able element. It was felt that in the near future EDTA will be virtually the only titrant necessary for the quality control testing of driers and pigments. Elements in mixed pigment systems are determined without prior separation by proper choice of p H and masking agents. The most important example given involved the production control testing of paint driers, metallic salts of carbosylic acids. The organic acid salt is dissolved in alcohol-benzene solution and escess aqueous E D T A is added. The unreacted EDTA is then backtitrated with zinc t o the Eriochrome Black-T end point. The metal contents of the octoate and naphthenate salts of calcium, lead, cobalt, manganese. and zinc can be determined in 10
minutes with the same accuracy obtained by the much more time-consuming ASTM methods (6). The new method is one of the few examples in which the EDTA titration is used in a largely nonaqueous medium. LITERATURE CITED
(1) Bicrrum. J.. “Metal AiniminPFormx‘ b o g in Aqueous Solution.” P. Haase and Son, Copenhagen, 1941: Chenz. Reis. 46,
381 (1950).
( 2 ) Bjerrum, J., Schwarzenbach, (3.. Sil-
len, L. G., “Stability Constants. Part 11. Inorganic Ligands.” The Chemical Society, Eondon, i958. (3) Kraus, K. .4.,Selson, F , “Anion Exchange Studies of the Fission Products,” Proceedings of International Conference on Peaceful Usee of Atomic Energy,
Geneva 1955, Vol. 7, pp. 113, 131, United Nations, 1956. (4) . , Kraus, K. A., Nelson, F., “Metal Separations by Anion Exchange,” Symposium on Ion Exchange and Chromatography in Analytical Chemistry, 1956: .4m. SOC. Testing Materials. Spec: Tech. Publ. 195 ( 195%);d (5) Kraus, K. A., Nelson, F., Structure of Electrolytic Solutions,” W. J. Hamer, ed., p. 340, Wiley, New York, 1959. (, 6,) Lucchesi, C. A , , Hirn, C. F., A N ~ L . CHEX 30,’1877(i958). ( T ) Marcus, Y., Acta Chem. Scand. 11, 329, 610, 811 (1957). (81 Mulay, L. Y., Selwood, P. W., J . A??&. Cherri. SOC.77, 2693 (195.5). ( 0 ; Xexmnn, I,., Hume, D. Ti.Ibid., , 79, 4571. 4.581 (1957). (10) Pchn-arzenbach, G.! .i;\..i~. CHEX 32, ti (1880r. (11) Gillen, L. G., Acta Chein. Scand. 8, 299 (1954). (12) Sullivan, J. D., Hindman, J. C., J . Ani. Cheni. SOC.74, 6091 (1952).
Relationships between Metal Complex Stability and the Structure of the Complexing Agents GEROLD SCHWARZENBACH EidgenGssische Technische Hochschule, 6 Universitufstrasse, Zurich, Switzerland With the exception of oxidation and reduction, the reactions shown by metal cations in aqueous solution are all substitution reactions by which water molecules from the solvation shell are replaced by other ligands. Unidentate (ammonia, acetate), chelating (ethylenediamine, oxalate, glycinate), and bridging ligands (hydrazine, OH-, SF2, C03-*, are distinguished. The last ones are rnultidentate like the chelating ligands because of steric reasons; however, they are unable to satisfy several coordination sites on the same individual metal ion. Instead, they add more than one cation, tying them together; they form polynuclear complexes and finally, insoluble precipitates.
