Q.2.73 - An Introduction to General, Organic, and Biological Chemistry

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?

Step-by-Step Solution

Answer

a. 661 g

b. 34 kg

c. 29 cm³

Step 1: Part (a) Given Information

The volume of a cube of copper is 74.1 cm³.

The density of copper is 8.92 g/mL.

Step 2: 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:

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

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.

Step 1: Part (b) Given Information

Volume of gas tank=2.0-gal 

Density of gasoline = 0.74 g/mL

Step 2: 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:

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

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.

Step 1: Part (c) Given Information

The mass of the ice cube = 27 g

The density of the ice cube =0.92 g/mL

Step 2: 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.