Domanda del libro di testo
(a) The density of diamond is 3.5 g/cm3, and that of graphite is 2.3 g/cm3. Based on the structure of buckminsterfullerene, what would you expect its density to be relative to these other forms of carbon?
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Ch.12 - Solids and Modern Materials
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232
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TOC.tableOfContents
- Ch.1 - Introduction: Matter, Energy, and Measurement177
- Ch.2 - Atoms, Molecules, and Ions231
- Ch.3 - Chemical Reactions and Reaction Stoichiometry216
- Ch.4 - Reactions in Aqueous Solution189
- Ch.5 - Thermochemistry175
- Ch.6 - Electronic Structure of Atoms168
- Ch.7 - Periodic Properties of the Elements150
- Ch.8 - Basic Concepts of Chemical Bonding177
- Ch.9 - Molecular Geometry and Bonding Theories200
- Ch.10 - Gases179
- Ch.11 - Liquids and Intermolecular Forces113
- Ch.12 - Solids and Modern Materials154
- Ch.13 - Properties of Solutions157
- Ch.14 - Chemical Kinetics199
- Ch.15 - Chemical Equilibrium128
- Ch.16 - Acid-Base Equilibria164
- Ch.17 - Additional Aspects of Aqueous Equilibria163
- Ch.18 - Chemistry of the Environment105
- Ch.19 - Chemical Thermodynamics164
- Ch.20 - Electrochemistry171
- Ch.21 - Nuclear Chemistry122
- Ch.22 - Chemistry of the Nonmetals82
- Ch.23 - Transition Metals and Coordination Chemistry79
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry16
Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Non è quello che usi tu?Cambia libro di testo
Capitolo 12, Problema 122b
(b) X-ray diffraction studies of buckminsterfullerene show that it has a face-centered cubic lattice of C60 molecules. The length of an edge of the unit cell is 14.2 Å. Calculate the density of buckminsterfullerene.
Guida verificata passo dopo passo1
Identify the type of lattice structure: Buckminsterfullerene has a face-centered cubic (FCC) lattice structure.
Determine the number of C60 molecules per unit cell in an FCC lattice: An FCC lattice has 4 atoms or molecules per unit cell.
Calculate the molar mass of a C60 molecule: The molar mass of carbon (C) is approximately 12.01 g/mol. Therefore, the molar mass of C60 is 60 times the molar mass of carbon, which is 60 * 12.01 g/mol.
Convert the edge length of the unit cell from Ångströms to centimeters: 1 Å = 1 x 10^-8 cm, so 14.2 Å = 14.2 x 10^-8 cm.
Calculate the density using the formula: \( \text{Density} = \frac{\text{Mass of molecules in unit cell}}{\text{Volume of unit cell}} \). Use the molar mass, Avogadro's number, and the converted edge length to find the mass and volume.
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Unit Cell and Lattice Structure
A unit cell is the smallest repeating unit in a crystal lattice that reflects the overall symmetry and structure of the entire crystal. In the case of buckminsterfullerene, it has a face-centered cubic (FCC) lattice, meaning that the unit cell is cubic with atoms located at each corner and the center of each face. Understanding the unit cell is crucial for calculating properties like density.
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Percorso guidato
01:27
Simple Cubic Unit Cell
Density Calculation
Density is defined as mass per unit volume and is typically expressed in grams per cubic centimeter (g/cm³). To calculate the density of a substance, one must know the mass of the unit cell and its volume. For buckminsterfullerene, the volume can be determined from the edge length of the unit cell, while the mass can be calculated based on the number of C60 molecules in the unit cell.
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Percorso guidato
01:56Density Concepts
Molar Mass and Avogadro's Number
The molar mass of a substance is the mass of one mole of its entities, typically expressed in grams per mole (g/mol). For buckminsterfullerene (C60), the molar mass is approximately 720 g/mol. Avogadro's number (6.022 x 10²³) relates the number of molecules in a mole to its mass, allowing for the conversion between the mass of the unit cell and the number of molecules it contains, which is essential for density calculations.
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02:11Molar Mass Concept
Pratica correlata
Domanda del libro di testo
The karat scale used to describe gold alloys is based on mass percentages. (a) If an alloy is formed that is 50 mol% silver and 50 mol% gold, what is the karat number of the alloy? Use Figure 12.18 to estimate the color of this alloy.
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Domanda del libro di testo
Germanium has the same structure as silicon, but the unit cell size is different because Ge and Si atoms are not the same size. If you were to repeat the experiment described in the previous problem but replace the Si crystal with a Ge crystal, would you expect the X rays to be diffracted at a larger or smaller angle u?
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Domanda del libro di testo
The karat scale used to describe gold alloys is based on mass percentages. (b) If an alloy is formed that is 50 mol% copper and 50 mol% gold, what is the karat number of the alloy? What is the color of this alloy?
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