { h / ( l - ~ ) [ T D G 2 - ] } must be independent of [ T D G 2-] and only a function of [OH-I: ( 1 -- h) [ T D G 2-] =
+
z.p,.
/[OH-] i
A plot of ~/(1 - h ) [ T D G z-] vs [ O H - ] is given in Fig. 3. All the points fall on a single straight line with positive intercept on the Y axis. This means that only two complexes seem to be predominant in solution, with the simplified formulas A 1 T D G + and A I O H T D G . T h e stability constants of the complexes found can be calculated from the slope and the intercept of this curve, but these values are only approximate because a was derived in Equation (4) on the assumption that 8, L. G. Sill~n, Acta chem. scand. 10, 186 (1956). 9. W. R. Busing and H. A. Levy, O R N L TM-271 (1962).
1228
A. NAPOL1
0"5 h 0"4 0"3 0"2
• o • A
C~'m IV) CH 7.66 7.72 4.94 12.87 5.12 7.60 2"56 10"15
0
I
n
0
0
5.1:1o.15
o
0'I
EIAO 0.0 • 40
OA
I
I
30
-,o [ToG-ff
2.5
Fig. 2. Formation function of aluminum thiodiglycolic acid system.
5.10 =
$1 SJS -"
I
ss S
0
0-0
I 05
1.0
[OH'].IO '° Fig. 3. Aluminum thiodiglycolic acid system. Symbols are the same of Fig. 2.
neither mixed nor polynuclear complexes are present in solution. To obtain the correct values of the stability constants, the following equations can be written, assuming the AITDG ÷ and A I O H T D G complexes are present (charges are omitted): CM = [AI] + [AITDG] + [AIOHTDG]
(5)
CL = [H2TDG] + [HTDG] + [TDG] + [AITDG] + [AIOHTDG] Ch, = 2[H2TDG] + [HTDG] + [H] -- [OH] - [A1OHTDG]
(6) (7)
/31 = [AITDG]/[AI][TDG] ~tl = [AIOHTDG]/[AI][OH][TDG] K1 = [HTDG]/[H][TDG] KIK~ = [H2TDG]/[H]2[TDG].
(8) (9) (10)
Aluminum complexes
1229
If a = 1 + KI[H] + K1 K2 [H] 2, from Equations (5, 6 and I 0) we obtain: [AI] = C M - C t . + a [ T D G ] .
(11)
By combining Equations (7, 9 and 10) ( [ O H - ] is negligible in the acid range): flH =
( K I [ H ] [ T D G ] + 2KIK2[H]2[TDG]+[H]--Cn)/[AI][OH][TDG] •
(12)
F r o m Equations (6, 7 and 11 ): f l l a [ T D G ] 2 + (KI[H] + 2KIK2 [H] 2+ or+
CM~ 1 -- Cl.fll
)
× [TDG] + [H] - CL -- CH = 0.
( 13)
If/31 is known, Equation (1 3) allows a calculation of the correct value of [TDG] and Equation (I 2) the value of/3H. Table 1. Aluminum-thiodiglycolic acid system. T = 25°C, NaCIO4 0.5 M Experimental data: --log [H+]; --log [ T D G 2 - ] * ; 1311 × 10 - ~ M-'-' (fl~ = 85 M - 1 ) CM=7.66mM 3.177 3-263 3.331 3.380 3.417 3.448 3.483
CH=7.72mM 3.42 3.27 3-15 3-07 3.00 2.95 2.89
CM = 4.94 m M 3.017 3,148 3.241 3.309 3.363 3-407 3.453 3.488
C,= 3.47 3.24 3.08 2.97 2.88 2.81 2.73 2-68
2.20 2.22 2.11 2.14 2.22 2.28 2-10
12-87 m M 2"41 2"36 2.19 2.15 2,05 1,96 1,84 1,81
CM=5-12mM 2,732 2,897 3,031 3,133 3,207 3.371 3-439
*Calculated from Equation ( 13).
