Question

Use the density values in Table 2.8 to solve each of the following problems:

a. What is the mass, in grams, of a cube of copper that has a volume of 74.1 cm³?

b. How many kilograms of gasoline fill a 12.0-gal gas tank?

c. What is the volume, in cubic centimeters, of an ice cube that has a mass of 27 g?

Short answer

a. 661 g

b. 34 kg

c. 29 cm³

Step-by-step solution

Part (a) Given Information

The volume of a cube of copper is 74.1 cm³.

The density of copper is 8.92 g/mL.

Part (a) Explanation

Density is defined as the ratio of mass over volume. Every substance has a unique density, which distinguishes it from others. It is given by:

$\mathrm{Density}=\frac{\mathrm{mass}\mathrm{of}\mathrm{substance}}{\mathrm{volume}\mathrm{of}\mathrm{substance}}$

Unit conversion of cm³ into mL:

$$\begin{gathered} 1c{m}^3=1mL \\ 74.1c{m}^3=74.1mL \end{gathered}$$

On rearranging and substituting the values:

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{Copper}=\mathrm{Density}\mathrm{of}\mathrm{copper}\times \mathrm{Volume}\mathrm{of}\mathrm{copper} \\ \mathrm{Mass}\mathrm{of}\mathrm{Copper}=8.92\mathrm{g}/\mathrm{mL}\times 74.1\mathrm{mL} \\ \mathrm{Mass}\mathrm{of}\mathrm{Copper}=660.97\mathrm{g}\approx 661\mathrm{g} \end{gathered}$$

Thus, the mass of copper is 661 g.

Part (b) Given Information

Volume of gas tank=2.0-gal

Density of gasoline = 0.74 g/mL

Part (b) Explanation

Density is defined as the ratio of mass over volume. Every substance has a unique density, which distinguishes it from others. It is given by:

$\mathrm{Density}=\frac{\mathrm{mass}\mathrm{of}\mathrm{substance}}{\mathrm{volume}\mathrm{of}\mathrm{substance}}$

Unit conversion for gallons into mL:

$$\begin{gathered} 1gal=3785.41mL \\ 12gal=12\times 45424.92mL \end{gathered}$$

On rearranging and substituting the values:

$$\begin{gathered} \mathrm{Mass}\mathrm{of}\mathrm{Gasoline}=\mathrm{Density}\mathrm{of}\mathrm{Gasoline}\times \mathrm{Volume}\mathrm{of}\mathrm{Gasoline} \\ \mathrm{Mass}\mathrm{of}\mathrm{Gasoline}=0.74\mathrm{g}/\mathrm{mL}\times 45424.92\mathrm{mL} \\ \mathrm{Mass}\mathrm{of}\mathrm{Gasoline}=33614.4\mathrm{g}\mathrm{or}33.61\mathrm{kg}\approx 34\mathrm{kg} \end{gathered}$$

Thus, the mass of gasoline is 34 kg.

Part (c) Given Information

The mass of the ice cube = 27 g

The density of the ice cube =0.92 g/mL

Part (c) Explanation

Density is defined as the ratio of mass over volume. Every substance has a unique density, which distinguishes it from others. It is given by:

$\mathrm{Density}=\frac{\mathrm{mass}\mathrm{of}\mathrm{substance}}{\mathrm{volume}\mathrm{of}\mathrm{substance}}$

On rearranging and substituting the values:

data-custom-editor="chemistry" $$\begin{gathered} \mathrm{Volume}\mathrm{of}\mathrm{ice}=\frac{\mathrm{Mass}\mathrm{of}\mathrm{ice}}{\mathrm{Density}\mathrm{of}\mathrm{ice}} \\ \mathrm{Volume}\mathrm{of}\mathrm{ice}=\frac{27\mathrm{g}}{0.92\mathrm{g}/\mathrm{mL}} \\ \mathrm{Volume}\mathrm{of}\mathrm{ice}=29.34\mathrm{mL}\approx 29\mathrm{mL} \\ \mathrm{OR} \\ \mathrm{Volume}\mathrm{of}\mathrm{ice}=29{\mathrm{cm}}^3 \end{gathered}$$

Thus, the volume of ice is 29 cm³.