Chromium radii

Calculate the atomic radius of each of the following elements from the data given (a) silver, fee structure, density 10.500 g-cm 3 (b) chromium, bcc structure, density 7.190 g-cm-3. 

The curve of single-bond metallic radii for the elements of the first long period has a characteristic appearance (Fig. 3) which must be attributed in the main to variation in the type of bond orbital. The rapid decrease from potassium to chromium results from increase in bond strength due to increasing s-p and d-s—p hybridization. The linear section of the curve from chromium to nickel substantiates the assumption that the same bonding orbitals (hybrids of 2.56 3d orbitals, one 4s orbital, and 2.22 4p orbitals) are effective throughout this series. The increase in radius from nickel to copper is attributed not... 

A suitable extrathermodynamic approach is based on structural considerations. The oldest assumption of this type was based on the properties of the rubidium(I) ion, which has a large radius but low deformability. V. A. Pleskov assumed that its solvation energy is the same in all solvents, so that the Galvani potential difference for the rubidium electrode (cf. Eq. 3.1.21) is a constant independent of the solvent. A further assumption was the independence of the standard Galvani potential of the ferricinium-ferrocene redox system (H. Strehlow) or the bis-diphenyl chromium(II)-bis-diphenyl chromium(I) redox system (A. Rusina and G. Gritzner) of the medium. 

Chromium has a similar electron configuration to Cu, because both have an outer electronic orbit of 4s. Since Cr3+, the most stable form, has a similar ionic radius (0.64 A0) to Mg (0.65 A0), it is possible that Cr3+ could readily substitute for Mg in silicates. Chromium has a lower electronegativity (1.6) than Cu2+ (2.0) and Ni (1.8). It is assumed that when substitution in an ionic crystal is possible, the element having a lower electronegativity will be preferred because of its ability to form a more ionic bond (McBride, 1981). Since chromium has an ionic radius similar to trivalent Fe (0.65°A), it can also substitute for Fe3+ in iron oxides. This may explain the observations (Han and Banin, 1997, 1999 Han et al., 2001a, c) that the native Cr in arid soils is mostly and strongly bound in the clay mineral structure and iron oxides compared to other heavy metals studied. On the other hand, humic acids have a high affinity with Cr (III) similar to Cu (Adriano, 1986). The chromium in most soils probably occurs as Cr (III) (Adriano, 1986). The chromium (III) in soils, especially when bound to... 

The chemistry of aluminium combines features in common with two other groups of elements, namely (i) divalent magnesium and calcium, and (ii) trivalent chromium and iron (Williams, 1999). It is likely that the toxic effects of aluminium are related to its interference with calcium directed processes, whereas its access to tissues is probably a function of its similarity to ferric iron (Ward and Crichton, 2001). The effective ionic radius of Al3+ in sixfold coordination (54 pm) is most like that of Fe3+ (65 pm), as is its hydrolysis behaviour in aqueous solution ... 

Chromium has more electrons than scandium. Why, then, does scandium have a larger atomic radius ... 

There arc some features of the coarse of the values in the sequences that merit comment. First, what is the cause of the rapid decrease in single-bond radius from potassium to chromium, and the corresponding decreases for the other sequences We may be sure that fcbis... 

We conclude instead that the rapid decrease in radius from potassium to chromium is due to the nature of the bonding orbitals. It has been... 

The unique ligating behavior of the bridging 2,6-dimethoxyphcnyl ligand with respect to promoting a substantial decrease in the metal atom separation for molybdenum(II) dimers is even more prominent in the case of chromium. The chromium-chromium distance of 1.847(1) A in Cr2(DMP)4 (90) is more than 0.1 A less than the corresponding value in any other chromous dimer yet reported. To compare homonuclear multiple bonds among elements with inherently different atomic radii, Cotton, Koch, and Millar proposed a normalized value for intemuclear distances based on Pauling s atomic radius of the element in question (209). A simple definition of formal shortness as t/(M—M)/2r(M) then follows as a measure of the relative compactness of the attractive interaction (90). The formal shortness ratio of 0.778 for the quadruple bond in... 

Identify the element with the larger atomic radius in each of the following pairs (a) cobalt and manganese (b) copper and zinc (c) chromium and molybdenum. 

Explain in terms of electron configurations why the atomic radius of manganese is larger than that of chromium. 

Comparison of the r/-band width IV and the d-band energy obtained by fitting the bands of Fig. 20-1 with values of and , from the Solid State Table (abbreviated as SST). The latter were obtained by using parameters from Andersen and Jcpsen (1977) and values fitted to chromium. All energies are in eV. Also shown is the atomic sphere radius tq. 

These metals have an atomic radius below 1.3 A. Iron (1.16 A), chromium (1.17 A) and manganese (1.17 A) form carbides with properties intermediate between the salt-like and the interstitial. Structurally FcgC, MugC and NigC have C atoms inside the trigonal prisms formed by the metal atoms. They are easily decomposed by acids and water. In CrgC2 the carbon atoms form chains in the solid. 

The ionic radius of Cr(IV), 69 pm, is smaller than that of Ti(lV), 75 pm. The unit cell and c/spacings will shrink as a result of the smaller radius of chromium. The XRD pattern for Cr02 will show identical reflections to those of rutile TiO (see Figure 8.4) but shifted to slightly higher diffraction angles. 

It was very interesting to determine the pore volume and size distribution through N2 porosimetry. Fig. 4 shows the distribution of the pores radius of the AIF3 support and of the sample containing 10 wt% chromiiun thermally treated (CrlOiT). Note that the former is characterized by a wide distribution of the pore radii, while the latter has a more homogeneous distribution, with a value of about 20 A. It can be assumed that the mixed phase containing chromium covers the porosity of the support, determining the porosity of the solid after thermal treatntent (Fig. 5). 

Fig. 4. Distribution of the pore radius of AIF3 and of the san le with 10 wt% chromium thermally treated (CrlOiT)...

The AIF3 support, characterized by different allotropic phases, has a wide distribution of the pore radii. Incipient wetness impregnation method has allowed the introduetion on the support of chromium phases with amorphous or mierocrystalline structure. The N2 porosimetry has shown that these phases cover the surface of the support, determining a more homogeneous pore radius distribution of the catalytic material. 

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