CoreChem:6.8 The Sizes of Atoms and Ions

From ChemEd Collaborative

6.8 THE SIZES OF ATOMS AND IONS

Atomic Sizes

The sizes of atoms and ions are important in determining the properties of both covalent and ionic compounds. You should already have some appreciation of the factors which govern atomic sizes from the color-coded dot-density diagrams in Plates 4 and 5. By far the largest atom illustrated in these color plates is Li. Because Li has an electron in the n = 2 shell, it is larger than H or He whose 1s electron clouds are much closer to the nucleus. Li is also larger than Be, B, or C. In the latter atoms, the 2s and 2p electron clouds are attracted by a greater nuclear charge and hence are held closer to the center of the atom than the 2s cloud in Li. Thus two important rules may be applied to the prediction of atomic sizes.

1 As one moves from top to bottom of the periodic table, the principal quantum number n increases and electrons occupy orbitals whose electron clouds are successively farther from the nucleus. The atomic radii increase.

2 As one moves from left to right across a horizontal period, then n value of the outermost electron clouds remains the same, but the nuclear charge increases steadily. The increased nuclear attraction contracts the electron cloud, and hence the atomic size decreases.

It is difficult to measure the size of an atom very exactly. As the dot-density diagrams show, an atom is not like a billiard ball which has a definite radius. Instead of stopping suddenly, an electron cloud gradually fades out so that one cannot point to a definite radius at which it ends. One way out of this difficulty is to find out how closely atoms are packed together in a crystal lattice. Figure 6.9 illustrates part of a crystal of solid Cl₂ at a very low temperature. The distance AA′ in this figure has the value of 369 pm. Since this represents the distance between adjacent atoms in different Cl₂ molecules, we can take it as the distance at which different Cl atoms just “touch.” Half this distance, 184 pm, is called the van der Waals radius of Cl. The van der Waals radius gives an approximate idea of how closely atoms in different molecules can approach each other. Commonly accepted values of the van der Waals radii for the representative elements are shown in Fig. 6.10. Note how these radii decrease across and increase down the periodic table.

Also given in Fig. 6.10 are values for the covalent radius of each atom. Returning to Fig. 6.9, we see that the distance AB between two Cl atoms in the same molecule (i.e., the Cl—Cl bond length) has a value of 202 pm. The covalent radius is one-half of this bond length, or 101 pm. Covalent radii are approximately additive and enable us to predict rough values for the internuclear distances in a variety of molecules. For example, if we add the covalent radius of C (77 pm) to that of O (66 pm), we obtain an estimate for the length of the C―O bond, namely, 143 pm. This is in exact agreement with the measured value in ethyl alcohol and dimethyl ether discussed in the previous section.

Ionic Sizes

The size of an ion is governed not only by its electronic structure but also by its charge. This relationship is evident from Fig. 6.11. Ions in the first row of this figure, H^–, Li⁺, and Be²⁺, all have the same 1s² electronic structure as the helium atom.

Species which have the same electronic structure but different charges are said to be isoelectronic. For any electronic series, such as H^–, He, Li⁺, Be²⁺, in which the nuclear charge increases by 1 each time, we find a progressive decrease in size due to the increasingly strong attraction of the nucleus for the electron cloud. Each row in Fig. 6.11 corresponds to an isoelectronic series involving a different noble-gas electron configuration. As we move from the more negative to the more positive ions in each row, there is a steady decrease in size. If we move down any of the columns in Fig. 6.11, ionic sizes increase due to the increasing principal quantum number of the outermost electrons. The sizes of singly charged cations, for example, increase in the following order: Li⁺ < Na⁺ < K⁺ < Rb⁺ < Cs⁺.

A further point of interest is the size of an ion relative to the atom from which it was formed. Figure 6.1 at the beginning of this chapter showed that when an Li atom lost its electron and became an Li⁺ ion, its size decreased dramatically. The radii given in Fig. 6.10 and 6.11 reveal that this is also true for the other alkali metals. For example, the van der Waals radius of K is 280 pm, while the ionic radius of K⁺ is only 133 pm.

The large reduction in size is in sharp contrast to what occurs when an atom accepts one or more electrons to attain a noble-gas structure. Since the added electron goes into a subshell which already has occupants, rather than starting on a new subshell, there is very little change in size. This is clearly seen in Fig. 6.1 where formation of an H^– ion from an H atom produces no perceptible increase in size. Comparing Fig. 6.10 and 6.11, we also find that the van der Waals radii of nonmetals are only slightly smaller than the radii of their anions.

The sizes of the ions involved have considerable influence on both the chemical and physical properties of ionic compounds. There is a strong correlation, for example, between ionic size and the melting point of an ionic compound. Among the halides of sodium the melting point decreases in the order of NaF (995°C) > NaCl (808°C) > NaBr (750°C) > NaI (662°C). The larger the anion, the farther it is from the sodium ion, and the weaker the coulombic force of attraction between them. Hence the lower the melting point. When a very small cation combines with a very large anion, the resulting compound is less likely to exhibit the characteristic macroscopic properties of an ionic substance.