Domanda del libro di testo
Calcium crystallizes in a body-centered cubic structure at 467°C. (a) How many Ca atoms are contained in each unit cell?
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Ch.12 - Solids and Modern Materials
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement146
- Ch.2 - Atoms, Molecules, and Ions200
- Ch.3 - Chemical Reactions and Reaction Stoichiometry176
- Ch.4 - Reactions in Aqueous Solution155
- Ch.5 - Thermochemistry126
- Ch.6 - Electronic Structure of Atoms131
- Ch.7 - Periodic Properties of the Elements126
- Ch.8 - Basic Concepts of Chemical Bonding123
- Ch.9 - Molecular Geometry and Bonding Theories143
- Ch.10 - Gases147
- Ch.11 - Liquids and Intermolecular Forces91
- Ch.12 - Solids and Modern Materials122
- Ch.13 - Properties of Solutions126
- Ch.14 - Chemical Kinetics174
- Ch.15 - Chemical Equilibrium101
- Ch.16 - Acid-Base Equilibria139
- Ch.17 - Additional Aspects of Aqueous Equilibria146
- Ch.18 - Chemistry of the Environment72
- Ch.19 - Chemical Thermodynamics129
- Ch.20 - Electrochemistry142
- Ch.21 - Nuclear Chemistry101
- Ch.22 - Chemistry of the Nonmetals68
- Ch.23 - Transition Metals and Coordination Chemistry66
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry10
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Non è quello che usi tu?Cambia libro di testo
Capitolo 12, Problema 34
Sodium metal (atomic weight 22.99 g/mol) adopts a body-centered cubic structure with a density of 0.97 g/cm3. (a) Use this information and Avogadro’s number (NA = 6.022 × 1023/mol) to estimate the atomic radius of sodium. (b) If sodium didn't react so vigorously, it could float on water. Use the answer from part (a) to estimate the density of Na if its structure were that of a cubic close-packed metal. Would it still float on water?
Guida verificata passo dopo passo1
Identify the type of crystal structure for cubic close-packed (ccp), which is also known as face-centered cubic (fcc).
Recall that in a face-centered cubic structure, there are 4 atoms per unit cell.
Use the formula for density: \( \text{Density} = \frac{\text{Mass of atoms in unit cell}}{\text{Volume of unit cell}} \).
Calculate the mass of the atoms in the unit cell using the atomic weight of sodium and Avogadro's number.
Estimate the volume of the unit cell using the relationship between the atomic radius and the edge length in a face-centered cubic structure, then calculate the density and compare it to the density of water (1 g/cm³) to determine if it would float.
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Density
Density is defined as mass per unit volume, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that determines whether a substance will float or sink in a fluid. In this context, understanding the density of sodium in different crystal structures helps assess its buoyancy in water.
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Percorso guidato
01:56
Density Concepts
Crystal Structures
Crystal structures refer to the orderly arrangement of atoms in a solid. The body-centered cubic (BCC) and cubic close-packed (CCP) structures are two common types. The arrangement affects the packing efficiency and, consequently, the density of the material, which is essential for estimating how sodium would behave in water.
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01:42Resonance Structures
Buoyancy
Buoyancy is the upward force exerted by a fluid that opposes the weight of an object immersed in it. An object will float if its density is less than that of the fluid. In this case, determining whether sodium would float on water involves comparing its estimated density in a cubic close-packed structure to the density of water (1 g/cm³).
Pratica correlata
Domanda del libro di testo
Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (a) Which structure(s) corresponds to the densest packing of atoms?
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Domanda del libro di testo
Consider the unit cells shown here for three different structures that are commonly observed for metallic elements. (b) Which structure(s) corresponds to the least dense packing of atoms?
454
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