sample solution can be evaluated and the amount of chromium in the ruby sample calculated. The results obtained by spectrophotometric and polarographic methods for different ruby samples are listed in Table 11. When the polarographic method is applied to a ruby sample after converting its chromic oxide into chromate by fusion and then estimating it polarographically, the results obtained are in
reasonable agreement with those obtained by chemical methods. ACKNOWLEDGMENT
The author expresses deep gratitude to Kartar Singh, director, for suggesting the problem and his keen interest during the progress of the work and H. K. Acharya, assistant director, for providing the necessary facilities.
LITERATURE CITED
(1) Chirnside, R. C., Cluley, H. J., Powell, R. J., Profitt, P. M.C., Analyst 88, 851 (1963). (2) Dodson, E. M., ANAL.CHEM.34, 966 (1962). (3) Lingane, J. J., Kolthoff, I. M., J. Am. Chem. SOC.62, 852 (1940). (4) Verneuil, M. A,, Ann. Chim. Phys. 3, 20 (1904). S. S. SINGH
Chemistry Division Defence Science Laboratory Metcalfe House, Delhi-6 India
otentiometric Determination of Stabilities of Molybdenum(VI) ungste n (VI) Chelates SIR: Although hexavalent molybdenum and tungsten coordinate with a great number of ligands, only limited stability data exist for such complexes. Recent work in this laboratory on the structural and bonding characteristics of various Mo(V1)-aminopolycarboxylic acid complexes has led t o the evaluation of stability constants from proton nuclear magnetic resonance (K'MR) data (9, 3 ) . These studies have suggested the possibility of using potentiometric pH titration techniques to measure the stabilities of Mo(V1) and W(VI) complexes. One advantage of using potentiometric methods is that the solution ionic strength may be kept low and constant, a condition not possible using NMR techniques because of the high concentrations required. The ligand systems which have been studied are iminodiacetic acid (IDA), N-methyliminodiacetic acid (MIDA), nitrilotriacetic acid (NTA), and (ethylenedinitrilo) tetraacetic acid (EDTA). Comparisons are made of the potentiometrically determined constants among the ligands and between Mo(V1) and W(VI). These constants are also compared to those determined by NMR methods. I n the usual potentiometric method for evaluating metal-ligand stability constants, the competition between metal ion and hydrogen ion for the ligand is studied, and the pH region of interest is from about 1 to 5 (6). In the i\Io(VI) and W(V1) (hereafter indicated as just Mo and W) systems, however, the complication of metal polymerization is introduced in acidic solutions. Because the polymerization equilibria are not well understood, this pH region is not useful for stability determinations. In more alkaline solutions, on the other hand, a pH-dependent process involving the competition between molybdate or tungstate formation and metal-ligand complexation-Le., a competition between ON- and ligand for the metal ion-can be utilized. This process was
determined from the NMR studies to be important from about pH 6 t o 9 and can be represented by
where M represents either 310or W and L represents the aminopolycarboxylic acid ligand. I n the pH region above 6 no evidence was found for any Mo species containing fewer than three oxygen atoms-e.g., Mo02'2-as has been proposed for other systems (8). The molybdenum coordinating species in all the aminopolycarboxylic acid systems above pH 6 is Mo03, and by analogy we have assumed that the corresponding coordinating unit in the tungsten systems is WOa. EXPERIMENTAL
