2.72 - 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. A graduated cylinder contains 18.0 mL of water. What is the new water level, in milliliters, after 35.6 g of silver metal is submerged in the water? 

b. A thermometer containing 8.3 g of mercury has broken. What volume, in milliliters, of mercury spilled? 

c. A fish tank holds 35 gal of water. How many kilograms of water are in the fish tank? 

Step-by-Step Solution

Answer

a. 21.39 mL

b. 0.610 mL

c. 132.48 kg

Step 1: Part (a) Given Information

Mass of silver = 35.6 g

Volume of graduated cylinder=18.0 mL

Density of silver metal =10.5 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: 

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

On rearranging and substituting the given values :

$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{silver}=\frac{\mathrm{mass} \mathrm{of} \mathrm{silver}}{\mathrm{density} \mathrm{of} \mathrm{silver}} \\ \mathrm{Volume} \mathrm{of} \mathrm{silver}=\frac{35.6 \mathrm{g}}{10.5 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Volume} \mathrm{of} \mathrm{silver}=3.390 \mathrm{mL} \end{gathered}$$

The new water level, in milliliters, after 35.6 g of silver metal is submerged in the water is:

$$\begin{gathered} \mathrm{Total} \mathrm{volume} = 3.390 \mathrm{mL}+18.0 \mathrm{mL} \\ \mathrm{Total} \mathrm{volume}=21.39 \mathrm{mL} \end{gathered}$$

Thus, the new water level is 21.39 mL.

Step 2: Part (b) Given Information

Mass of mercury = 8.3 g

Density of mercury= 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 and substituting the given values:

$$\begin{gathered} \mathrm{Volume} \mathrm{of} \mathrm{mercury}=\frac{\mathrm{mass} \mathrm{of} \mathrm{mercury}}{\mathrm{density} \mathrm{of} \mathrm{mercury}} \\ \mathrm{Volume} \mathrm{of} \mathrm{mercury}=\frac{8.3 \mathrm{g}}{13.6 \mathrm{g}/\mathrm{mL}} \\ \mathrm{Volume} \mathrm{of} \mathrm{mercury}=0.610 \mathrm{mL} \end{gathered}$$

Thus, the volume of mercury is 0.610 mL.

Step 1: Part (c) Given Information

The volume of fish tank =35 gal of water

The density of water= 1.00 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 for gallons into mL:

$$\begin{gathered} 1 gal=3785.41 mL \\ 35 gal = 132489.35 mL \end{gathered}$$

On rearranging and substituting the values:

$$\begin{gathered} \mathrm{Mass} \mathrm{of} \mathrm{water}=\mathrm{Volume} \mathrm{of} \mathrm{water} \times \mathrm{Density} \mathrm{of} \mathrm{water} \\ \mathrm{Mass} \mathrm{of} \mathrm{water}=132489.35 mL\times 1.00 g/mL \\ \mathrm{Mass} \mathrm{of} \mathrm{water}=132489.35 \mathrm{g} or 132.48 \mathrm{kg} \end{gathered}$$

Thus, the mass of water is 132.48 kg.