Coordination in the Second Sphere - ACS Publications

13 Coordination in the Second Sphere JANNIK BJERRUM

Downloaded by MICHIGAN STATE UNIV on February 18, 2015 | http://pubs.acs.org Publication Date: January 1, 1967 | doi: 10.1021/ba-1967-0062.ch013

The H . C. Orsted Institute, University of Copenhagen, Copenhagen, Denmark

The concept of coordination in the second sphere was intro duced by Werner. All authors agree that such outer– sphere association exists in solution, but they disagree about the kind and the extent of this association. Some advocate a second-sphere coordination which is closely analogous to the inner-sphere coordination. The data which support this hypothesis are not very convincing and can be criticized in various ways. The present author finds that the electrostatic theories of N. Bjerrum, Fuoss, and Kraus, according to which the formation of the ion-asso ciates is a result of coulombic attraction, both qualitatively and quantitatively, give the most trustworthy picture of the outer-sphere association. However, this does not exclude the fact that some preferred mutual orientation exists in the ion pairs.

T n the third edition of his famous "Inorganic Chemistry," Alfred Werner introduces the concept of coordination in the second sphere and distinguishes between the following possibilities: (1) A group in the second sphere is directly coordinated to a ligand in the first sphere. (2) A complex with fully occupied first sphere has residual affinity to attach groups (addition compounds in the second sphere). (3) A n added group is attached at the same time to the complex and to a group in the second sphere of the original complex (substitution reaction in the second sphere). As an example of the first kind of outer-sphere complex formation, Werner (44) studied the interaction of thiocyanato complexes of cobalt (IH)ammines with silver ions. In these complexes nitrogen is bound to the metal, and the sulfur atom in the thiocyanate group is free to complex

178 In Werner Centennial; Kauffman, G.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

13.

BJERRUM

179

The Second Sphere

metal ions with affinity to this atom. In most cases 1:1 complexes are formed (41) \ D . N . Purohit, Rajasthan, has in this laboratory with a silver electrode determined that the formation constants for the addition of silver ions to various thiocyanatochromium(III) and cobalt (III) complexes are of the 10 order of magnitude. This type of reaction is a special case of the more general category— reactions of coordinated ligands—which has recently been discussed (19). However, one has the feeling that the concept "second-sphere coordina t i o n , " as understood by modern research workers, no longer includes this category of important reactions. The second possibility considered by Werner comes more closely to what is understood today by second-sphere coordination. As an example of this kind of outer-sphere coordination, Werner (43) mentions the addi tion compounds of tris(acetylacetonato) complexes of trivalent metals with various amines. Strangely enough Werner also considers double salts Cl of the Carnallite type formulated as [Me(OH ) ]Q-£ to be compounds of this category. Such double salts are today interpreted as lattice com pounds, but it must be remembered that Werner was without any knowl edge of crystal structures and had to draw his conclusions from the stoichiometrical composition of the solid compounds alone. In order to explain Werner's viewpoints with regard to his third kind of second-sphere coordination, one may consider the fact that a great number of tris(ethylenediamine) complexes of divalent metals crystallize with two moles of water while, on the other hand, tris(ethylenediamine)cobalt(III) halides crystallize with three moles of water. Werner expresses this through formulas of the type: (OH Cl) [Co en ](OH Cl) (OH Cl)


4

2

2

6

2

3

2

2

In a similar way the seventh mole of water in N i S 0 - 7 H 0 , for ex ample, and the fifth mole of water in C u S 0 4 * 5 H 0 are considered to be bound to the sulfate ion in the second sphere. W i t h our present knowledge of the crystal structures of these salts (2, 8), this interpretation is not far from being correct. In crystal lattices one always has an ordered configura tion in the second sphere, and the question discussed in recent years is to what extent one has an arranged and spatially well-defined configuration in the second sphere also for complex ions in solution. 4

2

2

Outer-sphere Association in

Solution

One way, in some cases usable, of obtaining qualitative information about compound formation in solution is to determine the ionic or molecular weight of the association products either by diffusion or dialysis experi-

In Werner Centennial; Kauffman, G.; Advances in Chemistry; American Chemical Society: Washington, DC, 1967.

