Q.2.74 - 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. If a bottle of olive oil contains 1.2 kg of olive oil, what is the volume, in milliliters, of the olive oil? 

b. A cannon ball made of iron has a volume of 115 cm³. What is the mass, in kilograms, of the cannon ball? 

c. A balloon filled with helium has a volume of 7.3 L. What is the mass, in grams, of helium in the balloon?

Step-by-Step Solution

Answer

a. Volume of olive oil is 1.3 L.

b. The mass of a cannonball is 0.9 kg. 

c. The mass of helium gas is 0.13 kg.

Step 1: Part (a) Given Information

Mass of olive oil = 1.2 kg

Density of olive oil =0.92 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 for kg into g:

$$\begin{gathered} 1 kg= 1000 g \\ 1.2 kg=1.2\times 1000=1200 g \end{gathered}$$

On rearranging and substituting

$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{olive} \mathrm{oil}=\frac{\mathrm{mass} \mathrm{of} \mathrm{olive} \mathrm{oil}}{\mathrm{density} \mathrm{of} \mathrm{olive} \mathrm{oil}} \\ \mathrm{Volume} \mathrm{of} \mathrm{olive} \mathrm{oil}=\frac{1200 \mathrm{g}}{0.92 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Volume} \mathrm{of} \mathrm{olive} \mathrm{oil}=1304.34 \mathrm{mL} \mathrm{or} 1.3 \mathrm{L} \end{gathered}$$ the given values:

Thus, the volume of olive oil is 1.3 L.

Step 1: Part (b) Given Information

Volume of cannon iron ball = 115 cm³

Density of iron=7.86 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: 

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

$1 c{m}^3=1 mL$

On rearranging and substituting the given values:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{iron} \mathrm{ball}=\mathrm{Volume} \mathrm{of} \mathrm{iron} \mathrm{ball}\times \mathrm{Density} \mathrm{of} \mathrm{iron} \mathrm{ball} \\ \mathrm{Mass} \mathrm{of} \mathrm{iron} \mathrm{ball}=115 \mathrm{mL}\times 7.86 \mathrm{g}/\mathrm{mL} \\ \mathrm{Mass} \mathrm{of} \mathrm{iron} \mathrm{ball}=903.9 \mathrm{g} \mathrm{or} 0.9 \mathrm{kg} \end{gathered}$$

Thus, the mass of cannon ball that is made up of iron is 0.9 kg.

Step 1: Part (c) Given Information

Volume of helium gas = 7.3 L

Density of helium gas = 0.179 g/L

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:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{Helium} \mathrm{gas}=\mathrm{Volume} \mathrm{of} \mathrm{Helium} \mathrm{gas} \times \mathrm{Density} \mathrm{of} \mathrm{Helium} \mathrm{gas} \\ \mathrm{Mass} \mathrm{of} \mathrm{Helium} \mathrm{gas}=7.3 \mathrm{L}\times 0.179 \mathrm{g}/\mathrm{L} \\ \mathrm{Mass} \mathrm{of} \mathrm{Helium} \mathrm{gas}=1.30 \mathrm{g} \mathrm{or} 0.13 \mathrm{kg} \end{gathered}$$

Thus, the mass of helium gas is 0.13 kg.