concentration, the larger the slope of Equation 6 , the greater is its extraction into chloroform. The values of Kx in Table I give an idea about the relative ease of extraction of the anions by the extractant, cetyltrimethylammonium ion. A larger value means greater interference with dye extraction. From Table I, it follows that the ease of extraction of the ions investigated follows the order, C1- < NOS- < Br- < I- < CIO1- < dye base. The extraction of the ions follows the same sequence as that determined by Diamond and coworkers (9, IO) for amine extraction systems. Diamond interpreted the results in terms of ion hydration. The most strongly hydrated ions should have the least tendency to enter a much less powerful ion solvating organic phase. The ion hydration depends upon the size and basicity of the ions and follows the order, CI- > Br- > I- > C104- (11). Very strongly hydrated ions, such as F- and S042-,have hardly any tendency t o be extracted into the organic phase and therefore do not interfere with dye extraction. The dye ion has large hydrophobic portions and therefore has a large tendency to be ejected from the aqueous environment. Among all the ions studied, KX for the dye ion is therefore the largest.
With the nonquaternary ammonium surfactants used here, the slopes of the lines in Figure 4 decrease in the following order: c104- > C1- > SO4?-. The same reason as above applies here also. The absence of the extraction data at various concentrations of the different acids does not permit us t o determine the KX values for the ammonium surfactants. The slopes for the various ammonium salts (Table 11) in any given acid differ from one another. This points out that the interference from the conjugate base of the acid to the dye extraction varies with the nature of'the ammonium ions. For the invariance of the intercepts with these extractants, it follows from Equation 7 that either K,,Dis so large as not to affect the intercept beyond the range of experimental error or it has the same value for all the systems studied here. The former conclusion seems to be more tenabie. ACKNOWLEDGMENT
The authors are indebted t o S. R. Palit for encouragement throughout the course of the work. Thanks are due to Imperial Chemical Industries, London, for providing the dye disulfine blue VN 150 as a gift.
(9) W. Muller and R. M. Diamond, J. Phys. Chem., 70, 3469 (1966). (10) J. J. Bucher and R. M. Diamond, ibid., 69, 1565 (1965). (11) R . M,Diamond and D. G. Tuck, Prog. Inorg. Chem., 2 , 109 (1960).
RECEIVED for review October 4, 1971. Accepted March 1, 1972. One of us (H. K. B.) thanks the Scientific Man-Power Committee of the Government of India for financial assistance.
Interaction of Methanehydroxyphosphonic Acid and Ethane-1-hydroxy-1,l-diphosphonicAcid with Alkali and Alkaline Earth Metal Ions Hiroko Wada and Quintus Fernando Department of Chemistry, University of Arizona, Tucson, Ariz. 8.5721
A potentiometric method has been used to study the complex formation reactions between Mg2+, Ca2+, Li+, Na+, and K + and the ligands, methanehydroxyphosphonic acid and ethane-1-hydroxy-1,l-diphosphonic acid. The interaction between the monophosphonic acid ligand and the metal ions was found to be primarily electrostatic and only 1:l complexes were formed in solutions containing a large excess of metal ion. The diphosphonic acid formed 1:l complexes in which one of the protons in a phosphonic acid group remained undissociated, and in the presence of an excess of metal ion, binuclear complexes were formed. The values of the formation constants of the calcium complexes indicated that the hydroxy group in the mono- as well as the diphosphonic acid may be involved in complex formation.
