1127
A SPECTROSCOPIC STUDY OF BINUCLEAR COPPER COMPLEXES
A Spectroscopic Study of Binuclear Copper Complexes in Aqueous Poly( methacrylic acid) Solutions by J. C. Leyte, L. H. Zuiderweg, and M. van Reisen Laboratory of Physical Chemistry, The University of Leyden, The Netherlands Accepted and Transmitted by The Faraday Society
(July 3,1967)
The changes in the ir, visible, and uv spectra and the static magnetism of aqueous solutions of the PMACu(I1) system as a function of the degree of neutralization of the polyacid have been recorded. It is concluded that at low polyelectrolyte charge a binuclear copper complex exists which dissociates, yielding mononuclear complexes, on increasing the charge of the polyion. It is shown that the ir intensities of the carboxylate groups may be of considerable use in the identification of binuclear carboxylates.
Introduction The existence of a complex of Cu(I1) and poly(methacrylic acid) (PMA) was established some time ago' and this complex has been the subject of several publications s i n ~ e . ~The , ~ binding of copper ions by PMA is conveniently discussed in terms of the ratio f = [equivalent concentration of ionized PMA]/ [equivalent concentration of Cu(II)]. With the help of several experimental methods (potentiometry, viscosity, electrophoresis, and spectrophotometry) it was shown that Cu(I1) ions are chelated by two carboxylate groups per metal ion for f 5 1.2.s At higher charge densities of the polyelectrolyte (f > 1.2), a decrease was observed in the intensities of the visible and uv spectrum characteristic of the complex. As was done in the case of the Cu(I1)-poly(acrylic acid) c ~ m p l e xthis , ~ was interpreted in terms of a partial disintegration of the complex and possible competition between site binding and interaction with the over-all electrostatic field of the polymer. The nonspectroscopic methods mentioned before do not admit a definite interpretation of this phenomenon. We have, therefore, investigated this system using spectroscopic methods directed a t the binding sites (ir) and the chelated ions (visible region) directly. I n this way it is possible to gain information about the environment of the Cu(I1) ion while the changes in the ir spectrum associated with the carboxylate group yield quantitative information on the amount of these groups involved in binding Cu(I1) ions.
experimentally convenient to work with solutions containing 30% equiv of Cu(C104)z with respect to PMA. The titrations were performed with a variablepathlength titration cell. As the spectral changes in the region f = 1.3-3.3 occur smoothly throughout this range, we have only represented the extremes in Figures 1 and 2. The infrared region was studied with a Unicam SPlOO instrument equipped with a rock salt prism and grating. Because of the low-energy conditions in the region studied in DzO solution, large slit widths had to be used. Although no influence of the slit width on the peak height could be detected on decreasing the slit width by SO%, the quantitative measurements were carefully performed at the same slit width for a given wave number in a series of solutions. The solutions in the concentration range of 0.07-0.16 equiv/l. with respect to PNIA were measured in cells with CaFz windows at pathlengths of about 0.01 cm. Compensation for the solvent was carried out with variable pathlength cells at 1310 cm-l. Transmission values were determined by the base line method. For the absorptions a t 1610 and 1550 cm-' the same base line was used. From the copper-free solutions we verified that at 1600-1610 em-' the absorption due to the 1550-cm-I peak is negligible. PMA of molecular weight 7.5 X lo5 was synthesized and fractionated as described before.6 Solution of PMA in DzO and subsequent evaporation of DzO was repeated five times before the final solution for ir work was prepared. Analytical grade CuClz.2H20 was
Experimental Part The measurements in the visible and uv regions were performed using Unicam SP700 and Zeiss PMQII spectrophotometers. The spectra of the PIMA-Cu(I1) system a t different f values were obtained by spectrophotometric titration of aqueous PMA-Cu(I1) solutions with NaOH. Although the same results are obtained a t different Cu(I1) concentrations, it proved
(1) H. P. Gregor, L. B. Luttinger, and E. AM.Loeble, J . Phys. Chem., 59, 366 (1955). (2) A. M. Kotliar and H. Morawetz, J . Amer. Chem. Soc., 7 7 , 3692 (1 955). (3) M. Mandel and J. C. Leyte, J . Polym. Sci., Part A-2, 2883, 3771 (1964). (4) F. T. Wall and S. J. Gill, J . Phys. Chem., 5 8 , 1128 (1954). (5) J. C. Leyte and M. blandel, J . Polym. Sci., Part A-2, 1879 (1964).
