Textbook Question
Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: b. a cup of coffee
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Ch.1 - Introduction: Matter, Energy, and Measurement
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970
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Table of contents
- Ch.1 - Introduction: Matter, Energy, and Measurement111
- Ch.2 - Atoms, Molecules, and Ions166
- Ch.3 - Chemical Reactions and Reaction Stoichiometry138
- Ch.4 - Reactions in Aqueous Solution127
- Ch.5 - Thermochemistry104
- Ch.6 - Electronic Structure of Atoms109
- Ch.7 - Periodic Properties of the Elements107
- Ch.8 - Basic Concepts of Chemical Bonding102
- Ch.9 - Molecular Geometry and Bonding Theories120
- Ch.10 - Gases122
- Ch.11 - Liquids and Intermolecular Forces79
- Ch.12 - Solids and Modern Materials102
- Ch.13 - Properties of Solutions99
- Ch.14 - Chemical Kinetics153
- Ch.15 - Chemical Equilibrium83
- Ch.16 - Acid-Base Equilibria109
- Ch.17 - Additional Aspects of Aqueous Equilibria117
- Ch.18 - Chemistry of the Environment60
- Ch.19 - Chemical Thermodynamics109
- Ch.20 - Electrochemistry113
- Ch.21 - Nuclear Chemistry79
- Ch.22 - Chemistry of the Nonmetals52
- Ch.23 - Transition Metals and Coordination Chemistry57
- Ch.24 - The Chemistry of Life: Organic and Biological Chemistry7
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
Chapter 1, Problem 68
A copper refinery produces a copper ingot weighing 150 lb. If the copper is drawn into wire whose diameter is 7.50 mm, how many feet of copper can be obtained from the ingot? The density of copper is 8.94 g/cm3. (Assume that the wire is a cylinder whose volume π=ππ2β, where r is its radius and h is its height or length.)
Verified step by step guidance1
Convert the weight of the copper ingot from pounds to grams using the conversion factor: 1 lb = 453.592 g.
Calculate the volume of the copper ingot using the formula: \( \text{Volume} = \frac{\text{mass}}{\text{density}} \), where the mass is in grams and the density is given as 8.94 g/cm\(^3\).
Convert the diameter of the wire from millimeters to centimeters, and then calculate the radius by dividing the diameter by 2.
Use the formula for the volume of a cylinder \( V = \pi r^2 h \) to express the height (or length) \( h \) in terms of the volume and radius. Rearrange the formula to solve for \( h \): \( h = \frac{V}{\pi r^2} \).
Convert the length of the wire from centimeters to feet using the conversion factor: 1 cm = 0.0328084 ft.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Density
Density is defined as mass per unit volume and is a crucial property of materials. In this problem, the density of copper (8.94 g/cmΒ³) allows us to convert the mass of the copper ingot into volume. Understanding how to manipulate the density formula (Density = Mass/Volume) is essential for determining how much space the copper occupies.
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Density Concepts
Volume of a Cylinder
The volume of a cylinder can be calculated using the formula V = ΟrΒ²h, where r is the radius and h is the height (or length) of the cylinder. In this context, the copper wire is modeled as a cylinder, and knowing this formula is necessary to relate the volume of the copper ingot to the length of wire that can be produced.
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02:35Constant-Volume Calorimetry
Unit Conversion
Unit conversion is the process of converting a quantity from one unit to another, which is often necessary in chemistry problems. In this case, converting the weight of the copper ingot from pounds to grams and the diameter of the wire from millimeters to centimeters is essential for consistent calculations. Mastery of unit conversions ensures accurate results in the final answer.
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01:56Conversion Factors
Related Practice
Textbook Question
(b) A(n) _________ reliably predicts the behavior of matter, while a(n) _________ provides an explanation for that behavior.
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Textbook Question
Classify each of the following as a pure substance, a solution, or a heterogeneous mixture: c. a wood plank
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Textbook Question
Gold can be hammered into extremely thin sheets called gold leaf. An architect wants to cover a 100 ft x 82 ft ceiling with gold leaf that is five-millionths of an inch thick. The density of gold is 19.32 g/cm3. If gold costs \$1768 per troy ounce (1 troy ounce = 31.10348 g), how much will it cost the architect to buy the necessary gold?
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