2.69 - An Introduction to General, Organic, and Biological Chemistry

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.

Step-by-Step Solution

Answer

a. $4.51 g/mL$

b. $1.42 g/mL$

c. $2.70 g/mL$

Step 1: Part (a) Given Information

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

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 into mL:

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

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.

Step 1: 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.  

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 of pt into mL:

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

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

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.

Step 1: Part (c) Given Information

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

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 L into mL:

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

Unit conversion of kg into g:

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

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.