Q.2.67 - An Introduction to General, Organic, and Biological Chemistry

Question

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

a. A 20.0-mL sample of a salt solution has a mass of 24.0 g. 

b. A cube of butter weighs 0.250 lb and has a volume of 130.3 mL. 

c. A gem has a mass of 4.50 g. When the gem is placed in a graduated cylinder containing 12.00 mL of water, the water level rises to 13.45 mL. 

d. A 3.00-ml sample of medication has a mass of 3.85 g. 

Step-by-Step Solution

Answer

a.$1.20 g/mL$ 

b. $0.871 g/mL$

c. $3.10 g/mL$

d. $1.28 g/mL$

Step 1: Part (a) Given Information

Volume = 20.0 mL

Mass = 24.0 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:

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

On substituting the given values in the above formula:

$$\begin{gathered} \mathrm{Density}=\frac{24.0 \mathrm{g}}{20.0 \mathrm{mL}} \\ \mathrm{Density}=1.20 \mathrm{g}/\mathrm{mL} \end{gathered}$$

 Thus, the density of the sample is 1.20 g/mL.

Step 1: Part (b) Given Information

Mass =0.250 lb

Volume = 130.3 mL

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:

$$\begin{gathered} 1 lb =454 g \\ 0.250 lb = 0.250\times 454 =113.5 g \end{gathered}$$

On substituting the given values in the above formula:

$$\begin{gathered} \mathrm{Density} = \frac{113.5 \mathrm{g}}{130.3 \mathrm{mL}} \\ \mathrm{Density} = 0.871 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Thus, the density cube of butter is 0.871 g/mL.

Step 1: Part (a) Given Information

Mass = 4.50 g

When the gem is placed in a graduated cylinder containing 12.00 mL of water, the water level rises to 13.45 mL.  

Total volume = 13.45-12.00 = 1.45 mL

Step 1: 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:

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

On substituting the values in the above formula:

$$\begin{gathered} \mathrm{Density} = \frac{4.50 \mathrm{g}}{(13.45-12.00) \mathrm{mL}}=\frac{4.50 \mathrm{g}}{1.45 \mathrm{mL}} \\ \mathrm{Density} = 3.10 \mathrm{g}/\mathrm{mL} \end{gathered}$$

Step 1: part (d) Given Information

Mass= 3.85 g

Volume= 3.00 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:

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

On substituting the values:

$$\begin{gathered} \mathrm{Density} = \frac{3.85 \mathrm{g}}{3.00 \mathrm{mL}} \\ \mathrm{Density} = 1.28 \mathrm{g}/\mathrm{mL} \end{gathered}$$