Q.2.68 - An Introduction to General, Organic, and Biological Chemistry

Question

Determine the density (g/mL) for each of the following: 

a. The fluid in a car battery has a volume of 125 mL and a mass of 155 g. 

b. A plastic material weighs 2.68 lb and has a volume of 3.5 L. 

c. A 4.000-mL urine sample from a person suffering from diabetes mellitus has a mass of 4.004 g. 

d. A solid object has a mass of 1.65 lb and a volume of 170 mL.

Step-by-Step Solution

Answer

a.  $1.24 g/mL$

b.  $0.347 g/mL$

c.  $1.00 g/mL$

d.  $4.40 g/mL$

Step 1: Part (a) Given Information

Mass= 155 g

Volume= 125 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 substituting the given values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{155 \mathrm{g}}{125 \mathrm{mL}} \\ \mathrm{Density}=1.24 \mathrm{g}/\mathrm{mL} \end{gathered}$$

 Thus, the density of the fluid is 1.24 g/mL.

Step 1: Part (b) Given Information

Mass = 2.68 lb

Volume =3.5 L

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 lb into grams:

$$\begin{gathered} 1 lb=454 g \\ 2.68 lb =2.68\times 454 =1216.72 g \end{gathered}$$

Unit conversion of L into mL:

$$\begin{gathered} 1 L=1000 mL \\ 3.5L =3.5\times 1000 mL=3500 mL \end{gathered}$$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{1216.72 \mathrm{g}}{3500 \mathrm{mL}} \\ \mathrm{Density}=0.347 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the plastic material is 0.347 g/mL.

Step 1: Part (c) Given Information

Mass=4.004 g

Volume=4.00 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:

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

On substituting the given values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{4.004 \mathrm{g}}{4.00 \mathrm{mL}} \\ \mathrm{Density}=1.00 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of the urine sample is 1.00 g/mL.

Step 1: Part (a) Given Information

Mass= 1.65 lb

Volume= 170 mL

Step 2: Part (d) 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 lb into grams:

$$\begin{gathered} 1 lb=454 g \\ 1.65 lb=1.65\times 454=749.1 g \end{gathered}$$

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{749.1 \mathrm{g}}{170 \mathrm{mL}} \\ \mathrm{Density}=4.40 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density of a solid is 4.40 g/mL.