Q.2.71 - 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. How many liters of ethanol contains 1.50 kg of ethanol? 

b. How many grams of mercury are present in a barometer that holds 6.5 mL of mercury? 

c. A sculptor has prepared a mold for casting a silver figure. The figure has a volume of 225 cm³. How many ounces of silver are needed in the preparation of the silver figure?

Step-by-Step Solution

Answer

a. 1.9 L of ethanol

b. 88 g of mercury

c.  83.4 oz of silver

Step 1: Part (a) Given Information

The mass of ethanol is 1.50 kg.

The density of ethanol is 0.79 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:

$$\begin{gathered} 1 kg=1000 g \\ 1.50 kg=1.50\times 1000=1500 g \end{gathered}$$

On rearranging the formula and substituting the values:

$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{ethanol}=\frac{\mathrm{mass} \mathrm{of} \mathrm{ethanol}}{\mathrm{density} \mathrm{of} \mathrm{ethanol}} \\ \mathrm{Volume} \mathrm{of} \mathrm{ethanol}=\frac{1500 \mathrm{g}}{0.79 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Volume} \mathrm{of} \mathrm{ethanol}=1898.73 \mathrm{mL} \\ \mathrm{or} \\ \mathrm{Volume} \mathrm{of} \mathrm{ethanol}=1.9 \mathrm{L} \end{gathered}$$

Thus, the volume of ethanol is 1.9 L.

Step 1: Part (b) Given Information

The volume of mercury is 6.5 mL.

The density of mercury is 13.6 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: 

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

On rearranging the formula and substituting the values:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{mercury}= \mathrm{Density} \mathrm{of} \mathrm{mercury}\times \mathrm{Volume} \mathrm{of} \mathrm{mercury} \\ \mathrm{Mass} \mathrm{of} \mathrm{mercury}=13.6 \mathrm{g}/\mathrm{mL}\times 6.5 \mathrm{mL} \\ \mathrm{Mass} \mathrm{of} \mathrm{mercury}=88.4 \mathrm{g} \end{gathered}$$

Thus, the mass of mercury is approximately 88 g.

Step 1: Part (c) Given Information

The volume of the silver figure is 225 cm³.

The density of silver is 10.5 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: 

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

Unit conversion of cm³ into mL:

$$\begin{gathered} 1 c{m}^3=1 mL \\ 225 c{m}^3=225 mL \end{gathered}$$

On rearranging the formula and substituting the values:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} silver= \mathrm{Density} \mathrm{of} silver\times \mathrm{Volume} \mathrm{of} silver \\ \mathrm{Mass} \mathrm{of} silver=10.5 \mathrm{g}/\mathrm{mL}\times 225 \mathrm{mL} \\ \mathrm{Mass} \mathrm{of} silver=2362.5 \mathrm{g} \\ \mathrm{or} \\ 1 \mathrm{oz} =28.3 \mathrm{g} \\ 1\mathrm{g} =\frac{1}{28.3}\mathrm{oz} \\ 2362.5 \mathrm{g}=\frac{2362.5}{28.3}\mathrm{oz}=83.4 \mathrm{oz} \end{gathered}$$

Thus, the mass of silver is 83.4 oz.