Physical Chemistry , 1st ed.

mechanics and its probabilistic interpretation of wavefunctions do not allow

us to define a certain “size” for the electrons about an ion. But by measuring

the crystalline parameters of unit cells of various crystals, we can determine a

general size that an ion contributes to a crystal lattice and define that as the size

(diameter or radius) of the ion. Table 21.4 lists the experimentally determined

ionic radii for some ions. There are also several entries for polyatomic ions.

Although it is not possible to assign a specific, single radius to polyatomic

21.7 Rationalizing Unit Cells 753

Ice VI

Ice V

Ice I

Ice III

Ice I

6000

0

200

Temperature (K)

700

Ice

II

Pressure (bar)

4000

2000

218

1

2

0.006

600

647.30

400 500

273.15 273.16 373.15

300

Critical point

Triple

point

Liquid (water)

Gas (steam)

Liquid (water)

Figure 21.27 Phase diagrams can include dif-
ferent kinds of solid phase, as well as liquid and
gas phase. H 2 O, for example, has many different
crystalline structures, depending on the tempera-
ture and the pressure. Each region represents a
different solid phase of H 2 O.

Table 21.4 Crystalline ionic radii for various ions

Ion Radius (Å) Ion Radius (Å)

Ag 1.26 K 1.33

Al^3  0.51 Mg^2  0.66

Au^3  1.37 Na 0.97

Ba^2  1.34 O^2  1.31

Be^2  0.35 Pb^2  1.20

Br 1.96 S^2  1.84

Ca^2  0.99 Ti^4  0.68

Cl 1.81 Zn^2  0.74

Cr^3  0.63 NH 4  1.48

Cs 1.67 BF 4  2.28

F 1.33 SO 42  2.30

I 2.20