March 20, 1960
COMPLEXES OF NICKEL(II)ION
[CONTRIBUTION FROM MCPHERSON CHEMICAL
LABORATORY, THEOHIO
1333 STATE UNIVERSITY]
The Complexes of Nickel(I1) Ion in Aqueous Solutions Containing Oxalate Ion and Ethylenediamine BY JAMES I. WATTERS AND ROBERT DEU'ITT~ RECEIVED MAY21, 1959 T h e composition and complexity constants of the nickel(I1) complexes in solutions containing mixtures of ethylenediamine and oxalate ion have been determilied. Two new saturated mixed complex species, Ni( ( 2 2 0 , hen-* and S i ( C20ri(e!i)P, have been identified in aqueous solutions containing a n excess of oxalate and the corresponding stoichiometric proportlons of nickel(I1) ion and ethylenediamine. LVith less oxalate present, the mixed complex SiCZ01en0 also was obtained. The stepwise equilibria of nickel(I1) with one to three oxalate ions have been established and the previously unreported formation constants have been solved on the basis of PH titrations. The stepwise formation constants of Ni(C204)3-4 are K1 = Ks = 103.06and K 8 = 101.86. The over-all complexity constants of the mixed complexes in terms of equilibria with the aquo NiC204(en)zo, PIZ = 10l6.l5. nickel(I1) ion and the free ligands are: NiC20aenO. lal, = 1011.29; Si(CsO4)2en-*, Pzl = 1013.02; These constants were obtained in 1 ill KXOS at 25".
Introduction The equilibria of tetracoordinate copper (11) ion with mixtures of oxalate ion and ethylenediamine have been discussed in previous paper^.^^^ Since nickel forms hexacoordinate complexes with ethylenediamine and other ligands, the possibility of forming a t least three mixed complexes with two bidentate ligands was recognized. The system nickel(I1) ion, oxalate ion and ethylenediamine, was investigated with the purpose of gaining more insight on the factors influencing the stability and the absorption spectra of complexes, especially those containing different kinds of ligands. The stepwise addition of three ethylenediamine ligands (hereafter indicated by the symbol, en) to nickel(I1) ion has been extensively investigated.6J Poulsen and Bjerrum' recently obtained the values 106.35 and 104,42 for the successive formation constants and 1018.28 for the over-all complexity constant of Ni(en)3+zin the presence of 1 M KNO, a t 25") in close agreement with the values obtained in this Laboratory. The oxalate complex has been investigated a t very low ionic strengths by means of conductivitys and solubilitys measurements, but no previous systematic study of the stepwise equilibria has been reported. In the latter study it was found that two oxalate ions are bound even in millimolar oxalate concentrations. The total complexity constant for bis-(oxa1ato)-nickelate(I1) was found to be a t 25'. In the present investigation it will be shown that a third oxalate ion can also be bound to nickel(I1) in solutions containing larger oxalate ion concentrations. Sartori'O found that the polarographic electrode reaction of nickel(I1) (1) Presented in part before the Division of Physical and Inorganic Chemistry, 131st meeting of the American Chemical Society, Miami, Florida, April, 1957. (2) Based in part on a thesis submitted by Robert DeWitt in partial fulfillment of the requirements for the M.S. degree, June, 19.56. JOURNAL, 76, 3810 (1954). (3) R . DeWitt and J. I. Watters, THIS (4) J. I. Watters, ibid., 81, 1560 (1959). (5) J. Bjerrum, G. Schwarzenbach and L. G. Sillen, "Stability" Constants," Part I, Organic Ligands. Special Publication No. 6, The Chemical Society, Burlington House, W. 1 , London, 1957. (6) J. Bjerrum, "Metal Ammine Formation in Aqueous Solution," P. Haase and Son, Copenhagen, 1941. (7) J. Poulsen and J. Bjerrum, Acta Chem. Scand., 9, 1407, 1955. (8) R. W. Money and C. W. Davies, Trans. Faraday SOC.,%e, 609 (1932). (9) J. E. Barney, W. J. Argersinger, Jr., and C. A. Reynolds, THIS JOURNAL, 78, 3785 (1951). (IO) G. Sartori, Gam. chim. i t d , 64, 3 (1934).
in oxalate solution was irreversible, so the shift in half wave potential is not a reliable criterion for complex stability .