Volume 72, Number 4 April 1968
1128 e l
J. C. LEYTE,L. H. ZUIDERWEG, AND M, VAN REISEN 1
8
9 100
Figure 1. Ultraviolet spectrum of the PMA-Cu(I1) system a t f = 1.3 (I) and a t f = 3.3(11): PMA, 3.00 x 10-8 equiv/l.; Cu(ClO& 9.00 X 10-4 equiv/l.
IO
CP
I/
12
(40
Figure 3. Lambert-Beer plots for the PMA-Cu(I1) system: 0, 38,000 cm-l (f = 1.5); X, 38,000 cm-1 (f = 3.0); 0, 14,500 cm-1 (f = 1.3); A, 14,500 cm-' (f = 2.3).
indebted to Dr. J. W. Roelofsen, who kindly obtained the results for them. zoo
Figure 2. Visible and near-uv spectrum of the PMA-Cu(I1) system a t f = 1.3 (I) and a t f = 3.3 (11): PMA, 3.00 X 10-2 equiv/l.; Cu(ClO& 9.00 X 10-3 equiv/l.
recrystallized four times from D 2 0 to exchange the water. NaOD solutions were prepared by dissolving freshly cut sodium in D20 in a nitrogen atmosphere. D 2 0 of 99.8% was obtained from the Dutch Reactor Center. Solutions of PMA containing 30% CuCl2 (equivalent with respect to PMA) were mixed in varying proportions with identical solutions in which PMA was fully neutralized with NaOD to obtain PMA-CuC12 solutions at the degrees of neutralization wanted. Below f = 1.3, the complex is insoluble a t the PMA concentrations used for ir work. All operations involving the D20solutions were performed in a drybox. The magnetic measurements on the aqueous PMACu system were performed at room temperature according to the Gouy principle. The authors are The Journal of Physical Chemistry
Results and Discussion In Figure 1 and Figure 2, the visible and uv spectra of the Cu(I1)-PMA system are shown for two f values, At f = 1.3 absorptions are observed at 37,800 and 14,500 cm-'. A shoulder may be seen at 26,000 cm-l, while symmetrical analysis of the absorption at 14,500 cm-1 reveals another maximum at 11,250 cm-l ( E ~ 2 5 ) . At f = 3.3, the band at 26,000 cm-l has disappeared and the uv maximum shifts to 38,750 cm-l while its intensity decreases. The intensity decrease in the visible region is accompanied by a shift to 14,250 cm-'. The absorption at 11,250 cm-l decreases some 20%. When a t f = 3.3 the solvent was replaced by dioxane, the band a t 26,000 cm-' reappeared. The magnetic moment shows an interesting dependence on f . From 1.91 p B at f = 0, it drops to 1.54 pB at f = 1.3. At f = 3.0 the moment has increased to 1.66 pB. The application of both ir and uv spectroscopy to the same system often meets some experimental difficulties, as the concentrations that have to be used for convenient work in these regions generally differ by a factor of 100. Figure 3 shows that Lambert-Beer's law is obeyed (for 1.3 < f < 3) in a concentration range that connects the regions in which the ir (0.1 equiv/l.) and uv (0.01-0.003 equiv/l.) results were obtained. A discussion of these results in terms of the same complex at a given value off is, therefore, permitted. An important conclusion which was tentatively reached earlier3 may be confirmed from Figure 1: the ligands around a given Cu(I1) ion are situated on one polymer molecule only. This explains the insensitivity of the relative complex concentration to dilution.
1129
A SPECTROSCOPIC STUDY OF BINUCLEAR COPPERCOMPLEXES
“‘i 700
1770
1700
I
1670
I
1600
I
1550
l
1700cm.i
l
Figure 4. Infrared spectra of the aqueous PRIIA-Cu(I1) system at three different CL values. The solutions contain 30.070equiv CuCL with respect to PMA.