4.13 3-81 3.56 3-38 3.24 2.97 2.86
CM = 5"12 m M 2.909 3-092 3.221 3.314 3.380 3.443
CM = 2'56 m M
M e a n value: /311 = (2"16+-0"26) × 1012M -z
C,=I0.15mM
2.910 3.050 3.163 3.250 3'319 3.443
2.49 2.47 2.19 2.35 2.46 1.96 1.92
Cn = 7'60 m M 3.93 3-58 3.36 3-20 3.08 2.98
2.57 2-29 2-28 2-21 2.30 2.00
C~1 = 10.15 m M 3'78 3'52 3-32 3" 18 3.06 2'87
1.83 2'54 2'05 2' 14 2.14 1"22
1230
A. N A P O L I
Then/311 was calculated for a set of/31 values near the approximate value. The standard deviation o- corresponding to/311 for each/31 value was minimized by an original computation programme and the best values of the constants were deduced: log/31--- 1.93___0.08 log f l l l = 12.34±0.05. The experimental data are reported in Table 1 corresponding to the best value
of/31Protonation constants of the acids Protonation constants of the acids were determined at 25°C in 0.5 M NaCIO4 by potentiometric titrations, using the formation function: aL = (CH-- [H] + [OH] )/CL.
The constants were calculated by the minimization method mentioned above [9]. The formation functions for diglycolic and thiodiglycolic acids are plotted in Figs. 4 and 5 respectively. The obtained values, together with the formation constants of the complexes found are reported in Table 2. DISCUSSION
At - l o g [H +] < 3.5 and in the investigated concentration ranges (2.56 mM ~< C~ ~ 7.66 raM; 2.0 m M <~ CL ~< 12.5 raM) aluminum ion forms with diglycolic 2.0 CL (raM)
& o
•
1.0
~9.80 37.30
/
i
0"0
5.0
I
+o
s.O_~ogCH:! 2.o
Fig. 4. Formation function of diglycolic acid. Full curve calculated with the protonation constants obtained in this work: log K1 = 3.76; log K1K2 = 6.56.
Aluminum complexes
1231
20 Ct (raM) nL
o
5000
~z
15
7.0
0.5
0.0 50
I ~0
I 3.0
2"0 - Iog ~H*_7
F i g . 5. Formation function of thiodiglycolic acid. Full curve calculated with the protnnation constants obtained in this work: log K~ = 4 . 0 3 ; log K~ K._, = 7.13.
Table 2. Stability constants of aluminum complexes. T = 2 5 ° C , N a C I O 4 0.5 M
Diglycolic acid
Thiodiglycolic acid
log K1 = 3.76 ___0-01 log K I K 2 = 6-56___0-01 log/3~ = 3.t6___0-012 log/32 = 5.25 ± 0 . 0 2
l o g K t = 4-03 _ 0.01 log K I K 2 = 7 . 1 3 ± 0 . 0 1 log/3l = 1 . 9 3 ± 0 . 0 8 l o g / 3 ~ = 12-34 ± 0.05
acid two different mononuclear complexes with 1 : 1 and 1 : 2 metal:ligand molar ratios. With thiodiglycolic acid only the 1:1 complex can be found, the stability constant of which is lower than that of the corresponding complex with diglycolic acid. Furthermore, a hydrolytic complex, with the simplified formula AIOHTDG. is found. This fact could be explained by the lower affinity of the sulfur atom towards the aluminum ion. Probably stable five-membered rings in the chelate are not formed and hydrolytic phenomena are favored.
ALUMINUM
Pergamon Press. Printed in Great Britain
COMPLEXES WITH DIGLYCOLIC THIODIGLYCOLIC ACIDS*
AND
ALDO NAPOLI Istituto di C h i m i c a Analitica, Universith di R o m a (Received 9 August 1971 )
A b s t r a c t - C o m p l e x e s formation b e t w e e n a l u m i n u m ions and diglycolic and thiodiglycolic acids was studied at 25°C in 0"5 M N a C I O , by potentiometric m e a s u r e m e n t s . In the investigated concentration ranges (--log IH+I < 3-5; 2.55 m M ~< CM ~< 7"66 m M ; 2-0 m M ~< CL ~< 12'5 m M ) experimental data can be explained for the a l u m i n u m diglycolate ( D G 2-) with the formation of two m o n o n u c l e a r complexes and for the a l u m i n u m thiodiglycolate ( T D G 2-) with the formation of a I :1 c o m p l e x and a mixed c o m p l e x with O H - , according to the equilibria: A I 3 + + D G 2- ~ A I D G + AI 3+ + 2 D G 2- ~ AI(DG)2AI a+ + T D G z- ~ A I T D G + AI3++OH-+TDG2~ AIOHTDG
log/3~ = 3.16_+0.012 log/3z = 5'25 -+ 0.02 log 131 = 1.93 -+ 0.08 Iog/3n -- 12"34-+0'05.
