What is Density?
Density is an intrinsic physical property of a substance that quantifies how much mass is contained within a unit volume. It describes how tightly packed the matter is in a given space and is independent of the amount of substance present.
The fundamental density formula:
This relationship allows us to calculate any one of these three quantities when the other two are known.
Rearranging the Density Formula
The density formula can be rearranged to solve for any of the three variables:
Calculate Density
Calculate Volume
Calculate Mass
Units of Density
Density is expressed in units that combine mass and volume. Common units include:
- g/cm³ (grams per cubic centimeter) - commonly used for solids and liquids
- kg/m³ (kilograms per cubic meter) - SI unit, used in scientific calculations
- g/mL (grams per milliliter) - equivalent to g/cm³, often used for liquids
- mg/L (milligrams per liter) - used for very dilute solutions
Unit conversion note:
1 g/cm³ = 1 g/mL = 1000 kg/m³
Worked Examples
Example 1: Calculating Volume
Problem: Olive oil has a density of 0.92 g/cm³. What volume does 460 grams of olive oil occupy?
Given: Density = 0.92 g/cm³, Mass = 460 g
Formula: Volume = Mass ÷ Density
Solution: V = 460 g ÷ 0.92 g/cm³ = 500 cm³
Answer: The olive oil occupies 500 cm³ of space.
Example 2: Calculating Density
Problem: A metal cube has a mass of 216 g and occupies a volume of 27 cm³. What is its density?
Given: Mass = 216 g, Volume = 27 cm³
Formula: Density = Mass ÷ Volume
Solution: D = 216 g ÷ 27 cm³ = 8.0 g/cm³
Answer: The metal has a density of 8.0 g/cm³ (likely iron or steel).
Common Density Values
Here are some typical density values for reference:
| Substance | Density (g/cm³) |
|---|---|
| Air (at sea level) | 0.001 |
| Water | 1.00 |
| Ice | 0.92 |
| Olive Oil | 0.92 |
| Aluminum | 2.70 |
| Iron | 7.87 |
| Lead | 11.34 |
| Gold | 19.32 |
Real-World Applications
Understanding density is crucial in many fields:
- Materials Science: Identifying unknown substances and quality control
- Engineering: Designing structures with appropriate weight-to-strength ratios
- Geology: Identifying minerals and understanding Earth's structure
- Cooking: Understanding why oil floats on water
- Medicine: Bone density measurements and fluid analysis
- Environmental Science: Studying ocean currents and atmospheric layers
Key Properties of Density
- Intensive Property: Density doesn't depend on the amount of substance
- Temperature Dependent: Most substances become less dense when heated
- Pressure Dependent: Gases are highly compressible, affecting their density
- Composition Specific: Each pure substance has a characteristic density
Practice Problem
Problem:
A rectangular block of wood measures 10 cm × 5 cm × 4 cm and has a mass of 150 g. Calculate its density.
Show Solution
Step 1: Calculate the volume
Volume = length × width × height = 10 cm × 5 cm × 4 cm = 200 cm³
Step 2: Apply the density formula
Density = Mass ÷ Volume = 150 g ÷ 200 cm³ = 0.75 g/cm³
Answer: The wood has a density of 0.75 g/cm³