Q.2.70 - An Introduction to General, Organic, and Biological Chemistry

Question

What is the density (g/mL) of each of the following samples? 

a. An ebony carving has a mass of 275 g and a volume of 207 cm³.

b. A 14.3-cm³ sample of tin has a mass of 0.104 kg. 

C. A bottle of acetone (fingernail polish remover) contains 55.0 mL of acetone with a mass of 43.5 g.

Step-by-Step Solution

Answer

a. $1.32 g/mL$

b. $7.27 g/mL$

c. $0.709 g/mL$

Step 1: Part (a) Given Information

An ebony carving has a mass of 275 g and a volume of 207 cm³. 

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 cm³ to mL:

$$\begin{gathered} 1 L=1000 c{m}^3 \\ or \\ 1 c{m}^3=\frac{1}{1000}L \\ So, 207 c{m}^3=\frac{207}{1000}=0.207 L \\ 1 L=1000 mL \\ 0.207 L =0.207\times 1000 mL=207 mL \end{gathered}$$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{275 \mathrm{g}}{207 \mathrm{mL}} \\ \mathrm{Density}=1.32 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the sample is 1.32 g/mL.

Step 1: Part (b) Given Information

A 14.3-cm³ sample of tin has a mass of 0.104 kg. 

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 cm³ to mL:

$$\begin{gathered} 1 L=1000 c{m}^3 \\ or \\ 1 c{m}^3=\frac{1}{1000}L \\ So, 14.3 c{m}^3=\frac{14.3}{1000}=0.0143 L \\ 1 L=1000 mL \\ 0.0143 L =0.0143\times 1000 mL=14.3 mL \end{gathered}$$

Unit conversion of kg into g:

$$\begin{gathered} 1 kg=1000 g \\ 0.104 kg=0.104\times 1000=104 g \end{gathered}$$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{104 \mathrm{g}}{14.3 \mathrm{mL}} \\ \mathrm{Density} =7.27 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the sample is 7.27 g/mL.

Step 1: Part (c) Given Information

A bottle of acetone contains 55.0 mL of acetone with a mass of 43.5 g. 

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 substituting the given values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{43.5 \mathrm{g}}{55.0 \mathrm{mL}} \\ \mathrm{Density} =0.790 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the sample is 0.709 g/mL.