Theoretical The general equation for the various complex equilibria, assuming the absence of polynuclear species is (MA&) M Jr aA 4- bB J_ MAaBb; bob = (M)(A)"(B)b
Throughout this paper the numerical subscripts after the complexity constant, p, or the stepwise constant, K , indicate the numbers of A and B ligands, respectively, in the higher complex involved in the equilibria. In the present study M indicates Ni+2,A indicates CzOa-2 and B indicates en. The coefficients, a and b, may vary from zero to three, but their sum does not exceed three. Parentheses indicate concentrations and brackets indicate activities. N' indicates the maximum number of bound ligands. One mav write for the mean number of bound A
The coordination by hexacoordinate nickel (11) of three bidentate ligands, instead of two as is usual for copper (11), makes the mathematical treatment more involved than that in the previous paper in which the calculations were e ~ p l a i n e d . ~ Just as in the former case, the formation functions can be solved for the cases in which f i b is equal to or close to a half integer while fi, is equal to or close to an integer. The calculations are further complicated by the simultaneous existence of several complex species in practically all of the solutions. In this study, the complex species which must be considered are MA, MA2, MA,, MB, MB2, MBs, MAB, MAzB and MAB2. Since there is an unknown complexity constant for each of these nine complex species, a t least nine, or, in general, (N'+3)N'/2 equations
1334
JAMES
Vol. s3
I . WATTERS AND ROBERTDEWITT
are required. In general, three additional equations where the subscript r after K indicates that K are required since the oxalate ion concentrations is a replacement constant, and the numerical are unknown in the ligand deficient solutions. The subscript indicates the number of B ligands present following f i b equations fulfill the requirements for in the complex after the replacement of an X solving the complexity constants, while ( C Z O ~ - ~ligand. ) A combination of equations 1 and 17 can be solved by means of the fi, equations. yields the relations (18-20) between complexity In the present study the fia function can be and replacement constants. Temporary values written for this constant can be obtained from the known
Substituting complexity constants for complex concentrations yields
The latter equation can be rearranged as follows t o collect terms
+ ( 2 - iia)$m(A)' + (1 -
(3 - iia)P30(A)~
Ea)Plu(A)
+ ( 2 - ffa)Pzl(A)' B + (1 - na)P11(-4VB)' + (1 Eo)PiI(A)(B)
=
+
+
fiaP03(B)~ iiaB~?(B)~ ffi,Pui(B)
fia
(6)
For the particular case in which R , has the values 1 or 2 the later equation takes the following forms For E , = 1 i t becomeq
+
+
+
+
2Pi0(-4)~ $,u(A)' P2:(-4)*(B) = P u J ( B ) ~ PudB)' +PG.(B) 1 For iio = 2 it becomes &(AI3 - Diu(A) - Pi?(A)(B)' - Pi:(A)(B) = ~ P o ~ ( B 2802(B)' )~ ~PoI(B) 2 Equations 9 and 10 for f i b correspond t o equations 4 and 5 for f i a
+
(3 -
nb)
For
- P u ~ ( Bf ) ~( 2 - na)Puz(B)'
fib
=
(7)
+
(8)
+ (1 -zb)Pu1(B) + (2 - Zb)Pn(A)(B)' + (1 - %)L%i(A)'(B) $. (1 ( 4 ) ( B ) = naP30(-4)~+ ?ibPio(A)' + ?ibBiu(A) f Et
nb)P11
(11)
1/2 it becomes
+ + &(B) + 381?(A)(R)' + P?i(A)'(B) + Pl:(A)(B) = P ~ o ( A+) ~Pd-4)' + Plu(.4) f 1 For f i b = 3 '2 it becomes ~ P ~ o (+ A 382o(A)' )~ + 38iu(A) + 3 3Pu3(BI3 + PodB)' - Pui(B) + Pn(A)(B)' - D;i(A)*(B) - Bii(A)(B) For f i b = 5/2 i t becomes P O ~ B-) Puz(B)' ~ - 3Pui(B) - Pip(A)(B)' - 3&i(A)*(B) - 3&(A)(B) = ~ P J ~ ( + A )5PdA)' ~ + 5Pio(A) + 5 ~ P o ~ ( B 3Po?(B)' )~
One set of conditions which often can be used to solve the complexity constants of the saturated species is that in which the exccss concentration of ligand A is large enough so that most of the coordination positions are occupied. Under these conditions certain unsaturated species can be omitted from eauations 9 to 13. Equations of the form fi, = N' f i b are equivalent t6 the corresponding f i b equations. The stepwise addition of B to unsaturated species can be used to correlate and consequently to solve complexity constants from data obtained in ligand deficient solutions, thus
(12)
(13)
(14)
evaluating complexity constants in solutions containing sufficient excess of ligand A so that most of the coordination positions of iLI are occupied by A or B ligands. The general expression for these equilibria is MAW1Bb- i
+B
MAaBh
+ A;
(hlA,Ba)(A)
Krb
=
