Sodium interionic distance

The above calculation applies to independent sodium and fluoride ions, and does not take into account the electrostatic attraction between the oppositely charged ions, nor the repulsive force which operates at small interionic distances. In the crystal of NaF the distance of nearest approach of the sodium and fluoride ions is 231 pm, and Coulomb s law may be used to calculate the energy of stabilization due to electrostatic attraction between individual ion pairs ... 

Q Calculate the standard enthalpies of formation for the compounds (i) sodium chloride and (ii) potassium iodide. The interionic distances in the compounds are 282 and 353 pm, respectively. Compare your answers with the accepted experimental values for these quantities, which are -411 and -327.6 kJ mol1, respectively. 

The total potential energy of an ionic crystal MX with the sodium chloride arrangement can be obtained by summing the terms Va over all the pairs of ions in the crystal, and the quotient of this quantity by the number of stoichiometric molecules MX in the crystal is the potential energy of the crystal per molecule MX. Since in the crystal all of the interionic distances are related to the smallest interionic distance R by geometrical factors, the potential energy of the crystal can be written as... 

It is possible to make an approximate quantum-mechanical calculation of the forces operating between ions in a crystal and to predict values for the equilibrium interionic distance, the crystal energy, the compressibility, and other properties of the crystal. This calculation has been made in a straightforward manner for lithium hydride (Li+H-, with the sodium chloride structure) hy Hylleraas, with results in good agreement with experiment.10 A thorough theoretical treatment of... 

Since the electron distribution function for an ion extends indefi-finitely, it is evident that no single characteristic size can be assigned to it. Instead, the apparent ionic radius will depend upon the physical property under discussion and will differ for different properties. We are interested in ionic radii such that the sum of two radii (with certain corrections when necessary) is equal to the equilibrium distance between the corresponding ions in contact in a crystal. It will be shown later that the equilibrium interionic distance for two ions is determined not only by the nature of the electron distributions for the ions, as shown in Figure 13-1, but also by the structure of the crystal and the ratio of radii of cation and anion. We take as our standard crystals those with the sodium chloride arrangement, with the ratio of radii of cation and anion about 0.75 and with the amount of ionic character of the bonds about the same as in the alkali halogenides, and calculate crystal radii of ions such that the sum of two radii gives the equilibrium interionic distance in a standard crystal. 

These salts have been found to have the sodium chloride arrangement when deposited from the vapor onto cleavage surfaces of mica or certain other crystals L. G. Schulz, J. Chem. Phys. 18, 996 (1950). The observed interionic distances CV—Cl = 3.47, Cs+—Br = 3.62, Os+--T 3.83 A. 

Table 13-6.—Interionic Distances for Alkali Halogenide Crystals with the Sodium Chloride Structure...

Fia. 13-7.—The function F(p) showing the effect of radius ratio on equilibrium interionic distance of crystals with the sodium chloride arrangement. 

Crystals with the Rutile and the.Fluorite Structures Interionic Distances for Substances of Unsymmetrical Valence Type.—In a crystal of a substance of unsymmetrical valence type, such as fluorite, CaFs (Fig. 13-10), the equilibrium cation-anion interionic distance cannot be expected necessarily to be given by the sum of the crystal radii of the bivalent calcium ion and the univalent fluoride ion. The sum of the univalent radii of calcium and fluoride, 2.54 A, would give the equilibrium interionic distance in a hypothetical crystal with attractive and repulsive forces corresponding to the sodium chloride arrangement. 

Ionic Size. The size of an ion is a somewhat hazy concept because the modern notion of atoms pictures the electron distribution to extend to infinity. Nevertheless, it is true that there are definite distances established between the centers of atoms in a compound. It is thus natural to attempt to conceive of the distance between, say, Na+ and CT in solid sodium chloride as being made up as a sum of two contributions, one from the negative ion and the other the positive ion. This amounts to defining the sizes of ions in such a manner that in each ionic compound the sum of the ionic radii equals the observed interionic distance at equilibrium. 