Reagents. Analytical reagent grade sodium tungstate dihydrate and molybdenum trioxide were used without purification. N-methyliniinodiacetic acid (Aldrich Chemical Co.) (ethylenedinitrilo)tetraacetic acid (Baker Chemical Co.), and nitrilotriacetic acid (Eastman Organics) were also used as received. Disodium iminodiacetate (Aldrich Chemical Go.) was twice recrystallized from aqueous solution before use. Stock solutions of 0.010M KTA and MIDA and of 0.150M Ka2TV04 were prepared determinately. A diacid solution (0.010M) of IDA was prepared by titrating a solution of disodium iminodiacetate with HC1. EDTA solutions were prepared by dissolving the requisite amounts of the solid metal chelates, Na4(Mo03)zEDTA.8Hz0 and Na4(W03)2EDTA.8Hz0,synthesized by the method outlined previously (4). Stock 0.150M Kzhf004 was prepared by titrating a slurry of MOO3 with KOH. A 1.OM KN03 solution was prepared using reagent grade KNOa which had been twice recrystallized from water. All solutions were made up with triply distilled water which was degassed with Nz before use. Potentiometric Titrations. Solutions to be titrated were 1.00 X 10-3M
in ligand, 0.0150M in metal (&$f.004 ) , 0.10X in KN03. The or N ~ ~ W O Iand titrant was 0.0931M KOH prepared from a 45% Cos-free KOH solution. The solutions for titration of the free ligands for determination of the acid dissociation constants mere 1.00 x 10-aM in ligand and 0.10M in KNOa. The solution p H was monitored a8 KOH was added using either a Corning Model 12 or a Leeds and Northrup line-operated pH meter, standardized before and after each titration with saturated potassium acid tartrate (pH 3.66) and 0.01X sodium borate ~ D H 9.18). All work was carried ou< a t 25 f 0.5' C. Equilibrium Calculations. The method used for determining the acid dissociation constants of the protonated ligands was exactly analogous to that outlined by Schwarzenbach (6). The method for calculating the metalligand formation constants was similar to that outlined for metal-EDTA titrations (6),but was modified to take into account the different species present. For the IDA, MIDA, and NTA ligand systems, NMR studies indicate that only one metal-ligand species exists above pH 6, MOIL-.. The following equations and equilibria were considered in the IDA and MIDA systems:
+
+ L-' + HzO; K f
~1fo4-~ 2H+
MO&-2
HL-
s H*
+ L-2;
K, =
3
12.0
t
-,_,-
I
7-01
---_ I D A
I
I
MD-IDA W-IDA
APPARENT
Kf
APPARENT K f
1.0 -
0.0. 0.0
1
I
I
I
I
I .o
0.5
I
I .5
b I
I
,
0.5
I .O
1.5
Figure 2. Calculated formation constant as a function of b a s e a d d e d for Mo and W with iminodiacetate 28
b
Figure 1 .
pH titration curves for the iminodiacetate system
HzlDA = 1.00 X 1OmsM KNOs = 0.1OM MOO^-^ and W04-2 = 0.01 5M moles OH- added b = moles HzlDA Solution conditions:
where illt = total metal concentration in all solution forms; L t = total ligand concentration in all solution forms; b = moles OH- added/moles Lt. Combining these expressions, neglecting small terms, and assuming A f t remains constant, one obtains:
where
The corresponding expression derived for the NTA system is:
Kf
=
IMO~L-~J
=
[iM04-'] [H+]'[L-a]
+
[H+](2 - b) Ka(3 - b) Mt (b - 1)[H'I2 Ka
(8)
From the experimental titration curves [H+]and b values are obtained and K f is computed at varying b values. The calculations for the EDTA systems are similar but somewhat more involved because more metal-ligand species are formed. From the NLfR data M03EDTA-4, M03HEDTA-3, and (L1103)2EDTA-4 are known to exist (5). The resulting expression for these systems is: (b
- 4)KS + (b - 3) [H+l Kf bil.It'[Hf]4 KaKjz
+
+
+
Expression 9 is of the form P/Kf QKD R / K s = S. From the titration curves, values of b and [H+] are used to calculate P , Q, R , and S, giving a series of linear equations in three unknowns (Kf, K f z ,and K3). Suitable sets of three equations are selected and the constants are determined by diagonalization of the 3 x 3 matrix. All computations were carried out on a CDC 1604 computer.