(MA=+, B ~ - ~ ) ( B ) (17)
A and B concentrations by assuming that (Rf-kaBb) and (kfAa+lBb--) are equal a t f i b = b - '2. Pab K7b = ___ I?(.+
(18)
l ) ( b - 1)
K,i.K,,.....'KvnP o n / P n o K,,,Kv,.Kr, =
Pu3/P30
(19)
(20)
The exact procedure for solving the formation functions for the various complexity constants depends somewhat on the relative stabilities of the where the subscripts after the K indicate the for- various complexes. If the bonding of oxalate ion mula of the product after the stepwise addition of by nickel(I1) had been essentially quantitative one molecule of B. It is possible to use these tem- when present in (1 : 1) or ( 2 : 1) ratios, the calculaporary constants obtained for mixed complexes tions of complexity constants on the basis of tema t half integer values of f i b t o solve mixed com- porary stepwise constants, K,b or &,, would have plexity constants by successive approximations.6 been relatively easy. That such was not the case For example, the complexity constant P ~ of z M A ~ B z was discovered when (CzOI-2) was calculated by can be expressed as /&.K11.K12. substituting the temporary constants and the Replacement equilibria prove very useful in known (en) into the fior = 1 or a,, = 2 equations,
March 20, 1960
1335
COMPLEXES OF NICKEL(II)ION
particularly in the later case, where the subscript OX indicates oxalate. When this situation became evident, the complexity constants of the saturated species and of bis-(oxalato)-nickelate(II), as well, were calculated first by successive substitutions of data for solutions containing an excess of oxalate into the appropriate fzenequations containing only the terms for these species, with alternate corrections of the free oxalate ion concentration for loss through complex formation. The complexity constants of the unsaturated species, Ni (C204)2-2, NiC20d0 and NiC20Aeno were then solved simultaneously in determinant form by substituting data for solutions which were deficient or low in ligand concentration into the appropriate fie, equations. The oxalate concentrations were solved alternately by substituting the improving temporary constants and the known en concentration into the appropriate fioxequation. The values of aOxwere successively corrected for free ion concentration. Details of the calculation will be discussed in the next section. Spectrophotometric calculations are based on the expression 3
3
A = lOgIo/I =
€abCobl a-0
(21)
b=O
where A is the absorbance and €ab and C a b are the molar absorbance coefficient and the molar concentration, respectively, of the complex species MAaBb. The cell's light path length in cm. is indicated by 1. After solving PB from the known f i b value or pH with a known excess concentration of A, i t is possible to solve the concentration of each species by the equation (MAaBb) = @ab(A)n(B)* X
CM
N,
N,
a=O
b=O
BdA)b(B)" (22)
f
In solutions containing so large an excess of ligands that only saturated species are present, the two absorbance curves obtained with pure ligands A and B and two obtained in the presence of known $B or f i b are sufficient for the calculation of the molar absorbance coefficients and the absorbance curves of the two saturated mixed complex species. Experimental T h e apparatus, spectrophotometric techniques and preparation of the ethylenediamine are described in a previous paper.l In addition, stock solutions of 0.500 M nickel (11) nitrate were prepared and standardized by the conventional electrolytic and gravimetric'2 dimethylglyoxime methods. Separate portions of potassium oxalate were weighed to prepare concentrated 1 X oxalate solutions. h stock solution of 1 M K2C204 was used in preparing t h e more dilute oxalate solutions for the PH titrations. The pH titrations a t p = 1 were performed by adding 2.372 N H N O I from a microburet to 50 ml. of the solution containing 0.02 M Xic2, 0.06 M en, and varied concentrations of C Z O ~ - ~T. h e ionic strength was adjusted t o 1 M with KN03. T h e solutions were stirred by bubbling purified nitrogen through them until the PH readings became constant. Most of the spectrophotometric experiments were made in 1 M K~C204. All experiments were performed a t 25". (11) J. I. Watters and E. Dan Loughran, THIS JOURNAL, 76, 4819 (1953). (12) W. F. Hildebrand, G. E. F. Lundell, H. A. Bright and J. I. Soffman,"Applied Inorganic Analysis,'' 2nd Ed., John Wiley and Sons, Inc., New York, N.Y..1953, p. 408.
