Chemistry - A Molecular Science

melting points are highest for ionic substances with small, highly charged ions that are closely packed.

Table 8.3

Ionic Radii of Group 1A and Group 7A Ions

Cation Radius (Å)

Anion

Radius(Å)

The distance between two adjacent ions in

a crystal is equal to the sum of their

ionic

radii

. For example, the distance between Li

1+ and I

1- ions in a crystal of LiI is 2.96 Å, so

we can write r

• rLi

= 2.96 Å. Ionic radii have been determined by examining many such I

distances. The ionic radii of the alkali metal ions (Group 1A) and the halide ions (Group 7A) are given in Table 8.3.

1+Li

0.90

1-F

1.19

Na

1+ 1.16

Cl

1- 1.67

1+K

1.52

Br

1- 1.82

Rb

1+ 1.66

1-I 2.06

Cs

1+ 1.81

(a)

(b)

contact is alongthe face diagonal

void spaceon edge

Li

ions fill

1+ void space

Figure 8.12 Filling void space with cations (a) fcc structure of iodide ions wi

th no cations. In this arrangement,

the ions touch along the diagonal. (b

) fcc structure of iodide ion with

lithium ions inserted into the void spaces on the edge. The iodide ions no longer touch along the diagonal.

Figure 8.13 LiCl unit cell

Example 8.6

What is the ionic radius of Mg

2+, if the Mg-Cl distance in MgCl

is 2.53 Å? 2

Express the distance as the sum of the ionic radii: 2.53 = r

Mg

+ r

(^) Cl
Set r
= 1.67 Å from Table 8.3 and solve for the ionic radius of MgCl
2+^
rMg
= 2.53 - 1.67 = 0.86 Å
Not all of the particles in an ionic solid are identical, but the same structural
descriptions that are applied to metallic
solids can be used to understand the crystal
structure of many ionic compounds. For example, most of the alkali halides have a preference for a structure in which the anions pack in a face-centered cubic unit cell, as shown in Figure 8.12a. The three anions along a diagonal of a face touch in a fcc unit cell, but there is void space along each of the cell
edges and in the body center. Much smaller
cations can fit into these ‘holes’ as shown for
LiI in Figure 8.12b. Each ion is surrounded
by six ions of opposite charge, so both Li
1+ and I
1- ions have coordination numbers of six
and octahedral coordina
tion geometries. Using geometry, we can calculate that to fill these
holes perfectly, the radius of the cation should be
a little less than half the radius of the
anion (r
cation
= 0.414 r
anion
). LiI nearly adopts the ideal structure (r
/rLi
= 0.44) and has a I
very high packing efficiency. However, the Li
1+ ions are slightly too large to fit into the
holes, so the I
1- ions are pushed apart slightly and do not make contact. Chloride ions are
smaller than iodide ions, so their fcc arrangement has even smaller holes along the edge. As a result, they are pushed apart
even farther to accommodate the Li
1+ ions in crystalline
LiCl (Figure 8.13). Example 8.7 determines the distance between chloride ions.
Sodium chloride adopts the same structur
e type as lithium chloride. In fact, this
structure type is called the sodium chloride structure, and LiCl is said to crystallize in the sodium chloride structure

. In sodium chloride, the sodium

cation is considerably larger

than the ideal hole created by cl

osest packed chloride anions. As shown in Figure 8.14, the

Chapter 8 Solid Materials

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