Grade by Grade
C. Matter and Energy · Fluids

Density of Solids, Liquids and Gases

C2.3 C2.2 A1.2 A1.5About 45 minutes
Learning goals
  • I can use the particle theory to explain why solids, liquids and gases of the same substance have different densities.
  • I can explain why ice is an unusual exception and why it matters in a Canadian winter.
  • I can explain how heating and cooling change the density of a fluid.
  • I can build a density column and explain the order of the layers.

Words to know

particle theory of matter
The model that says all matter is made of tiny moving particles with spaces between them that attract each other.
state of matter
The form matter is in: solid, liquid or gas.
density
The mass of a substance in a certain volume (mass ÷ volume).
density column
Layers of liquids that don't mix, stacked in order of density, with the densest at the bottom.
expansion
An increase in volume, usually caused by heating.

Why does the ice stay on top?

Every winter, Ontario's lakes and ponds freeze from the top down. Under the ice, fish keep swimming in liquid water all winter. If ice sank, lakes would fill up with ice from the bottom, and many could freeze nearly solid.

So why does ice float? To answer that, let's look at how particles are arranged in solids, liquids and gases.

A frozen lake with a crack in the ice near the snowy shore showing dark liquid water underneath.
Ice floats on top of the liquid water below it. Ice is less dense than liquid water, so lakes freeze from the top down. AI-generated image

Density and the particle theory

Density is mass ÷ volume. For the same substance, the particles have the same mass. What changes from solid to liquid to gas is how much space they take up.

  • Solid: particles are packed tightly in fixed positions and only vibrate. Lots of mass in a small volume → highest density (for most substances).
  • Liquid: particles are still close, but they can slide past each other. Slightly more space between them → usually a bit less dense than the solid.
  • Gas: particles are very far apart and move fast in all directions. The same mass spreads out over a huge volume → much lower density.

For example, 1 g of liquid water takes up about 1 mL. Boiled into water vapour at 100 °C, that same 1 g takes up about 1700 mL. Same mass, much more volume, so the gas is far less dense.

solidliquidgasmost denseless denseleast dense
Particle models of the same substance as a solid, a liquid and a gas, each in the same space. More particles packed into the same space means more mass in that volume, so a higher density.

The ice exception

Water is unusual. When water freezes, its particles lock into an open, spread-out pattern with more space between them than in liquid water. So ice takes up about 9% more volume than the water it came from. Same mass, more volume → lower density.

  • Ice: about 0.92 g/cm³. Liquid water: about 1.00 g/cm³. So ice floats.
  • This is why water pipes can burst in a freezing house, and why a full glass bottle of water left in the freezer can crack.
  • It's also why lakes freeze from the top, which protects the life underneath.
An Ontario lake in winter (cross-section, not to scale)ice floats on top (0.92 g/cm³)air: −15 °Cwater just under the ice: near 0 °Cdensest water (about 4 °C) sinks to the bottomStill swimming, thanks!
Because ice is less dense than liquid water, it floats and forms a lid on the lake. The water below stays liquid all winter, so the fish survive.

Heating and cooling change density

Remember from Grade 7: when matter is heated, its particles move faster and spread a little farther apart. It expands. Its mass stays the same, so its density decreases.

  • Warm air is less dense than cool air, so it rises. That's how a hot-air balloon flies (Grade 6) and how convection currents form (Grade 7).
  • Warm water is slightly less dense than cold water, so in a lake in summer, the warm water stays near the top.
Worked example

Let's explain an observation with the particle theory

A sealed bag of chips is packed in Toronto and taken on a flight. Nothing is added or removed from the bag. Compare the density of the solid chips with the density of the air sealed in the bag, and explain the difference using the particle theory.

  1. Step 1. Recall the formula. Density = mass ÷ volume.
  2. Step 2. Describe the solid. In the chips, particles are packed close together, so there is a lot of mass in a small volume.
  3. Step 3. Describe the gas. In the air, particles are far apart with big spaces between them, so there is very little mass in a big volume.
  4. Step 4. Compare. The chips have a much higher density than the air.
  5. Step 5. Write it clearly. Use "because" and particle words.

The chips are much denser than the air because the particles in a solid are packed tightly together, while the particles in a gas are far apart, so the gas has much less mass in each millilitre.

Just for fun

What did the ice say to the lake water in December?

"I'm totally over you." (Less dense, remember?)