05 w
z 204 0
c m
0 3
C 2
(
1
6CO
IOOC WAVELENGTH,
I200
T!A
Fig. 1.-Absorbance curves of nickel(I1) complexes with ethylenediamine, oxalate and their mixtures. Effect of varying the ratio (h'i+2):(C204-2):(eo) by varying the amount of ethylenediamine added. All solutions contained 0.05 M Xis04 and 1.0 M KzC20n. Absorbance = log I d I : 1 cm. cells were used: (1) no en; (2) 0.05 M en; (3) 0.10 M en; (4) 0.3 M en; ( 5 ) calculated for Ni(CzO&en-2; (6) calculated for NiC204(en)oa.
Results and Discussion The first phase of the research2 consisted of spectrophotometric experiments in which the concentrations and ratios of oxalate ion to ethylenediamine were varied stoichiometrically or by the addition of acid. It was observed that with en absent the absorption of 0.025 M nickel(I1) increased greatly as the concentration of potassium oxalate increased from 0.1 M to 1 M . On the basis of published complexity constants, the conversion to bis(oxa1ato)-nickelate(I1) should have been essentially quantitative a t the lower oxalate concentration. That a third oxalate ion is bound by the nickel (11) ion in high oxalate ion concentrations was confirmed in pH titration experiments discussed later. Most of the spectrophotometric studies were performed on solutions containing 1 M KzC204 in order to shift the equilibrium between Ni(Cz04)2-2 and Ni(Cz04)3-4nearly quantitatively toward the latter. Absorbance curves of solutions containing 0.05 M Ni+2, 1.0 M KzC204, and with concentrations of en increased by 0.01 M increments, were obtained in the wave length range of 500 to 1300 mp. A third absorbance band in the ultraviolet was not investigated because of its proximity to the oxalate band. For clarity only the absorbances of solutions containing nickel ion and en in integral concentration ratios of 1:0, 1: 1, 1:2 and 1:6 are included in Fig. 1. The theoretical absorbance curves 5 and 6 for the pure species Ni(C20&en-2 and NiC204enzo can be compared to curves 2 and 3, respectively, for the actual equilibrium mixture containing the same ratios of (Ni+2): (en).
1336
Jams I . WATTERSAND ROBERTDEIYITT
Curve 4,Fig. 1,for Ni (en)1+* contains a maximum i n the visible region a t 540 tnp and one 1ri the photoelectric infrared region a t 890 mp. Curve 1 for
VOl. s2
the first, but not the second, inflection. Increasing concentrations of oxalate caused the lowering in PH to decrease without changing the shapes of the Ni(C204)3-4contains two corresponding maxima titration curves. a t 668 and 1105 tnp. The absorbances of all the The titration data are given in Table I. The intermediate solutions exceeded those of the simple total added concentrations of Cz04-2and H + are complexes in the region between 540 and 665 mp, listed under the columns indicated by Coxand CH, proving the presence of other complex species. respectively. The values of pen and fien were The absorbance was much greater than was ob- calculated in the usual way6 from the pH and tained by a similar change in en concentration in the CH,using the values Kl = 1 0 - 7 . 5 6 and K 2 = 10-10,22 absence of oxalate ion, indicating the presence of for the acidic dissociation constants of H2enf2 oxalate ions in addition to the en in the intermediate in 1 hf KS03 a t 25". These values decreased to complexes. The first few curves of solttions hav- 10-7.66and 10-10.30,respectively, when the ionic ing (Ni+*):(en) ratios of 1:0 to 1 : 1 had isosbestics strength was maintained a t unity with 0.25 close to 485, 660, 800, 1090 and 1240 mp. The KzC204 and 0.25 M KNOa a t 25". The pen values last curves in the (Ni+2): (en) ratios of 1 : 2 to 1:6 had a t half integral values of fie,, were obtained by ina different set of isosbestics close to 470, 710 and terpolation. Duplicate series of titrations using 840 mp. These effects can be accounted for by the 0.05 Ad Ni+* and 0.15 M en are not included since presence of at least two new species. The failure they yielded nearly identical results. of the isosbestics to persist in the region of (Ni+') : The stepwise formation constants of the simple (en) ratios of 1:1 and 1:2 indicated the simultaneous Ni(en)3t2 complex were calculated by Bjerruni's presence of more than two complex species in these method6 of successive approximations in which the solutions, with stepwise replacement constants temporary formation constants were substituted differingby less than 100 fold. into the formation functions. The calculated By analogy with the observed behavior of copper stepwise formation constants for Ni(en)3+2 were (11) in similar solutions, the presence of saturated 107.61,106.39 and 104.35,all with a niaximum deviamixed complexes having formulas Ni (C204) (en)zO tion of l0*O.O4. These values agree well with the and Ni(C204)2en-2 was postulated. Precipitates corresponding values 107.61,106.35and reformed quickly in the solutions having compositions