Dec. 5 , 1961
POLAROGRAPHIC STUDYOF MIXED-LIGAND COMPLEX FORMATION
(6) Magnetic moments and A values of a particular complex anion, [CoX4I2- vary, somewhat (usually ~ 4 occasionally % ~ as much as 1 0 ~ cfrom ) one compound to another due, presumably, to variations in compression forces in the crystal lattices. (7) Solvent effects on the spectra of [CoX4I2species are often significant. True spectra can usually be obtained in nonaqueous solutions by a.dding excess X- ion, but in aqueous solutions, even saturated with H X or LiX, full conversion of Co(I1) to COX^]^- species does not seem to occur. (8) C O ( O H ) ~dissolves in concentrated alkali metal hydroxide to form, a t least partly, one or more tetrahedral species. It is believed that these are [Co(OH)3(H20)]-, [Co(OH)4I2- or both. (9) The intensities of the v2 and v3 bands in all tetrahedral Co(I1) complexes studied to date appear to be -lo2 times as great as the band intensities in octahedral Co(I1) complexes. This ratio is comparable to those found for Ni(II)21 and
[COXTRIBUTION X O . 1023 FROM
THE
4699
M I I ( I I ) ~and ~ in agreement with previously reported observations, notably those of Gill and Nyholm, l1 Ballhausen and J@rgensen*and Buffagni and Dunn.I6 (10) The A values for COX^]^- complexes are 80-85~c of those in the corresponding [NiX412complexes.21 Whereas the [NiI4I2- and [NiB1-41~-complexes had A values which were equal within experimental error, the A value for [CoBr4I2- is 5 1 0 % greater than that for [CoI4I2-. Acknowledgments.-We thank Dr. Richard H. Holm for some of the data on aqueous solutions. Financial support was provided by the United States Atomic Energy Commission (Contract No. AT(30-1)-1965) and the National Institute of Health (Research Grant No. 7445). We also thank Dr. H. A. Weakliem and Professor H . G. Drickamer for communicating some of their results in advance of publication. (29) D. hl. L. Goodgame and F. A. Cotton, J . Chem. Soc., 3735 (1961); F. A. Cotton, D. M . L. Goodgame, M . Goodgame, J . Am. Chem. SOL.,in press.
DEPARTMENT O F CHEMISTRY,
INDIASA
UNIVERSITY, BLOOMIKGTON, ISDIASA]
A Polarographic Study of Mixed-ligand Complex Formation ; Complexes of Copper and Cadmium with Oxalate Ion and Ethylenediamine BY WARDB. SCHAAP AND DOXALD L. MCMASTERS' RECEIVED MAY 15, 1961 The polarographic method for the study of mixed-ligand complexes is discussed and then applied to the determination of the formation constants of the mixed-ligand complexes of copper(I1) and cadmium(I1) in the presence of both oxalate ion (ox) and ethylenediamine (en). Results for the one mixed complex of copper, [Cu(en)(ox)], agree well with results based on other physical measurements. The constants for the three possible mixed complexes of cadmium are log Kll = 7.9 for [Cd(en)(ox)], log K I Z = 8.8 for [ C d ( e n ) ( o x ) ~ ]and - ~ log KZI= 11.5 for [Cd(en),(ox)]. The effects of the relative charges of the unsaturated complex and the incoming ligand on the stepwise formation constants are those predicted by charge neutralization and entropy considerations when a.second ligand adds to either copper or cadmium ; abnormal effects accompany the addition of a third ligand to cadmium.
Introduction An increasing number of studies of mixed-ligand complex formation has appeared during the past decade. Mixed-ligand complexes are those in which more than one kind of ligand, other than the solvent molecule, are present in the innermost coordination sphere of the central metal ion and can be represented by the general formula [MXiYjzk. . . 1. &lost of the previous studies have made use of spectrophotometric measurements, *-12 some have involved potentiometric measurements using metal-metal ion or oxidation-reduction elec(1) Based in part on the P h . D . thesis of Donald L. McMasters submitted June, 1959. (2) G. Schwarzenbach and A. Willi, Hels. Chim. A d a , 34, 528 (1951). (3) G. Schwarzenbach and J. Heller, ibid., 676, 1876, 1889 (1951). (4) J. I. Watters and E. D. Loughran, J . A m . Chem. Soc., 76, 4819 (1953). (5) J. I . Watters, J. Mason and A. Aaron, ibid., 76, 5212 (1953). ( 6 ) R . DeWitt a n d J. I. Watters, ibid., 76, 3810 (1954). (7) M . W. Lister and D E. Rivington, Can. J . Chem., 33, 1591, 1603 (1955). (8) W. E. Bennett, J . A m . Chem. SOL.,79, 1290 (1957). (9) D. L. Leussing and R . C. Hansen, ibid., 79, 4270 (1957). (10) L. S e w m a n a n d D . N. Hume, i b i d . , 79, 4571, 4581 (1957). (11) A. A. Schilt, ibid., 79, 5421 (1957). (12) A A . Schilt, ibid.. 82, 3000 (1960).
