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Chapter 10: Problem 73

A certain metal fluoride crystallizes in such a way that the fluoride ions occupy simple cubic lattice sites, while the metal ions occupy the body centers of half the cubes. What is the formula of the metal fluoride?

Short Answer

Expert verified
In the given lattice structure, fluoride ions occupy simple cubic lattice sites, while metal ions occupy the body centers of half the cubes. The ratio of metal ions to fluoride ions in the lattice is 1:2. Therefore, the formula of the metal fluoride is \(MF_2\), with M representing the metal ion and F representing the fluoride ion.

Step by step solution

01

1. Understand the Lattice Structure

: First, let's visualize the given structure: - Fluoride ions occupy simple cubic lattice sites. - Metal ions occupy the body centers of half the cubes. In a simple cubic lattice, there is one atom/ion at each corner of the cube. As there are 8 corners, there is a total of 1 ion per unit cell (each corner contributes 1/8 of an ion to the unit cell). So, for the fluoride ions, we have an equivalent of 1 ion per unit cell. The metal ions are in the body center of half the cubes. In a body-centered cubic lattice, there is 1 atom/ion in the center of the cube, which contributes the whole 1 ion to the unit cell. As only half the cubes have metal ions, on average, there is 0.5 metal ion per unit cell.
02

2. Determine the Ratio between Metal and Fluoride Ions

: Now that we have the number of metal and fluoride ions per unit cell, we can determine the ratio between them: - Metal ions: 0.5 per unit cell - Fluoride ions: 1 per unit cell The ratio of metal ions to fluoride ions in the lattice is 0.5:1, which simplifies to 1:2.
03

3. Establish the Formula of the Metal Fluoride

: As there is a ratio of 1 metal ion to 2 fluoride ions in this lattice structure, we can represent the metal fluoride's formula with MF2, with M representing the metal ion and F representing the fluoride ion. Therefore, the formula of the metal fluoride is MF2.

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Most popular questions from this chapter

Explain the following: You add \(100 \mathrm{~mL}\) water to a \(500-\mathrm{mL}\) round-bottom flask and heat the water until it is boiling. You remove the heat and stopper the flask, and the boiling stops. You then run cool water over the neck of the flask, and the boiling begins again. It seems as though you are boiling water by cooling it.

Predict which substance in each of the following pairs would have the greater intermolecular forces. a. \(\mathrm{CO}_{2}\) or \(\mathrm{OCS}\) b. \(\mathrm{SeO}_{2}\) or \(\mathrm{SO}_{2}\) c. \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) or \(\mathrm{H}_{2} \mathrm{NCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}\) d. \(\mathrm{CH}_{3} \mathrm{CH}_{3}\) or \(\mathrm{H}_{2} \mathrm{CO}\) e. \(\mathrm{CH}_{3} \mathrm{OH}\) or \(\mathrm{H}_{2} \mathrm{CO}\)

Rationalize the differences in physical properties in terms of intermolecular forces for the following organic compounds. Compare the first three substances with each other, compare the last three with each other, and then compare all six. Can you account for any anomalies? $$ \begin{array}{|lccc|} \hline & \text { bp }\left({ }^{\circ} \mathrm{C}\right) & \operatorname{mp}\left({ }^{\circ} \mathrm{C}\right) & \Delta H_{\text {vap }}(\mathbf{k J} / \text { mol }) \\ \hline \text { Benzene, } \mathrm{C}_{6} \mathrm{H}_{6} & 80 & 6 & 33.9 \\ \text { Naphthalene, } & & & \\ \mathrm{C}_{10} \mathrm{H}_{8} & 218 & 80 & 51.5 \\ \text { Carbon tetra- } & & & \\ \text { chloride } & 76 & -23 & 31.8 \\ \text { Acetone, } & & & \\ \mathrm{CH}_{3} \mathrm{COCH}_{3} & 56 & -95 & 31.8 \\ \text { Acetic acid, } & & & \\ \mathrm{CH}_{3} \mathrm{CO}_{2} \mathrm{H} & 118 & 17 & 39.7 \\ \text { Benzoic acid, } & & & \\ \mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CO}_{2} \mathrm{H} & 249 & 122 & 68.2 \\\ \hline \end{array} $$

Consider two different organic compounds, each with the formula \(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O} .\) One of these compounds is a liquid at room conditions and the other is a gas. Write Lewis structures consistent with this observation, and explain your answer. (Hint: The oxygen atom in both structures satisfies the octet rule with two bonds and two lone pairs.)

How does each of the following affect the rate of evaporation of a liquid in an open dish? a. intermolecular forces b. temperature c. surface area
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