ported by Poulsen and Bjerrum7based on the values corresponding to Ni(Cz04)en-* and NiC204en2°. K1 = 10-7.4yand K 2 = 10-10.17for the acid disConsequently, Job's method was now applied to sociation constants of Hpen + 2 under identical conthe absorbance in a somewhat different way to ditions. indicate the existence of complexes containing Ni+2 4 t this point six equilibrium constants remained and en in 1:l and 1 : 2 ratios. In this study the to be determined. Furthermore, the oxalate ion role of the oxalate ligand became analogous to concentrations were unknown in the ligand dethat of water in the usual Job's method, since its ficient solutions but could be estimated quite acconcentration was kept large and constant. Fur- curately in the presence of excess ligand. Atthermore, any of nickel's six coordination positions tention first was directed to those solutions connot occupied by en were assumed to be occupied by taining a relatively large excess of both ligands, so bidentate oxalate ions. The solutions containing that the only species besides Nie113+~present in (Ni+2): (en) ratios of 1:0 and 1:3, respectively, cor- significant concentrations were NiC204(en)2', Niresponded to the solutions to be mixed, while the (C204)2en-2, Ni (CaoJa-4 and Ni (C204)2 -2. Temporary constants were obtained for Ni solutions containing intermediate ratios of (Ni+2): (en) corresponded to their mixtures in various Cz04(en)Z0,n'i(Cp04!2en-2 and Ni(Cp0.1)3-~on the ratios. The presence of species containing Ni+2 basis of the following considerations. When fien and en in ratios of 1: 1 and 1 : 2 was indicated by changes from 3 to 2.5, in the presence of excess oxamaxima a t x = 0.33 a t 640 mp and at x = 0.67 a t late, stoichiometry considerations indicate the 540 mp. presence of approximately equal concentrations of As a consequence of the simultaneous presence of Nien3+2 and NiC204en20. At %en = 1.5, approxiseveral complex species in most of the solutions, mately equal concentrations of NiC204 (en)yo and the pH method based on formation functions proved Ni(C204)~en-~are indicated. At f i e , = 0.5, to be less cumbersome and more accurate than approximately equal concentrations of Nispectrophotometric methods for calculating the (Cz0&en-2 and a mixture of Ni(Cz04)~-~and various equilibrium constants. The procedure Ni(C204)2-2 should be obtained. These temfor the calculations differed somewhat from that in porary constants, indicated by primes, were obthe previous publication4 because the oxalate was tained from the titration in the presence of 0.25M not always quantitatively bound in the ligand de- oxalate as indicated: a t fieri = 2.5, neglecting the ficient solutions, or even in the presence of a moder- trace of Ni(Cp04)2-2, the free oxalate ion is Cdlate excess of oxalate. In Table I are summarized culated to be 0.24M , so pox = 0.62. Substitution the pertinent data from the $H titrations of 0.06 of the data into equations 17 and 18 yielded M ethylenediamine solutions in the presence of K'"3 = 102.13, so p'12 = 1016,2j. At aen = 1.5, 0.02 ?If nickel(I1) ion and concentrations of neglecting Ni(C204)2-2, (C204-2) = 0.22 M , SO oxalate equal to zero or integral multiples of the pox = 0.66. Substitution of these data into equanickel(I1) concentration. Just as in the cor- tions 13 and 15 yielded K1,2 = lo3,% and P'ZI = responding copper system, the presence of nickel 10*2.sg.Xt %en = 0.5, no significant error was in(11) resulted in the lowering of the pH titration troduced in (C204-*) by neglecting Ni(CzO&-', SO curve by nliout 3 p€I units and the elimination of (C204-'j = 0.20 Ad arid pox = 0.70. Substitution
March 20, 1960
1337
COMPLEXES OF NICKEL(II)ION
TABLE I TITRATION DATAAND CALCULATIONS WITH VARIEDOXALATE CONCENTRAT~ON Fifty ml. of the solution titrated contained 0.06kl ethylenediamine, 0.02Af Nii2 and varied concentrations of C204-I ion, with KSOa added to produce a n ionic strength of unity a t 25'. Nitric acid, 2.372N , was added from a 10 ml. microburet. The total concentration of nitric acid in 50 ml. of solution is indicated under the heading CH,while pen and pox indicate -log (en) and -log (CzOr-2). COX
0.0
CH
0 010 ,015
k03
4.37
K
2'544} 2.375
3.85
1.469
5.42
0.470
3 19 (Eox = 0.97)
Kll
7.11
3.47 3.79 5.00 5.12 6.36 6.57 3.26 3.56 4.58 4.71 6.04 6.17
2.526 2.338
1.52
Kr3
1.91
Krz
3.01
1.86
K21
6.46
1.30
Krs
1.99
1.52
Kr2
3.10
1.84
K~I
4.22
.loo .010
.loo
8.80 8.37 7.42 7.15 6.38 6.26
0.010 .015 .050 .055 .095 ,100
8.99 8.57 7.50 7.40 6.54 6.44
.010 .015
9.10 8.66 7.69 7.58 6.80 6.70 9.36 8.94 7.84 7.72 6.90 6.70 9.57 9.16
,015 .050
.055 .095
.040
.045 .OX5 .090
.010 .015 .040 .045 .085 .090
.25
0.0
Log temporary
3.77 4.06 5.33 5.45 6.95 7.17
5,79
.O1 .015 ,040 .045 .080 .OS5
8.01
7.90 7.24 7.15
3.14 3.45 4.32 4.45 5.56 5.87 2.92 3.18 4.15 4.29 5.46 5.76 2.74 3.02 3.97 4.10 4.95 5.11
2.433
Equil. const.
