What is Density?
- Definition:
Density is a measure of how much mass is contained in a given volume.
- It tells us how compact or concentrated the material is.
The formal formula for density is:
**Density (ρ) = Mass (m) ÷ Volume (V)**
Where:
- ρ (rho) = density (measured in kg/m³ or g/cm³)
- m = mass (measured in kilograms, kg, or grams, g)
- V = volume (measured in cubic meters, m³, or cubic centimeters, cm³)
Units of Density:
- SI unit: kilograms per cubic meter (kg/m³)
- Other commonly used units: grams per cubic centimeter (g/cm³)
- Conversion: 1 g/cm³ = 1000 kg/m³
3. Properties:
- Denser materials (like metals) sink when placed in less dense
substances (like water).
- Less dense materials (like wood) float on denser liquids.
Applications of Density:
- Floating and Sinking:
Objects denser than water (density = 1 g/cm³) will sink, while objects less
dense than water will float
- Material Identification
Density helps distinguish between materials, e.g., gold (19.3 g/cm³) vs.
fake gold.
- Construction:
Engineers use density to choose materials suitable for specific purposes,
like lightweight materials for airplanes.
Worked Example 1:
A block of metal has a mass of 500 g and a volume of 100 cm³. Find its
density.
Using the formula:
ρ=m÷V
ρ = 500 g ÷ 100 cm³
ρ = 5 g/cm³
The metal’s density is 5 g/cm³, which is higher than water’s density, so it
would sink if placed in water.
Worked Example 2: Rearranging the Formula
Sometimes, you might need to calculate mass or volume using the density
formula
An object has a density of 2.5 g/cm³ and a volume of 40 cm³. What is its
mass?
Rearrange the formula:
m=ρ×V
m = 2.5 g/cm³ × 40 cm³
m = 100 g
Conclusion: The object’s mass is 100 g
Density of Liquids and Gases
1. Liquids:
- Example: Water has a density of 1 g/cm³** or 1000 kg/m³
- Oil (less dense than water) floats on water.
2. Gases:
- Gases have much lower density than liquids and solids.
- Example: Air density is approximately 1.2 kg/m³at room temperature
and pressure.
Experiment to Measure Density
You can measure density experimentally using the following steps:
1. Measure the Mass
- Use a digital balance to measure the mass of the object.
2. Measure the Volume (for Regular Shapes):
- Use mathematical formulas to calculate the volume.
- Example: For a cube, Volume = side³.
3.Measure the Volume (for Irregular Shapes):
- Use a displacement method:
- Fill a measuring cylinder with water and note the initial volume
- Submerge the object in the water.
- Note the final volume.
- Volume of the object = Final volume - Initial volume.
4. Calculate Density:
- Use the formula ρ = m ÷ V
Practical Example: Water Displacement
A rock is placed in a measuring cylinder containing 50 mL of water. The
water level rises to 65 mL. If the rock’s mass is 30 g, calculate its density.
- Volume of the rock = Final volume - Initial volume
= 65 mL - 50 mL = 15 mL (or 15 cm³)
- Density = Mass ÷ Volume
ρ = 30 g ÷ 15 cm³ = 2 g/cm³
:The rock’s density is 2 g/cm³**, so it will sink in water.
1. Density of Solids
To find the density of a solid, follow these steps:
Regularly Shaped Solids (e.g., cubes, spheres):
1. Measure the Mass:
- Use a digital or mechanical balance to find the mass of the solid in
kilograms (kg) or grams (g).
2. Measure the Volume:
- Use appropriate formulas for volume based on the shape of the solid:
3. Calculate Density:
- Use the formula:
- Ensure units are consistent.
Example:
- A metal cube has sides of 2 cm and a mass of 64 g.
Irregularly Shaped Solid
1. Measure the Mass:
- As with regular solids, use a balance.
2. Determine the Volume (Displacement Method):
- Fill a measuring cylinder partially with water and record the initial
volume.
- Submerge the solid completely in the water and record the new volume.
- Volume of the solid = Final volume - Initial volume.
3. Calculate Density
Example:
- A rock with a mass of 200 g displaces water from 50 mL to 90 mL in a
cylinder.
2. Density of Liquids
To find the density of a liquid:
1. Measure the Mass:
- Weigh an empty container (e.g., beaker or measuring cylinder) and
record its mass
- Fill the container with a known volume of liquid and weigh it again.
- Mass of the liquid = Mass of the filled container - Mass of the empty
container.
2. Measure the Volume:
- Use a measuring cylinder or pipette to accurately determine the volume
of the liquid.
3. Calculate Density:
Example:
- An empty beaker weighs 100 g. When filled with 200 mL of liquid, it
weighs 350 g.
3. Density of Gases
To find the density of a gas:
1. Measure the Mass:
- Use a sealed container of known mass. Evacuate the container to
remove all air and weigh it (mass of empty container).
- Allow the gas to fill the container and weigh it again (mass of container
+ gas).
- Mass of the gas = Mass of the full container - Mass of the empty
container.
2.Measure the Volume:
- Use the volume of the container as the volume of the gas (since gases
expand to fill the container).
3. Calculate Density:
Example
- A container has a volume of 5 L. Its mass increases from 200 g (empty)
to 202 g when filled with gas.
