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.

Short answer

a.$1.32g/mL$

b. $7.27g/mL$

c. $0.709g/mL$

Step-by-step solution

Part (a) Given Information

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

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:

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

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.

Part (b) Given Information

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

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:

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

Unit conversion of kg into g:

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

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.

Part (c) Given Information

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

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.