Ch.1 - Introduction: Matter, Energy, and Measurement

Brown - Chemistry: The Central Science 14th Edition

Brown14th EditionChemistry: The Central ScienceISBN: 9780134414232Not the one you use?Change textbook

Brown 14th Edition

Ch.1 - Introduction: Matter, Energy, and Measurement

Problem 4aii

Chapter 1, Problem 4aii

Consider the two spheres shown here, one made of silver and the other of aluminum. (a) What is the mass of each sphere in kg?

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Determine the volume of each sphere using the formula for the volume of a sphere: \(V = \frac{4}{3} \pi r^3\), where \(r\) is the radius of the sphere.

Identify the density of silver and aluminum from a reliable source. The density of silver is approximately 10.49 g/cm³, and the density of aluminum is approximately 2.70 g/cm³.

Convert the volume of each sphere from cubic centimeters to cubic meters if necessary, as the density is given in g/cm³ and the mass is required in kg.

Calculate the mass of each sphere using the formula: \(\text{mass} = \text{density} \times \text{volume}\). Ensure that the units are consistent, converting grams to kilograms if needed.

Verify the calculations and ensure that the mass is expressed in kilograms for both spheres.

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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. It is typically expressed in grams per cubic centimeter (g/cm³) or kilograms per cubic meter (kg/m³). Knowing the density of a material allows us to calculate its mass if we know its volume, using the formula: mass = density × volume.

Volume of a Sphere

The volume of a sphere can be calculated using the formula V = (4/3)πr³, where r is the radius of the sphere. This formula is essential for determining how much space the sphere occupies, which is necessary for calculating its mass when combined with the material's density.

Material Properties

Different materials have distinct properties, including density, which affects their mass for a given volume. Silver and aluminum have different densities (approximately 10.49 g/cm³ for silver and 2.70 g/cm³ for aluminum), which means that even if the spheres are the same size, their masses will differ significantly based on the material they are made from.

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Related Practice

Textbook Question

Musical instruments like trumpets and trombones are made from an alloy called brass. Brass is composed of copper and zinc atoms and appears homogeneous under an optical microscope. The approximate composition of most brass objects is a 2:1 ratio of copper to zinc atoms, but the exact ratio varies somewhat from one piece of brass to another. (a) Would you classify brass as an element, a compound, a homogeneous mixture, or a heterogeneous mixture?

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Textbook Question

Identify each of the following as measurements of length, area, volume, mass, density, time, or temperature: (a) 25 ps, (b) 374.2 mg, (c) 77 K, (d) 100,000 km2, (e) 1.06 mm, (f) 16 nm2, (g) -78 °C, (h) 2.56 g>cm3, (i) 28 cm3.

Which of the following diagrams represents a chemical change?

Consider the two spheres shown here, one made of silver and the other of aluminum. (d) If you release the spheres simultaneously, they will have the same velocity when they hit the ground. Will they have the same kinetic energy? If not, which sphere will have more kinetic energy?

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Textbook Question

Is the separation method used in brewing a cup of coffee best described as distillation, filtration, or chromatography?