8.53 8.16 i.06 6.97 6.0s 5.96
.095
.15
4.25
90x at half integer
.010
.060
.08
half integer
nen
5.70
.055
.06
pen at
-
.loo .015
.04
8.15 7.88 6.54 6.43
Ben
4.46 6 38 6 16 7.53 7.68
.05A ,060 .095 ,02
9H
}
6.38
0
k02
6.38
0'645) 0.485
7.67
.o
KO1
7.67
2.00
Kra
1.83
2.42
K12
5.42
1.447
(ZOX = 0.81)
. I
1.401 0.439
2,517 2.311
3.29
1.427
1
0.400
2'513 2.301 1.597 1.463
3.16
1.15
Krs
2.01
4.41
1.30
KT2
3.11
0'570 0.492
5.84
1.46
Kr1
4.38
0.85
Kra
2.08
-92
Kr2
3.29
0.354
.99
Kr1
4.48
2.396
.62
Kra
2.13
1.352
.66
K 1 2
3.36
.70
Kr1
4.38
2.228 4.21
1.444
o'680} 0.465
of these data in equations 17 and 18 yielded K',l = 104.3s and ,830 = 10sJ1'. More accurate values of P 1 2 , ,821 and ,830 were obtained by means of successive approximations in the appropriate equation 12, 13 or 14, with successive corrections of (C204-2) for bound oxalate in saturated complexes and finally in Ni(C20&-2 as well. Temporary values of and 108.61 were obtained for the complexity constants of the bis- and tris-(oxa1ato)-complexes by simultaneously solving equations of the form of equation 13 containing the data obtained for the titration in the presence of 0.15 M and 0.25 M oxalate a t Ben = 0.5. Then, values of 1016.1sand l O I 3 . O 4 for ,812 and ,821, respectively, were recalculated
5.08
by means of equations 13 and 14, from the data of the titration in the presence of 0.08 M oxalate a t rten = 2.5 and 1.5. At this stage, the constants ,811 and ,810 for unsaturated species, NiC204eno andT.INiC2040, were unknown and pz0for Ni(C20,J2-2 needed confirmation. Equation 7 for rtox = 1 contains no Pll or 810 terms, so this expression was first solved for (C204-7 using the penvalues of the titration in the presence of 0.02 M oxalate a t rten = 0.5 and 1.5. These results indicated that Cz04-2was essentially quantitatively bound only a t rt,, = 0.5 in the titration in the presence of 0.02 M oxalate, and not even approximately in the presence of 0.04 M
1338
JAMES
I. ITTATTERS .4ND ROBERTn E n 7 1 T T
oxalate. Consequently (C204-2) was solved by successive approximations in general equation 6, with alternate corrections of fiOx for free oxalate ion concentration. The sinal1 contribution of NiC204eno was solved by the use of a temporary constant calculated from the 0.02-11oxalate titration data a t aen= 3 / 2 . Substitution of these data into equations 18 and 19 yielded Klz = and Ptll = 1010.77. These improved data were substitutedinto equation 11to obtain P'11 = 1011.z9. Finally, values of plo, pz0and pll for the unsaturated complexes were solved simultaneously by means of determinants. The data of the 0.02 -11oxalate titration a t fieri = 0.5 and 1.5, and the titration in the presence of 0.06 L1 oxalate a t ?Zen = 0.5 were substituted into equations 12 and 13 along with (C204-2) previously solved according to equation 6 by means of successive approximations. All of the constants converged quickly. The complexity constants values obtained for the mixed complexes are
Vol. 52
The remaining six of eight probabilities are equally divided between MA42Band MAB2. The statistical probability of forming either of the latter is three times that of either simple complex. On the basis of these considerations one would predict a complexity constant for N i ( C ~ 0 ~ ) ~ eof n -3? X P 2 0 2 / ' X P03"', or 1012.29, compared to 1Ol3.O2 observed. The enhancement is Similar calculations for N i C ~ 0 4 ( e n lead ) ~ ~ to a calculated complexity constant of 1015.55, corresponding to an enhancement of
10+o.57. In the calculation of the complexity constant,
PII, for NiC204eno,the statistical factor favoring
