Ionic radii. Ion size. Ionic and crystal radii Ionic radii of elements table

The problem of ion radii is one of the central ones in theoretical chemistry, and the terms themselves "ionic radius" And " crystal radius", characterizing the corresponding sizes, are a consequence of the ionic-covalent structure model. The problem of radii develops primarily within the framework structural chemistry(crystal chemistry).

This concept found experimental confirmation after the discovery of X-ray diffraction by M. Laue (1912). The description of the diffraction effect practically coincided with the beginning of the development of the ionic model in the works of R. Kossel and M. Born. Subsequently, diffraction of electrons, neutrons and other elementary particles, which served as the basis for the development of a series modern methods structural analysis (X-ray, neutron, electron diffraction, etc.). The concept of radii played a decisive role in the development of the concept of lattice energy, the theory of closest packing, and contributed to the emergence of the Magnus-Goldschmidt rules, the Goldschmidt-Fersman isomorphism rules, etc.

Back in the early 1920s. two axioms were accepted: the transferability of ions from one structure to another and the constancy of their sizes. It seemed quite logical to take half the shortest internuclear distances in metals as radii (Bragg, 1920). Somewhat later (Huggins, Slater) a correlation was discovered between the atomic radii and distances to the electron density maxima of the valence electrons of the corresponding atoms.

Problem ionic radii (g yup) is somewhat more complicated. In ionic and covalent crystals, according to X-ray diffraction analysis, the following are observed: (1) a slight shift in the overlap density to a more electronegative atom, as well as (2) a minimum electron density on the bond line (electron shells of ions at close distances should repel each other). This minimum can be assumed to be the area of ​​contact between individual ions, from which the radii can be measured. However, from structural data on internuclear distances it is impossible to find a way to determine the contribution of individual ions and, accordingly, a way to calculate ionic radii. To do this, you must specify at least the radius of one ion or the ratio of ion radii. Therefore, already in the 1920s. a number of criteria for such a definition were proposed (Lande, Pauling, Goldschmidt, etc.) and created different systems ionic and atomic radii (Arens, Goldschmidt, Bokiy, Zachariazen, Pauling) (in domestic sources the problem is described in detail by V.I. Lebedev, V.S. Urusov and B.K. Weinstein).

Currently, the system of ionic radii Shannon and Pruitt is considered the most reliable, in which the ionic radius F“(r f0W F" = 1.19 A) and O 2_ (r f0W O 2- = 1.26 A) is taken as the initial one (in monographs by B.K. Weinstein (these are called physical). A set of radius values ​​for all elements is obtained. periodic table, for various oxidation states and CN, as well as for transition metal ions and for various spin states (the values ​​of the ionic radii of transition elements for CN 6 are given in Table 3.1). This system provides accuracy in calculating internuclear distances in the most ionic compounds (fluorides and oxygen salts) of the order of 0.01 A and allows for reasonable estimates of the radii of ions for which there are no structural data. Thus, based on the data of Shannon - Pruitt in 1988, the radii of ions unknown at that time were calculated d- transition metals in high oxidation states, consistent with subsequent experimental data.

Table 3.1

Some ionic radii r (according to Shannon and Pruitt) of transition elements (CN 6)

0.7 5 LS

End of table. 3.1

							0.75 lls

th CC 4 ; b CC 2; LS- low spin state; H.S.- high spin state.

An important property of ionic radii is that they differ by approximately 20% when the CN changes by two units. Approximately the same change occurs when their oxidation state changes by two units. Spin crossover

Examples of periodic property changes

Because quantum mechanics prohibits the exact determination of particle coordinates; the concepts of “atomic radius” and “ion radius” are relative. Atomic radii are divided into radii of metal atoms, covalent radii of non-metal atoms and radii of noble gas atoms. They are defined as half the distance between layers of atoms in crystals of the corresponding simple substances(Fig. 2.1) by x-ray or neutron diffraction methods.

Rice. 2.1. To the definition of the concept “atomic radius”

In general, the radius of an atom depends not only on the nature of the atoms, but also on the character chemical bond between them, state of aggregation, temperature and a number of other factors. This circumstance once again indicates the relativity of the concept of “atomic radius”. Atoms are not incompressible, motionless frozen balls; they always take part in rotational and oscillatory movement. In table Tables 2.1 and 2.2 show the radii of some metal atoms and the covalent radii of non-metal atoms.

Table 2.1

Atomic radii of some metals

Metal	r a , pm	Metal	r a , pm
Li		Rb
Be		Sr
Na		Y
Mg		Zr
Al		Nb
K		Mo
Ca		Tc
Sc		Ru
Ti		Rh
V		Pd
Cr		Ag
Mu		Cd
Fe		In
Co		Cs
Ni		Ba
Cu		La
Zn		Hf

Table 2.2

Covalent radii of nonmetal atoms

The radii of noble gas atoms are significantly larger than the radii of non-metal atoms of the corresponding periods (Table 2.2), since in noble gas crystals the interatomic interaction is very weak.

