Question

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

a. A lightweight head on a golf club is made of titanium. The volume of a sample of titanium is 114 cm³ and the mass is 514.1 g.

b. A syrup is added to an empty container with a mass of 115.25 g. When 0.100 pt of syrup is added, the total mass of the container and syrup is 182.48 g.

c. A block of aluminum metal has a volume of 3.15 L and a mass of 8.51 kg.

Short answer

a.$4.51g/mL$

b.$1.42g/mL$

c.$2.70g/mL$

Step-by-step solution

Part (a) Given Information

The volume of a sample of titanium is 114 cm³ and the mass is 514.1 g.

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 into mL:

$$\begin{gathered} 1L=1000c{m}^3 \\ Or \\ 1c{m}^3=\frac{1}{1000}L \\ 114c{m}^3=\frac{114}{1000}=0.114L \\ 1L=1000mL \\ 0.114L=0.114\times 1000=114mL \end{gathered}$$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{514.1\mathrm{g}}{114\mathrm{mL}} \\ \mathrm{Density}=4.51\mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of a sample is 4.51 g/mL.

Part (b) Given Information

A syrup is added to an empty container with a mass of 115.25 g. When 0.100 pt of syrup is added, the total mass of the container and syrup is 182.48 g.

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 of pt into mL:

$$\begin{gathered} 1pt=473mL \\ 0.100pt=0.100\times 473=47.3mL \end{gathered}$$

$\mathrm{Total}\mathrm{mass}=182.48\mathrm{g}-115.25\mathrm{g}=67.23\mathrm{g}$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{67.23\mathrm{g}}{47.3\mathrm{mL}} \\ \mathrm{Density}=1.42\mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of syrup is 1.42 g/mL.

Part (c) Given Information

A block of aluminum metal has a volume of 3.15 L and a mass of 8.51 kg

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 L into mL:

$$\begin{gathered} 1L=1000mL \\ 3.15L=3.15\times 1000=3150mL \end{gathered}$$

Unit conversion of kg into g:

$$\begin{gathered} 1kg=1000g \\ 8.51kg=8.51\times 1000=8510g \end{gathered}$$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{8510\mathrm{g}}{3150\mathrm{mL}} \\ \mathrm{Density}=2.70\mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the block is 2.70 g/mL.