MERCURY (11) HALIDE MIXEDCOMPLEXES IN SOLUTION
Sept., 1962
entrance of hydrogen brings about disturbances of the *3!-M bonds. Some of the changes show lengt!henirig of some M-RII bond classes along with a fihorteiiing of other M-M bond classes. The hexagonal structure of pure hafnium is of lion-ideal axial ratio. Since initial directional preferences are present in the pure metal, it is not surprising to see the distortion which is met in the face-centered cubic structure. One can infer that the distortion of the M-M bonds by hydrogen is itself endothermic since the sign of the relative partial molal enthalpy of hafnium is positive. Both deformation and energetics indicate that the process is much more than a simple filling of interstitiall holes. The fact that diatomic hydrogen enters a number of metals exothermally while a t the same time undergoing dissociation has always seemed somewhat startling from an energetic point of view to those thinking in terms of a simple “solution” of a gas in a solid. The bonding of a hydrogen atom to its surrounding metal atoms is thus
1661
even stronger than its covalent bonding to another
hydrogen atom in diatomic hydrogen. Sidhu, et u E . , ~ have stated that the M-H bonds are stronger than AI-31 bonds, but this is misleading. The important factor i s that the hydrogen atoms within the interstitial positions yield additional bonding beyond the normal &I-AI bonding. That is, due to the small size of the hydrogen atom, one gains 11-H bonding while retaining most of the &AI bonding. If the assumption is made that the hydrogen bonding energy is divided among four bonds associated with its four nearest metal neighbors, use of the thermodynamic data here obtained, the dissociation energy of diatomic hydrogen, and the sublimation energy of hafnium leads to a greater energy for the AI-31 bond than for the 31-H bond. Acknowledgment.-The support of the ONR and AFOSR during the course of this study is gratefully acknowledged. We wish to thank Prof. S.E. Wood for valuable discussions.
MERCURY(I1) HALIDE MIXED COMPLEXES I N SOLUTION. V. COMPARISON O F CALCULATED AKD EXPERIMESTAL STABILITY CONSTANTS1 BY Y. MARCUS AND I. ELIEZER Israel Atomic Energy Commission Laboratories, Rehovoth, Israel Received March 10,1961
The equililiriuni constants for the formation of mercury( 11) halide ternary (mixed ligand) complexes from the parent binary complexes have been calculated on the basis of a “polarized ion” model. The values obtained agree fairly well with the experimental results available.
Introduction an extent the experimental results can be explained The stability of ternary complexes MA& as by applying theoretical consideratioils along the comparcd with that of the binary complexes MA, lines mentioned Theory, a. Definitions.-We can write for and MB,, where n = i j , has not been studied much as yet but the basis for its theoretical treat- the formation of the mixed complex from the ment was laid by Bjerrum in his study of the ratio parent complexes hctween consecutive formation constants of binary Bjerrum divided the factors influcnciiig the complex formation constant’s into a “statistical effect” and a “ligand effect” further subequilibrium co~is t:in t f< If (1) dividing the latter into an “electrostatic effect” and a “resit effect.” Of late Kida has discussed Using thr coiivciitional10over-all stability coiistants some of the above factor^.^ ,B one obtains The mixed complexes of mercury@) with C1, Br, and I have been thoroughly investigated by one K M = Pi, X X Pori-'/'' (11) of while very recently Hume and Spiro8 Lct us now analyze KRZsomewhat similarly to studied spectrophotometrically the uncharged mixed mercury halides confirming the results ob- Bjerrum’s ideas. We can write tained in ref. 5 . We have tried to ascertain to what log KM = log &tat log K i log KR (111)
+
(1) Presented at the 7th International Conference on Coordination Chemistry, Stockholm, June, 1962.
(2) J. Bjerrum, “Metal Ammine Formation in Aqueous Solution,” P. Haase & Sons, Copenhagen, 1957. (31 S. Kida, Bull. Chem. Soc. J a p a n , 34,962 (1961). (4) Y . Marcus, Acta C h e k . Scand., 11, 329 (1957). ( 5 ) I’. Marcus, ibzd., 11, 599 (1957). (6) Y . Marcus, ibid., 11, 610 (1957). (7) Y . Marcus, ibid., 11, 811 (1957). (8) T. 0.Spiro a n d D. N. Hume, J . Am. Chem. Soc., 83, 4305 (1961).
