Density
Section: Chemistry | Syllabus: Cambridge Lower Secondary Checkpoint Science (0893)
What is Density?
- Density describes how much mass is contained in a given volume of a substance
- A substance with a high density has a lot of mass packed into a small volume
- A substance with a low density has less mass packed into the same volume
- Density: the mass of a substance per unit volume
The Density Formula
- Density = Mass ÷ Volume
- Rearranged:
- Mass = Density × Volume
- Volume = Mass ÷ Density
Units of Density
- Density is usually measured in grams per cubic centimetre (g/cm³) or kilograms per cubic metre (kg/m³)
- Mass is measured in grams (g) or kilograms (kg)
- Volume is measured in cubic centimetres (cm³) or cubic metres (m³)
The density formula triangle: density = mass ÷ volume
Calculating Density
- To calculate density, measure the mass and volume of a substance, then divide mass by volume
- For a regular solid (e.g. a cube or cuboid), volume can be calculated directly from its dimensions
- For an irregular solid, volume can be found by displacement - measuring the volume of water it displaces
- For a liquid, volume can be measured directly using a measuring cylinder
Worked Example: Density of a Regular Solid
Muumbe has a metal block measuring 2 cm × 3 cm × 5 cm with a mass of 240 g, and wants to find its density.
- Step 1: Volume = 2 × 3 × 5 = 30 cm³
- Step 2: Density = Mass ÷ Volume = 240 ÷ 30 = 8 g/cm³
Worked Example: Density of an Irregular Solid
Museli drops a small rock of mass 158 g into a measuring cylinder containing 50 cm³ of water. The water level rises to 70 cm³, and she wants to find the rock's density.
- Step 1: Volume of rock = 70 − 50 = 20 cm³ (volume of water displaced)
- Step 2: Density = Mass ÷ Volume = 158 ÷ 20 = 7.9 g/cm³
Worked Example: Density of a Liquid
Muchindu measures 25 cm³ of a liquid and finds it has a mass of 20 g, and wants to find the liquid's density.
- Step 1: Density = Mass ÷ Volume = 20 ÷ 25 = 0.8 g/cm³
Exam Tip
- Always check the units of mass and volume before calculating density, and give your answer with the correct unit (g/cm³ or kg/m³)
Comparing Densities of Solids, Liquids and Gases
- Density depends on how closely packed the particles of a substance are
- Solids usually have the highest density - particles are packed tightly together in a fixed arrangement
- Liquids usually have a slightly lower density than solids - particles are close together but can move past each other
- Gases have a much lower density than solids or liquids - particles are far apart with lots of empty space between them
| State | Particle Arrangement | Typical Density |
|---|---|---|
| Solid | Tightly packed, fixed positions | Highest |
| Liquid | Close together, able to move past each other | Slightly lower than solid |
| Gas | Far apart, moving freely | Much lower than solid or liquid |
Particle arrangement in solids, liquids and gases, and how it relates to density
Comparing Different Substances
| Substance | State | Approximate Density (g/cm³) |
|---|---|---|
| Gold | Solid | 19.3 |
| Iron | Solid | 7.9 |
| Ice | Solid | 0.92 |
| Water | Liquid | 1.0 |
| Cooking oil | Liquid | 0.92 |
| Air | Gas | 0.0012 |
Common Mistakes
- Ice is less dense than liquid water, which is why ice floats - this is unusual, as most solids are denser than their liquid form
- A larger object does not always have a greater mass or a higher density - density depends on how tightly packed the particles are, not on size alone
Density in Everyday Life
- An object floats in a fluid if it is less dense than the fluid, and sinks if it is more dense than the fluid
- Wood floats on water because wood is less dense than water
- A steel ship floats because its overall shape displaces enough water, even though steel itself is denser than water
- Hot air balloons rise because hot air is less dense than the cooler air surrounding it
- Oil floats on water because oil is less dense than water - this is why oil spills spread across the surface of the sea
Exam Tip
- When comparing whether one substance will float on another, compare their densities directly - the less dense substance will float on top
For a fuller look at floating and sinking - including how dissolving a solute changes a solution's density, and worked examples ranking objects by volume - see the Mass, Volume and Density topic.
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