Elements, crystal radii

The high-temperature contribution of vibrational modes to the molar heat capacity of a solid at constant volume is R for each mode of vibrational motion. Hence, for an atomic solid, the molar heat capacity at constant volume is approximately 3/. (a) The specific heat capacity of a certain atomic solid is 0.392 J-K 1 -g. The chloride of this element (XC12) is 52.7% chlorine by mass. Identify the element, (b) This element crystallizes in a face-centered cubic unit cell and its atomic radius is 128 pm. What is the density of this atomic solid ... 

ACTINIDE CONTRACTION. An effect analogous to the Lanthanide contraction, which lias been found in certain elements of the Actinide series. Those elements from thorium (atomic number 90) to curium (atomic number 96) exhibit a decreasing molecular volume in certain compounds, such as those which the actinide tetrafluoiides form with alkali metal fluorides, plotted in Eig. 1. The effect here is due to the decreasing crystal radius of the tetrapositive actinide ions as the atomic number increases. Note that in the Actinides the tetravalent ions are compared instead of the trivalent ones as in the case of the Lanthanides, in which the trivalent state is by far the most common. 

Each rubidium halide (Group VIIA element) crystallizing in the NaCl-type lattice has a unit cell length 30 pm greater than that for the corresponding potassium salt of the same halogen. What is the ionic radius of Rb+ computed from these data ... 

Atomic number Element Electronic configuration Crystal radius r, nm (Ln3+) Standard redox potential, E°273 Volt Ln3+(aq.) + 3e = Ln(s)... 

Despite the development of microscale modeling for reaction—diffusion in zeolite, the complex of MTO reaction mechanism impedes the application of microscale modeling to MTO process. Up to now, the reliable reaction kinetics based on element reactions in MTO process is still under development (van Speybroeck et al., 2014). However, a reduced or simplified microscale model could be applied. Basically, the diffusion effect is negligible if the crystal radius is small enough. Then mass equation, i.e., Eq. (1), could be simplified by neglecting the species ffux term. In this case, MTO processes over ZSM-5 and SAPO-34 catalyst could be simulated by use of the single-event kinetics by Alwahabi and Froment (2004a) as an input. 

The radius of an atom or an ion is a function of its environment An extreme example is the hydrogen atom, which must be assigned one radius when it combines with itself, a second radius when it combines with elements of the second period, a third radius when it combines with elements of the third period, and so on. Most ionic radii, however, may be treated as fairly constant. It is, therefore, advantageous for many purposes to assign a radius to each atom, called the COVALENT RADIUS, and to each ion, called the IONIC or CRYSTAL RADIUS. 

Element Atomic Radius (nm) Crystal Structure Electro- negativity Valence... 

The atom radius of an element is the shortest distance between like atoms. It is the distance of the centers of the atoms from one another in metallic crystals and for these materials the atom radius is often called the metal radius. Except for the lanthanides (CN = 6), CN = 12 for the elements. The atom radii listed in Table 4.6 are taken mostly from A. Kelly and G. W. Groves, Crystallography and Crystal Defects, Addison-Wesley, Reading, Mass., 1970. 

Space-Filling Models. For most of this century, chemists have tried to answer the size question by using a special set of molecular models known as space-filling or CPK models. The space-filling model of an atom is simply a sphere of fixed radius. A different radius is used for each element, and the radii are chosen to reproduce certain experimental observations, such as the compressibility of a gas, or the spacing between atoms in a crystal. 

Valence, 286 Valence electrons, 269 and ionization energies, 269 Vanadium atomic radius, 399 eleciron configuration, 389 oxidation numbers, 391 pentoxide catalyst, 227 properties, 400, 401 van der Waals forces, 301 elements that form molecular crystals using, 301 and molecular shape, 307 and molecular size, 307 and molecular substances, 306 and number of electrons, 306 van der Waals radius, 354 halogens, 354 Vanillin, 345... 

Steel is an alloy of about 2% or less carbon in iron. Carbon atoms are much smaller than iron atoms, and so they cannot substitute for iron in the crystal lattice. Indeed, they are so small that they can fit into the interstices (the holes) in the iron lattice. The resulting material is called an interstitial alloy (Fig. 5.48). For two elements to form an interstitial alloy, the atomic radius of the solute element must be less than about 60% of the atomic radius of the host metal. The interstitial atoms interfere with electrical conductivity and with the movement of the atoms forming the lattice. This restricted motion makes the alloy harder and stronger than the pure host metal would be. 

Figure 3. Cartoon illustrating the lattice strain model of trace element partitioning. For an isovalent series of ions with charge n+ and radius entering crystal lattice site M, the partition coefficient,, can be...

Ionic radii are quoted in Tables 2.3 and 2.5 for a large number of cations including those of the elements in groups 13, 14, 15, and 16, which do not form predominately ionic bonds. These values were obtained by subtracting the fluoride or oxide ion radius obtained from predominantly ionic solids from the length of a bond that is not predominantly ionic. The very small values for the radii of cations obtained in this way do not bear much relation to the real size of the atom in the crystal or molecule. 

Element Atomic Number Electronic Configuration Electronegativity Crystal Ionic Radius A°... 

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... 

Table 2.3 gives the self-diffusion coefficients of some important ions in submerged soils and Figure 2.2 shows the values for the elemental ions plotted against ionic potential ( z /r where z is the absolute ionic charge and r the crystal ionic radius). As the ionic potential increases the hydration layer of water molecules around the ion increases, and therefore the mobility tends to decrease. Also, at the same ionic potential, cations diffuse faster than anions. The mobilities... 

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