In Figure 4 the ir spectra are shown of the PMA-Cu(11) Rystem at several degrees of neutralization. The identification in the region from 1500 to 1750 cm-l presents no difficulties. The peaks at 1550 and 1700 em-1 may be assigned to the antisymmetric stretching mode of the carboxylate group ( V I ) and the carbonyl stretching mode ( vZ), respectively. An absorption at about 1600 cm-l has been observed in the spectra of many Cu(I1)-carboxylate complexessJ and as there is no absorption of PbIA in this region in the absence of cupric ions this peak may be identified with the antisymmetric stretching mode of the chelating carboxylate groups (4. The negligible intensity of v g at a = 0 shows that the nnneutralized polyacid binds practically no Cu(I1) ions. This is in agreement with previous r e ~ u l t s . ~ Figure 5 shows the absorbance A = c,-l d-’ log T-’ (c, is the polymer concentration in equiv/l., d is the cell length in centimeters, and T is the transmission) plotted against the degree of neutralization a for VI, v2, and v3. The values plotted here were determined by the base line method and refer to the absorption maxima. Extinction coefficients determined from plots will be designated a to emphasize that they were not obtained from integrated intensities. First the titration of PMA will be discussed. Whereas A ( v 1 ) follows an intramolecular Beer’s law, this is not true for A ( v 2 ) . I n the region where A(vZ) deviates from the straight line, PMA is well known to exhibit a conformational transition from densely coiled to extended conformations.6+8 As A(vl)/a = i ( v l ) does not change in this region, we may conclude that the first hydration sphere of the carboxylate groups is the same in both groups of conformations. From the validity of Beer’s law for A(vl),the important conclusion may be drawn that the carboxylate groups along the
0
OF++-
c
Figure 5 . Absorbance, (see text) from ir spectrophotometric titrations: PMA: VI (D), YZ (V), PMA 30.0% equiv Cu(I1): Y1 (b), Y2 (-01, Y8 ( 0 ) .
+
polymer chain are optically independent, even at high degrees of ionization of the polyacid. In Figure 5, the plot of A ( v 1 ) for the PMA-Cu(I1) system is shifted 0.3 unit parallel to the CY axis with respect to the copper-free system. As in the former case, 30.0% equiv of Cu(I1) is present (referred to PMA); it is confirmed3 that two carboxylate ions are bound per copper ion. = The equality of the slopes of the two lines 597 1, mol-’ cm-‘ for the titration of pure PMA and = 600 1. mol-’ cm-’ in the other case) proves that once the point of equivalence with respect to Cu(I1) has been reached (a = 0.3) the number of bound carboxylate ions is constant. The original explanation of the intensity decrease of the electronic spectrum for f > 1.2 in terms of a dissociation producing copper ions and carboxylate ions is therefore abandoned (in Figure 5, LY = 0.3.f). As pointed out b e f ~ r e ,the ~ band at 26,000 cm-l and its disappearence on increasing f is important in the interpretation of the binding phenomena in the present system. Starting with the work of Tsuchida, et al.,1° evidence has been presented that an absorption in this region and of the strength observed (6) K. Nakamoto, “Infrared Spectra of Inorganic and Coordination Compounds,” John Wiley and Sons, Inc., New York, N. Y., 1963. (7) L. L. Shevchenko, Ukr. Khim. Zh., 2 9 , 1247 (1963). (8) J. C. Lyte, Polym. Letters, 4, 245 (1966); M. Mandel, J. C. Leyte, and M. G. Stadhouder, J. Phgs. Chem., 71, 603 (1967). (9) J. C. Leyte, Kolloid-Z., 212, 168 (1966). (10) R. Tsuchida and S. Yamada, Nature, 176, 1171 (1955).
