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A steel cylinder has a length of 2.16 in, a radius of 0.22 in, and a mass of 41 g. What is the density of the steel in g/cm3?
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Ch.1 - Matter, Measurement & Problem Solving
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217
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TOC.tableOfContents
- Ch.1 - Matter, Measurement & Problem Solving118
- Ch.2 - Atoms & Elements106
- Ch.3 - Molecules and Compounds131
- Ch.4 - Chemical Reactions and Chemical Quantities56
- Ch.5 - Introduction to Solutions and Aqueous Solutions82
- Ch.6 - Gases114
- Ch.7 - Thermochemistry96
- Ch.8 - The Quantum-Mechanical Model of the Atom60
- Ch.9 - Periodic Properties of the Elements90
- Ch.10 - Chemical Bonding I: The Lewis Model89
- Ch.11 - Chemical Bonding II: Molecular Shapes, VSEPR & MO Theory85
- Ch.12 - Liquids, Solids & Intermolecular Forces51
- Ch.13 - Solids & Modern Materials47
- Ch.14 - Solutions90
- Ch.15 - Chemical Kinetics115
- Ch.16 - Chemical Equilibrium68
- Ch.17 - Acids and Bases136
- Ch.18 - Aqueous Ionic Equilibrium153
- Ch.19 - Free Energy & Thermodynamics93
- Ch.20 - Electrochemistry106
- Ch.21 - Radioactivity & Nuclear Chemistry74
- Ch.22 - Organic Chemistry140
Tro6th EditionChemistry: A Molecular ApproachISBN: 9780137832217Non è quello che usi tu?Cambia libro di testo
Capitolo 1, Problema 126
A solid aluminum sphere has a mass of 36 g. Use the density of aluminum to find the radius of the sphere in inches.
Guida verificata passo dopo passo1
Identify the density of aluminum, which is typically 2.70 g/cm³.
Use the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \) to find the volume of the sphere. Rearrange it to \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).
Substitute the given mass (36 g) and the density of aluminum (2.70 g/cm³) into the volume formula to calculate the volume in cm³.
Use the formula for the volume of a sphere: \( V = \frac{4}{3} \pi r^3 \) to solve for the radius \( r \). Rearrange it to \( r = \left(\frac{3V}{4\pi}\right)^{1/3} \).
Convert the radius from centimeters to inches using the conversion factor 1 inch = 2.54 cm.
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Density
Density is defined as mass per unit volume and is a key property of materials. For aluminum, the density is typically around 2.70 g/cm³. Understanding density allows us to relate the mass of an object to its volume, which is essential for solving problems involving geometric shapes like spheres.
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Percorso guidato
01:56
Density Concepts
Volume of a Sphere
The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius. This formula is crucial for determining the volume of the aluminum sphere based on its mass and density. By rearranging this formula, we can solve for the radius once we have the volume.
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Percorso guidato
02:35Constant-Volume Calorimetry
Unit Conversion
Unit conversion is the process of converting a quantity expressed in one set of units to another. In this problem, we need to convert the radius from centimeters to inches, as the final answer requires the radius in inches. Knowing the conversion factor (1 inch = 2.54 cm) is essential for accurate results.
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Percorso guidato
01:56Conversion Factors
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