Density is mass divided by volume, usually in grams per cubic centimeter.
Density Mass per unit volume.
Step 1: Something to Notice
Watch first. The explanation comes later.
Cut a bar of gold in half and each half weighs half as much, occupies half the volume, and has exactly the same density.
Which properties survive being cut in half, and why does that matter?
Step 2: Find Out
Isolate the property that identifies a material regardless of sample size.
Step 1 — Predict
A gold bar is cut in half. What happens to its density?
Choose what you think will happen. You cannot see the experiment until you do — guessing first is what makes it worth watching.
Step 3: So Here Is Why
Now the explanation, after you have seen it happen.
Intensive properties do not scale
Density, melting point and color are the same for any amount, which is what makes them identifying.
Intensive property A property that does not depend on the amount of substance.
Extensive properties do
Mass, volume and length depend on how much you have, so they identify nothing on their own.
Heavy is not dense
A tonne of polystyrene is heavy and barely dense. A large enough piece of anything is heavy.
Which is why density identifies
Measure mass and volume of any sample and the ratio names the material.
A property that does not depend on how much
Cutting a block of aluminum in half halves the mass and the volume and leaves the density unchanged. Intensive properties like density identify a substance; extensive ones like mass do not.
Density identifies materials
Measuring mass and volume and dividing gives a number that can be looked up. It is how Archimedes is said to have tested a crown, and it is still a standard identification method.
Step 4: A Common Mistake
Lots of people think
“Heavy things are dense and light things are not.”
Step 5: Why Ice Floats and Almost Nothing Else Does
The same idea somewhere new.
Nearly every substance is denser as a solid than as a liquid, because cooling packs the particles closer. Water is the exception: hydrogen bonding holds the molecules in an open lattice when it freezes, so ice is about 9% less dense than liquid water. Lakes therefore freeze from the top down, which is why fish survive winters.
Step 6: Think It Through
Practice makes it stick.
Cut in Half
Problem 1 of 2
A gold bar is cut in half. Which properties change?
A Tonne of Polystyrene
Problem 2 of 2
A tonne of polystyrene weighs more than a copper coin. Which is denser?
Which Properties Identify
1 of 5
Which are intensive properties?
2 of 5
A sample has mass 89.0 g and volume 10.0 cm³. What is its density?
3 of 5
Why can mass not identify a substance?
4 of 5
Why does ice float on water?
5 of 5
How is the volume of an irregular solid found?
Step 7: Quick Check
Show what you know.
Question 1 of 1
Is a tonne of polystyrene dense?
Step 8: Explain It in Writing
Claim, evidence, then reasoning.
The question
Explain why density identifies a substance when mass does not, and why a tonne of polystyrene is not dense.
Fill in all three boxes. The reasoning box is the one that matters most.
What You Found Out
- Density is mass per unit volume and does not depend on the amount.
- Intensive properties identify a substance; extensive ones do not.
- Heavy and dense are different questions, and a large enough piece of anything is heavy.
- Ice floats because hydrogen bonding holds an open lattice — almost nothing else does this.