Textbook Question
Cesium chloride crystallizes in a cubic unit cell with Cl- ions
at the corners and a Cs+ ion in the center. Count the numbers
of + and - charges, and show that the unit cell is electrically
neutral.
Ch.12 - Solids and Solid-State Materials
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement170
- Ch.2 - Atoms, Molecules & Ions160
- Ch.3 - Mass Relationships in Chemical Reactions169
- Ch.4 - Reactions in Aqueous Solution199
- Ch.5 - Periodicity & Electronic Structure of Atoms102
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory92
- Ch.7 - Covalent Bonding and Electron-Dot Structures61
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure59
- Ch.9 - Thermochemistry: Chemical Energy122
- Ch.10 - Gases: Their Properties & Behavior155
- Ch.11 - Liquids & Phase Changes54
- Ch.12 - Solids and Solid-State Materials73
- Ch.13 - Solutions & Their Properties120
- Ch.14 - Chemical Kinetics98
- Ch.15 - Chemical Equilibrium125
- Ch.16 - Aqueous Equilibria: Acids & Bases110
- Ch.17 - Applications of Aqueous Equilibria147
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium86
- Ch.19 - Electrochemistry154
- Ch.20 - Nuclear Chemistry96
- Ch.21 - Transition Elements and Coordination Chemistry156
- Ch.22 - The Main Group Elements187
- Ch.23 - Organic and Biological Chemistry51
Chapter 12, Problem 50
Sodium hydride, NaH, crystallizes in a face-centered cubic unit cell similar to that of NaCl (Figure 12.11). How many Na+ ions touch each H- ion, and how many H- ions touch each Na+ ion?
Verified step by step guidance1
Identify the structure of the face-centered cubic (fcc) unit cell, which is characterized by atoms at each of the eight corners and one atom at the center of each face of the cube.
Recognize that in a NaCl-type structure, the cations (Na+) and anions (H-) alternate positions in the lattice. Each type of ion is surrounded by the other type in the structure.
Determine the coordination number for each ion, which is the number of nearest neighboring ions of the opposite charge that an ion touches directly. In an fcc lattice like NaCl, each ion is surrounded by six ions of the opposite charge.
Apply this understanding to NaH, where Na+ ions and H- ions alternate in the same manner. Each Na+ ion is surrounded by six H- ions and vice versa.
Conclude that in the NaH structure, each Na+ ion touches six H- ions, and each H- ion touches six Na+ ions.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Ionic Bonding
Ionic bonding occurs when atoms transfer electrons, resulting in the formation of charged ions. In sodium hydride (NaH), sodium (Na) donates an electron to hydrogen (H), creating Na+ and H- ions. Understanding ionic bonding is crucial for analyzing the interactions between these ions in the crystal lattice.
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Chemical Bonds
Crystal Lattice Structure
A crystal lattice structure is a three-dimensional arrangement of atoms or ions in a crystalline material. In the case of NaH, it adopts a face-centered cubic (FCC) structure similar to NaCl, where each ion occupies specific positions in the lattice. This arrangement influences how ions interact with each other, including how many of one type of ion are in contact with another.
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Coordination Number
The coordination number refers to the number of nearest neighbor ions surrounding a given ion in a crystal lattice. For NaH, determining how many Na+ ions touch each H- ion and vice versa involves calculating the coordination numbers for both ions based on their positions in the FCC structure. This concept is essential for understanding the spatial relationships and interactions between ions in the lattice.
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Related Practice
Textbook Question
Silicon carbide, SiC, is a covalent network solid with a structure
similar to that of diamond. Sketch a small portion of
the SiC structure.
Textbook Question
If the edge length of an NaH unit cell is 488 pm, what is the
length in picometers of an Na¬H bond? (See Problem 12.50.)
Textbook Question
The density of a sample of metal was measured to be
6.84 g>cm3. An X-ray diffraction experiment measures the
edge of a face-centered cubic cell as 350.7 pm. What is the
atomic weight, atomic radius, and identity of the metal?
Textbook Question
If a protein can be induced to crystallize, its molecular structure
can be determined by X-ray crystallography. Protein crystals,
though solid, contain a large amount of water molecules
along with the protein. The protein chicken egg-white lysozyme,
for instance, crystallizes with a unit cell having angles of
90° and with edge lengths of 7.9 * 103 pm, 7.9 * 103 pm,
and 3.8 * 103 pm. There are eight molecules in the unit
cell. If the lysozyme molecule has a molecular weight of
1.44 * 104 and a density of 1.35 g>cm3, what percent of the
unit cell is occupied by the protein?
Textbook Question
Iron crystallizes in a body-centered cubic unit cell with an
edge length of 287 pm. Iron metal has a density of 7.86 g>cm3
and a molar mass of 55.85 g. Calculate a value for Avogadro's
number.