180

WERNER

merits. Brintzinger and co-workers have developed the last-mentioned method and determined the ionic weights of complex ions in strong salt solutions using selected reference ions of opposite sign (10-18). From their data they draw far-reaching conclusions with regard to the constitu tion of complex salts in aqueous solution. Thus Brintzinger and Osswald (12) think they have proof that complex cobalt (III) cations such as C o ( N H ) , C o ( N H ) C l + , and C o ( N H ) S 0 + form two-shelled complexes of the general type [ C o a ] X - with anions such as S 0 ~ , C 0 ~ , and H P 0 " but curiously enough not with S20 ~ . According to ionic weight determinations of Brintzinger and Osswald the complex formation is nearly complete in 1-2 molar solutions of the anions in question. Other unex pected results of Brintzinger and co-workers are that the divalent metal ions of the first transition group in 2M ( N H ) S 0 or N a S 0 have ionic weights corresponding to the general formula Me (S0 ) "~ (10), and that the tris (ethylenediamine) cobalt (III) ion, contrary to C o ( N H ) 6 and Cren + , is found to have an ionic weight corresponding to the formula Co en (13). These results, as also many other results from the work of Brintzinger, must be taken with all possible reservation for various reasons (88), but mainly because they were carried out with filters whose pores were too narrow (40). Pore size is very critical, and those which are too narrow sometimes cause ionic weights which are too high. Thus, Kiss and Acs (23), by repeating the measurements of Brintzinger and co-workers using better filters, showed the nonexistence of the complex [Co(NH )5Cl] ( S 0 ) - and found that C o ( N H ) C l + i n 2M ( N H ) S 0 has an ionic weight corresponding to the cobalt (III) complex itself (found 174, calc. 180) to be compared with the value 563 found by Brintzinger and Osswald (11). Further, Kiss and Acs (23) have disproved the existence of the binuclear complex M e ( S 0 ) ~ and found that C u S 0 in 2M ( N H ) S 0 has an ionic weight corresponding to the complex C u ( S 0 ) . They have also confirmed that C o e n is not dimeric, in agreement with J . Bjerrum's redox potential measurements of the couple Coen3 /Coen3 (6). 3

6

+ 3

3

2

5

3

6

4

4

4

u

2

4

2

4


CENTENNIAL

3

2

4

2

2

4

2

4

2

2

4

4

4

4

3

+ 3

3

3

2

6

+ 6

3

4

4

6

3

2

4

4

5

2

4

4

2

4

4

4

4

3

2

2

4

- 2

+3

+3

+2

Thus, Brintzinger's dialysis measurements are not reliable even as qualitative evidence for coordination in the second sphere. However, Laitinen et al. (25) have obtained such evidence from polarographic i n vestigations of hexamminecobalt(III) ions in various supporting elec trolytes. The half-wave potential of C o ( N H ) 6 is found to be shifted towards more negative values in the presence of certain ions—e.g., S0 ~~ , and diffusion rates are slower than in a pure chloride or nitrate medium. T o explain these findings, the authors assume that the ions of the support ing electrolytes are clustered about the central complex owing to electro static attraction similar to that on which the ion-association concept of Bjerrum (9) and of Fuoss and Kraus (17) is based. In Bjerrum's theory (9), two ions of opposite charge constitute an ion pair if they are closer together than a certain critical distance: 3

+ 3

4


2

13.

