Ch.12 - Solids and Solid-State Materials

Problem 138

Chapter 12, Problem 138

Assume that 1.588 g of an alkali metal undergoes complete reaction with the amount of gaseous halogen contained in a 0.500 L flask at 298 K and 755 mm Hg pressure. In the reaction, 22.83 kJ is released 1ΔH = -22.83 kJ2. The product, a binary ionic compound, crystallizes in a unit cell with anions in a face-centered cubic arrangement and with cations centered along each edge between anions. In addition, there is a cation in the center of the cube. (c) Sketch a space-filling, head-on view of the unit cell, labeling the ions. Are the anions in contact with one another?

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Identify the type of unit cell described: The problem states that the anions form a face-centered cubic (FCC) arrangement, and the cations are located at the center of each edge and one in the center of the cube.

Visualize the FCC unit cell: In an FCC unit cell, anions are located at each corner and the centers of each face of the cube. This means there are 8 corner anions and 6 face-centered anions.

Determine the positions of the cations: The cations are located at the center of each edge of the cube and one in the center. There are 12 edges, so there are 12 edge-centered cations, and 1 cation in the center of the cube.

Sketch the unit cell: Draw a cube and place anions at each corner and face center. Then, place cations at the center of each edge and one in the center of the cube.

Consider the contact between anions: In an FCC arrangement, anions at the face centers are in contact with those at the corners. Therefore, the anions are indeed in contact with one another.

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Key Concepts

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

Stoichiometry and Molar Mass

Stoichiometry involves the calculation of reactants and products in chemical reactions. Understanding the molar mass of the alkali metal is essential to determine how many moles are present in the 1.588 g sample. This information is crucial for relating the mass of the reactant to the amount of halogen gas consumed and the energy released during the reaction.

Thermodynamics and Enthalpy Change

Thermodynamics studies the relationships between heat, work, and energy in chemical processes. The enthalpy change (ΔH) indicates the heat released or absorbed during a reaction. In this case, the negative ΔH of -22.83 kJ signifies an exothermic reaction, meaning energy is released when the alkali metal reacts with the halogen, which is important for understanding the reaction's energetics.

Crystal Lattice Structure

The crystal lattice structure describes the arrangement of ions in a solid ionic compound. In this scenario, the anions are arranged in a face-centered cubic (FCC) structure, while the cations occupy specific positions within the unit cell. Understanding this arrangement is key to visualizing the spatial relationships between ions, including whether the anions are in contact with one another, which affects the compound's stability and properties.

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A group 3A metal has a density of 2.70 g/cm³ and a cubic unit cell with an edge length of 404 pm. Reaction of A 1.07 cm³ chunk of the metal with an excess of hydrochloric acid gives a colorless gas that occupies 4.00 L at 23.0 °C and a pressure of 740 mm Hg. (a) Identify the metal.

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Textbook Question

A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (b) Use the data in Figure 5.19 to identify the alkali metal.

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Textbook Question

A cube-shaped crystal of an alkali metal, 1.62 mm on an edge, was vaporized in a 500.0 mL evacuated flask. The resulting vapor pressure was 12.5 mm Hg at 802 °C. The structure of the solid metal is known to be body-centered cubic. (c) What are the densities of the solid and the vapor in g>cm3?

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Textbook Question

Europium(II) oxide is a semiconductor with a band gap of 108 kJ/mol. Below 69 K, it is also ferromagnetic, meaning all the unpaired electrons on europium are aligned in the same direction. How many f electrons are present on each europium ion in EuO? (In lanthanide ions the 4f orbitals are lower in energy than the 6s orbitals.)

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The mineral wustite is a nonstoichiometric iron oxide with the empirical formula FexO, where x is a number slightly less than 1. Wustite can be regarded as an FeO in which some of the Fe sites are vacant. It has a density of 5.75 g>cm3, a cubic unit cell with an edge length of 431 pm, and a facecentered cubic arrangement of oxygen atoms. (c) Each Fe atom in wustite is in either the +2 or the +3 oxidation state. What percent of the Fe atoms are in the +3 oxidation state?

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Textbook Question

The mineral wustite is a nonstoichiometric iron oxide with the empirical formula FexO, where x is a number slightly less than 1. Wustite can be regarded as an FeO in which some of the Fe sites are vacant. It has a density of 5.75 g>cm3, a cubic unit cell with an edge length of 431 pm, and a facecentered cubic arrangement of oxygen atoms. (d) Using X rays with a wavelength of 70.93 pm, at what angle would third-order diffraction be observed from the planes of atoms that coincide with the faces of the unit cells? Third-order diffraction means that the value of n in the Bragg equation is equal to 3.

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