Volume 76, Number 4
April 1968
1130 here is characteristic of the formation of binuclear copper carboxylates both in the solid state and in solution. As was discussed in a review" of the early results, the 26,000-cm-l band is no proof of Cu-Cu interaction in complexes. Still, for the carboxylates the subnormal magnetic moments that are found when this band is observed indicate that its appearance is characteristic for copper acetate type dimeric structures. Recently, this was confirmed for a series of copper complexes of unsaturated acids by Edmondson and Lever. l 2 I n connection with the present polyacid (-CH2C(CH,) (GOOH)-), especially, the results on the qo-dicarboxylic acids are of interest. Dubicki, et a1.,'3 and Figgis and Martin14 found that the copper complexes of these acids from the succinate upward in the homologous series behave as magnetically isolated dimers. For these complexes the 26,000-cm-l band is present in the spectrum. I n the spectra of the oxalate and the malonate, the band is absent and the magnetic behavior excludes the acetate type dimer structure. It is suggestive that in PMA the number of C atoms between neighboring carboxylate groups equals that in the glutarate. I n view of these results, the optical spectrum and the low magnetic moment of the present system strongly suggest the presence of binuclear copper complexes at f = 1.3. At f = 3.3 the characteristics of the dimer are absent and, from the ir results, it is seen that each copper ion still binds two carboxylate groups. Therefore, the explanation for the spectral changes seems to be a dissociation of the dimers into monomer complexes. This dissociation is probably due to the greater accessibility of water molecules to the interior of the polyelectrolyte molecule as a result of the expansion of the polymer on increasing its charge. This is confirmed by the reappearance of the 26,000-cm-l band on replacing the solvent by dioxane. In this connection, it is of interest that 30 vol % of water in acetic acid solutions of cupric acetate completely destroys the dimer.15 A detailed discussion of the general decrease of extinction coefficients in the electronic spectrum is hampered by the absence of dependable term schemes, especially in the case of the dimer. From general considerations the observed decrease is, however, quite consistent with the dissociation of the dimer complexes. It is now accepted16-1s that in the dimer the coppercopper interaction is weak and that the d manifold is probably only slightly disturbed if compared to mononuclear complexes. The absorption in the 10.000-15.000-cm-1 region may, therefore, still be related to d-d transitions in the dimer. I n the dimer carboxylates the Cu ions are bridged by four carboxylate groups, forming a structure of approximately D4h symmetry with two additional solvent ligands on the C4axis. The symmetry center is halfway between the metal ions and the ligand charge T h e Journal of Physical Chemistry
J. C. LEYTE,L. H. ZUIDERWEQ, AND M.
VAN
REISEN
distribution is, therefore, asymmetrical for a given Cu(I1) ion. In this situation d-d transitions are allowed, resulting in an intense visible spectrum. I n monomeric complexes the Cu(I1) ions tend to surround themselves with a deformed octahedron of negative ligand charge. As the metal ion is in the symmetry center d-d transitions are in principle forbidden here, resulting in low visible intensities. For the uv region, analogous considerations hold. It will now be shown that the ir spectra yield additional information in connection with the discussion just presented. In the same range off values where the changes in the electronic spectrum occur, the intensity A(v3) due to the chelated carboxylate ions increases considerably (Figure 5). Integration of some of the bands involving correction for the neighboring v1 obtained from spectra of Cu(I1)-free solutions confirms this. Considering the insensitivity of ;(vl) (and of a(vJ outside the conformational transition region) with respect to the electrostatic charge of the polymer and the fact that the number of bound carboxylate groups is constant (as shown by the absorption of the free ions), it is concluded that the behavior of A(v3) is due to a change in the nature of the complex. It should be noted that a considerable change in the nature of the copper carboxylate bonding does not seem to occur, as the shift in v3 is small if existent at all (see discussion below). The conservation of the number of bound carboxylates per Cu(I1) ion, therefore, suggests a rearrangement of ligands: a structure in which the contributions of the individual ligands to the transition moment partially cancel is replaced by a structure in which this happens to a lesser degree. First, starting from the assumption that at f = 1.3 only mononuclear complex is present, any rearrangement reducing the symmetry of the orientation of the carboxylate groups with respect to each other necessarily reduces the symmetry of the orientation of these ions with respect to the central ion. This reduces the symmetry of the distribution of negative charge around this ion. Even without consideration of the 26,000-cm-' band, this is quite in conflict with the general decrease of intensity in the visible and uv region as this, in view of the invariance of the number of bound carboxylate ions per (11) M. Kato, H. B. Jonassen, and J. C. Fanning, Chem. Rev.,64, 99 (1964). (12) B. J. Edmondson and A. B. P. Lever, Inorg. Chem., 4, 1608 (1966). (13) L. Dubicki, C. M. Harris, E. Kokot, and R. L. Martin, ibid., 5 , 93 (1966). (14) B. N. Figgis and D. J. Martin, ibid., 5 , 100 (1966). (15) J. K. Kochi and R. V. Subramanian, ibid., 4, 1527 (1965). (16) A. E. Hansen and C. J. Ballhauser, Trans. Faraday Soc., 61, 631 (1965). (17) L. Dubicki and R. L. Martin, Inorg. Chem., 5 , 2203 (1966). (18) G. F. Kokoszka, H. C. Allen, and G. Gordon, J. Chem. Phye., 46, 3013 (1967).
