Problem 4 - Chemistry: The Central Science

Question

Three spheres of equal size are composed of aluminum (density \(=2.70 \mathrm{~g} / \mathrm{cm}^{3}\) ), silver (density \(\left.=10.49 \mathrm{~g} / \mathrm{cm}^{3}\right)\) and nickel (density \(\left.=8.90 \mathrm{~g} / \mathrm{cm}^{3}\right)\). List the spheres from lightest to heaviest.

Step-by-Step Solution

Answer

The spheres can be listed in the order of their weight, from lightest to heaviest, as follows: Aluminum sphere (with a density of \(2.70\:g/cm^3\)), Nickel sphere (with a density of \(8.90\:g/cm^3\)), and Silver sphere (with a density of \(10.49\:g/cm^3\)).

Step 1: Identifying the given densities for each material

From the problem, we know that the density of each material is: - Aluminum: 2.70 g/cm³ - Silver: 10.49 g/cm³ - Nickel: 8.90 g/cm³ Step 2: List the spheres based on density

Step 2: List the materials in ascending order of their densities

Looking at the densities, we find the following order: 1. Aluminum (2.70 g/cm³) 2. Nickel (8.90 g/cm³) 3. Silver (10.49 g/cm³) Step 3: List the spheres based on their weights

Step 3: Concluding the order of the spheres based on the density comparison

Since all three spheres are of equal size, the sphere with the lowest density will also have the lowest weight, and the sphere with the highest density will have the heaviest weight. With this, we can conclude the following order: 1. Aluminum sphere (lightest) 2. Nickel sphere 3. Silver sphere (heaviest)

Key Concepts

Density Comparison

Density is a property of materials that helps us understand how much mass they have within a certain volume. Different materials have different densities, and by comparing these values, we can determine which material is heavier or lighter when they have the same size. For instance, when comparing the density of aluminum, nickel, and silver, we observe that aluminum is the lightest because it has the lowest density, while silver is the heaviest due to its highest density. This comparison is crucial in applications where weight plays a vital role, like in selecting materials for aerospace or automotive components.

• Lowest density means the material is the lightest for a given volume.
• Highest density indicates the material is the heaviest for the same volume.

When materials are of the same volume, their weight will directly relate to their density. This kind of comparison is practical for understanding the physical attributes and suitability of different materials in various applications.

Aluminum Density

Aluminum is a popular material known for its relatively low density of 2.70 g/cm³. This characteristic makes aluminum lightweight, which is one of the primary reasons for its widespread use in industries where reducing weight is crucial, such as the automotive and aerospace sectors. Despite being lightweight, aluminum is strong and resistant to corrosion, making it ideal for manufacturing frames, panels, and various structural components.

• Lightweight nature due to lower density.
• Corrosion-resistant, enhancing durability.
• Used extensively in transportation industries to lower overall weight.

Understanding the density of aluminum helps us appreciate why it's chosen over other materials for these specific purposes. Its low density translates to improved fuel efficiency when used in vehicles or aircraft, leading to cost savings and reduced environmental impact.

Material Comparison

When choosing a material for a specific application, comparing different materials based on their physical properties like density is essential. In the exercise, we examined aluminum, nickel, and silver. Each has its distinct benefits and uses due to their density:

• Aluminum: Lightweight and versatile, ideal for high-strength and low-weight needs.
• Nickel: Moderately dense with excellent thermal and corrosion resistance, used in high-stress environments.
• Silver: Dense and conductive, used in electronics and high-end jewelry.

Such comparisons help in deciding which material best suits a project based on priority needs, be it weight, strength, resistance, or conductivity. The choice depends not just on density but also on how these materials perform under different conditions and requirements.

Measurement of Density

Density is measured as the mass of a material per unit volume, typically in grams per cubic centimeter (g/cm³). It's an intrinsic property that does not change with the size of the object; it depends solely on the material's composition. To calculate density, use the formula:
density = \( \frac{mass}{volume} \)
This means if you know the mass and volume of a sample, calculating its density is straightforward. During measurement:

• Mass is usually measured using a balance.
• Volume can be found using geometric formulas or water displacement methods.

Precise measurement of density aids in identifying materials and understanding their suitability for various applications. It also helps in quality control and ensures consistency in industrial and laboratory settings. Understanding how density is measured allows for better control over manufacturing processes and material selection.