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Chapter 2: Problem 114

What is the density of an object with a volume of 15 \(\mathrm{mL}\) and a mass of \(42 \mathrm{~g}\) ? A. \(0.352 \mathrm{~g} / \mathrm{mL}\) B. \(2.80 \mathrm{~g} / \mathrm{mL}\) C. \(630 \mathrm{~g} / \mathrm{mL}\) D. \(6.30 \mathrm{~g} / \mathrm{mL}\)

Short Answer

Expert verified
B. 2.80 \( \mathrm{g/mL} \)

Step by step solution

01

- Understand the Formula

Density is calculated using the formula: \[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]
02

- Identify Given Values

From the problem statement, the mass of the object is given as 42 grams (\(42 \, \mathrm{g}\)) and the volume is given as 15 milliliters (\(15 \, \mathrm{mL}\)).
03

- Substitute the Values

Substitute the given mass and volume values into the density formula: \[ \text{Density} = \frac{42 \, \mathrm{g}}{15 \, \mathrm{mL}} \]
04

- Calculate the Density

Divide the mass by the volume: \[ \text{Density} = \frac{42}{15} = 2.8 \, \mathrm{g/mL} \]
05

- Choose the Correct Answer

From the calculated density, the correct option is B. \(2.80 \, \mathrm{g/mL}\)

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Key Concepts

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

Mass
Mass is a measure of how much matter an object contains. It is typically measured in grams (g) or kilograms (kg). In this exercise, we are given the mass of the object, which is 42 grams. Mass can be understood as the 'heaviness' of an object.

To find out the density of an object, knowing the mass is crucial. If you do not have the mass, you cannot calculate density. In some problems, you might have to measure the mass using a balance or scale. Always double-check units; ensure you're using grams if your volume is in milliliters to keep units consistent.
Volume
Volume is the amount of space that an object occupies. It is usually measured in cubic centimeters (cm³), milliliters (mL), or liters (L). In this exercise, the volume of the object is 15 milliliters.

Think of volume as how much 'room' the object takes up. For liquids, you can often measure volume using a graduated cylinder. For solids, you may need to use formulas or water displacement methods. Like mass, the unit consistency here is key. If your mass is in grams, your volume should typically be in milliliters for density calculations.
Formula for Density
Density is a measure of how much mass is contained in a given volume. The formula to calculate density is:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

This means you take the object's mass and divide it by its volume. In our exercise, the mass is 42 grams, and the volume is 15 milliliters. Plug these values into the formula, and you get:

\[ \text{Density} = \frac{42 \text{ g}}{15 \text{ mL}} \]

Which simplifies to 2.8 grams per milliliter (g/mL). This formula is fundamental in understanding density, and it's often used for various types of materials, from liquids to solids and gases.
Division
Division is a mathematical operation where you split a number into equal parts. In this exercise, division is used to calculate density. Specifically, we are dividing the mass by the volume:

\[ 42 \text{ g} \frac{15 \text{ mL}} \]

When we perform this division, we get:

\[ 2.8 \text{ g/mL} \]

Understanding division is crucial for solving density problems. It helps to practice basic division skills if you find this part challenging. Use a calculator if needed, but ensure that you understand the logic behind dividing mass by volume to find density.

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