A SPECTROSCOPIC STUDY OF BINUCLEAR COPPERCOMPLEXES copper ion, clearly indicates an increase of the symmetry of the charge distribution around the metal ion. Also, the low magnetic moment at f = 1.3 cannot be explained this way. Therefore, the consequences for A ( v 3 ) will be considered for the dissociation of a binuclear copper carboxylate with the well-known acetate structure into mononuclear complexes. The binuclear complex will be represented by a model consisting of 16 point masses: two Cu(I1) ions and two solvent particles on the Cg axis and four carboxylate ions (consisting of 3 point masses each) with the carbon atoms in Qh of Dah. Standard symmetry analysis yields the ir active vibrations: 4Azu 6E,. Using the C-0 distance of the carboxylate ion as an internal coordinate,lQit is found that the ir-active vibrations involving this coordinate are Az, and E,. From the behavior under (TI, it is clear that the A2, vibration stems from the antisymmetric stretching vibration of the free carboxylate ions, while the E, vibrations arise from a combination of symmetric stretching vibrations of carboxylate groups. I n other words, when four carboxylate ions react to form the binuclear complex, the antisymmetric vibrations of the free ions combine in different ways to yield Az, E, 3. Bzu. Of these only Azu is ir active, and this is only one of the four possible combinations. As these combinations are about equally probable (the ground states will not show energy differences which are appreciable with respect to AT) the intensity of va will he sharply reduced relative to the free ion if no large increase of the transition moment occurs as a result of the electronic interaction with the Cu(I1) ion. As this is improbable, the extinction coefficient of vg in a binuclear copper carboxylate with a structure analogous to that of the acetate should be some 25% of the extinction coefficient of v1 of the free carboxylate ion. For the present system a value of 33% is found at f = 1.3 from integration of the bands. As at this f value part of the binuclear complexes are probably dissociated already (the intensities in the uv and visible spectrum start to decrease a t f = 1.2), this result is satisfactory. For the mononuclear complex we will first consider a structure of symmetry D z in ~ which both carboxylate ions and the central ion are in (Th. The same analysis that was applied to the dimer shows that in the monomer only one of the two possible combinations of the antisymmetric stretching vibrations of the carboxylate group is active. At f = 3.3 the extinction coefficient of va is found to be 47% relative to the free ion while roughly 50% should be expected. It should be stressed that any other model for the monomer is necessarily of lower symmetr,y with respect to the relative carboxylate orientation. Even higher extinction coefficients for the ligands are then expected. An increase of A(vJ is, therefore, expected for the dissociation of a
+
+
1131
dimer irrespective of the type of the resulting monomer. It is concluded that the dissociation of binuclear complexes existing to some extent at f = 1.3 into monomers is responsible both for the changes in the spectrum of the complex and its magnetic behavior on increasing f. Several attempts have been made to correlate the position of q with the type of interaction between metal ions and the carboxylate groups.20 It has been established that for some metal ions the frequency order is more or less independent of the physical state of the compounds. It is assumed that the position of v3 with respect to VI and v2 is a measure of the covalence of the metal-carboxylate bond. The principle is of little use, however, in the interpretation of the spectrum of an isolated compound. Still a shift in v3 would be expected in our case if the type of bonding of the carboxylate groups changes when the binuclear complex dissociates. From Table I, it is seen that V I , vz, and v3 shift to lower frequencies on increasing a. This effect also occurs in the absence of Cu(I1) ions for v1 and vz and has been discussed previously for that case.21 These shifts are connected
Table I a
0 0.4
0.7
1.o
VI
... 1554 1552 1550
V I
Y8
1698 1692 1685
1612 1611 1608 1604
...
with the expansion of the polyelectrolyte molecule upon increase of its charge density. Any small change in v3 due to a change in the nature of the copper complex will be superimposed on the shifts mentioned and it must be concluded that the small displacement of v3 cannot be used as an indication for a transformation of the complex. It is of interest to note that the poly(glutamic acid)-Cu(I1) system shows an analogous behavior to the system treated here.22 The authors mainly investigated the influence of Cu(I1)-ion binding on the helix-coil transition, and for an explanation of the spectral phenomena, they leave the choice open between exciton interaction (disappearing when the copper ions become more widely spaced along the polymer chain) and direct copper(19) E.B. Wilson, J. C. Decius, and P. C. Cross, “Molecular Vibrations,” McGraw-Hill Book Co., Inc., New York, N. Y . ,1956. (20) J. D. Donaldson, J. F. Knifton, and S. D. Ross, Spectrochim. Acta, 20, 847 (1964). (21) J. C. Leyte, L. H. Zuiderweg, and H. J. Vledder, ibid., 234, 1397 (1967). (22) H. Takesada and H. Yamaaaki, Biopolumers, 4, 713 (1966). V o l u m e 72, N u m b e r 4
April 1068
J. STEIGMAN, R. DE IASI,H. LILENFELD, AND D. SUSSMAN
1132 copper interaction. Our results on PMA, especially those from the vibrational spectrum, favor the latter explanation.
