(b) Three cubes of equal mass are composed of gold (density = 19.32 g/cm 3 ), platinum (density = 21.45 g/cm 3 ), and lead (density = 11.35 g/cm 3 ). List the cubes from smallest to largest.

Hi everyone here we have a problem telling asking us to list a potassium cube density equals 0.862 g per centimeters cube. A cesium cube density equals 1.9 g per centimeters cube. And rubidium cube density equals 1.63 g per centimeter cube that have similar masses from smallest to largest. So density equals mass over volume. We know all of their densities and we know that their masses are similar. So we want to solve for volume. So we're going to multiply both sides by volume to cancel that out, which gives us density times volume equals mass. So then we want to divide both sides by density to cancel that out. And I sleep volume. So we get volume equals mass over density. So we're going to assume that each cube is one g. So for potassium We have one g Divided by 0.862 g per cm cube. So our grams are going to cancel out here And that's going to give us 1.16 cm cute. We have cesium Which equals one g Divided by 1.9 grams per centimeters cubed. And our g cancel out. And that gives us 0.52 cm cubed. And lastly we have rubidium Which is one g divided by 1.63 g per centimeters cubed. And our grams cancel out that equals 0. centimeters cubed. So now we just have to list the smallest to largest. So we have cesium is less than rubidium is less than potassium. And that is our final answer. Thank you for watching Bye!

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

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Brown 14th Edition

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

Problem 7b

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Chapter 1, Problem 7b

(b) Three cubes of equal mass are composed of gold (density = 19.32 g/cm³), platinum (density = 21.45 g/cm³), and lead (density = 11.35 g/cm³). List the cubes from smallest to largest.

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Identify that the problem involves comparing the volumes of three cubes made of different materials but with equal mass.

Recall the formula for density: \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \). Rearrange it to find the volume: \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Since the mass of each cube is the same, the volume of each cube is inversely proportional to its density.

Compare the densities of the materials: gold (19.32 g/cm^3), platinum (21.45 g/cm^3), and lead (11.35 g/cm^3).

List the cubes from smallest to largest volume based on their densities: platinum (smallest volume), gold, lead (largest volume).

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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, typically expressed in grams per cubic centimeter (g/cm³). It is a crucial property that helps determine how much matter is packed into a given space. In this question, the densities of gold, platinum, and lead are provided, which will be used to compare the relative sizes of the cubes when their masses are equal.

Volume Calculation

Volume can be calculated using the formula: Volume = Mass / Density. Since the cubes have equal mass, their volumes will differ based on their respective densities. A lower density indicates a larger volume for the same mass, which is essential for determining the order of the cubes from smallest to largest.

Comparison of Materials

Comparing materials based on their physical properties, such as density, allows us to rank them effectively. In this scenario, understanding how the densities of gold, platinum, and lead relate to their volumes will enable us to list the cubes from smallest to largest. This concept emphasizes the importance of material properties in practical applications.

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(b) Three cubes of equal mass are composed of gold (density = 19.32 g/cm3), platinum (density = 21.45 g/cm3), and lead (density = 11.35 g/cm3). List the cubes from smallest to largest.

Verified Solution

Key Concepts

Density

Volume Calculation

Comparison of Materials

(b) Three cubes of equal mass are composed of gold (density = 19.32 g/cm³), platinum (density = 21.45 g/cm³), and lead (density = 11.35 g/cm³). List the cubes from smallest to largest.