t r o d e ~ , ~ ,while ~ , ' ~others . ~ ~ made use of data obtained from pH titration curve^.^.^^-^^ The formation constants evaluated in the above studies, as well as purely statistical considerations, indicate that mixed-ligand complex formation is a general and common phenomenon whenever two or more ligands are present in solution and that actually mixed complexes should be preferred over simple complexes whenever the concentrations of the ligands involved are such that the products of the formation constants for the simple complexes and the concentrations of the ligands, raised to the appropriate power, are approximately equal, ie., Khlxi[XIi = K h I Y , [ Y ] j= KhlZk[Zlk.. . . Although the polarographic method has been widely used in the study of single-ligand systems, no general discussion of the application of the method to the study of mixed-ligand complexes (13) J. L. Watters and J. Masou. ibid.. 1 8 , 285 (1956). (14) J. I. Watters, J. Mason and 0. E. Schupp, 111, ibid., 78, 5782 (1956). (15) S. Fronaeus, Acta Chem. Scand.. 4, 72 (1950). (16) A. E. Martell, e1 at., J . A m . Chem. SOL.,79, 3036 (1957): i b i d , 80, 2121, 4170 (1958). (17) W. E. Bennett, i b i d . , 81, 246 (1959). (18) J. I. X'atters, i b i d . , 81, 1560 (1959). (19) J. I. Watters and R , DeWitt, ibid.. 62, 1333 (ISGO).
4700
U'ARD
B.
SCIIAAP A N D
DONALD L. MCMASTERS
has been published. This application involves an extension of the DeFord and Hume polarographic method for studying single-ligand complexes.20 Such an extension was made by Davisz1 in this Laboratory in an unpublished study of basic tin pyrophosphate complexes. Also, Watters and Mason13 derived the equation of the polarographic wave for the special case of mixed-ligand complexes of mercury and used their equation to test polarographic reversibility of the mixed complexes but not to determine their formation constants. The copper-ethylenediamine-oxalate system was investigated prior to this study by DeWitt and W a t t e d using spectrophotometric techniques. It was included in the present study to allow comparison of results obtained by the two methods. Recently, Wattersls has reinvestigated this system using p H titration measurements and has obtained essentially the same results as in his spectrophotometric study. The cadmium-ethylenediamine-oxalate system provides an example of a hexacoordinate system and has not been studied previously. A study of the analogous nickel system with these ligands was reported recently by Watters and DeWitt. l9
Theoretical
Pw ... (X,Y . . . I
Vol. 83
=
2
i+j+
K i , J ,.. [x]i[y]i"./faaXtYj.
(4)
...e0
If the expression for [MI in eyn. 3 is substituted into the Nernst equation describing the potential of a dropping mercury electrode a t whose surface the metal ion is reduced to a soluble amalgam, then Ed.m.0.
=
Ea'
.[XI'[YI'.../~MX~P~...
!Y n5
In
[$
1
1
(5)
[MXiYj... ] O / ~ M X.~. Y ~ .
The definitions of the various symbols used in equation 5 and below are well known and will not be repeated here.1av20J3 It can be shown that C a o = i / k I a and that (id
- i)
E
k i+j+
5...
lij
...(CMxiYi... -
C'MXiYi
...I
-0
It is not necessary to assume that the diffusion coefficient for each complex, I i j . . ., is the same, as done by Watters and Mason, rather let IC be the observable "weighted average" diffusion coefficient for all diffusing species giving rise to the electrode current in a given solution.20 Thus
The inathematical treatment of polarographic data for the determination of the formation constants of successive single-ligand complexes has [MXiYj., .]o/fMXiUj.. . = ( i d - i ) / k I o been described in detail by DeFord and HumeZa (6) +j+...=O and makes use of the graphical approach of LedeaZ2 This treatment can be extended to the more general The equation of the polarographic wave then becase in which more than one kind of ligand can add comes to a given central ion to form mononuclear comp l e x e ~ , ' i.e. ~.~~
5
hi
+ iX + j W + ... ,
MXiYj
... .
(1)
(For simplicity and generality, charges will not be included in the equations.) The activity of each species may be expressed
.