+
+
where K s t a t = the value of K Mif formation of the mixed complex proceeds statistically; K,I = the stabilization constant of the mixed complex due to the electrostatic effect; K R = any additional stabilization, which Bjerrum calls the rest effect. Y.Marcus, Bull. Res. C o m c d Israel, IOA, N o 3 , 2 (1961). 110) J. BJertum, G bchmaraenbach, and L G Sill6n “Stab~lity Conhtants ” The Chemical Society, London, 1958. (9)
Y.MARQUE AND I. ELIEZER
I.662
Vol. 66
The energy for dipole-dipole interaction was found to be quite small and therefore we shall neglect it in the following treatment. We shall assume the dipoles at the anion centers to be due solely to the cation charge. We shall deal first with the linear17-21uncharged complexes as shown in Fig. 1. Figure 1.
We shall now discuss each of these in turn. b.-Kstat can be evaluated as follows: Let us assume that M has N coordination positions. Let us denote the probability of a ligand A or ligand B to be found a t a coordination position by u or b, respectively, which are assumed to be independent. Then the probability of a solvent molecule S being a t the coordination position will be 1 - u - b and the number of molecules n'lAiB,S,v-, will be proportional to &(l - a - b ) N - i - j N !
i!j! (N - i - j)!
will be given by
AEe1
=
Eel
(MAB) -
'/&e1
(n9A2)
-
- &'(I - a - b)"-"iV! i ! j ! (W - n)!
Writing similar expressions for the number of MAn and MB, molecules and introducing them into the expression for the stability constant (I), M-cobtain
that, is Kstat is independent of the cobrdination number, of the occupation of coordination positions by solvent molecules, and of the affinity of the ligands for the central metal ion. The number of complexes for which the experimental value of Kbl is found identical with Kstatis rather small. Usually Knt > &tat. c. The Electrostatic Effect.-The modcl on which the following treatment is bawd i s depicted in Fig. 1 for the casc of the BIAB linear ternary complexcs. The following synibols will be used : AEel = difference in electrostatic encrgy of intcraclion between the ternary complex and the binary complexes, thus In KG1 = AE,l/kT ZR~,XA,ZR= charges on thc metal c:ilioii and anioii A and 13 (in units of clectron charge) d.dx = distance bctmecn the ceiitcrs oi the ions M-A, niid M-B, respectively E = dielcctric constant We shall write -J- for attraction ~ i i d- for rppulsion . The molecule will be treatedl1-l6 as a system of point charges and point dipoles a t the center of the ions given by p = aF where F is the field strength a t the center of the ion in which p is induced and O( its polarizability. We then obtain for the iowdipole interaction energy
W =
AEel
l/zp.F =
'/z~uF'
(11) E. S. Rittner, J . Chem. Phys., I D , 1030 (1951). (12) 6 . A. Rice and W. Klemperer, zbzd., 27, 573 (1957). (13) K. P. Lawley, Trans. Paraday Soc., 67, 1809 (1061). (14) G. 14. Rothberg, J . Chem. Phys., 34, 2069 (1961). (15) K. S.Krasnov, Dokl. Akad. Nauk S S S R , 128, 326 (1959). (16) C. J. F. Rottoher, "Theory of Dielectric Polarization,'' Elsevier, 1952, pp. 143, 150.
I n the case of the halides X A = XB = 1 so that wc obtain finally EAE~I (X - 1)' a x ( x 2 - 1)2 - __(VI) e2 4d4x 1) + 2(dx)4
+
Iii the case of the tetrahedral complcxcs of the type MA3B we obtain .-
ffM f%
3%AZB
_ _ I _ _
d y'l
-a%2\
I
iVT1)
+ x 2 I- 3 z 2
Ncglectiiig polarization cffects mid putting x = 1 and E = 1 we obtain AEei 32/G _ I. - _(Xn - Zl3)Z e2 8d which is the cxpressioii obtaincd by liida in Iris discussion of the problcm.3 For l,hc casc of thc mercury halides ( X A = ZB = 1) wc obtain
The same expression, of course, holds for the MAB, complexes. For the MAzBz complexes we obtain (17) P. -4.Akishin, V. P. Spiridonov, and A. N. Hodchenkov, Zh. Fiz. Khim., 83, 20 (1959). (18) C. L. van P. van Eok, Thesis, Leyden, 1958. (19) J. D. E. McIntyre, Dissertation Abstr., 22, 754 (1961). (20) A. R. Tourky and H. A. Rizlc, Can. J . Chem., 36, 630 (1957). (21) A. R. Tourky, H. A. Risk, and Y . 11. Girgis, J . Phys. Chem., 64, 665 (1960).
