Chemistry - A Molecular Science

Chapter 8 Solid Materials

identical to Figure 8.24 except that space-filli

ng representations are used rather than ball-

and-stick. Note that the atomic sphere

s of X penetrate one another in an X

molecule, 2

which means that the two atoms are much closer

than the sum of their van der Waals radii.

Two atoms much closer than the sum of their van der Waals radii are interacting strongly, so there is a bond between the two X atoms. The spheres on adjacent molecules are touching but not penetrating, so the X atoms of different X

molecules interact only 2

weakly. Figure 8.26 compares the ball-and-

stick, covalent radius, and space-filling

representations of X

. In the ball-and-stick representation, the spheres indicate the 2

positions but not the sizes of the atoms. When

atomic size is represented with covalent

radii, bonds are indicated by the contact of spheres, but when atomic size is given by van der Waals radii (space-filling), bonds are indicated by the penetration of spheres. Table 8.4 gives the covalent and van der Waals radii of selected nonmetals.

rcov

rvdw

rcov

(a) (b) (c)

Figure 8.26 Representations of X

2

(a)

Ball-and-stick representation:

The sizes of the spheres are

not usually meaningful.

(b)

Covalent radii:

When atoms are represented by their covalent

radii, bonds are represented by

contact of the two spheres.

(c)

Space-filling model

: The atomic size is represented by the

van der Waals radius and bonds by the penetration of the atomic spheres.

Example 8.8 a) What is van der Waals distance in graphite (Figure 8.16), and what is the van der

Waals radius of carbon as determined from this distance? The carbon atoms in adjacent layers are t

ouching but not penetrating, so the van der

Waals distance is the distance between layers, which is 3.4Å. The van der Waals radius is one-half of the van der Waals distance, so the

van der Waals radius of a carbon atom is

1.7 Å, in agreement with its entry in Table 8.4.

b) How does the C-C bond length in graphite compare to that predicted from the

covalent radii in Table 8.4? The C-C bond length predicted from Table 8.4 is

twice the covalent radius of carbon, so L

= 2r

= 2(0.77) = 1.54Å. The obserC

ved C-C length in graphite is 1.4Å. The reason for the

difference is that the covale

nt radii are determined for single bonds, but the C-C bond

order in graphite is 1.5 due to the delocalized

π system.

Example 8.9

Use the covalent radii in Table 8.4 to determine the Ge-Cl bond length. The bond length is the sum of the covalent ra

dii of the bound atoms. Obtain the two

covalent radii from Table 8.4 and

sum them to get the bond length.

L(Ge-Cl) = r

cov

(Ge) + r

cov

(Cl) = 1.22 + 0.99 = 2.21 Å

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