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General Chemistry Principles, Patterns, and Applications, 2011

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. What is the length of one edge of the unit cell? (Hint: there is no empty space between<br />

atoms.)<br />

c. Calculate the volume of the unit cell.<br />

d. Determine the packing efficiency for this structure.<br />

e. Use the steps in Problem 11 to calculate the packing efficiency for a bcc unit cell with a<br />

metallic radius of 1.00 Å.<br />

A N S W E R S<br />

1. four<br />

2.<br />

3. fcc<br />

4.<br />

5. molybdenum<br />

6.<br />

7. sodium, unit cell edge = 428 pm, r = 185 pm<br />

8.<br />

9. d = 0.5335 g/cm 3 , r =151.9 pm<br />

12.3 Structures of Simple Binary Compounds<br />

L E A R N I N G O B JE C T I V E S<br />

1. To use the cation:anion radius ratio to predict the structures of simple binary<br />

compounds.<br />

2. To underst<strong>and</strong> how x-rays are diffracted by crystalline solids.<br />

The structures of most binary compounds can be described using the packing schemes we have just discussed for<br />

metals. To do so, we generally focus on the arrangement in space of the largest species present. In ionic solids, this<br />

generally means the anions, which are usually arranged in a simple cubic, bcc, fcc, or hcp lattice. (For more<br />

information about anions, see Chapter 7 "The Periodic Table <strong>and</strong> Periodic Trends",Section 7.2 "Sizes of Atoms <strong>and</strong><br />

Ions".) Often, however, the anion lattices are not truly “close packed”; because the cations are large enough to prop<br />

them apart somewhat, the anions are not actually in contact with one another. In ionic compounds, the cations<br />

usually occupy the “holes” between the anions, thus balancing the negative charge. The ratio of cations to anions<br />

Saylor URL: http://www.saylor.org/books<br />

Saylor.org<br />

1089

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