Determination of the Coordination Number

Problem The previous experiment roughly shows, qualitatively, that there is a specific amount of NH3 molecules, which is attached to the central copper ion in 

Material 8 small beakers, plastic pipettes, measuring cylinders, scales, photometer 0.1 -M solutions of copper sulfate and ammonia, ammonium nitrate. 

Procedure Prepare mixtures A - H as indicated below. In order to avoid the precipitation of copper hydroxide during mixing, add 10 g of ammonium nitrate beforehand and dissolve. Measure the extinction of all solutions at a wavelength of 600 nm using the photometer. 

Observation Extinction measurement values range from 0.01 to 0.58 the maximum extinction is reached in solution E, after that the extinction remains practically constant. 

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By Fourier transforming the EXAFS oscillations, a radial structure function is obtained (2U). The peaks in the Fourier transform correspond to the different coordination shells and the position of these peaks gives the absorber-scatterer distances, but shifted to lower values due to the effect of the phase shift. The height of the peaks is related to the coordination number and to thermal (Debye-Waller smearing), as well as static disorder, and for systems, which contain only one kind of atoms at a given distance, the Fourier transform method may give reliable information on the local environment. However, for more accurate determinations of the coordination number N and the bond distance R, a more sophisticated curve-fitting analysis is required. 

The relative sizes of the cation and anion are not the only determinant of the coordination number the bonding strength of the anion also plays an important role and explains how the same cation can display different coordination numbers in different compounds. 

It has recently been shown (34) that the commonly used EXAFS analysis procedures [Eq. (3)] may introduce large errors in the determination of the coordination numbers of small particles. The fact that the motion of the atoms in small particles is highly anharmonic, especially at high tempera-... 

Determination of the Coordination Number from Diol-Titration Experiments. Early in the research on the diol-boric acid reaction it was recognized that two possible complexes could form (3), one with a diol coordination number of one, the other with a coordination number of two. A generalized expression for the overall complex reaction can be written as follows,... 

Through the years there has been some conflict in the literature over the determination of the coordination numbers of various diol-boric acid complexes. Most of these conflicts can be resolved by making the proper approximations in these three conservation equations as determined by the experimental conditions. 

The coordination number can sometimes be established by coordinated physical measurements such as conductance, molecular weight measurement, infrared, UV-VIS-near IR, and emission spectroscopy [16]. The coordination numbers of solid complexes can be obtained by X-ray diffraction methods. Infrared spectroscopy and the conductance methods were used in the determination of the coordination numbers of Nd(NCh)3 4DMSO and Dy(N03>3 3DMSO complexes [17]. 

Nuclear magnetic resonance spectroscopy of the 27Al nucleus, both in solution and the solid state, has proved useful for the determination of the coordination numbers and, to some extent, the stereochemistry of Al. Four-, 5-, and 6-coordinate geometries can be differentiated on the basis of their chemical shifts. 

The idea of one of the authors to employ the double-double effect to the determination of the coordination number of the inner transition elements in solutions57 has been developped in his recent works95,96. Thus, the double-double effect has proved to be a useful instrument to solve some difficult problems of the f-element coordination chemistry when other methods are often deceiving. 

Both studies show very clearly the problems when solutions are studied with X-rays. The nuiin problem is that an X-ray experiment provides the sum of all atom pair correlation functions, weighted wilh the mole fraction and the electron number of the corresponding atom pairs. If (he concentration of the solute is not very high, die contribution of Ihc atom pairs, from which the local structure can be deduced, to the iota] atom pair correlation function is too small for an unambiguous assignment of certain peaks to definite atom pairs and for a reliable determination of the coordination number. Nevertheless, the X-ray studies of liquids or solutions have their merits, when they arc combined with other experimental methods and arc compared with theoretical calculations. 

This determination of the coordination number of the ion is predicated on the electrical neutrality principle given earlier (see page 19). This principle is also called the electrostatic valence principle and is part of Pauling s second rule In a stable ionic structure the valence of each anion, with changed sign, is exactly or nearly equal to the sum of the strengths of the electrostatic bonds to it from the adjacent cations. (Pauling, 1960)... 

Figure 18 shows a well resolved triplet spectrum of tin in alkaline silicate glasses. According to [16] the isomeric shift permits determination of the coordination number of the Sn(IV) and Sn(II) ions. As the glass composition and... 

