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Chapter 12: Problem 64

The rutile and fluorite structures, shown here (anions are colored green), are two of the most common structure types of ionic compounds where the cation to anion ratio is 1: 2 . (a) For \(\mathrm{CaF}_{2}\) and \(\mathrm{ZnF}_{2}\) use ionic radii, \(\mathrm{Ca}^{2+}(r=114 \mathrm{pm})\), $\mathrm{Zn}^{2+}(r=88 \mathrm{pm})\(, and \)\mathrm{F}^{-}(r=119 \mathrm{pm})$, to predict which compound is more likely to crystallize with the fluorite structure and which with the rutile structure. (b) What are the coordination numbers of the cations and anions in each of these structures?

Short Answer

Expert verified
CaF2 is more likely to crystallize in the fluorite structure, and ZnF2 is more likely to crystallize in the rutile structure. For the fluorite structure, the cation coordination number is 8, and the anion coordination number is 4. For the rutile structure, both cation and anion coordination numbers are 6.

Step by step solution

01

Calculate cation-anion radius ratio for each compound

For CaF2, we need to calculate the ratio of the Ca2+ and F- ion radii: Cation-Anion Radius Ratio (CaF2) = \( \frac{r_{Ca^{2+}}}{r_{F^{-}}} \) = \( \frac{114 \, pm}{119 \, pm} = 0.958 \) Similarly, for ZnF2: Cation-Anion Radius Ratio (ZnF2) = \( \frac{r_{Zn^{2+}}}{r_{F^{-}}} \) = \( \frac{88 \, pm}{119 \, pm} = 0.739 \)
02

Compare the calculated radius ratios with known ratios for fluorite and rutile structures

In general, the cation-anion radius ratio for the fluorite structure (CaF2-type) is around 0.75 to 1, while for the rutile structure (TiO2-type) it is around 0.7 to 0.85. Comparing the calculated cation-anion radius ratios for CaF2 (0.958) and ZnF2 (0.739) with the known radius ratios for the fluorite and rutile structures, we can predict that CaF2 is more likely to crystallize in the fluorite structure, and ZnF2 is more likely to crystallize in the rutile structure.
03

Determine the coordination numbers for cations and anions in each structure

Coordination number can be defined as the number of nearest neighbors of a species (cation or anion) in the crystal structure. In the fluorite structure, the cations are surrounded by eight anions forming a cubic coordination polyhedron, while the anions are surrounded by four cations forming a tetrahedral coordination polyhedron. Thus, for the fluorite structure: Cation Coordination Number: 8 Anion Coordination Number: 4 In the rutile structure, both cations and anions are surrounded by six nearest neighbors in an octahedral arrangement. Thus, for the rutile structure: Cation Coordination Number: 6 Anion Coordination Number: 6
04

Summary

CaF2 is more likely to crystallize in the fluorite structure, and ZnF2 is more likely to crystallize in the rutile structure. For the fluorite structure, the cation coordination number is 8, and the anion coordination number is 4. For the rutile structure, both cation and anion coordination numbers are 6.

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Most popular questions from this chapter

An ideal quantum dot for use in TVs does not contain any cadmium due to concerns about disposal. One potential material for this purpose is InP, which adopts the zinc blende (ZnS) structure (face-centered cubic). The unit cell edge length is \(586.9 \mathrm{pm} .(\mathbf{a})\) If the quantum dot is shaped like a cube, how many of each type of atom are there in a cubic crystal with an edge length of \(3.00 \mathrm{nm} ? 5.00 \mathrm{nm} ?(\mathbf{b})\) If one of the nanoparticles in part (a) emits blue light and the other emits orange light, which color is emitted by the crystal with the \(3.00-\mathrm{nm}\) edge length? With the \(5.00-\mathrm{nm}\) edge length?

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