Gas He Ne Ar Kr Xe

r a , rm 122 160 191 201 220

The scale of ionic radii, of course, cannot be based on the same principles as the scale of atomic radii. Moreover, strictly speaking, not a single characteristic of an individual ion can be objectively determined. Therefore, there are several scales of ionic radii, all of them are relative, that is, built on the basis of certain assumptions. The modern scale of ionic radii is based on the assumption that the boundary between ions is the point of minimum electron density on the line connecting the centers of the ions. In table Table 2.3 shows the radii of some ions.

Table 2.3

Radii of some ions

Ion	r i pm	Ion	r i, pm
Li+		Mn 2+
Be 2+		Mn 4+
B 3+		Mn 7+
C 4+		Fe 2+
N 5+		Fe 3+
O2–		Co2+
F –		Co 3+
Na+		Ni 2+
Mg 2+		Cu+
Al 3+		Cu 2+
Si 4+		Br –
P5+		Mo 6+
S 2–		Tc 7+
Cl –		Ag+
Cl 5+		I –
Cl 7+		Ce 3+
Cr 6+		Nd 3+
		Lu 3+

The periodic law leads to the following patterns in changes in atomic and ionic radii.

1) In periods from left to right, in general, the radius of the atom decreases, although unevenly, then at the end it sharply increases for the noble gas atom.

2) In subgroups, from top to bottom, the radius of the atom increases: more significant in the main subgroups and less significant in the secondary ones. These patterns are easy to explain from the perspective electronic structure atom. In a period, during the transition from the previous element to the next, electrons go to the same layer and even to the same shell. The growing charge of the nucleus leads to a stronger attraction of electrons to the nucleus, which is not compensated by the mutual repulsion of electrons. In subgroups, an increase in the number of electronic layers and shielding of attraction to the nucleus outer electrons deep layers leads to an increase in the radius of the atom.

3) The radius of the cation is less than the radius of the atom and decreases with increasing charge of the cation, for example:

4) The radius of the anion is greater than the radius of the atom, for example:

5) In periods, the radii of ions of d-elements of the same charge gradually decrease, this is the so-called d-compression, for example:

6) A similar phenomenon is observed for ions of f-elements - during periods, the radii of ions of f-elements of the same charge smoothly decrease, this is the so-called f-compression, for example:

7) The radii of ions of the same type (having a similar electron “crown”) gradually increase in subgroups, for example:

8) If different ions have same number electrons (they are called isoelectronic), then the size of such ions will naturally be determined by the charge of the ion nucleus. The smallest ion will be the one with the highest nuclear charge. For example, Cl –, S 2–, K +, Ca 2+ ions have the same number of electrons (18); these are isoelectronic ions. The smallest of them will be the calcium ion, since it has the largest nuclear charge (+20), and the largest will be the S 2– ion, which has the smallest nuclear charge (+16). Thus, the following pattern emerges: the radius of isoelectronic ions decreases with increasing ion charge.

Relative strength of acids and bases (Kossel diagram)

All oxygen acids and bases contain in their molecules the fragment E n+ – O 2– – H +. It is well known that the dissociation of a compound according to the acidic or basic type is associated with the degree of oxidation (more strictly, with the valence) of the element’s atom. Let us assume that the bond in this fragment is purely ionic. This is a rather rough approximation, since as the valence of an atom increases, the polarity of its bonds weakens significantly (see Chapter 3).

In this rigid fragment, cut from an oxygen acid or base molecule, the site of bond cleavage and dissociation, respectively, with the release of a proton or hydroxyl anion, will be determined by the magnitude of the interaction between the E n+ and O 2– ions. The stronger this interaction, and it will increase with an increase in the charge of the ion (oxidation state) and a decrease in its radius, the more likely the rupture of the O–H bond and acid-type dissociation are. Thus, the strength of oxygen acids will increase with an increase in the oxidation state of an element's atom and a decrease in the radius of its ion .

Note that here and below, the stronger of the two is the electrolyte that, at the same molar concentration in solution, has a greater degree of dissociation. We emphasize that in the Kossel scheme two factors are analyzed - the oxidation state (ion charge) and the ion radius.

For example, it is necessary to find out which of two acids is stronger - selenic H 2 SeO 4 or selenous H 2 SeO 3 . In H 2 SeO 4 the oxidation state of the selenium atom (+6) is higher than in selenous acid (+4). At the same time, the radius of the Se 6+ ion is less than the radius of the Se 4+ ion. As a result, both factors show that selenic acid stronger than selenium.

