Chapter 2, Problem 88QAP

For the masses and volumes indicated, calculate the density in grams per cubic centimeter.

1. mass = 4.53 kg; volume = 225 cm³
2. mass = 26.3 g; volume = 25.0 mL
3. mass = 1.00 lb; volume = 500. cm³
4. mass = 352 mg; volume = 0.27 1 cm³

Interpretation Introduction

Interpretation:

The density in grams per cubic centimeter for the mass 4.53 kg and volume 225 cm³ should be determined.

Concept Introduction:

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$.

Answer to Problem 88QAP

The density in grams per cubic centimeter for the mass 4.53 kg and volume 225 cm³ is 20.13 g/cm³.

Explanation of Solution

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$

Mass = 4.53 kg (given)

Since, 1 kg = 1000 g

So, 4.53 kg = 4.53 * 1000 = 4530 g

Substituting the values:

$\begin{array}{l}\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{4530\text{g}}{225\text{c}{\text{m}}^3}\hfill \\ \text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=20.13\text{g}/\text{c}{\text{m}}^3\hfill \end{array}$.

Interpretation Introduction

Interpretation:

The density in grams per cubic centimeter for the mass 26.3 g and volume 25.0 mLshould be determined.

Concept Introduction:

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$.

Answer to Problem 88QAP

The density in grams per cubic centimeter for the mass 26.3 g and volume 25.0 mL is 1.052 g/cm³.

Explanation of Solution

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$

Volume = 25.0 mL (given)

Since, 1 mL = 1 cm³

So, 25.0 mL = 25.0 cm³

Substituting the values:

$\begin{array}{l}\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{26.3\text{g}}{25.0\text{c}{\text{m}}^3}\hfill \\ \text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=1.052\text{g}/\text{c}{\text{m}}^3\hfill \end{array}$.

Interpretation Introduction

Interpretation:

The density in grams per cubic centimeter for the mass 1.00 lb and volume 500 cm³ should be determined.

Concept Introduction:

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$.

Answer to Problem 88QAP

The density in grams per cubic centimeter for the mass 1.00 lb and volume 500 cm³ is 0.908 g/cm³.

Explanation of Solution

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$

Mass = 1.00lb (given)

1 lb = 453.592 g

Substituting the values:

$\begin{array}{l}\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{453.592\text{g}}{500\text{c}{\text{m}}^3}\hfill \\ \text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=0.908\text{g}/\text{c}{\text{m}}^3\hfill \end{array}$.

Interpretation Introduction

Interpretation:

The density in grams per cubic centimeter for the mass 352 mg and volume 0.271 cm³ should be determined.

Concept Introduction:

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$.

Answer to Problem 88QAP

The density in grams per cubic centimeter for the mass 352 mg and volume 0.271 cm³ is 1.299 g/cm³.

Explanation of Solution

The ratio of mass to volume of a substance is said to be the density of a substance. The formula is:

$\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{\text{m}\text{a}\text{s}\text{s}}{\text{v}\text{o}\text{l}\text{u}\text{m}\text{e}}$

Mass = 352 mg (given)

Since, 1 mg = 0.001 g

So, $352\text{m}\text{g}=352\times 0.001=0.352\text{g}$

Substituting the values:

$\begin{array}{l}\text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=\frac{0.352\text{g}}{0.271\text{c}{\text{m}}^3}\hfill \\ \text{D}\text{e}\text{n}\text{s}\text{i}\text{t}\text{y}=1.299\text{g}/\text{c}{\text{m}}^3\hfill \end{array}$.