T
most important points for the characterization of a ligand are the nature and basicity of its ligand atom. For aqueous solution chemistry, only the atoms of the halogens (ligands: F-, C1-, Br-, I-), oxygen (ligands and ligand groups: OH-, C03-*, SOC-’, Po4+,aliphatic and aromatic R-OH and R-0-, ether oxygen, keto oxygen, carboxylate oxygen), sulfur (ligands and ligand groups: HS-, S+, mercaptan sulfur R-SH and R-S-, ether sulfur, keto sulfur, mono- and dithiocarboxylate sulfur), nitrogen (ligands and, ligand groups: ammonia and organic amine nitrogen, nitrogen of Schiff HE
6
ANALYTICAL CHEMISTRY
bases, amides, nitroso groups, and azo groups), and carbon (cyanide) are iniportant. Comparison of Coordination Tendencies. The tendency of the Larious metal ions t o substitute a molecule of n a t e r with a ligand group can be inyestigated a t present n i t h the aid of complex stabilities. The values 1 of log K 1 or ;log Pn can be compared with K1 as the stability constant of the 1 to 1 complex and Pn the over-all stacomplex bility constant of the 1 to with an unidentate ligand. Chelate complex stabilities may also he conipared if due consideration is given to the chelate effect and the possible strain within the chelate rings. I n the case of bridging ligands, solubility products of precipitates having the same type of crystal lattice can be used for comparison. Furthermore, with precipitates in equilibrium there are usually mononuclear complexes existent within the solution. Their stability constants can be obtained with the aid of solubility measurements and then it is possible to compare again the log K1 values so obtained. General a n d Selective Complexing Agents. A comparison shows t h a t oxygen donors and fluorides are general complexing agents, combining with a n y metal ion with a charge more t h a n one. Acetates, citrates tartrates, and 8-diketones sequester all metals in general, and hydroxides,
fluorides, carbonates, and p1iosphntc.s are common precipitating agents. T11~ strength of the coordinating bond formed increases enormously with the charge of the metal ion and decreases with its radius, which is known as elecB>- comparing trovalent behavior. various oxygen donors the observation is made that bond stability increasts regularly with the basicity (measured by proton addition) of the ligand atom. Cyanide, heavy halides, sulfur donors, and to a smaller extent the nitrogen donors, in contrast to oxygen donors, are selective complexing agents. These ligands do not combine with the cations of A metals (having a noble-gas electronic structure). Only B-metal cations (having 18 outer electrons) and transition-metal cations are coordinated to carbon, sulfur, nitrogen, chlorine, bromine, and iodine, and the solution stabilities of the complexes show that charge and radius of the metal ion no longer are the dominant factors for bond strength. A nonelectrovalent behavior exists, comprising the formation of covalent bonds and possible crystal field stabilization. n hich is most pronounced Kith cations of noble metals of low charge (the electrovalent behavior being as small as possible), such as CuT, Ag-, and du+. The largest of these three ions forms the most stable bonds, and by comparing the stabilities of the halogen complexes the series is found to be F- naphthylacetamide, diethyldithiocarbamate, and xanthogenate. There exist also organic VOL. 32, NO. 1, JANUARY 1960
7
bridging agents, giving precipitates of special insolubility like dithiooxalamide. Strong General Sequestering Agents. The anion of (ethylenedinitri1o)tetraacetic acid (EDTA) has the best structure for a general sexidentate sequestering agent. Substitution of some of the acetic acid residues by propionic acid or substitution of the ethylene bridge connecting the til-o nitrogens by a trimethylene bridge-Le., by enlarging some of the five-membered chelate rings of the EDTA complexes to six-membered chelate rings-reduces the complex stability. As mentioned before, nitrogen must be used a t the branching positions of the molecule. If the general nature of the sequestering agent has to be preserved, the terminal ligand atoms should be oxygen. Instead of carbosylate oxygen, phenolate oxygen may be and has been used, the