Actually, the quadrupolar nature of the nucleus does not allow the observation of the structurally significant fine structure of the bands, limiting the applicability of Al MAS-NMR to little more than the determination of the coordination number at the aluminum atom. However, new techniques such as Al MQ MAS NMR [95] and A1]- H REAPOR NMR (REAPOR = rotational echo adiabatic passage... 

Muller, D., W. Gessner and A.-R. Grimmer. 1977. Determination of the coordination number of aluminum in solid aluminates from the chemical shift of alumi-num-27. Zeitschrift fiir Chemie 17, 453-454. 

Unlike its analogue FCIO3 it forms adducts with BF3 and AsFs, possibly by F" donation to give [I03]+[BF4 ] and [I03]+[AsF6]", though the structures have not yet been determined. Alternatively, the coordination number of the central I atom might be increased. SO3 reduces FIO3 to iodyl fluorosulfate ... 

Some quantitative characteristics of disordered packings have been discussed in Section 9.4 through Section 9.6. Let us begin this section with the specificity of determination of a coordination number for random packing (RP) of hard monospheres. 

Even if the connectivity is not known, one can predict many properties if one can make a reasonable estimate of the coordination number. Chapter 6 describes the different factors that determine the coordination number, but at this point in the discussion it is sufficient, and simpler, to work with coordination numbers that are determined experimentally. 

Cation coordination numbers using Rule 4.1 as a criterion have been determined for some 14000 cation environments (Brown 1988a). Some cations, such as are known with only one coordination number (4 in this case), but others, such as Cs+, can be found with every coordination number between 3 and 12. Whatever the total range, the frequency distribution of the coordination number for a given cation usually peaks close to the average. It is therefore convenient to take the average observed coordination number as a characteristic chemical property of the cation. 

CN depends not only on the composition of a coordination compound, but also on the type of a- and n-bonds present in it. Chromium carbonyl-pyridine complexes are the classic example to illustrate the difficult task of determining unambiguously the coordination numbers. Only a-bonds are present in Cr(py)(CO)5 and CN = 6 (12). However, in the a, n-complex 13, as well as in 9, the coordination number is quite questionable (compare formulae 9 IT). 

FIGURE 3 Selectivity for N2 formation as a function of the coordination number of Ti determined by EXAFS in the photocatalytic decomposition of NO into N2 and 02 on various titanium oxide catalysts including highly dispersed, chemical mixture and bulk Ti02 powder. (Reproduced with permission from Yamashita and Anpo (2004).)... 

Some 20 years ago, analysis of the coordination numbers for large numbers of coordination compounds of yttrium and the lanthanides indicated that coordination numbers of 8 and 9 are almost equally common, accounting for around 60% of the known structures, and it is unlikely that this distribution has changed significantly. As already pointed out, it is steric factors that determine the coordination number (and geometry) adopted by a lanthanide ion (see e.g. X.-Z. Feng, A.-L. Guo, Y.-T. Xu, X.-F. Li and P.-N. Sun, Polyhedron, 1987, 6, 1041 J. Margalo and A. Pires de Matos, Polyhedron, 1989, 8, 2431). Saturation in the coordination sphere of the metal can come about in one of two ways. 

While complete X-ray analysis will establish the structure in the solid state, it is useful to have NMR data on the solution state that illustrate the increase of the coordination number of silicon. It would seem that NMR spectroscopy of nuclei participating directly in donor-acceptor interaction is especially important in investigating silicon compounds with an expanded coordination sphere. This requires the use of Si NMR spectroscopy since the electron shell of the silicon atom, the bond angles and lenghts are strongly affected upon complexation. Valuable information could also be obtained with by " N, N, 0, F NMR data since these elements act as donors. Chemical shifts of nuclei other than hydrogen are determined by various factors and not yet understood well anough to provide easily applied correlations of other physical properties of the molecules. 

At least in compounds with metals of lower oxidation states up to three or four, the metal-fluorine bond is almost purely ionic and the small, least polarizable fluoride ion behaves as a small hard sphere with an ioitic radius which varies, depending on the coordination number, between 1.285 (CN 2) and 1.320 A (CN 6). The structures of fluorides are therefore determined mainly by simple geometrical and electrostatic principles, such as sphere packing, the rigid sphere concept, which allows derivation of the coordination number around... 

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