Since the sum of the ionic radii is known (from x-ray studies), both radii may then be evaluated. Similarly, if the S values for the argon, krypton, and xenon structures are known, the interionic distances in KC1, RbBr, and Csl may be used to calculate ionic radii for K+, Rb+, Cs4, Cl, Br, and I . The values for cesium and iodide ions must be regarded cautiously (for, as we shall see presently, the structure of the cesium halides is different from that of the other alkali halides) but the radii of the retnaining ions fit into a self-consistent system. Thus, adding from sodium fluoride (0.95 k) to R Br from rubidium bromide (1.95 A) yields a sum not greatly different from the observed interionic distance in solid sodium bromide (2.98 A). 

It would appear that the radius of sodium or that of fluoride might be used to calculate the radii of both the magnesium and oxide ions, since all four of these ions are iso-electronic. However, the ionic radii so calculated do not add up to the interionic distance observed in magnesium oxide, even though this compound has the same structure as sodium fluoride later it will be shown how this sum must be adjusted downward to obtain the correct distance. 

Sodium fluoride and magnesium oxide have the same structure, and the interionic distances in the two compounds are not greatly different. Explain why magnesium oxide is so much harder, higher melting, and less water soluble than sodium fluoride. 

If the ionic radii are used to calculate the interionic distances in crystals of the sodium chloride type, good agreement is obtained with the experimental values for the salts of potassium and rubidium, but it is less satisfactory with the salts of sodium and agreement is poor for lithium. Thus in LiGl, the experimental interionic distance is 2 57 A whereas the sum of the ionic... 

It is clear that from the observed interionic distances we can deduce only the sum of two ionic radii, but that if any one radius is known then other radii may be found. Various independent methods are available for estimating the radii of certain ions, and the values so determined, taken in conjunction with data from the crystal structures not only of the alkali halides but also of many other compounds, lead to the semi-empirical ionic crystal radii shown in table 3.02 and in fig. 3.05. The interpretation of the radii given in this table is subject to a number of qualifications which will be discussed below. For the present, however, it is sufficient to treat the radii as constant and characteristic of the ions concerned. For the alkali halides with the sodium chloride structure it will be seen that the interatomic distances quoted in table 3.01 are given with fair accuracy as the sum of the corresponding radii from table 3.02. 

The distribution of chloride ions round a sodium ion (a) in the crystal lattice, (b) in a solution of sodium chloride. In the solution the interionic distances are greater, and the distribution is not as regular, but near to the sodium ion there are more chloride ions than sodium ions,... 

The accumulation of lattice constants gave rise to a growing Hbrary of interatomic (and interionic) distances, providing atomic and ionic radii. In 1929 Pauling published five principles (rules) that formed the first rational basis for understanding aystal structures. For example, the ratio of the ionic radii of cations to anions determines coordination number in crystals coordination number 6 for each chlorine and sodium ion in NaCl coordination number 8 for each ion in CsCl. 

Because the Madelung constant has been computed by a summation over all lattice sites, it adopts characteristic values for all structure types [5,8]. To give a few examples, M arrives at (dimensionless) values of 1.6381 (zinc-blende-type), 1.7476 (sodium chloride-type), 1.7627 (caesium chloride-type), 5.0388 (fluorite-type), and 25.0312 (corundum-type) and does not scale with (= is independent of) the interionic distances. For the case of NaCl, the Madelung constant shows that the three-dimensional lattice surpasses the ionic pair in energy by almost 75%. This is what has made the formation of solid NaCl possible, a collective stabilization. 

For larger counterions, like Cs, dissociation into free anions and cations was observed at very low concentrations. However, the dissociation constants are much lower than those of polystyryl ion pairs and the contribution of free anions to polymerization is negligible in most cases, except for [Na, 222], that is, the sodium ion encaged by cryptand 222, which has a large interionic distance (see Figure 3). ... 

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