oxyphenyl group being linked t o the nitrogen in ortho position by means of -CH2(16). Using the oxygens of phosphonic acid groups as terminal ligand atoms in conethylenediaminetetraphosstructing phonic acid was also tried (4,BS). The complexes of this acid, however, proved to have less stability than the EDTA complexes. Apparently it is a disadvantage to use terminal ligand groups which are charged doubly negative because of the larger energy needed to bring these charges close to one another during coordination. The tetraacetic acid of trans-diaminocyclohexane forms complexes of higher stability than EDTA (16). Unfortunately, the basicity of its anion is also greater (PIX,), which partly offsets the stability gain of the complexes if the complex formation takes place below p H 10. A long-chain diaminetetraacetic acid is much more inferior to EDTA. HOTever, the loss in stability of the complexes can be compensated partly if new ligand atoms are used within the chain connecting the two nitrogens. Even oxygen in this position is effective in P,/Y-diaminodiethyl ether tetraacetic acid and bis(P-aminoethy1)glycol ethertetraacetic acid (19). The anions of these acids have seven and eight ligand atoms and their characteristics are such that they preferably chelate large ions before corresponding small cations; the complexes of Caf2, S F , and Ba+2 are more stable than the complex of Mg+2. The anion of diethylenetriaminepentaacetic acid (DTPA) also contains eight ligand atoms. Partly because of its larger negative charge and partly because the heavy metal cations can increase their coordination number to eight, its complexes are generally more stable than the complexes of EDTA 8
ANALYTICAL CHEMISTRY
(3, 7 ) . DTPA is superior especially with the heavy alkaline earths, the first members of the lanthanide cations, and Th+4. Another characteristic of DTPA is the presence of hydrogen and bimetallic complexes within the equilibria mixtures. Attention should be paid also t o the pyridine carbonic acids. Picolinic acid forms complexes as strong as iminodiacetic acid, and 2,6-pyridinedicarboxylic acid complexes as strong as nitrilotriacetic acid. Because of the weak proton-addition tendency of the pyridine nitrogen (low pK) these pyridine derivatives have a decisive advantage in low p H regions. Nitrogen Donors of Low Basicity. Polyamines are much mole selective sequestering agents than aminopolycarbouylates, but they have the disadvantage t h a t the apparent stability constants of their complexes decrease rapidly with decreasing pH. This property is a result of the high and multibasicity of aliphatic polyamines; several protons are added to the free amine and the reactions correspond to pK values between 8 and 11. At pH values below 8, the metal cation stands in competition with several hydrogen ions and complex stability decreases rapidly with increasing acidity. Oximes of polyacetonylamines are much more favorable in this respect. For instance, tris(acetony1trioxime)amine, N(-CHrC-CH3)3, which is
/I
N-OH protonated only below p H = 5, has been synthesized. I n spite of this lorn basicity, the formation constants of Bmetal complexes are rather high, as a constant of lo8 has been determined for the copper complex. The complexes are proton donors with pK values from 6 to 10, and three protons being given off from the oxime hydroxyls, therefore stabilizing the complex by going up the p H scale. Unfortunately, the oximes are rather sensitive to hydrolytic decomposition. Stereochemistry of EDTA Complexes. RIost E D T A nietal complexes add a proton a t p H values around 3. RIany years ago it was assumed t h a t this proton nould be attached t o a carbovylate group of EDTA which is not used by the metal as a ligand, or that one of the chelate rings is opened rather easily by the attack of the hydrogen ion. Furthermore, it is possible to add to the nietalEDTA complexes a further unidentate ligand, such as OH-, ammonia, or SCN-, which also hints the possibility that EDTA acts as a quinquedentate ligand only or that the new unidentate ligand opens a ring, replacing a carboxylate group by doing so (11). The five condensed chelate rings which must be present when EDTA is