Another example is manganese acid (HMnO 4) and rhenium acid (HReO 4). The oxidation states of Mn and Re atoms in these compounds are the same (+7), so the radii of the Mn 7+ and Re 7+ ions should be compared. Since the radii of ions of the same type in the subgroup increase, we conclude that the radius of the Mn 7+ ion is smaller, which means manganese acid is stronger.

The situation with grounds will be the opposite. The strength of bases increases with a decrease in the oxidation state of an element's atom and an increase in the radius of its ion . Hence, if the same element forms different bases, for example, EON and E(OH) 3, then the second of them will be weaker than the first, since the oxidation state in the first case is lower, and the radius of the E + ion is greater than the radius of the E 3+ ion. In subgroups, the strength of similar bases will increase. For example, the most strong foundation of the alkali metal hydroxides will be FrOH, and the weakest is LiOH. Let us emphasize once again that we are talking about comparing the degrees of dissociation of the corresponding electrolytes and does not concern the issue of the absolute strength of the electrolyte.

We use the same approach when considering the relative strength of oxygen-free acids. We replace the E n– – H + fragment present in the molecules of these compounds with an ionic bond:

The strength of interaction between these ions, of course, is determined by the charge of the ion (the oxidation state of the element's atom) and its radius. Bearing in mind Coulomb's law, we obtain that the strength of oxygen-free acids increases with a decrease in the oxidation state of an element's atom and an increase in the radius of its ion .

The strength of oxygen-free acids in solution will increase in the subgroup, for example, hydrohalic acids, since with the same degree of oxidation of an element’s atom, the radius of its ion increases.

Ionic radius- value in Å characterizing the size of ion cations and ion anions; the characteristic size of spherical ions, used to calculate interatomic distances in ionic compounds. The concept of ionic radius is based on the assumption that the size of ions does not depend on the composition of the molecules in which they are found. It is influenced by the quantity electron shells and the packing density of atoms and ions in the crystal lattice.

The size of an ion depends on many factors. With a constant charge of the ion, as the atomic number (and, consequently, the charge of the nucleus) increases, the ionic radius decreases. This is especially noticeable in the lanthanide series, where the ionic radii monotonically change from 117 pm for (La3+) to 100 pm (Lu3+) at a coordination number of 6. This effect is called lanthanide contraction.

In groups of elements, ionic radii generally increase with increasing atomic number. However, for d-elements of the fourth and fifth periods, due to lanthanide compression, even a decrease in the ionic radius can occur (for example, from 73 pm for Zr4+ to 72 pm for Hf4+ with a coordination number of 4).

During the period, there is a noticeable decrease in the ionic radius, associated with an increase in the attraction of electrons to the nucleus with a simultaneous increase in the charge of the nucleus and the charge of the ion itself: 116 pm for Na+, 86 pm for Mg2+, 68 pm for Al3+ (coordination number 6). For the same reason, an increase in the charge of an ion leads to a decrease in the ionic radius for one element: Fe2+ 77 pm, Fe3+ 63 pm, Fe6+ 39 pm (coordination number 4).

Comparisons of ionic radii can only be made when the coordination number is the same, since it affects the size of the ion due to repulsive forces between counterions. This is clearly seen in the example of the Ag+ ion; its ionic radius is 81, 114 and 129 pm for coordination numbers 2, 4 and 6, respectively.
The structure of an ideal ionic compound, determined by the maximum attraction between unlike ions and the minimum repulsion of like ions, is largely determined by the ratio of the ionic radii of cations and anions. This can be shown by simple geometric constructions.

The ionic radius depends on many factors, such as the charge and size of the nucleus, the number of electrons in the electron shell, and its density due to the Coulomb interaction. Since 1923, this concept has been understood as effective ionic radii. Goldschmidt, Arens, Bokiy and others created systems of ionic radii, but they are all qualitatively identical, namely, the cations in them, as a rule, are much smaller than the anions (with the exception of Rb +, Cs +, Ba 2+ and Ra 2+ in relation to O 2- and F-). The initial radius in most systems was taken to be K + = 1.33 Å; all others were calculated from interatomic distances in heteroatomic compounds, which were considered ionic according to their chemical type. communications. In 1965 in the USA (Waber, Grower) and in 1966 in the USSR (Bratsev), the results of quantum mechanical calculations of ion sizes were published, showing that cations are indeed smaller in size than the corresponding atoms, and anions are practically no different in size from the corresponding atoms. This result is consistent with the laws of the structure of electron shells and shows the fallacy of the initial assumptions adopted when calculating the effective ionic radii. Orbital ionic radii are not suitable for estimating interatomic distances; the latter are calculated based on the system of ionic-atomic radii.