181

The Second Sphere

BJERRUM

ZiZ e

2

2

q

=

2D k T

where z\ and z are the ion charges, e the charge of the electron, D the d i electric constant of the solvent, k is Boltzmann's constant, and T the K e l v i n temperature. According to this criterion considerable ion-pair formation must be expected to occur i n aqueous solutions i n the case of highly charged cations and anions. Such ion association has also been found i n numerous cases (39), and methods as different as those of solubil ity, conductivity, and spectrophotometry usually give values for the asso ciation constant which agree fairly well (33). I n the case of aquo cations it is not always easy to distinguish between coordination i n the inner sphere (normal complex formation with more or less covalent bonding) and the outer-sphere association. However, from the Bjerrum's theory it is possi ble to calculate the dimension of the ion pair from the experimental asso ciation constants extrapolated to zero ionic strength, and because the crystal radii are known one can estimate whether or not the water shell around the cation is penetrated by the anion. For example, the ion pair of the trivalent ions L a ( H 0 ) and Fe(CN) ~~ i n mixed solutions of water and organic solvents has been shown to be an outer-sphere complex i n agreement with Bjerrum's theory (20). More recently the relaxation methods developed by Eigen and co-workers (15) have made it possible to analyze the problem i n more detail and to determine the association con-, stant for the inner-sphere as well as for the outer-sphere complex. Using this technique, Behr and Wendt (4) have i n aluminum sulfate solutions at an average ionic strength J ~ 0.1M estimated the following values for the two kinds of constants:


2

2

N

+ 3

6

_ [ A l ( H O V , 80,-] _ " [A1(H 0) ][S0 - ] " 3

2

A

l

A l

o u t

in

3

2

6

+3

4

2

[A1B0«+, aq] ~ [A1(H 0) ][S0 - ] 2

6

+3

4

2

A

y

±

d

, D

A ligand such as SCN~~ shows a relatively higher tendency to inner complex formation than does S 0 ~ (36). Fronaeus and Larsson (16) as sume that the C — N stretching frequency is nearly the same for the free ligand as for thiocyanate bound i n the outer sphere, and under this as sumption they estimated from infrared absorption measurements the innerand outer-sphere association constant i n the nickel(II)-thiocyanate system at average ionic strengths to be: 4

2

K i m - 12 ±2 M~\

Ki out = 3 ± 2

For the special case of the metal ions i n the first transition group, the absorption spectra i n the visible and ultraviolet can also be used as criteria


182

WEKNER CENTENNIAL

to distinguish between substitution i n the first and the second sphere (45). Thus the ligand field bands characteristic of these ions are changed only by substitution in the first sphere (8), while the electron transference bands also are influenced by the substitution in the second sphere (30). I n the C u ( H 0 ) 6 , S0 ~ -system the ligand field band in the near infra red, which is responsible for the blue color of the solutions, depends only slightly on the sulfate ion concentration—contrary to the electron transfer ence band in the ultraviolet. B y careful analysis of the concentration influence on this band i n lithium sulfate solutions, with y/l varying from 0.2 to 2.6, Nasanen (34) obtained the following expression for the association constant of the ion pair at 2 5 ° C :


2

+2

l o g X

2

4

' =

-rTW/

2 1 0

+

0 0 5 2

7

Owing to the tetragonal distortion of the cupric ions (7), this ion pair must be considered an anisotropic complex as defined by J0rgensen (22)— i.e., an intermediate between an inner- and outer-sphere complex. I n the case of the octahedral robust complexes of cobalt (III) and chro mium (III), substitution i n the first sphere is hindered. This type of com plex ion is, therefore, especially suitable for studying association i n the second sphere. The hexammine and tris(ethylenediamine) cobalt(III) ions have especially been used for this kind of study. For the association of these ions with anions, such as sulfate and thiosulfate, the ion-pair constant is of the order of magnitude of 10 M at / = 0, somewhat smaller for C o e n than for C o ( N H ) (21), but strongly dependent on the ionic strength. Thus Posey and Taube (37), from spectrophotometric measure ments i n the ultraviolet, obtain the following expression for the associa tion constant of the ion pair [ C o ( N H ) ] S 0 4 i n solutions with y/l varying from 0.04 to 0.3: 3