+
RESULTS
The types of titration curves obtained in this investigation are illustrated in Figure 3. by the IDA system. The region from b = 0 t o 1 is apparently that portion of the titration in which the complex is being consumed, whereas from b = 1 to 2 the curves are nearly identical to the titration of free HIDAwith OH-. These results are in qualita-
tive agreement with the NMR results which indicate that from b = 1 to 2 the complexed form of the ligand is virtually nonexistent. The relatively flat pH profile for W a t low b values (b = 0 to 0.6) suggests that an additional factor must also be considered. This behavior is the result of tungstate polymerization in competition with metal-chelate formation, caused by the l&fold excess of metal over ligand. Thus, the first additions of base result in titration of the polymeric metal ions rather than titration of the complex. This situation causes little difficulty in the Mo systems because polymerization is not prevalent above about pH 6.5, but for the W systems polymerization is important up to about pH 7.4. The effect of this complication on the quantitative calculations can be seen in Figure 2 where the formation constants, calculated from Equation 7, have been plotted as a function of b for the IDA system. At low b values the calculated K, is changing rapidly because polymerization has not been included in the formation constant derivation. At higher b values (less than b = 1) K, approaches a constant value which we have ascribed to the apparent K I of the complex. Above b = 1 the calculated values again change rapidly because virtually all the complex has been consumed. The same behavior has been observed in the LIIDA and NTA systems where the linear portion of the calculated K , us. b curve is taken as the apparent K,. The calculated K f values are presented in Table I, along with the range of the values determined in the region where K f becomes constant. Similar considerations apply to the EDTA systems, but in the Mo case the VOL. 38, NO. 13, DECEMBER 1966
e
1935
Table 1.
Calculated Equilibrium Constants0
n,io Ligand IDA R’IIDA
PIC, 9.52 f 0.02 9.73 f 0.06
log K f b
Table I!.
pH Independent Equilibrium
log Kfn
pK3
W log Kfz
log K f
PKs
18.3 f 0.1 18.73 i 0.04 (18.2 f 0.3) 18.94 f 0.03 (18.90 i 0.08) 18.6 f 0 . 4 (18.5 f 0 . 3 )
18.5 f 0 . 2 18.70 f 0.01 (18.6 f 0 . 2 ) NTA 9.81 f 0.10 18.86 f 0.05 (19.1 f 0.2) EDTA 10.2 f 0 . 1 17.5i0.3 8.1 =t 0 . 4 18.9 3z 0 . 4 16.9 i: 0 . 2 (17.2 i 0 . 2 ) (7.5 =t 0 . 2 ) (18.7 i 0.3) (16.7 i 0 . 3 ) (7.5 f 0.2) a Potentiometricall determined constants at ionic strength = 0.15MJ T = 25”. b NMRdeterminelconstants are in parentheses (ionic strength ranges from 1.0 to 2 3 M , T = 35”). Estimated errors are giver1 as the range of calculated values.