Hands-on activity

Build a density column

Do this with a grown-up nearby. Dish soap is not food. Nothing in the finished column should be eaten or drunk.

You need: a tall clear glass or jar, honey (or corn syrup), dish soap, water with a drop of food colouring, cooking oil, a spoon, and small test objects such as a coin, a cork or bottle cap, and a grape.

  1. Pour about 50 mL of honey into the bottom of the glass.
  2. Slowly pour about 50 mL of dish soap down the inside wall of the glass, or over the back of a spoon so it doesn't mix.
  3. Slowly add about 50 mL of coloured water the same way.
  4. Slowly add about 50 mL of cooking oil.
  5. Let it settle for a minute. Draw and label the layers.
  6. Predict where each test object will stop, then gently drop each one in. Record the results.
  7. Explain: write a sentence about each layer using the word density.

What to look for: from bottom to top: honey (about 1.4 g/mL), dish soap (a little more than 1), water (1.00), oil (0.92). The densest liquid is at the bottom. The coin sinks to the bottom because metal is much denser than all four liquids. The cork floats on top because it is less dense than all of them. An object stops at the boundary where the liquid above it is less dense than the object and the liquid below it is more dense. (Your grape result depends on the grape: record what you see.)

Safety and clean-up: keep dish soap out of eyes and mouth. Wipe spills right away (soap and oil are slippery). Put the column in the garbage or a compost container with a grown-up's help, not down the drain, because oil and honey can clog pipes.

Your turn

1

For most substances, which state is the densest: solid, liquid or gas?

2

Use the particle theory to explain why a gas is much less dense than a liquid of the same substance.

3

Why does ice float on liquid water?

4

What happens to the density of air when it is heated? Why?

5

In a density column, which liquid ends up at the bottom?

6

Why can a water pipe burst in an unheated cottage in winter?

More practice: warm-up

1

True or false: the particles in a gas are close together.

2

Which is denser: liquid water or ice?

3

Does heating usually make a substance more or less dense?

4

In the density column, which is on top: water or cooking oil?

5

Which state has particles in fixed positions that only vibrate?

More practice: on your own

1

1 g of liquid water takes up about 1 mL. As water vapour at 100 °C, it takes up about 1700 mL. Estimate the density of the water vapour in g/mL.

2

Why do lakes in Ontario freeze from the top down instead of the bottom up?

3

Cork is a solid, but it floats on liquid water. Does that break the rule that solids are densest? Explain.

4

Why does warm air near a baseboard heater rise toward the ceiling?

5

A full glass bottle of water cracks in the freezer, but a half-full one does not. Explain.

Challenge

1

Ice has a density of 0.92 g/cm³. A 100 g ice cube melts. What is the volume of the ice before it melts, and of the water after? (Use 1.00 g/mL for water.)

2

Most solids sink in their own liquid (for example, solid candle wax sinks in melted wax). Imagine ice did the same. Describe what could happen to a pond and its fish over a long Canadian winter.

3

You pour equal volumes of water and maple syrup (1.33 g/mL) into a jar. Without stirring, which ends up on the bottom? If you weigh 100 mL of each, how different are their masses?

Check your understanding

Quiz

1.

For most substances, the gas state has...

2.

Why is a gas less dense than the liquid of the same substance?

3.

Ice floats on water because...

4.

When a fluid is heated, its density usually...

5.

Honey, water and cooking oil are poured gently into a glass. From bottom to top, the order is...

6.

Which observation is explained by water expanding when it freezes?

For parents and teachers

Big idea (C2.3): for the same substance, the arrangement of particles explains density: tightly packed solids are usually densest, liquids slightly less, gases far less. Water is the important exception: ice is less dense than liquid water, which is why lakes freeze from the top. Heating lowers density (links to convection from Grade 7 and hot-air balloons from Grade 6).

How to help: freeze a plastic container filled to the brim with water and look at the bulging top. Watch ice cubes in a drink: how much of the cube sits below the surface?

Common difficulties:

  • Thinking gas particles are lighter or smaller. They're the same particles, just farther apart.
  • Applying "solids are densest" to different substances (cork vs water). The rule compares states of the same substance.
  • Forgetting the ice exception.

Safety: you supervise the density column. Dish soap is not food. The column goes in the garbage, not down the drain. Never use glass bottles filled to the top in the freezer.