Chapter 5, Problem 62A

(a)

Interpretation Introduction

Interpretation: The mass of $\text{50}{\text{.0cm}}^{\text{3}}$ gold needs to be calculated.

Concept Introduction: Density is amount of matter present in a substance in given volume. That is, it is the ratio of mass of a substance to volume:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 62A

Mass of gold is 966g.

Explanation of Solution

Expression for density is as follows:

  $\text{Density=}\frac{\text{Mass}}{\text{Volume}}$

Given, density of gold is $\text{19}\text{.32}\text{g}/{\text{cm}}^{\text{3}}$ and volume is $\text{50}{\text{.0cm}}^{\text{3}}$

. Put these values in density expression as follows:

  $\begin{array}{c}19.32\text{g}/{\text{cm}}^{\text{3}}\text{=}\frac{\text{mass}}{{\text{50cm}}^{\text{3}}}\\ {\text{Mass=50cm}}^{\text{3}}\times 19.32\text{g}/{\text{cm}}^{\text{3}}\\ =966\text{g}\end{array}$

Thus mass of gold is 966g.

(b)

Interpretation Introduction

Interpretation: The mass of $\text{50}{\text{.0cm}}^{\text{3}}$ iron to be calculated.

Concept Introduction: Density is amount of matter present in a substance in given volume. That is, it is the ratio of mass of a substance to volume:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 62A

Mass of iron is 394g.

Explanation of Solution

Expression for density is as follows:

  $\text{Density=}\frac{\text{Mass}}{\text{Volume}}$

Given, density of iron is $\text{7}\text{.87}\text{g}/{\text{cm}}^{\text{3}}$ and volume is $\text{50}{\text{.0cm}}^{\text{3}}$ . Put these values in density expression as follows:

  $\begin{array}{c}7.87\text{g}/{\text{cm}}^{\text{3}}\text{=}\frac{\text{mass}}{{\text{50cm}}^{\text{3}}}\\ {\text{Mass=50cm}}^{\text{3}}\times 7.87\text{g}/{\text{cm}}^{\text{3}}\\ =393.5\text{g}\\ =394\text{g}\end{array}$

Thus mass of iron is 394 g.

(c)

Interpretation Introduction

Interpretation: The mass of $\text{50}{\text{.0cm}}^{\text{3}}$ lead to be calculated.

Concept Introduction: Density is amount of matter present in a substance in given volume. That is, it is the ratio of mass of a substance to volume:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 62A

Mass of lead is 567g.

Explanation of Solution

Expression for density is as follows:

  $\text{Density=}\frac{\text{Mass}}{\text{Volume}}$

Given, density of lead is $\text{11}\text{.34}\text{g}/{\text{cm}}^{\text{3}}$ and volume is $\text{50}{\text{.0cm}}^{\text{3}}$ . Put these values in density expression as follows:

  $\begin{array}{c}11.34\text{g}/{\text{cm}}^{\text{3}}\text{=}\frac{\text{mass}}{{\text{50cm}}^{\text{3}}}\\ {\text{Mass=50cm}}^{\text{3}}\times 11.34\text{g}/{\text{cm}}^{\text{3}}\\ =567\text{g}\end{array}$

Thus mass of lead is 567g.

(d)

Interpretation Introduction

Interpretation: The mass of $\text{50}{\text{.0cm}}^{\text{3}}$ aluminum to be calculated.

Concept Introduction: Density is amount of matter present in a substance in given volume. That is, it is the ratio of mass of a substance to volume:

  $\text{Density =}\frac{\text{mass}}{\text{volume}}$

Answer to Problem 62A

Mass of aluminum is 135g.

Explanation of Solution

Expression for density is as follows:

  $\text{Density=}\frac{\text{Mass}}{\text{Volume}}$

Given, density of aluminum is $\text{2}\text{.70}\text{g}/{\text{cm}}^{\text{3}}$ and volume is $\text{50}{\text{.0cm}}^{\text{3}}$ . Put these values in density expression as follows:

  $\begin{array}{c}2.70\text{g}/{\text{cm}}^{\text{3}}\text{=}\frac{\text{mass}}{{\text{50cm}}^{\text{3}}}\\ {\text{Mass=50cm}}^{\text{3}}\times 2.70\text{g}/{\text{cm}}^{\text{3}}\\ =135\text{g}\end{array}$

Thus, mass of aluminum is 135g.