Acknowledgment. The authors wish to thank Professor M. Mandel and Professor G. Gordon for their comments and interest.
Acid-Base Reactions in Concentrated Aqueous Quaternary Ammonium Salt Solutions. 111. Dicarboxylic Acids by Joseph Steigman, Richard De Iasi,l Harvey Lilenfeld, and Donald Sussman Department of Chemistry, Polytechnic Institute of Brooklyn, Brooklyn, New York
(Received July 11, 1967)
A number of dicarboxylic acids were titrated with KOH in aqueous 7.75 m tetra-n-butylammonium bromide solutions a t 25". The ratio of the two dissociation constants was greater than in water for the following acids : maleic, o-phthalic, malonic, dimethyl- and di-n-propylmalonic, and succinic. The maleic acid ratio was greater than in water by more than 4 X los. That for succinic acid was five times greater. The ratios for oxalic acid, for m- and p-phthalic acids, for fumaric acid, and for the longer-chain aliphatic dicarboxylic acids from glutaric to suberic were almost unchanged. Infrared spectra of some of these acids, their acid salts, and their fully neutralized salts were made in DZO and in 7.75 rn tetra-n-butylammonium bromide solutions in DzO. With the exception of oxalic acid, those compounds which showed small changes in their dissociation constant ratios on transfer from water to the quaternary ammonium salt solution had monoacid salt spectra which were simple composites of those of the free acid and the fully neutralized salt. Acids which showed large changes in their ratios had monoacid anion spectra in which the carbonyl frequency of the acid moved to a lower frequency and the asymmetric carboxylate stretching frequency of the fully neutralized salt moved t o a higher frequency, an effect which became larger in the quaternary ammonium salt solution. It was concluded that an internally hydrogen-bonded monoacid anion was formed by the latter acids and that water was a part of this structure. Since such a structure was not possible for the acid oxalate anion and since a dimer of this ion does not appear to exist in aqueous solution, it was concluded that the effects observed in the oxalic acid system are probably due t o electrostatic forces.
Introduction On statistical grounds, the ratio of the first to the second dissociation constant of a diprotic acid should be 4. In water, the first three members of the homologous aliphatic series-oxalic, malonic, and succinic acids-possess ratios which are much greater than 4, and the theoretical statistical value is not reached even for long-chain dicarboxylic acids. Bjerrum attributed these high ratios to the electrical work which is required to remove the second proton from the negatively charged monoanion, an approach which was further developed by other worker^.^^^ An alternative explanation for the first three members of the homologous series was put forth by Jones and Soper, who suggested that an internal hydrogen bond would stabilize the acid salt.4 This would resuIt in an increase in the value of the first dissociation constant and a decrease in the second constant, producing the high ratios which are observed. Eberson found that a,a'disubstituted racemic succinic acids had dissociation constant ratios which were very much larger than those The Journal of Physical Chemietrg
of the corresponding meso compounds and he concluded that the difference between them was due to a hydrogen-bonded intermediate for the acid salt in the preferred conformation of the racemic c ~ m p o u n d . ~Miles and his coworkers further supported the hypothesis of an internally hydrogen-bonded intermediate by a potentiometric and kinetic study of the dissociation of disubstituted malonic acids in water.'j On the other hand, Chapman, Lloyd, and Prince concluded from an examination of the infrared spectra of DzOsolutions of a number of dicarboxylic acids and their salts that the hydrogen malonate ion, the hydrogen maleate ion, and (1) Taken from a thesis submitted by R. De Iasi to the Graduate School of the Polytechnic Institute of Brooklyn in partial fulfillment of the requirements for the degree of Doctor of Philosophy. (2) N. Bjerrum, 2.Phys. Chem. (Leipzig), 106, 219 (1923). (3) J. G. Kirkwood and F, H. Westheimer, J . Chem. Phys., 6, 508 (1938). (4) I. Jones and F. G. Soper, J . Chem. SOC.,133 (1936). (5) L. Eberson, Acta Chem. Scand., 13, 211 (1959). (6) M.H.Miles, E. M. Eyring, W. W. Epstein, and R. E. Ostlund, J . Phys. Chem., 69, 467 (1965).