3

+3

3

6

3

1 l Q

1

-

+ 3

r,

o o «

g^- 3

3 2

6

+

6.10 V/ -i+2.oovr

The rather polarizable thiosulfate ion has a much higher influence on the ultraviolet absorption of the cobalt(Ill)-ammine complexes than the much less polarizable sulfate ion (24), but it is noteworthy that the sta bility of the ion pairs formed with the first mentioned ion is even smaller than those formed with the sulfate ion (18). This supports the electro static nature of the second-sphere association. Using Bjerrum's theory, M o n k and co-workers (18, 21) calculated the radii of the ion pairs i n question to have the expected order of magnitude 4-5 A . From the theory it can also be estimated that the constant for the formation of a triple ion [Coa ]X ~ of the considered type and dimensions: 6

2


13.

183

The Second Sphere

BJERRUM

[[Coa ]X j " [[Coa ]X+][X-'] 6

A a

2

6

at zero ionic strength is about 100 times smaller than K\ for the formation of [ C o a ] X . However, K depends much less on the ionic strength than K\ and, if [Coa ]X ~ is formed, which a priori is not very probable, then the value of +

6

2

6

3

3

_ [[Coa ]X,-3] ~ [[Coa ]X -][X->]

v

6


A s

6

2

should even increase with increasing ionic strength. R . Larsson recently has found evidence for a relatively rapid stepwise association i n the second sphere for complexes of the above type. Thus, anion-exchange investigations of Larsson and Tobiason (29) with the hexammine cobalt (III) ion i n sodium sulfate and thiosulfate solutions showed that three sulfate ions or thiosulfate ions were taken up i n about 1M solutions of the ligands. These results were supported by another method. It is well-known since the days of Werner (42) that the optical rotation of dissymmetric complex ions is sensitive to the nature of the accompanying ions, and, as pointed out by Kirschner and co-workers (1), this may be due to ion association. Larsson (26) studied the change in the optical rotation of the D-tris(ethylenediamine)cobalt(III) ion i n sulfate and thiosulfate solutions. It was here characteristic that the curves, which gave the molar rotation as a function of the anion concen trations, went through a minimum for C^ x ~ 0.05M. This gave some evidence for the formation of [Coen ]X+ and [Coen ]X ~, and Larsson assumed that a considerable amount of [Coen ]X - was formed at higher concentrations. I n an attempt to exclude the influence of activity factors, Larsson and Johansson (28) repeated the measurements of the C o e n , S 0 - s y s t e m i n an approximately constant salt medium (I = 2M (NaC10 )). The curve had here a somewhat different appearance from the curve i n pure thiosulfate solution. The minimum was less pronounced, occurred already for CNa s o ~ 0.005M, and was followed by a plateau for CNa s o ~ 0.04-0.06M before the curve increased smoothly. Larsson believed that the deviations from a monotonically increasing curve were a result of stepwise outer-sphere association, and by analysis of the curve he arrived at the following set of constants: &t

3

3

3

3

2

3

3

2

3

+3

_2

4

2

2

2

2

3

3

K

x

= 150,

K

2

- 50,

K

z

~ 20,

K

A

~ 1.

This result seemed to support Larsson's hypothesis (27, 29) that the same criterion shall apply to the outer sphere of coordination as to the inner one—i.e., the ligands must be assumed to occupy a limited n u m ber of so-called coordination sites which are spatially well-defined. H o w -


