This page needs the IB Demystified site-wide snippets. Ask the site administrator to install them.
IB DemystifiedMYP Sciences
Density
A kilogram of feathers and a kilogram of iron have the same mass, but not the same size. Density compares mass with the space it takes up, and it explains why ships float, balloons rise and oil sits on water.
Recommended for MYP 2 · About 3 lessons · Criteria A, B, C and D
Figure 1. Same volume, different numbers of identical particles, so different masses.
calculate density from mass and volume, and rearrange the equation to find mass or volume
find the volume of regular objects by measuring and of irregular objects by displacement
convert between g/cm³ and kg/m³
predict and explain floating and sinking using density
explain differences in density using the particle model
Before you start
You will use these skills. If any feel shaky, review them first.
the particle model of solids, liquids and gases
units of mass (g, kg) and volume (cm³, m³, mL)
volume of a cuboid: length × width × height
reading a scale, including a measuring cylinder
Key vocabulary
Mass
The amount of matter in an object, measured in grams (g) or kilograms (kg).
Volume
The amount of space an object takes up, measured in cm³ or m³. 1 cm³ = 1 mL.
Density
The mass of a substance per unit volume.
Displacement
Pushing a liquid aside. An object sinking in water displaces its own volume of water.
Meniscus
The curved surface of a liquid in a narrow tube. Read water levels at the bottom of the curve.
Buoyancy
The upward push of a fluid on an object in it. An object floats if it is less dense than the fluid.
Understanding density
What is it?
Density tells you how much mass is packed into each unit of volume. Aluminium has a density of 2.7 g/cm³: every cubic centimetre of it has a mass of 2.7 g.
density = mass ÷ volume
Why does it happen?
Density depends on two things: how heavy each particle is, and how closely the particles are packed. In Figure 1 the particles are identical, so the solid is densest because it packs the most particles into the same space. Lead is denser than aluminium because its atoms are much heavier.
How do we know?
We cannot see particles, but we can measure mass with a balance and volume with a ruler or by displacement, then calculate density. Because density is the same for every piece of a pure substance, it can identify materials. Scientists have used it to spot fake gold and to deduce that Earth has a dense iron core.
Why does it matter?
Density decides what floats and what sinks. Engineers use it to design ships and aircraft, recycling plants use it to sort plastics, and it explains why oil spills spread across the sea surface.
What does it connect to?
Density links to the particle model and changes of state, to pressure and buoyancy in physics, to ocean currents and Earth's layers in Earth science, and to ratio and proportion in mathematics.
Measuring mass and volume
Mass is measured with an electronic balance. How you find volume depends on the object:
Regular solids such as cuboids: measure the sides with a ruler and multiply length × width × height.
Irregular solids such as stones: lower the object into a measuring cylinder of water. The rise in the water level equals the object's volume.
Liquids: pour into a measuring cylinder and read the scale at the bottom of the meniscus, at eye level.
Take care with units: 1 cm³ = 1 mL, and 1 m³ = 1 000 000 cm³. To convert g/cm³ to kg/m³, multiply by 1000.
Density in the real world
Hot-air balloons rise because heated air expands and becomes less dense than the cooler air around it. Ocean water that is cold and salty is denser, so it sinks and drives currents around the planet. Submarines dive and surface by taking in or pumping out sea water, changing their average density.
Worked examples
Example 1: finding density
A pebble has a mass of 54 g. It raises the water in a measuring cylinder from 40 cm³ to 60 cm³. Calculate its density.
Find the volume: 60 cm³ − 40 cm³ = 20 cm³.
Write the equation: density = mass ÷ volume.
Substitute and add the unit: density = 54 g ÷ 20 cm³ = 2.7 g/cm³.
Example 2: finding mass
A fish tank holds 60 000 cm³ of water, density 1.00 g/cm³. What is the mass of the water in kilograms?
Rearrange: mass = density × volume.
Substitute: mass = 1.00 g/cm³ × 60 000 cm³ = 60 000 g.
Convert: 60 000 g ÷ 1000 = 60 kg.
Check your understanding
Quick questions on the ideas above. Try each one before using a hint.
Practice questions
Show
Investigation: can you make an egg float?
Guided investigation · about 50 minutes · pairs
Research question
How does the mass of salt dissolved in 100 cm³ of solution (0, 5, 10, 15 and 20 g) affect the density of the solution?
Scientific background
When salt dissolves, its particles fit between the water particles. The mass increases more than the volume, so the density of the solution rises.
Hypothesis
If more salt is dissolved in 100 cm³ of solution, then the density of the solution will increase, because more mass is added to almost the same volume.
Independent variable
Mass of salt in 100 cm³ of solution: 0, 5, 10, 15 and 20 g.
Dependent variable
Density of the solution, calculated from the mass of 50.0 cm³ of it.
Control variables
Temperature: all solutions at room temperature, because warm liquids expand and become less dense.
Same type of salt, fully dissolved.
Same measuring cylinder and balance throughout.
Same final volume, 100 cm³, for each solution.
Apparatus
Salt, water, 100 cm³ and 50 cm³ measuring cylinders, beakers, stirring rod, electronic balance, a fresh egg, spoon.
Method
Dissolve the mass of salt in some water and make it up to 100 cm³.
Find the mass of an empty 50 cm³ measuring cylinder.
Pour in exactly 50.0 cm³ of solution and find the new mass.
Density = mass of solution ÷ 50.0 cm³.
Lower the egg in gently with a spoon and record whether it sinks or floats.
Repeat for each concentration, three times if time allows.
Safety. Wipe up spills at once, as salty water makes floors slippery. Handle the egg gently and wash hands afterwards. Do not taste any solutions.
Results from one student are used in the Criterion C questions below. Then evaluate: why is it better to measure 50.0 cm³ than 10.0 cm³ of each solution?
Criterion-linked questions
Criterion B: inquiring and designing
Criterion C: processing and evaluating
Criterion D: reflecting on the impacts of science
Challenge questions
Harder problems in unfamiliar contexts. Plan before you calculate.
Topic check
Five questions picked at random from the whole topic. Take a new set whenever you like.
Review your mistakes
Questions you got wrong on this device appear here so you can try them again. Answer one correctly and it leaves the list.
Your progress
Tracked separately for each skill, on this device only.
