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Chapter 2: Problem 2

What is the volume of a sample that has a mass of 20 g and a density of 4 g/mL?

Short Answer

Expert verified
The volume of the sample with mass 20 g and density 4 g/mL can be calculated using the formula \(V = \frac{m}{\rho}\). Plugging in the given values, we get \(V = \frac{20\,g}{4\,g/mL}\), which simplifies to V = 5 mL.

Step by step solution

01

Identify the formula

We will use the formula for volume: Volume = Mass/Density \( (V = \frac{m}{\rho}) \), where V is the volume, m is the mass, and \(\rho\) is the density. Step 2: Plug in the given values
02

Plug in the given values

Now, let's plug the given values into the formula: Volume = Mass/Density V = \( \frac{20\, g}{4\, g/mL} \) Step 3: Calculate the volume
03

Calculate the volume

By dividing the mass by the density, we can find the volume: V = \( \frac{20}{4} \) V = 5 mL The volume of the sample is 5 mL.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Density
Density is a fundamental concept that describes how much mass is contained in a given volume. Think of it as the compactness of a material. When you hold two objects, the denser one will feel heavier even if they are the same size. This is because density relates mass to volume and is expressed as mass per unit volume.

Density is usually measured in units such as grams per milliliter (g/mL) or kilograms per cubic meter (kg/m鲁). The formula to find density is:
  • Density = Mass/Volume
With this formula, you can determine an object's density if you know its mass and volume. In our example, knowing the density helps calculate the volume when the mass is given.
Exploring the Concept of Mass
Mass is a measure of the amount of matter in an object. It's what most people refer to when they talk about "weight," but technically, weight is a force that results from gravity acting on mass. Mass remains constant regardless of an object's location, whether on a mountain or in space.

Mass is typically measured in grams (g) or kilograms (kg). It is an essential variable in many calculations, especially in determining volume and density. In our example, the mass of the sample is 20 grams, which is crucial for finding its volume using the given density.
Applying the Formula for Volume
The formula for volume is an essential tool in calculating how much space a substance occupies. When mass and density are known, you can find the volume using:
  • Volume = Mass/Density
This formula rearranges the density equation to solve for volume. By dividing the mass by the density, you determine the space that a mass occupies.

In our exercise, we have a mass of 20 grams and a density of 4 g/mL. Plugging these values into the formula gives:
  • Volume = \( \frac{20\, g}{4\, g/mL} \)
This calculation results in a volume of 5 mL, indicating that the sample occupies 5 milliliters of space. Understanding this formula helps in various scientific and real-world applications.

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Most popular questions from this chapter

When dividing numbers in scientific notation, what must you do with the exponents?

Challenge Express each quantity in regular notation along with its appropriate unit. \(\begin{array}{llllll}{\text { a. } 3.60 \times 10^{5} \mathrm{s}} & {\text { b. } 5.4 \times 10^{-5} \mathrm{g} / \mathrm{cm}^{3}} & {\text { c. } 5.060 \times 10^{3} \mathrm{km}} & {\text { d. } 8.9 \times 10^{10} \mathrm{Hz}}\end{array}\)

Complete the following multiplication and division problems in scientific notation. a. \(\left(4.8 \times 10^{5} \mathrm{km}\right) \times\left(2.0 \times 10^{3} \mathrm{km}\right)\) b. \(\left(3.33 \times 10^{-4} \mathrm{m}\right) \times\left(3.00 \times 10^{-5} \mathrm{m}\right)\) c. \(\left(1.2 \times 10^{6} \mathrm{m}\right) \times\left(1.5 \times 10^{-7} \mathrm{m}\right)\) d. \(\left(8.42 \times 10^{8} \mathrm{kL}\right) \div\left(4.21 \times 10^{3} \mathrm{kL}\right)\) e. \(\left(8.4 \times 10^{6} \mathrm{L}\right) \div\left(2.4 \times 10^{-3} \mathrm{L}\right)\) f. \(\left(3.3 \times 10^{-4} \mathrm{mL}\right) \div\left(1.1 \times 10^{-6} \mathrm{mL}\right)\)

Analyze Data Students collected mass data for a group of coins. The mass of a single coin is 5.00 g. Determine the accuracy and precision of the measurements \(\begin{array}{|c|c|c|c|c|}\hline \text {Number of coins} \ \ \ \ {5} & {10} & {20} & {30} & {50} \\ \hline \text {Mass (g)} \ \ \ \ 23.2 & {54.5} & {105.9} & {154.5} & {246.2} \\ \hline\end{array}\)

Perform the following calculations. Round the answers. a. 24 \(\mathrm{m} \times 3.26 \mathrm{m} \quad\) b. 120 \(\mathrm{m} \times 0.10 \mathrm{m} \quad\) c. 1.23 \(\mathrm{m} \times 2.0 \mathrm{m} \quad\) d. 53.0 \(\mathrm{m} \times 1.53 \mathrm{m}\)
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