184

WERNER

CENTENNIAL

ever, from an electrostatic point of view, it seems improbable that the voluminous tris (ethylenediamine) cobalt (III) ion should associate with such a relatively high affinity with four thiosulfate ions in 2M N a C 1 0 . Therefore, in cooperation with Inge Olsen, the author (35) has examined the system by a more traditional method. The association was followed spectrophotometrically in mixtures of sodium perchlorate and sodium thiosulfate at a constant ion normality (C + = 2.88M). Measurements were made at five wavelengths in the ultraviolet, and the data were treated as described by J . Bjerrum (5). It was found that the formation of the ion pair [ C o e n ] S 0 was sufficient to explain the data at least up to about 0 . 5 M N a S 0 . The ion-pair constant was calculated to be Ki = 1.3±0.1, a value which is more than 100 times lower than Larsson's value for Ki i n the same system. The most simple explanation of this discrepancy is that the irregularities found i n the concentration dependence of the rotation are only indirectly caused by second-sphere coordination. According to recent views (14), the dextro- as well as the levo-form of Coen + exists as an equilibrium mixture of four conformations, each with its own optical rotation. If now the equilibrium between the different conformations is disturbed by the ion-pair formation, a minimum i n the rotation curve is easily understood. Therefore, the measurements ought to be repeated with the optically active tris(diamine) complex of 1,2cyclohexanediamine which exists i n one conformation only. I n any case, it is noteworthy that the minimum is less pronounced i n solutions with a high concentration of N a C 1 0 , and Olsen and the author (85) have found that the minimum disappears completely in mixtures of N a S 0 and N a S 0 at a constant molarity of one. In this medium the rotation of D - C o e n at 546 and 578 m/* shows no anomaly and changes linearly with the mole fraction from 1M N a S 0 to 1M N a S 0 . 4


Na

3

2

2

3

3

2

+

3

3

4

2

2

2

3

4

3

+3

2

4

2

2

3

The idea that the instantaneous equilibrium between the different conformations of dissymmetric complex ions could be influenced by ionpair formation finds some support i n recent experiments of Mason and co workers with diastereoisomeric cobalt (III) complexes. Thus, Mason and Norman (31) have shown that the circular dichroism spectra of D - C o ( d - p n ) and L-Co(d-pn) + (pn = propylenediamine) are differently changed by oxo-anions such as P 0 , S 0 , and S 0 . According to these authors the oxo-anion and D - C o ( d - p n ) (or D-Coen + ), but not L - C o ( d - p n ) , should have a preferred mutual orientation i n the ion pairs. A t low concentrations the effect of sulfate and thiosulfate ions on the circu lar dichroism of D - C o ( d - p n ) is similar to that of phosphate but with these anions at concentrations > 0 . 2 M the previous changes are reversed— probably due to breaking down the specific orientation of the ion pair i n the denser ionic atmosphere. It is also interesting that Mason and Norman (32) have found that C o ( N H ) associated with d-tartaric acid produces a pronounced Cotton effect. These results show that some 3

+3

3

3

4

- 3

4

- 2

2

3

3

+3

3

- 2

3

3

+3

3

+3

3

6

+ 3


13.

BJERRUM

The Second Sphere

185

mutual orientation exists i n the outer-sphere association products, prob ably as a consequence of chelate hydrogen bonding. Future work in this field is awaited with interest.


