Density Calculations

Master the relationship between mass, volume, and density

Key Concept

Density (D) expresses how much mass is contained in a given volume of a substance. It connects three measurable quantities through the formula:

Density = Mass ÷ Volume

From this, we can rearrange:

Mass = Density × Volume
Volume = Mass ÷ Density

Common Metric Units

Quantity Unit Equivalent forms
Mass grams (g) kilograms (kg = 1000 g)
Volume cubic centimeters (cm³) milliliters (mL = cm³)
Density grams per cubic centimeter (g/cm³) grams per milliliter (g/mL)

Worked Examples

1

Copper Bar

Given Data:

  • • Mass = 216 g
  • • Volume = 24 cm³

Find:

Density of the copper bar

Formula Used:

D = m ÷ V

Step-by-Step Solution:

Step 1: Identify the given values

Mass (m) = 216 g

Volume (V) = 24 cm³

Step 2: Apply the density formula

D = m ÷ V

D = 216 g ÷ 24 cm³

Step 3: Calculate

D = 9 g/cm³

Final Answer:

9 g/cm³

2

Candy Bar

Given Data:

  • • Mass = 70 g
  • • Volume = 55 cm³

Find:

Density of the candy bar

Formula Used:

D = m ÷ V

Step-by-Step Solution:

Step 1: Identify the given values

Mass (m) = 70 g

Volume (V) = 55 cm³

Step 2: Apply the density formula

D = m ÷ V

D = 70 g ÷ 55 cm³

Step 3: Calculate

D = 1.27 g/cm³

Final Answer:

1.27 g/cm³

3

Ice Cube

Given Data:

  • • Mass = 33.2 g
  • • Volume = 36 cm³

Find:

Density of the ice cube

Formula Used:

D = m ÷ V

Step-by-Step Solution:

Step 1: Identify the given values

Mass (m) = 33.2 g

Volume (V) = 36 cm³

Step 2: Apply the density formula

D = m ÷ V

D = 33.2 g ÷ 36 cm³

Step 3: Calculate

D = 0.92 g/cm³

Final Answer:

0.92 g/cm³

4

Pure Water

Given Data:

  • • Density = 1 g/mL
  • • Volume = 2 L = 2000 mL

Find:

Mass of the water

Formula Used:

m = D × V

Step-by-Step Solution:

Step 1: Identify the given values

Density (D) = 1 g/mL

Volume (V) = 2 L = 2000 mL

Step 2: Apply the mass formula

m = D × V

m = 1 g/mL × 2000 mL

Step 3: Calculate

m = 2000 g

Step 4: Convert to kilograms

2000 g = 2.0 kg

Final Answer:

2000 g (2.0 kg)

5

Ethyl Alcohol

Given Data:

  • • Density = 0.789 g/mL
  • • Volume = 200.0 mL

Find:

Mass of the ethyl alcohol

Formula Used:

m = D × V

Step-by-Step Solution:

Step 1: Identify the given values

Density (D) = 0.789 g/mL

Volume (V) = 200.0 mL

Step 2: Apply the mass formula

m = D × V

m = 0.789 g/mL × 200.0 mL

Step 3: Calculate

m = 157.8 g

Final Answer:

157.8 g

6

Silver Metal

Given Data:

  • • Mass = 2500.0 g
  • • Density = 10.5 g/cm³

Find:

Volume of the silver metal

Formula Used:

V = m ÷ D

Step-by-Step Solution:

Step 1: Identify the given values

Mass (m) = 2500.0 g

Density (D) = 10.5 g/cm³

Step 2: Apply the volume formula

V = m ÷ D

V = 2500.0 g ÷ 10.5 g/cm³

Step 3: Calculate

V = 238.1 cm³

Final Answer:

238.1 cm³

Summary

  • Density links mass and volume, helping identify or compare materials.
  • Denser substances have more mass per unit volume.
  • Unit consistency is crucial: convert liters to milliliters or cm³ before calculating.
  • Always label your final answer with correct units (e.g., g/cm³, g/mL, g, cm³).

Explore More Chemistry Topics

Check out other chemistry topics or return to the main chemistry notes section.