MERCURY(II) HALIDEMIXEDCOMPLEXES IN SOLUTION
Sept., 1962
1663
I together with the experimental results available. 4-* Discussion Assuming for the MAzB complexes a pyramidal structure such that the meial is at the center of a tetrahedron three of the corners of which are occupied by the halide ions we obtain AEel(MA2B)
AEel(MAB2)
2 3
=-
AEel(MA3B)
Comparison with the Experimental ResultsIn order to calculate numerically the stabilization constant, values have to be chosen for the dielectric constant, the distances between the metal and the halide ions, and the polarizability of the metal ion. For our calculations we put E = 1,which seems not unreasonable. For the distances between the various ahoms we chose Akishin’s values obtained from electron diffraction,l’ which seem to be the most accurate and which are in good agreement with previous values.18s22They are dHg-Ct
=
2.29 ii.; dHg-Br = 2.41 ii.; = 2.59
From these the appropriate values for culated in each case.
2
h.
were cal-
For the polarizability of Hg2-+there is no generally accepted value. We chose two rather different values: 1.244 X cm.a23and 2.45 X cm.* 24 and calculated a separate set of results for each. The reasons for this will be discussed later. The results of the calculations are given in Table TABLE I log #or (calod.) log K M (obsd.) a~ = CZM= Mar2,45 1.244 2.45 cus4--1 H u m s
log K e l log Coniplex
CZM=
Kata& 1.244
ani =
0.30 0.09 0.13 0.39 HgClBr HgClI .75 .30 .45 .70 .30 .14 .22 .44 HgBrI ,4& .24 .30 .72 HgBrJHgBrIz.48 .24 .30 .T2 HgBrJZ‘- .GO .37 .44 .97 HgBr132.GO .37 .44 .97 HgBrzICr- .78 .49 .59 1.27
0 . 4 3 0 . 6 0.57 1 .OO I . 0 .68 0.52 0.54 .54 .78 .99 . . .78 .81 . . 1.04 1 . 3 ... 1.04 1.10 . 1.37 1.80 .
. .
(22) D. W. Allen a n d L. E. Sutton, Acta Cryst., 3, 46 (1950). (23) E. A. Moelwyn-Hughes, “Physical Chemistry,” 2nd Ed., Pergamon, 1961, p. 400. (24) J. A. A. Krtelaar, “Chemical Constitution,” 2nd Ed., Elsevier, 1958, p. 91.
From Table I we can see that there is a large measure of agreement between the theoretical and experimental values. However the following points should be noted. The theoretical considerations include many simplifications. The “polarized-ion” model used (Fig. 1; ref. 11--16)cannot take the partly covalent nature of the bonding fully into account. Some secondary effects, which would make the calculations very tedious, have been neglected. The effects of the solvent have not been introduced explicitly, but some are implicit in the value of a. The distances are strictly applicable only to the gaseous neutral molecules, and they were assumed to apply also to the complexes in solution.l* That an effect of the solvent exists may be shown by the differences in stability of the ternary complex in aqueous and benzene solutions.6 Hume and Spiro8report E. L. King’s suggestion that this is due to the interaction of the dipole of the ternary complex with the solvent. As long as such interactions cannot, be calculated explicitly, they might be included in a “rest effect.” There is no agreement on the value of a~ for mercury. The value 1.244 obtained by P a ~ l i n g ~ ~ - ~ ~ has been criticized by Fajans2* and a value approximately twice as large suggested by him was arrived at also by Ketelaar.24 Recently, MurgulescuZ9gave the value 3.18, while Berry3° thinks 1.0 to be still too high. Fortunately, the calculated values of Kel are not too sensitive to the value of CYM (Table I). Calculations on other metal-ligand systems are now in progress. Although there is obviously much room for improvement of the theory and removal of the various approximations and assumptions, this would seem of doubtful value unless at the same time more accurate experimental data become available. Acknowledgment.-We thank Prof. L. G. SillBn for helpful discussions. (25) L. Pauling, Proc. Roy. Sac. (London), A114, 181 (1927). (26) J. H. Van Vleck, “Eleotrio and Magnetic Susceptibilities,” Oxford, 1932, p. 225. (27) A. Heydweiller, Physik. 2.. 26, 526 (1925). (28) X. Fajans, et al., 2. Physik, 13, 1 (1924); 2. p h y s i k . Chem., B24, 103 (1934); J . Am. Chem. Soc., 64, 3023 (1942). (29) J. G. Murgulescu and E . Latiu, Rev. ehzm. Acad. rep. populaire Roumaine, 2, 27 (1954). (30) R. S. Berry, J . Chem. Phys., 30, 286 (1959).