SYMBOLS CM~-~
C H -~ C L -~
K n -~
total concentration of aluminum ions total concentration of hydrogen ion total concentration of ligand over-all stability constant of the complex species AIL~ over-all stability constant of the species AI(OH)nLi stepwise protonation constant of the acid species HnL.
Tins report deals with the species formed in aqueous solutions containing aluminum ions and diglycolic and thiodiglycolic acids (H2DG and H~TDG) and with the calculation of the stability constants of the complexes found. Investigation was carried out at 25°C in a 0.5 M medium (using sodium perchlorate as neutral salt). Measurements were performed by a potentiometric method measuring the hydrogen ion concentration with a glass electrode. EXPERIMENTAL Materials
Acids were recrystallized from water, dried at i 15°C and c h e c k e d by potentiometric titrations. T h e solutions of the titrant had the following composition: [Na +] = 0"5 M
[L 2-] = 0"050 M L 2- = acid anion.
O t h e r solutions were prepared as previously described [ 1]. I. A, Napoli, Talanta 5, 189 (1968). *Work carried out with the C N R aid. 1225
[ClO4-] = 0.4 M
1226
A. N A P O L I
Apparatus All emf measurements were performed at 25.0---0-I°(2 with a Radiometer valve potentiometer PHM4, a Thalamid glass electrode being used. The Wilhelm type half-cell, similar to that described by Forsling, Hietanen and Sill/m [2l was used: Ag, AgCI{NaCI 0.01 M, NaCIO4 0.49 M INaC104 0.50 M. The Ag,AgCl electrode was prepared as recommended by Brown [3]. According to Biedermann and Sill~n [4] the e m f o f the cell at 25°(2, in mV units, may be written as: E = E°+59-16 log [H +] + Es
(i)
where E ° is a constant and E j is the liquid junction potential given by J [ H ÷] ( = - 100[H +] mV under our experimental conditions). E ° was determined before and after each titration and later, from emf measurements, [H +] was derived from Equation (1), while [OH-] was calculated from: - log [H +] - log [OH-] = p ( Kw )c
(2)
where p (Kw)c is 13.73 at 25°C in 0"5 M NaCIO4 [5]. The emf measurements were repeated until two successive values agreed to within 0.1 mV. Titrations were performed by the Leden procedure [6]; the total concentrations of the metal and hydrogen ions were kept constant, while the ligand concentration was progressively increased from 2-0 to 12'5 mM. Air in the titration vessel was replaced by nitrogen, free from carbon dioxide, passed through 0'5 M NaCIO4. Calculations were carried out on a U N I V A C 1108 computer. RESULTS
Investigation was carried out at various total concentrations of metal and hydrogen ions in order to check the presence of polynuclear or mixed complexes. Measurements were carried out in a medium sufficiently acidic to minimize the hydrolysis of aluminum ions [7]. The concentration of the free ligand and the average number of ligands can be calculated from the relationships:
[L z-] = (Cu - [H +1) / (K1 [H +] + 2K1Kz [H +]2 )
(3)
t / = (CL -- [L 2-1 -- K1 [L2-][H +1 -- K~K2[L2-I[H+] z )/Cu.
(4)
If the formation function is found to be independent of C , no hydrolytic equilibria occur in solution. If ~ is independent of Cu polynuclear reactions can be ignored and only mononuclear complexes should exist in solution.
.4 luminum-diglycolic acid system Formation function for aluminum diglycolic acid system, h vs --log [DG2-], is plotted in Fig. I. The experimental points fall on the same curve for all C , and Cu values. This means that in the chosen concentration ranges (2.55 mM ~< C~ ~< 7.66 mM; 5.15 mM ~ Cn ~ 12.87 mM) polynuclear and mixed complexes are negligible. 2. 3. 4. 5. 6. 7.
W, Forsling, S. Hietanen and L. G. Sill~n, Acta chem. scand. 6, 901 (1952). A. S. Brown, J. Am. chem. Soc. 56, 646 (i 934). G. Biedermann and L. G. Sill~n, Ark. K e m i 5 , 425 (1953). G. Lagestrom, Acta chem. scand. 13, 722 (1959). I. Leden, Thesis, Lund (1943). J. Aveston, J. chem. Soc. 4438 (1965).