Literature

Cited

(1) Albinak, M. J., Bhatnagar, D. C., Kirschner, S., Sonnessa, A. J., Proc. 6th Intern. Conf. Coord. Chem., S. Kirschner, ed., p. 154, MacMillan Co., New York, 1961. (2) Beevers, C. A., Lipson, H., Proc. Roy. Soc. London 146A, 570 (1934). (3) Beevers, C. A., Schwartz, C. M., Z. Krist. 91, 157 (1935). (4) Behr, B., Wendt, H., Z. Elektrochem. 66, 223 (1962). (5) Bjerrum,J.,Kgl. Danske Videnskab., Selsk., Mat.-Fys. Medd. 11, No. 10 (1932). (6) Bjerrum, J., "Metal Ammine Formation in Aqueous Solution", p. 225, P. Haase and Son, Copenhagen, 1941. (7) Bjerrum, J., Ballhausen, C. J., Jørgensen, C. K., Acta Chem. Scand. 8, 1275 (1954). (8) Bjerrum, N., Z. Anorg. Chem. 63, 140 (1909). (9) Bjerrum, N., Kgl. Danske Videnskab. Selsk., Mat.-Fys. Medd., No. 9 (1926). (10) Brintzinger, H., Osswald, H., Z. Anorg. Chem. 221, 21 (1934). (11) Ibid. 223, 253 (1935). (12) Ibid. 225, 312 (1935). (13) Brintzinger, H., Plessing, H., Z. Anorg. Chem. 242, 193 (1939). (14) Corey, E. J., Bailar, J. C. Jr., J. Am. Chem. Soc. 81, 2620 (1959). (15) Eigen,M.,Pure Appl. Chem. 6, No. 1, 97 (1963). (16) Fronaeus, S., Larsson, R., Acta Chem. Scand. 16, 1433 (1962). (17) Fuoss, R.M.,Kraus, C. A., J. Am. Chem. Soc. 55, 2387 (1933). (18) Gimblett, F. G. R., Monk, C. B., Trans. Faraday Soc. 51, 793 (1955). (19) Gould, R. F., ed. ADVAN. CHEM. SER. 37 (1963).

(20) James, J. C.,J.Chem. Soc. 1950, 1094. (21) Jenkins, I. L., Monk, C. B., J. Chem. Soc. 1951, 68. (22) Jørgensen, C. K., Proc. Symp. Coord. Chem., Tihany 1964, Akadémiai Kiadó, Budapest, 1965, p. 11. (23) Kiss, A. v., Acs, V., Z. Anorg. Chem. 247, 190 (1941). (24) Kiss, A. v., Czeglédy, D. v., Z. Anorg. Chem. 239, 27 (1938). (25) Laitinen, H. A., Bailar, J. C., Jr., Holtzclaw, H. F., Quagliano, J. V.,J.Am. Chem. Soc. 70, 2999 (1948). (26) Larsson, R., Acta Chem. Scand. 16, 2267 (1962). (27) Ibid. 16, 2305 (1962). (28) Larsson, R., Johansson, L., Proc. Symp. Coord. Chem., Tihany 1964, Akadémiai, Budapest, 1965, p. 31. (29) Larsson, R., Tobiason, I., Acta Chem. Scand. 16, 1919 (1962). (30) Linhard, M., Z. Elektrochem. 50, 224 (1944). (31) Mason, S. F., Norman, B. J. (Miss), Proc. Chem. Soc. 1964, 339. (32) Mason, S. F., Norman, B. J. (Miss), Chem. Commun. 1965, 335. (33) Nancollas, G. H., Quart. Rev. 14, 402 (1960). (34) Näsänen, R., Acta Chem. Scand. 3, 179 (1949). (35) Olsen, I. (Miss), Bjerrum, J., to be published. (36) Phipps, A. L., Plane, R. A., J. Am. Chem. Soc. 79, 2458 (1957). (37) Posey, F. A., Taube, H., J. Am. Chem. Soc. 78, 15 (1956). (38) Schmitz-Dumont, O., Z. Anorg. Chem. 226, 33 (1936). (39) Sillén, L. G., Martell, A. E., "Stability Constants," Special Publication No. 17, The Chemical Society, London, 1964. (40) Spandau, H., Zillesen, D., Z. Anorg. Chem. 246, 100 (1941). (41) Waggener, W. C., Mattern, J. A., Cartledge, G. H., J. Am. Chem. Soc. 81, 2958 (1958).


186

WERNER CENTENNIAL

(42) Werner, A., Ber. Deutsch. Chem. Ges. 45, 121 (1912). (43) Werner, A., "Neuere Anschauungen auf dem Gebiete der anorganischen Chemie", 3rd ed., Vieweg und Sohn, Braunschweig, 1913. (44) Werner, A., Muller, H., Z. Anorg. Chem. 22, 91 (1900). (45) Williams, R. J. P., J. Chem. Soc. 1958, 457. 1966.


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