THEDISODIUM SALTS of the two diphosphonic acids, ethane-lhydroxy-1,l-diphosphonic acid, CH3C(OH)(P03H&, and methylenediphosphonic acid, HzC(PO3H2)z,have been found t o prevent calcification in vivo ( I , 2). Both diphosphonic acids contain the phosphorus-carbon-phosphorus bond; compounds containing a single carbon-phosphorus bond, e.g., the monophosphonic acids, however, were found t o have ( I ) H. Fleisch, R. G. G. Russell, and M. D. Francis, Science, 165, 1262 (1969). (2) M. D. Francis, R. G. G. Russell, and H. Fleisch, ibid., p 1264. 1640
no such biological activity. Although it has been suspected that complex formation with calcium is not the only factor that determines the biological activity of these compounds, it is of importance t o compare the metal complexing properties of the mono- and diphosphonic acids. Ethane-lhydroxy-1,l-diphosphonic acid, (EDPA), and methanehydroxyphosphonic acid, H2C(OH)(POsH2), (MPA), were selected as model compounds for a comparative study of their complexation behavior with the alkali and alkaline earth metal ions. Several workers have shown that a variety of complexes can be obtained in solutions containing calcium and EDPA. Complexes in which the ca1cium:ligand ratio is 1 : 1 have been postulated in which the proton in the 1-hydroxy group has either dissociated (3), or has not dissociated ( 3 - 3 , and also in which one of the protons in a phosphonic acid group is undissociated (6). In addition to these mononuclear com(3) M. I. Kabachnik, R. P. Lastovskii, T. Ya. Medved., V. V. Medyntsev, I. D. Kolpakova, and N. M. Dyatiova, Dokl. Akad. Nauk. S.S.S.R., 177, 582 (1967) [ Dokl. Chem., 177, 1060 (1 96711. (4) ~, R. J. Grabenstetter. 0. T. Quimby, and T. J. Flautt, J . Pliys. Chem., 71,4194 (1967). ( 5 ) R. L. Carroll and R. R. Irani, Znovg. Chem., 6 , 1994 (1967). (,6,) R. L. Carroll and R. R. Irani, J . Znorg. Nircl. Chem., 30, 2971 (1968).
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
plexes, it has been demonstrated experimentally that polynuclear complexes as well as micelles are obtained when the calcium ion concentration in solution exceeds 2 X 10-6M(7). In this work. we have used a potentiometric method to determine t h e formation constants of MPA and EDPA complexes of ?Ig2--, Ca", Li+, N a t , and K". Wherever possible, the same solution parameters have been employed with both ligands to facilitate the comparison of the complexation behavior of the two ligands.
Table I. Acid Dissociation Constants of MPA and EDPA at 25 "C and Ionic Strength 0.1 M PA concentration MPA PKl PK2 x 103:(~) ... 7.01 0.5 ... 7.00 3.4 1.7 1.6
7.02
10.0 24.5
...
EDPA concentration
EXPERIMENTAL
Synthesis of MPA. Methanehydroxyphosphonic acid was prepared by the method described by Page (8). One mole of trioxymethylene, (CH20)3,was added in small portions at a time to one mole of phosphorus trichloride, and the mixture was cooled thoroughly after every addition. The mixture was heated on a water-bath for one hour and the viscous oil that was obtained was allowed to stand at room temperature for 2 1 hours and then poured into 5 1. of water. After the oil had dissolved completely in the water, the resulting solution w2s c\,apornted 3 n a water-bath until no further reduction in thc volume was observed. Addition of sodium hydroxide to the oily residue gave the crude disodium salt of MPA M hich m a 5 pnrilicd hy rccrystallization from an ethanol-water mixture. A solution of the disodium salt was converted into thc free acid by passing the solution through the hydrogen form of the cation exchange resin, Amberlite IR 120. The acid solution was titrated with a standard solution of (CH,),VOH and uas found to be 100.4x pure. The lH N h l R spectrum of the compound in DsO exhibited the expected doublet that arises from the methyl protons that are split b y a phosphorus atom. Potentiometric Determination of Acid Dissociation Constants of MPA and Formation Constants of EDPA and MPA Complexes. All pH meahurements were made with a Beckman Model G pH meter equipped with a Beckman Type E2 glass electrode and a saturated calomel electrode and calibrated with Beckman buffers. Potentiometric titrations were carried out in the titration apparatus that has been described previously (9). Extensive precautions were taken to exclude CO? from the titration vessel, the solution being titrated, and the titrant (CH&NOH, which was freed from carbonate by passing it through the anion exchange resin Amberlite IRA-400. The solution of (CH3)1NOHwas standardized with NBS primary standard potassium hydrogen phthalate. The ionic strength in all the solutions was maintained at 0.1 by the addition of appropriate amounts of tetramethylammonium chloride which was purified by repeated recrystallization from ethyl alcohol. The value of pKl of MPA was determined by the titration of the monotetramethylammonium salt with a standard solution of HCIOI. The value of pK? was determined by the titration of the free acid, MPA, with a standard solution of (CH:&NOH. All pH meter readings were converted into hydrogen ion concentrations, [Hi] values, by using a correction factor (9) that was calculated from the titration curve of HC104 with (CH3)4NOHat an ionic strength of 0.1. All equilibrium constants that are reported in this work are therefore, concentration constants that are valid at an ionic strength of 0.1. Values of pKl and pK2 were determined at varying MPA concentrations (Table I). Solutions containing MPA or EDPA ( 9 ) metal ion (Lii, Na+, K-, Ca?+,or Mgr-), and (CH3)rNC1,were titrated with a standard solution of (CH3)4NOHto determine the hydrogen ions that were liberated upon complex formation. Values (7) R. J. Grabenstetter and W. A. Cilley, J. Phys. Chem., 75, 676 (1971). (8) H. J. Page, J . C/im7. Soc., 101, 423 (1912). (9) H. Wada and Q. Fernando, ANAL.CHEM., 43, 751 (1971).
PK2 ...
EDPA
... .
t
.
2.31 2.33 a
PK3
PKa
x 103:(~)
6.99 7.06 7.02 6.99
10.96 11.00 10.95 10.93
1.0 3.6 8.6 10.0" 11.3
...
...
Reference (9).
of the complex formation constants were calculated in solutions in which the concentration of the ligand was kept constant and the metal ion concentration varied and also in solutions in which the metal ion concentration was constant and the ligand concentration varied (Tables I1 and 111). RESULTS
Acid Dissociation Constants of MPA. MPA may be represented as follows:
>
H
The dissociation of
PH, -
4 = 0 \ O H
HO
"2Y
HY-
Yz-
and
The equations used to calculate Kl and K?,the acid dissociation constants of MPA, from potentiometric titration data have been reported in a previous paper (9). Formation Constants of MPA Complexes. In solutions containing an excess of metal ion and the ligand, MPA, 1 : 1 metal-MPA complexes are formed. At pH > 5 , MPA is present in solution predominantly in the form of HY- and Y 2 - . In the following equations, [B] represents the concentration of tetramethylammonium hydroxide added, CY and C ~ the I analytical concentrations of MPA and the metal ion, respectively. All the terms in square brackets represent concentrations in moles/l. and all charges are omitted for the sake of simplicity. (3)
+ [Yl + [MY1 [MI + [MY]
CY = [HYI CM =
(4) (5)
The formation constants of the 1 :1 metal-MPA complexes are defined by
Values of [MY], [MI, and [Y] can be obtained as functions of , the the experimentally observable quantities, [B], C ~ I CY,
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
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Table 11. Formation Constants of MPA Complexes at 25 "C and Ionic Strength 0.1 Meta1:ligand Metal ion Metal ion log G Y ratio concentration, M K+ 0.34 29:l 0 . 100 Na+ 0.61 29:l 0.100 Li+ 0.72 29:l 0 . 100 CaZ+ 1.81 8:l 0.011 1.84 8:l 0.020 1.89 9:l 0.045 1.93 1:s 0.001 Mgz+ 1.97 8:l 0.011 1.87 8.1 0.021 1.87 8:l 0.045 1.95 9:l 0.023 2.10 1:5 0.001
In the presence of an excess of alkali or alkaline earth ions, the monoprotonated species of EDPA, MHY, would be expected to react as follows: MHY
+M
e MzY
+H
(14)
The equilibrium constant for the above reaction is,
and its value can be calculated from the following equations: [B] - [OH]
=
3[MHY]
+ 4[MzY]
(16)
+ [MHYI [MI + 2[MzYl + LMHYI
CY Cif
=
=
[MzYl
(17)
(18)
Substitution for [M2Y], [MHYI and [MI from Equations 16-1 8 in Equation 15 gives : pH of the solution, and the second acid dissociation constant, Kz, of MPA, from Equations 2-4, and 5. Equation 7 was used to calculate the metal-MPA formation constants which are given in Table 11. KGy
=
[BI
- CY - (2Cy - [B]).