Aluminum complexes
1227
7'5 CM •
o a
CH (raM) 5.11 5'15 5.11 12"87 7"66 7"72
.~/
/
1"0_
05
00
----~'~1
50
I
~0
3O og ~D5~7 2"0
Fig. 1. Formation function of aluminum diglycolic acid system. Full curve calculated from the equilibrium constants obtained in this work: log/3, = 3.16; log/3..,= 5.25. By applying the graphical method described by Sill~n[8], the values of the formation constants can be obtained. Such values, refined by a computing minimization method [9], are: log/3, = 3.16___0.012
log fl,, = 5-25 ___0.02.
Aluminum thiodiglycolic acid system In Fig. 2 is shown the formation function of the aluminum thiodiglycolic acid system. By varying Cn the experimental points fall on different curves and, since t~ decreases on increasing CH, mixed complexes with O H - are certainly present in solution. Also, since the formation function is independent on CM, polynuclear complexes are negligible. The maximum value of t~ is less than 0-5, so probably only 1:1 complexes exist in solution. According to this hypothesis, a plot of { h / ( l - ~ ) [ T D G 2 - ] } must be independent of [ T D G 2-] and only a function of [OH-I: ( 1 -- h) [ T D G 2-] =
+
z.p,.
/[OH-] i
A plot of ~/(1 - h ) [ T D G z-] vs [ O H - ] is given in Fig. 3. All the points fall on a single straight line with positive intercept on the Y axis. This means that only two complexes seem to be predominant in solution, with the simplified formulas A 1 T D G + and A I O H T D G . T h e stability constants of the complexes found can be calculated from the slope and the intercept of this curve, but these values are only approximate because a was derived in Equation (4) on the assumption that 8, L. G. Sill~n, Acta chem. scand. 10, 186 (1956). 9. W. R. Busing and H. A. Levy, O R N L TM-271 (1962).
1228
A. NAPOL1
0"5 h 0"4 0"3 0"2
• o • A
C~'m IV) CH 7.66 7.72 4.94 12.87 5.12 7.60 2"56 10"15
0
I
n
0
0
5.1:1o.15
o
0'I
EIAO 0.0 • 40
OA
I
I
30
-,o [ToG-ff
2.5
Fig. 2. Formation function of aluminum thiodiglycolic acid system.
5.10 =
$1 SJS -"
I
ss S
0
0-0
I 05
1.0
[OH'].IO '° Fig. 3. Aluminum thiodiglycolic acid system. Symbols are the same of Fig. 2.
neither mixed nor polynuclear complexes are present in solution. To obtain the correct values of the stability constants, the following equations can be written, assuming the AITDG ÷ and A I O H T D G complexes are present (charges are omitted): CM = [AI] + [AITDG] + [AIOHTDG]
(5)
CL = [H2TDG] + [HTDG] + [TDG] + [AITDG] + [AIOHTDG] Ch, = 2[H2TDG] + [HTDG] + [H] -- [OH] - [A1OHTDG]
(6) (7)
/31 = [AITDG]/[AI][TDG] ~tl = [AIOHTDG]/[AI][OH][TDG] K1 = [HTDG]/[H][TDG] KIK~ = [H2TDG]/[H]2[TDG].
(8) (9) (10)
Aluminum complexes
1229
If a = 1 + KI[H] + K1 K2 [H] 2, from Equations (5, 6 and I 0) we obtain: [AI] = C M - C t . + a [ T D G ] .
(11)
By combining Equations (7, 9 and 10) ( [ O H - ] is negligible in the acid range): flH =
( K I [ H ] [ T D G ] + 2KIK2[H]2[TDG]+[H]--Cn)/[AI][OH][TDG] •
(12)
F r o m Equations (6, 7 and 11 ): f l l a [ T D G ] 2 + (KI[H] + 2KIK2 [H] 2+ or+
CM~ 1 -- Cl.fll
)
× [TDG] + [H] - CL -- CH = 0.
