CuI, CsI, and NaI each adopt a different type of structure. The three different structures are those shown in Figure 12.26. (a) Use ionic radii, Cs+ 1r = 1.81 A 2, Na+ 1r = 1.16 A 2, Cu+ 1r = 0.74 A 2, and, I- 1r = 2.06 A 2, to predict which compound will crystallize with which structure.

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Identify the ionic radii for each cation and the anion from the problem statement: Cs+ (1.81 Å), Na+ (1.16 Å), Cu+ (0.74 Å), and I- (2.06 Å).

Calculate the cation to anion radius ratio for each compound: CuI, CsI, and NaI.

Compare the calculated cation to anion radius ratios with the given ratios for ZnS, NaCl, and CsCl structures in the provided table.

Match each compound (CuI, CsI, NaI) with the structure (ZnS, NaCl, CsCl) that has the closest cation to anion radius ratio.

Assign the appropriate structure to each compound based on the closest match in cation to anion radius ratio.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ionic Radii

Ionic radii refer to the effective size of an ion in a crystal lattice, which influences how ions pack together in a solid. The size of cations (positively charged ions) and anions (negatively charged ions) affects the stability and structure of ionic compounds. Larger ions can lead to different coordination numbers and crystal structures, as seen in the comparison of Cs+, Na+, and Cu+ with I-.

Coordination Number

The coordination number is the number of nearest neighbor ions surrounding a central ion in a crystal lattice. It is determined by the relative sizes of the cations and anions, influencing the geometry of the crystal structure. For example, in NaCl, the coordination number is 6, indicating that each Na+ ion is surrounded by six Cl- ions, which is crucial for predicting the structure of compounds like CsI and CuI.

Crystal Structure Types

Different ionic compounds adopt distinct crystal structures based on the ionic sizes and charges of their constituent ions. Common structures include face-centered cubic (like NaCl) and body-centered cubic (like CsCl). Understanding these structures helps predict how compounds will crystallize, as seen in the question regarding CuI, CsI, and NaI, where the arrangement of ions is influenced by their ionic radii.

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A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 Å. (a) Calculate the density of HgS in this form. (c) Which of the two substances has the higher density? How do you account for the difference in densities?

Textbook Question

A particular form of cinnabar (HgS) adopts the zinc blende structure. The length of the unit cell edge is 5.852 Å. (b) The mineral tiemannite (HgSe) also forms a solid phase with the zinc blende structure. The length of the unit cell edge in this mineral is 6.085 Å. What accounts for the larger unit cell length in tiemmanite?

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Textbook Question

The coordination number for the Al3+ ion is typically between four and six. Use the anion coordination number to determine the Al3 + coordination number in the following compounds: (a) AlF3 where the fluoride ions are two coordinate.

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