[MX,Yj.. . ] =
Kij
... IM][X]'[YlJ.. . (2)
'The constants, Ki;. . ., are the over-all complexity constants for the indicated complexes. If the total analytical concentration of the metal ion present in all forms is designated z1hf and if AT is the maximum number of ligands coordinated, then [MI= P . /
:
i+j+
...-
Kij
(7)
The first three terms on the right-hand side of equation 7 represent the half-wave potential of the complexed metal, ( E I / ~ ) The ~. difference between the half-wave potential of the uncomplexed ("simple") metal ion, (,?31/~)~, and that of the complexed ion is
. . .[X]'[UI'.../fiaxiYj.. . ( 3 )
0
where f is an activity coefficient and Koa. . . 1. In equation 3, 2 h is easily known and [MI is obtainable from polarographic measurements, as described below. The activity coefficients are usually not known, so are most oiten held as constant as possible by maintaining a constant ionic strength and are incorporated into the equilibrium constants, which are then valid only for the conditions of the experiment. By definition, Leden's Fa function for this more general case becomes (20) D . D . DeFord and D . N. Hume, J . Am. C h e m SOC.,73, 5321 ( 19.5 1).
(21) J. A . Davis, P h . D . Thesis, Dept. of Chern., Indiana Univ. Bloomington, Ind., 1955. (22) I. Leden, 2. physik. Chcm., 1888, 160 (1941).
Thus, F w , , . (X,Y. . . ) =
All terms in equation 9 are readily evaluated from polarographic data except for f M , which is usually incorporated into the equilibrium constants. For the sake of brevity and clarity, the description of the analysis of the Foa,.. function for the formation constants of the mixed-ligand system will be restricted to the case of two different ligands of the same functionality, assuming that at most a total of three can add to the central ion. (23) I. M. Kolthoff and J. J. Lingane, "Polarography," Vol. I, 2nd Ed., Interscience Publishers, Inc., New York, New York, 1952, Chapters XI and XII.
Dec. 5, 1961
POLAROGRAPHIC STUDY OF MIXED-LIGAND COMPLEX FORMATION
(In the studies of C u f 2 and Cd+2 reported below, a total of two and three of the bidentate ligands can add, respectively.) Further extension of the treatment to apply to the addition of a total of four or more ligands, or to more than two types of ligands, will be obvious from the discussion below. I n the latter case, however, considerably more data would be needed t o evaluate the constants. The FW(X,Y) function can be factored and written in the form
+ KPl[YI + Koz[Yl* + Kod[YlaJ [XI0 + + KlJYl + KIZ[YI*l[XI + ( L o + K*l[YII[XI* + IKaoJ [XIa (10) Fw(X,Y) = A + B[X] + C[X]* + D[XI3 (11)
FoO(X,Y) = (Koo {KlO
or
where the quantities A , B, C and D are defined by eq. 10 and are constant a t each given value of [Y]. If experimental data are obtained under conditions such that the activity of one of the ligands remains constant while the other is varied, which is particularly easy to do if the ligands vary significantly in basicity, then the resulting FOO data can be readily analyzed by a Leden-type approach. The value of the constant A a t a given activity of Y can be calculated if the consecutive formation constants are known for the simple system containing the metal ion with Y alone. This value of A may be compared with the value of A obtained by plotting Fmversus [Xi a t the same value of [Y]. The plot represents a cubic equation whose intercept a t [XI = 0 is A and whose limiting slope a t [XI-tOisB. If the intercept value of A is subtracted from Fo0and the resulting quantity divided by [XI a t each value of [XI, then a plot of this FIOfunction versus [XI represents a quadratic function whose intercept is B and whose limiting slope is C, ;.e.
4701
Some judgment must be exercised in choosing the Y concentration range over which the various constants are evaluated. The concentrations should be chosen so that the corresponding complexes are present in solution in appreciable amounts. At concentrations far removed from these regions, the Fij values may vary widely and become meaningless.