mixed complex formation is two. In this case, however, the term P#?' also contains a gross statistical factor of 3 / 2 , since there are only two ligands in the complex whereas the aquo ion has a capacity for three ligands. Thus, the ligand factor becomes (2/3p)l/"''. The observed value, 10".29, is larger than the calculated value, 1010.70, by 1O0.j9. Similar calculations for the copper(I1) complexes, C U P ~ O ~ ( N H ~and ) ~ - CuC204eno, ~ indicate enhancements of about The enhancement may be due to some weak bonding between unlike bound ligands, possibly through hydrogen bonding between the oxygen atoms and the hydrogen of the amine. In any event these calculations indicate The values obtained for stepwise formation con- an interesting and fairly accurate method for estimating mixed complexity constants. Studies of stants of the oxalate complexes are this enhancement of the bonding in mixed complexes for various types of ligands are being continued. The calculations of the molar absorbance coefficients and the absorbance curves for NiCzOl(en)2' and Ni(C20&en-2 require the molar concentrations of the various species. Accordingly the titration procedure was used to calculate the complexity The latter correspond to a value of 10s.51i0.10for constants of the saturated species in the 1 M the over-all complexity constant P30 of tris- (oxalato) - K2C204 solutions in which the spectrophotometric nickelate (11), a value of * O . l o for the com- measurements were made. plexity constant P 2 0 of his-(oxa1ato)-nickelate(I1) The formation constants of N i ( e n ) ~ +a ~ tp = 3 and l O 4 . l o * O . l 0 for mono-(oxa1ato)-nickel(I1). were obtained in a solution containing 3 M KNO3 It is of interest to compare the mixed complexity with oxalate absent. In 3 M KN03 a t 25", pK1 constants with the values which one might predict and PKz of Hzenf2were found to be 7.80 and 10.40, from those of the simple complexes. The free while in 1 M KzC204 the values were 8.17 and energy change, AFO, due to the replacement of the 10.63. From the mean pen values of 7.70, 6.59 bound water in the aquo complex by N' ligands in and 4.64 a t fzen = 0.5, 1.5 and 2.5, respectively, were the simple saturated complex, is equal to - RT In calculated for the stepwise formation constants of P w . If all of the bonds are equivalent the free Ni(en)3+, in 3 Af KN03 a t 25" : K O= 1076.1,& = energy change for each bound ligand must be 106.67 and KO3= 104.65, which correspond to an over- ( R T / N ' ) In 0". Accordingly, the logarithm of all value of 1015.93 for Po3. the N'th root of PN' for a simple complex, log In 1 M KzCz04 the values were 4.60, 3.58 may be taken as a measure of this free energy change and 2.42 a t aen = 0.5, 1.5 and 2.5, respectively. per bound ligand. Bjerrum13has used this value as a From these data, these values were calculated for measure of the complex formation tendency of a the replacement constants in 1 M KzCz04 a t 25: ligand. KV1= 104.49,K,, = 103.69 and K r 3 = 102.49. 'The The gross statistical effect is absent in the com- 6 values obtained were NiCz04(en)20,Plz = 10'6.44; plexity constant of the saturated complex, since Ni(C204)2en-2, P ~ I= Ni(C~04)3-~,030 = there are N' ligands in the complex and N' positions 105.36. available in the aquo ion. However, there is a The absorbance calculations were made on the statistical factor in the complexity constant of basis of the spectrophotometric data for solutions mixed complexes which can be arrived a t thus: containing 0.05 M Ni(N03)2, 1.0 M KzCz04 and with equal concentrations of A and B ligands the these various (Ni+2): (en) ratios; 1:0, 1: 1, 1: 2 probability that the first bonded ligand will be A is and 1:lo. Values of 4.07 and 3.03 were calculated The probability that three successive A's will for p e n in the (1: 1) and (1:2) solutions, respectively, bond with M to form MA3 is i / z . 1 / 2 . i 2, or one in by means of the fie, formation functions assigned eight. The same probabilities hold for MBa. values of 1 and 2, respectively, proving that the en was essentially quantitatively bound. The con(13) J. Bjerrum, Chcm. Reu., 4 6 , 381 (1950). ,
1339
COMPLEXES O F NICKEL(I1) ION
March 20, 1960
TABLE I1 ABSORBAKCE DATA Visible band Species
a
Wave length, mw
Absorb, M -1 cm. -1
7 -
Half band width, cm. -1
K e n s +z 540 6.56 3220 SiC*O4(en)z0 562 13.44 3000 Ni( CzO&en-2 612 13.30 2910 3340" 668 9.44 Si(C2O4)8-4 These bands have a shoulder in the 700-800 mg range.