used as a sexidentate agent must form a rather strained structure, so that not much energy is needed to open one of the rings. This conclusion has been proved to be true by x-ray crystallography of the cobalt(II1) complex, KCoY (2B), revealing the exact geometry of the anion COY-. The EDTA anion, Yd4, satisfies all six coordination sites of Cof3, but the six ligand atoms form a strongly distorted octahedron. An especially large amount of strain apparently exists in the plane of the N-Co--T\’ chelate ring which contains also two K-Co-0 rings with bond angles deviating strongly from the normal values. One of these rings is opened in the compound KiH2Y.H20, the molecule of water replacing the carboxylate group which has been detached and is now carrying a proton ($0)
a
The anion of EDTA fits the steric requirements of the metal cation only approximately, the suit being too tight. The EDTA complexes could be stabilized considerably if the strain mentioned previously were released. This can be done by enlarging the chelate rings by just a few per cent. If some of the five-membered rings are replaced by six-membered chelate rings, not an increase but a decrease in complex stability is observed because of the smaller chelate effect. The astonishingly large differences in stability among the individual rare earth-EDTA complexes are probably due to differences in strain within the system of condensed chelate rings. Along the series from LaY- to LuYthere should be a release of strain because of the decrease of the ionic radius (lanthanide contraction) and this may partly be the reason for the large stability increase which amounts almost to 5 logarithmic units (18). The corresponding increase in stability of the nitrilotriacetate complexes is only about 1 to 3 units ( l 7 ) , whereas a reduction of the increase by a factor of 4/6 would be expected by replacing the sexidentate ligand, EDTA, by the quadridentate ligand, KTA. The lanthanides form with nitrilotriacetic acid not only 1 to 1 but also 1 t o 2 complexes and the stability of the latter is surprisingly large for the first members of the series, increasing from LaX2-S (log Kz = 7.7) to SmXz (log K z = 8.5). Around gadolinium there is a flat maximum in stability (log kz = 9.4) and then the stability decreases slightly again to (log Kz = 9.1) (2). Specific Chelating Agents. Coordination is a general tendency of metal cations. There is a selective behavior towards the various ligand atoms as pointed out previously, b u t the members of groups of cations of equal charge and of similar electronegativity behave very much alike. It is very
difficult to create specificity of a complexing agent for only one or two metal ions. Such a specificity could probably be achieved only by closely meeting the steric requirements of the ion in question. The following compound is a n example showing how specificity might be obtained. Ethylenediamino-bis(acety1acetone) (EDAA) : (-CH?-N=C-
I CH,
CH=C-O)2-2
I
CHI
is especially adapted to four coordination sites around a metal ion forming a planar square. Complex formation takes place with special ease with K'i+2, PdL2, Pt+2, and C u t 2 . The cations with a n octahedral sphere form EDAA complexes with two further unidentate ligands in trans- position to each other, this being the constitution, for instance, for cob:tlt(II)-EDAA, the two unidentate ligands being water molecules. By replacing EDAA with 1,2 - diaminocyclohexane - bis(acety1acetone) (DCAA), strain is created within the complex becausp of steric difficulties to make the three chelate rings coplanar. The DCAA complexes are less stable than the EDAA complexes and the strain is gwater in the transDCd-4 complex than in the one dcriv-