KMHY MzY
Formation Constants of EDPA Complexes. The diphosphonic acid, EDPA, exists in solution predominantly as H2Y2- and HY3-, between pH 5 and 8 (9). The alkali or alkaline earth metal ions will react with EDPA in approximately neutral solutions to form the monoprotonated complex, MHY. The formation constant of MHY is
{ ([BI - [OH]) - 3Cy ] * [HI (19) { CY - ([BI - [OH])} . { Cif CY - ([BI - [OH]))
+
The overall formation constant, KZ;, can now be evaluated from Equation 20.
All values of the formation constants of EDPA complexes are collected in Table 111. DISCUSSION
The potentiometric titration data for MPA and EDPA indicate that the former is a diprotic acid and the latter a tetraprotic acid, neither of which show any tendency to polymerize (9), at least in the concentration ranges that were employed (Table I). The dissociation of MPA can be represented, therefore, as follows:
and is calculated in a manner very similar to the formation constants of the 1 : 1 metal-MPA complexes. The symbols in the following equations have the same significance as stated above. =
2[HzYl
+ 3[HYl + 3[MHY]
+ [HYI + WHY1 [MI + WHY1
CY = [HzYl Chr
=
(9)
(10)
HH
MPA
The value of K2 for MPA is almost identical with the value of K3for EDPA as expected from the dissociation scheme shown below for EDPA. 0
(1 1)
I/ OH
0
Substitution for [MHY], [MI, and [HY] in Equation 8, in terms of quantities that can be obtained experimentally and K3, the third acid dissociation constant of EDPA, gives Equation 13 which was used for the calculation of the formation constants for the monoprotonated complexes, MHY.
[B]
-
-
(7)
[B]
-
0
"
EDPA
- 2 c y - (3CY - [B]). The presence of a second phosphonic acid substituent on the 1-carbon atom in EDPA results in the value of K2 (10-Z.31)for EDPA being considerably smaller than the corresponding value of Ki (lO-I.7) for MPA.
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ANALYTICAL CHEMISTRY, VOL. 44, NO. 9, AUGUST 1972
Metal ion K' Na+
Li'
Ca2+
Mgz+
Table 111. Formation Constants of EDPA Complexes at 25 OC and Ionic Strength 0.1 Metal ion log KsL log K&. Metal :ligand ratio concentration, M log KsEs ... 2.05 30: 1 0.1Ooo 0.60 ... 2.03 50: 1 0.0660 0.64 1 . 79a ... 1 :0.5-35 ... 0. 36a 0.78 ... 2.68 30: 1 0.1Ooo 0.84 ... 2.64 50: 1 0.0660 0.54& 2.07& ... 1: O . 5-35 ... 1.30 ... ... 3: 1 0.0100 1.47 ... 4.83 7: 1 0.0100 1.39 ... 4.80 26: 1 0.0340 1.27 ... 4.73 30: 1 0.1Ooo 1.35 ... 4.75 50: 1 0.0660 1.08 3.35 ... 1:0.5-35 ... 3.55 6.84 ... 1: 2 0.0013 6.40 ... 1.2:l 0.0021 3.53 ... 12.2 1.7:l 0.0042 ... ... 110.4-0.8 ... 5.74" 3.58" 6.04* ... ... ... 5.52 1:1, 3:2, & 4:3 ... 3.82 7.26 ... 1:3.2 O.oo08 7.30 ... 1:2.5 0.0010 3.80 ... 11.o 2.5:l 0.0066 3.68 ... 10.5 6.2:l 0.0170 3.50 ... 10.5 12.4:1 0.0200 ... ... ... 10.8 40: 1 0.1Ooo 3. 32a 6.39" ... 1 : 0.4-0.8 ...