( 13)
If/31 is known, Equation (1 3) allows a calculation of the correct value of [TDG] and Equation (I 2) the value of/3H. Table 1. Aluminum-thiodiglycolic acid system. T = 25°C, NaCIO4 0.5 M Experimental data: --log [H+]; --log [ T D G 2 - ] * ; 1311 × 10 - ~ M-'-' (fl~ = 85 M - 1 ) CM=7.66mM 3.177 3-263 3.331 3.380 3.417 3.448 3.483
CH=7.72mM 3.42 3.27 3-15 3-07 3.00 2.95 2.89
CM = 4.94 m M 3.017 3,148 3.241 3.309 3.363 3-407 3.453 3.488
C,= 3.47 3.24 3.08 2.97 2.88 2.81 2.73 2-68
2.20 2.22 2.11 2.14 2.22 2.28 2-10
12-87 m M 2"41 2"36 2.19 2.15 2,05 1,96 1,84 1,81
CM=5-12mM 2,732 2,897 3,031 3,133 3,207 3.371 3-439
*Calculated from Equation ( 13).
4.13 3-81 3.56 3-38 3.24 2.97 2.86
CM = 5"12 m M 2.909 3-092 3.221 3.314 3.380 3.443
CM = 2'56 m M
M e a n value: /311 = (2"16+-0"26) × 1012M -z
C,=I0.15mM
2.910 3.050 3.163 3.250 3'319 3.443
2.49 2.47 2.19 2.35 2.46 1.96 1.92
Cn = 7'60 m M 3.93 3-58 3.36 3-20 3.08 2.98
2.57 2-29 2-28 2-21 2.30 2.00
C~1 = 10.15 m M 3'78 3'52 3-32 3" 18 3.06 2'87
1.83 2'54 2'05 2' 14 2.14 1"22
1230
A. N A P O L I
Then/311 was calculated for a set of/31 values near the approximate value. The standard deviation o- corresponding to/311 for each/31 value was minimized by an original computation programme and the best values of the constants were deduced: log/31--- 1.93___0.08 log f l l l = 12.34±0.05. The experimental data are reported in Table 1 corresponding to the best value
of/31Protonation constants of the acids Protonation constants of the acids were determined at 25°C in 0.5 M NaCIO4 by potentiometric titrations, using the formation function: aL = (CH-- [H] + [OH] )/CL.
The constants were calculated by the minimization method mentioned above [9]. The formation functions for diglycolic and thiodiglycolic acids are plotted in Figs. 4 and 5 respectively. The obtained values, together with the formation constants of the complexes found are reported in Table 2. DISCUSSION
At - l o g [H +] < 3.5 and in the investigated concentration ranges (2.56 mM ~< C~ ~ 7.66 raM; 2.0 m M <~ CL ~< 12.5 raM) aluminum ion forms with diglycolic 2.0 CL (raM)
& o
•
1.0
~9.80 37.30
/
i
0"0
5.0
I
+o
s.O_~ogCH:! 2.o
Fig. 4. Formation function of diglycolic acid. Full curve calculated with the protonation constants obtained in this work: log K1 = 3.76; log K1K2 = 6.56.
Aluminum complexes
1231
20 Ct (raM) nL
o
5000
~z
15
7.0
0.5
0.0 50
I ~0
I 3.0
2"0 - Iog ~H*_7
F i g . 5. Formation function of thiodiglycolic acid. Full curve calculated with the protnnation constants obtained in this work: log K~ = 4 . 0 3 ; log K~ K._, = 7.13.
Table 2. Stability constants of aluminum complexes. T = 2 5 ° C , N a C I O 4 0.5 M
Diglycolic acid
Thiodiglycolic acid
log K1 = 3.76 ___0-01 log K I K 2 = 6-56___0-01 log/3~ = 3.t6___0-012 log/32 = 5.25 ± 0 . 0 2
l o g K t = 4-03 _ 0.01 log K I K 2 = 7 . 1 3 ± 0 . 0 1 log/3l = 1 . 9 3 ± 0 . 0 8 l o g / 3 ~ = 12-34 ± 0.05
acid two different mononuclear complexes with 1 : 1 and 1 : 2 metal:ligand molar ratios. With thiodiglycolic acid only the 1:1 complex can be found, the stability constant of which is lower than that of the corresponding complex with diglycolic acid. Furthermore, a hydrolytic complex, with the simplified formula AIOHTDG. is found. This fact could be explained by the lower affinity of the sulfur atom towards the aluminum ion. Probably stable five-membered rings in the chelate are not formed and hydrolytic phenomena are favored.