Experimental Chemicals.-All chemicals were of reagent grade and were uot purified further except the Eastman Kodak (white label) ethylenediamine, which was distilled twice under nitrogen from sodium a t reduced pressure. Standard solutions of copper( 11) sulfate, ethylenediamine, nitric acid and potassium oxalate were prepared and standardized according to generally accepted procedures. Apparatus.-All polarograms were recorded with a Sargent Model XXI Visible Recording Polarograph a t a sensitivity of 0.020 microamp. mm.-1 with no electrical damping. The effects from the very slight non-linearity in the slidewire were cancelled out, or minimized, by recording every polarogram over the same portion of the slidewire. Potential measurements were made before and after the wave to the nearest 0.01 mv. with a potentiometer. Potentials a t various points along the wave were obtained by interpolation. Voltages were corrected for iR drop arising from the resistance of the cell and the measuring resistor of t h e Polarograph The dropping mercury electrode, when inserted into a solution containing 1.0 hl NaN03, had a drop time of 4.36 sec. per drop and a flow rate of 1.78 mg. set.-' of mercury a t a column height of 49.0 cm. and a t the potential of the saturated calomel electrode. The H-type electrolysis cell and the water-jacketed s.c.e. reference electrode were kept a t a constant temperature of 25.0 f 0.05'. The current and voltage data obtained from the recorded polarograms were analyzed for the least-squares-best El/, values and slopes using an IBM 650 computer program described previously.26 Measurement of pK. Values of the Ligands.-The ionization constants of oxalic acid and the acid form of ethylenediamine were measured a t several different concentrations in solutions of ionic strength 1.0, adjusted with sodium nitrate, so that these constants would be known under conditions corresponding as closely as possible to those employed in the mixed complex studies. To obtain the two pKa values for each ligand, the calculated amount of sodium nitrate was added so that the ionic strength would be 1.0 a t the or a t the J/4-point of the total titration curve. Thus, two titrations were required a t each concentration of ligand employed. The basic forms of the ligands were titrated a t 25 f 0.1' with a standard nitric acid solution. The pH measurements were made with a Beckman Model G PH meter. The PKa values read from the titration curves are given in Table I.
.
Continuing this procedure, the F 2 0 function is seen to be linear with slope C, and F30 is equal to the constant D,the F W vs. [XI plot being horizontal to the [ X J axis. In actual practice, least squares intercepts and slopes, calculated from the Fij TABLE I data with an IBM 650 electronic computer, as described p r e v i o u ~ l y ,were ~ ~ used to guide the IONIZATION CONSTANTS OF THE ACIDFORMS OF ETHYLENEgraphical extrapolations in order to obtain more DIAIIINE AND OXALATE ION accurate intercepts, and ligand concentrations a t Conrn., \. 1 PIC1 PKr constant ionic strength were used in place of activiEthylenediamine: ( p = 1.0) ties. 0.002 7.38 10.10 Equations 10 and 11 show that D is equal t o .02 7.38 10.06 K30, the over-all complexity constant of the simple .2 7.31 9.85 system containing the metal ion with X alone. The value of C is equal to Kzo Kzl [ Y ]and allows Potassium oxalate: ( p = 1.0) the value of K21 to be calculated directly if Kzo is 0.002 2.77 3.60 known for the simple system. The expression for .02 1.90 3.43 B contains two unknown constants, Kl1 and K I ~ , .2 (PPt.1 (PPt.) in addition to Klo, which can be known from the simple system; thus B must be measured a t a miniFormation Constants of Single-Ligand Complexes of Copmum of two different values of [Y] to evaluate the per,-The formation constants of the complexes of copper two unknown constants. (and cadmium) with ethylenediamine and with oxalate
+
(24) D. L. McMasters and W. B. Schaap, Proc. Indiana Acad. Sci., 67, 111 (1958).
were measured separately prior t o the study of the mixed-
-
(35) D. L. McMasters and
W.B. Schaap, ibid., 6T, 117
(1058).
4702
M’ARD B. SCHAAP AND DONALD L. MCMASTERS
ligand system. The conditions used corresponded as closely as possible t o those planned for the mixed system, i.e., p = 1.0, adjusted with sodium nitrate. The values obtained for the single-ligand system are needed in the calculation of the formation constants of the mixed-ligand complexes or may be compared with the results of the mixed system. I n the studies with ethylenediamine, all solutions conM C U +and ~ O . O O l ~ o “Triton X-100” as tained 4.8 X maximum suppressor. The pH was adjusted with ” 0 3 and sufficient NaN03 was added to make the ionic strength equal t o 1.O. The concentration of “free” ethylenediamine, [en],was calculated from the pH and the total amount present, using the appropriate pK values from Table I. The experimental data and the Fj(X) values for the single-ligand systems will not be included here, only the results. In the oxalate system, the same concentration of C U + ~ was used, but no maximurn suppressor was needed. The concentration of the divalent oxalate anion, [ox], was varied either by varying the total concentration of potassium oxalate ( p H > 5) or by decreasing the p H below 5 and calculating [ox]using the ionization constants in Table I. The half-wave potential of the simple cupric ion, (E1/2)8, measured to &O.l mv. in 1 M hTaN03a t the time of each series of polarograms was run, varied between +0.025 t o $0.029 v . GS. s.c.e. for the various series on which the calculations are based. The average of the experimental values of &(en), which is equal t o