(6) Cotton, F. A., Harris. F. E.. J . Phus. Chem. 59, 1203 (1955). ( 7 ) Durham, E. J., Ryskiewich, D. P., J . A m . Chem. SOC. 80, 4812 (1958). (8) Honda, M., Schwarzenbach, G..'Helv. M(EDAA) > M(cis-DCAA) > Chim. Acta 40. 27 11957). M( ~ T U ~ S - D C A A )(9) Irving, H., J+illia&s,-R. J. P., Kature (London) 162, 764 (1948); Analyst 77, 813 (1952); Chem. SOC.(London). Spec. On the other hand, the metal sequence Pub11 1953,'3192. for any of the three complexing agents (10) Schwarxenbach, G., Ezperientia 12, is : 162 (1956). (11) Schwarxenbach, G., Helv. Chim. Acta Pt(che1) > Pd(che1) > Cu(che1) > 32. 839 11949'1. Ni(che1) > Co(che1) (12) '%id., 35,2344 (1952). (13) Ibid., 36, 23 (1953). (14) Schwarxenbach, G., Z. anorg. u. K i t h these two sequences in mind, allgem. Chem. 282, 286 (1956). i t is understandable that cis-DCAA (15) Schmarxenbach, G., Ackermann, H., does not react any more with cobalt, Helv.Chim. Acta 32. 1682 (1949). whereas complexes still are formed with (16) Schwarxenbach, G., Anderegg, G., Sallmann, R., Ibid., 35, 1785 (1952). nickel, copper, palladium, and plati(17) Schwarzenbach, G., Gut, R., Zbid., num. With trans-DCAA the com39, 1589 (1956). plexes of nickel and copper are also (18) Schwarzenbach, G., Gut, R., Anno longer formed and this agent has deregg, G., Ibid., 37, 937 (1954). (19) Schwarxenbach, G., Senn, H., Andertherefore become specific for palladium egg, G., Ibid., 40, 1886 (1957). and platinum (8). (20) Smith, G. S., Hoard, J. L., J . Am. Chern. Soe. 81, 556 (1959). (21) Spike, C. G., Perry, R. W.,Ibid., LITERATURE CITED 75, 2726, 3770 (1953). (1) Agren, rl., Schwarzenbach, G., Helv. ( 2 2 ) Weakliem, H. .4.> Hoard, J. L., Ibid., Chim. Acta 38, 1920 (1955). 81,549 (1959). (2) Anderegg, G., unpublished results. (23) Kesterback, S. J., Martell, A., A'ature (3) Anderegg, G., Nageli, P., Muller, F., (London) 178, 321 (1956). Schwarzenbach, G., Helv. Chim. Acta 42, 827 (1959). RECEIVEDfor review October 6, 1959. (4) Banks, C. V., Yerick, R. E., Anal. Sccepted October 15, 1959. 12th Annual Chim. Acta 20. 301 119.59). Summer Symposium Division of Analyti(5) Charles, R. G , - > . Am. Chem. SOC. cal Chemistry, ACS, and ASALYTICAL 76, 5854 (1954). C H E v I s T R Y , Urbana, Ill., June 1959. ing from cis-diaminocyclohexane. We get the following stability series for a n y metal:
.I-
\ - - - - ,
Use of an Unbalanced Bridge Circuit in High-Frequency Titrimetry JOE M. WALKER,' JACK L. LAMBERT, and LOUIS D. ELLSWORTH Departments o f Chemisfry and Physics, Kansas Sfafe University, Manhaftan, Kan.
b The feasibility of using a modulated off-balance radio-frequency signal originating from the detector side of a high-frequency impedance bridge as a method for performing high-frequency titrations was investigated. The use of an unbalanced bridge circuit was found to b e applicable to the acid-base titrations studied. Several relationships were inferred relating admittance changes to specific conductivity changes. An equation was derived relating the unbalance of the bridge, as measured by a voltmeter, to that of the true admittance obtained under balanced conditions. Frequency, electrolyte concentration, and the dielectric constant of the solvent were found to affect the titration curves in a manner predicted by the equations for admittance values. A new titration cell utilizing magnetic stirring is de-
scribed. An off-balance bridge circuit instrument should prove useful for titrations within the electrolyte concentration conditions studied, and the mathematical relationships derived should contribute to the theoretical knowledge of the circuitry of highfrequency titrimetry.
T
principles of high-frequency titrimetry have been studied previously ( I , 2, 4). The purpose of this investigation n-as to study the feasibility of using a modulated off-balance radio-frequency signal originating from the detector side of a high-frequency impedance bridge as a method for performing high-frequency titration. A bridge-type circuit similar in principle to that described by Hall and Gibson HE
(3) was used with a magnetically-stirred titration cell. APPARATUS
The apparatus was selected to measure parallel Capacitance and highfrequency conductance independent of other circuit components (Figure 1). A General Radio Type 1001-A standard signal generator was used as the highfrequency source (oscillator and modulator in Figure 1). Independent measurements of high-frequency conductance and capacitance were made with the General Radio Type 821-A Twin-T impedance bridge. A National communications receiver Model-NC-98 was used to amplify the unbalanced modulated signal from the bridge. Present address, Department of Physical Science, Kansas State College, Pittsburg, Kan. VOL. 32, NO. 1, JANUARY 1960
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