Ionic strength 0.5. In 0.10M KC1.
The formation constants of the 1 : l alkali metal-MPA complexes are very small and could be determined only in the presence of a large excess of the alkali metal ion. The alkaline earth metal ions form somewhat stronger complexes with MPA, and variation of the concentration of the metal ion as well as that of the MPA did not change the value of the 1 : 1 formation constant to any significant extent (Table 11). The nature of the interaction of the alkali and alkaline earth metal ions with MPA is, therefore, largely electrostatic and polynuclear complexes are not present in the concentration ranges of the metal ion and ligand that have been employed in this study. Magnesium forms a slightly stronger complex than calcium and, in general, the stability order for the metal ions in Table I1 i s that which is expected if the metal-ligand interaction is electrostatic (5). Although the formation constants increase with increasing values of (charge)2/(radius) or the ionization potential of the metal ions, this increase is not linear. The nonlinearity is due either to the formation constant of the calcium-MPA complex being too large, or that of the magnesium-MPA complex being too small. It is possible that the hydroxy group in MPA acts as an additional bonding site and thereby increases the stability of the calcium complex. It is also possible that the lower stability of the magnesium complex is caused by intramolecular short-range repulsion forces (6). It is difficult to choose between these alternatives in the absence of additional experimental evidence. In solutions that are approximately neutral, the diphosphonic acid, EDPA, forms monoprotonated complexes with the alkali and alkaline earth metal ions. These complexes follow the same stability sequence that was found with the MPA complexes: Mgzt > CaZT > Lit > Na' > K+. The magnesium complex is slightly more stable than the calcium complgx despite the much smaller crystal radius of magnesium (0.65 A) when compared with the crystal radius of calcium (0.99 A). Therefore, it appears that the ionization potential of the calcium or the magnesium ion is not the only factor that
affects the stability of the EDPA as well as the MPA complexes of these two metal ions. It has been reported that EDPA forms binuclear complexes with the alkali metal ions (5). This observation has been confirmed and the formation constants of the binuclear complexes of K', Na+, and Li+ have been determined in the presence of a large excess of the alkali metal (Table 111). Polynuclear complexes are probably not formed to any significant extent since the values of the formation constants remain practically unchanged when the concentration of the alkali metal ion as well as that of the EDPA is varied (Table 111). As expected, lithium forms the most stable complexes and the potassium complexes are the least stable. When the metal :EDPA ratio is increased, the calciumEDPA complexes precipitate when the ratio exceeds 2 :1. However, no precipitate formation was observed in solutions containing magnesium and EDPA even when the magnesium : EDPA ratio was increased to 40: 1. It was assumed that in solutions containing a large excess of magnesium ion, the only complex that was present in solution was the binuclear complex. On the basis of this assumption, the formation constant of the binuclear complex was calculated and was found to remain approximately constant when the magnesium : EDPA ratio was varied from about 6 : 1 to 40 : 1. The value of the constant, however, indicates that the binuclear complex of calcium is more stable than the corresponding binuclear complex of magnesium, which is a reversal of the usual stability order that has been found with these complexes. This suggests that in the calcium complexes of EDPA and of MPA, the hydroxy group influences the complex formation to a marked extent and confers an extra degree of stability to the calcium complexes.
RECEIVED for review January 27, 1972. Accepted April 11, 1972. This work was supported by a research grant from the National Science Foundation.
ANALYTICAL CHEMISTRY, VOL. 44, NO. 9 , AUGUST 1972
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