Textbook Question
Potassium metal crystallizes in a body-centered cubic structure. Draw one unit cell, and try to draw an electron-dot structure for bonding of the central K atom to its nearestneighbor K atoms. What is the problem?
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Ch.12 - Solids and Solid-State Materials
McMurry8th EditionChemistryISBN: 9781292336145
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Table of contents
- Ch.1 - Chemical Tools: Experimentation & Measurement143
- Ch.2 - Atoms, Molecules & Ions134
- Ch.3 - Mass Relationships in Chemical Reactions149
- Ch.4 - Reactions in Aqueous Solution157
- Ch.5 - Periodicity & Electronic Structure of Atoms92
- Ch.6 - Ionic Compounds: Periodic Trends and Bonding Theory73
- Ch.7 - Covalent Bonding and Electron-Dot Structures47
- Ch.8 - Covalent Compounds: Bonding Theories and Molecular Structure51
- Ch.9 - Thermochemistry: Chemical Energy104
- Ch.10 - Gases: Their Properties & Behavior138
- Ch.11 - Liquids & Phase Changes43
- Ch.12 - Solids and Solid-State Materials56
- Ch.13 - Solutions & Their Properties98
- Ch.14 - Chemical Kinetics79
- Ch.15 - Chemical Equilibrium107
- Ch.16 - Aqueous Equilibria: Acids & Bases94
- Ch.17 - Applications of Aqueous Equilibria125
- Ch.18 - Thermodynamics: Entropy, Free Energy & Equilibrium66
- Ch.19 - Electrochemistry130
- Ch.20 - Nuclear Chemistry73
- Ch.21 - Transition Elements and Coordination Chemistry122
- Ch.22 - The Main Group Elements155
- Ch.23 - Organic and Biological Chemistry43
Chapter 12, Problem 52
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.)
Verified step by step guidance1
Identify the type of crystal structure for NaH. Sodium hydride (NaH) typically crystallizes in the face-centered cubic (fcc) structure.
Understand the relationship between the edge length of the unit cell and the atomic positions in an fcc lattice. In an fcc lattice, atoms are located at each corner and the centers of all the faces of the cube.
Determine the position of Na and H in the unit cell. In NaH, Na and H atoms alternate positions at the corners and face centers of the cube.
Calculate the distance between a corner atom and a face-centered atom along the face diagonal. This distance represents half the face diagonal, since the face-centered atom is midway along the diagonal.
Use the Pythagorean theorem to find half the face diagonal: half the face diagonal = \(\sqrt{\left(\frac{a}{2}\right)^2 + \left(\frac{a}{2}\right)^2}\), where \(a\) is the edge length of the unit cell. This distance is the length of the Na-H bond.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Unit Cell Structure
A unit cell is the smallest repeating unit in a crystal lattice that reflects the symmetry and structure of the entire crystal. In ionic compounds like NaH, the unit cell can be cubic, and its edge length is crucial for determining the distances between ions within the lattice. Understanding the geometry of the unit cell helps in calculating bond lengths and other structural properties.
Ionic Bonding
Ionic bonding occurs when atoms transfer electrons, resulting in the formation of positively and negatively charged ions. In NaH, sodium (Na) donates an electron to hydrogen (H), creating Na⁺ and H⁻ ions. The bond length in ionic compounds is influenced by the size of the ions and their arrangement in the crystal lattice, which is essential for calculating the Na-H bond length.
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Bond Length Calculation
Bond length is the distance between the nuclei of two bonded atoms, typically measured in picometers (pm). In a simple cubic unit cell, the bond length can often be derived from the edge length of the unit cell, as it relates to the distance between ions. For NaH, the bond length can be approximated as half the edge length of the unit cell, assuming a direct relationship between the unit cell dimensions and the ionic distances.
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Related Practice
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.
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Textbook Question
Silicon carbide, SiC, is a covalent network solid with a structuresimilar to that of diamond. Sketch a small portion ofthe SiC structure.
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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?
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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?
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Textbook Question
Carbon and oxygen combine to form the molecular compound CO2, while silicon and oxygen combine to form a covalent network solid with the formula unit SiO2. Explain the difference in bonding between the two group 4A elements and oxygen.
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