Constants
nr 0 Ligand IDA MIDA NTA EDTA
lo!$
w loq
Kf
10.5 10.9 11.1 10.8
k‘fz
log Kf’
log Kfz’
9.7
10.4 10.6 10.8 10.8
8.8
useful b range is from about 0.2 to 3. This enables a wide selection of b values for solving K f , K f 2 ,and K3 from the simultaneous equations and, even though the contribution from the K 3 term is small, a meaningful value of this constant can be determined. I n the case of TV, however, the b range is limited from about b = 2 to 3. As a consequence the small contribution from the K 3term cannot be detected and only K f and Kfz may be evaluated with any accuracy. For both M o and W with IDA, MIDA, and EDTA the reaction of complex with the added base was fairly rapid, pH equilibrium being established within 10 minutes. For the Rlo and W-NTA systems, however, up to 1.5 hours were required to achieve equilibrium after each addition of base. DISCUSSION
This study indicates the feasibility of using potentiometric techniques for stability measurements of Mo(V1) and W(V1) chelates. The results obtained by this method are comparable to those obtained by NMR methods, but have the advantage of maintaining low ionic strength conditions. Furthermore, the method is not confined to systems in which the ligand exchange rate is slow. Using the potentiometric technique, results obtained for simple one to one metal-ligand chelates are more precise than for higher complexes, such as those formed with EDTA. In fact, for the multicomplex systems the NMR data are probably more reliable than the potentiometric data as indicated by the range of calculated values for the EDTA systems. A comparison of the formation 6
ANALYTICAL CHEMISTRY
constants shows that within experimental error there is essentially no difference between the stabilities of the corresponding Rlo and JV chelates. This does not seem too surprising in view of the similarities of the two ions and their nearly equal ionic radii ( 1 ) . However, N3lR work currently in progress does show that the 14’ chelates are significantly more labile with respect to individual metal-ligand bonds than are the Mo chelates. Perhaps a better stability correlation may be expected if the pH dependence of the formation constants were eliminated. This may be accomplished by combining the pHdependent formation constants with the acid dissociation constants of molybdic and tungstic acids obtained by Schwarzenbach (7):
2H+
+ RIo04-2 g
cally. Due to the uncertainty in the potentiometric results, this factor cannot be substantiated in the present investigation. There is little question that the first metal ion is bound more strongly to EDTA than is the second. This difference in stabilities and the decrease of the dissociation constants, K3, compared to K , for EDTA were noted previously (3) and seem to be the result of either an inductive or a steric influence from the first X03group. The slowness with which pH equilibrium was attained in the NTA chelates may be explained by the higher negative charge of this complex compared to the other complexes and the subsequently slower reaction with OH-:
+ OH- $2
A110sNTA-3
M04-2
HzhI004; K y , = lO’*’
2H’
+ T’VOI-’
e H2WO4; KTV= lo8*’
Then, assuming that H&04 is equivalent to X 0 3 .HzO, the following equilibrium results:
+
“TA-2 Although an even greater negative charge exists on the EDTA complexes, (M03)2EDTA-4 and (,1/I03)EDTA-4, the hydroxide addition in these complexes is confined to the metal a t one end of the ligand where the effective charge is still only -2. LITERATURE CITED
These new Constants are summarized in Table I1 and suggest that the XI0 complexes may be slightly stronger than the corresponding W complexes. Comparison of the formation constants for different ligands shows essentially only one trend. That is, the stabilities of the one-to-one complexes approximately parallel the basicities of the ligands with respect to addition of the first proton: IDA < MIDA c EDTA < NTA. The greater stability of MIDA over IDA is probably a result of inductive effects from the methyl group. The higher stability of NTA than of IDA and N I D A complexes is the result of having more ligand donor groups available for coordination. From NMR studies the stability of the one to one niIoEDTA complex was greater than that of MoMIDA by about a factor of 2, just as predicted statisti-
(1) Day, RI. C., Selbin, J., “Theoretical Inorganic Chemistry,” p. 101, Reinhold, Kew York, 1962. (2) Kula, R. J., ANAL.CHEW 38, 1382 (1966). i 3 i -Ihid.. - - - > I). 1,581. ~ ~ (4)Pecsok, R. L., Sawyer, D. T., J . Am. Chem. SOC.78, 5496 (1956). (5) Rossotti, F. J. C., Rossotti, H., “T? Determination of Stability Constants, McGraw-Hill, New York, 1961. (6) Schwarzenbach, G., Ackermann, H., Helv. Chim. Acta 31, 1029 (1948). \-,
I
(7) Schwarzenbach,G., Neier, J., J.Inorg. Ajucl. Chenz. 8, 302 (1958). (8) Spengler, G., Gansheimer, J., Angew. Chem. 69, 523 (1957).
RICHARDJ. KULA DALLAS E. RABENBTEIS Department of Chemistry University of Wisconsin Rladison, Wis. WORK supported by a grant (GP-4423) from the Piational Science Foundation and by a Graduate School Research ,Assistantship (D. L.R.) from the Wisconsin Alumni Research Foundation.