centrations of the four saturated species in equilibrium then were solved by means of equation 22. These values in turn were substituted into equation 21 to obtain the absorbance data of Table I1 for the two absorbance peaks in the 400 to 1300 mp region. No detailed study has been made as yet in this Laboratory of the theoretical significance of the absorbance curves. In a series of papers on the application of ligand field theory to complex ions, Jorgensen14 has included calculations on Ni(en)B+2 which agree well with the experimental values for the absorbance maxima. There are indications that a similar treatment of the mixed complexes may not be too involved. First, the frequency of either absorbance maximum was found to be essentially a linear function of the logarithm of the complexity constant of the corresponding complex. As expected, other ligands having a different number of coordination positions, for example, ammonia and ethylenediaminetetraacetic acid, did not fit this relation. This is reasonable, since the statistical and other entropy factors, which also contribute to the equilibrium constant, must be different for ligands having a different number of coordination positions. This linear relation indicates that, a t least to a first approximation, the energy level is a linear function of the ligand field strength. This follows if one may assume that for a particular type of complex the logarithms of the complexity constants are proportional to the bond strength13and, in turn, to the field strength. Although both maxima shifted to higher frequencies with increasing log K , the frequency ratio of the two maxima for a particular complex retained the constant value of 1.65. This effect, which depends on the fact that the various d-orbitals are subjected to the same ligand fields, indicates that the bond type and electron distribution are not changed in this series of complexes. A third characteristic is the enhanced molar absorbance of the mixed complexes compared to (14) C. K. Jorgensen, Acta Chem. Scand., 8, 1495 (1954); 9, 1362 (1955); 10, 887 (1956); 11, 1223 (1957); 12, 903 (1958).
Wave length, mw
Near infrared band-
890 924 1010 1105
Absorb.,
M-1 cm. -1
7.12 9.46
8.88 8.08
Half band width, cm. -1
3050" 2820 2790 2220
Freq. ratio
1.648 1.644 1.650 1.654
that of the simple complexes. This effect may be associated with a greater multiplicity of the dorbital energy levels associated with the unsymmetrical electric field of the mixed octahedral complex. In this connection, the polyethylenediamine15 complexes with nickel(I1) also exhibit exceptionally high absorbances. Since there is evidence of some strain in these complexes, these fields may also be quite unsymmetrical. In this connection, i t should be mentioned that during the stepwise addition of ammonia to nickel(I1) to form Ni(NH3)sf2, the molar absorbance coefficients increases regularly to a maximum for Ni(NH3)4f2, after which i t decreases. N ~ ( N H S ) ~ + ~ and Ni(NH3)b+2,as well as one of the geometric isomers of Ni(NH3)4+2, are unsymmetrical. Statistically, the probability of forming the latter unsymmetrical isomer is two out of three. This enhancement does not necessarily occur in complexes having different geometric configurations. For example, the corresponding copper (11) complex, CuC204eno, which has a square configuration, has a molar absorbance coefficient3 which is intermediate between those of the simple species, Cu(C204)2-* and Cu(en)2+2. In all of the curves there is either a small peak or a shoulder in the wave in the 700-800 mp range. This is believed to correspond to a relatively improbable additional electronic transition in all of the species, rather than to other species such as a hydroxy complex, because this characteristic persists independently of p H variations. Jorgensenl8 has discussed some low intensity bands of transition metal complexes. All curves having the same maxima have the same shoulders even though the composition and @Hare varied. The half band widths given in Table I1 do not yield any unique information. Except for the shoulders and the exceptionally narrow near infrared band of Ni(Cz04)3-4, the widths are 3000 200 cm.-'.
*
COLUMBUS, OHIO
(1.5) T. A. Youness, Ph.D. Thesis, The Ohio State University, 1959. (16) C. K . Jorgensen, Acta Chcm. Scand., 8, 1502 (1954).
