Solutions and Density
Density, and how to measure it
Calculate density from mass and volume, find the volume of an irregular solid by displacement, and say what heating does to density.
A wooden stick and an iron rod can be exactly the same size, and the iron rod still feels much heavier. Saying iron is heavier than wood is loose talk unless you say heavier for the same amount of space — and that is the quantity this chapter is about.
Density
Density is the mass present in a unit volume: density equals mass divided by volume. Since the SI units of mass and volume are the kilogram and the cubic metre, the SI unit of density is kg/m³. For liquids and small solids it is usually more convenient to use g/mL or g/cm³. A substance's density does not change with its shape or size, though it does change with temperature and pressure.
Worked example
A block of aluminium turns out to have a density of 2.7 g/cm³, and water has a density close to 1 g/cm³. What does the chapter make of that?
Divide one density by the other: aluminium is 2.7 times as dense as water.
The two densities are in the same units, so the units cancel and what is left is a bare number.
Try it together
A stone is weighed on a digital balance and comes to 16.400 g. Its volume is then found with a measuring cylinder. Work out its density.
Answer with a bare number each time.
1.The water stood at 50 mL, and rose to 55 mL when the stone was lowered in. What is the stone's volume, in cubic centimetres?
Have a go
Have a go on your own. A metal key has a mass of 90 g and a volume of 12 cm³. What is its density, in grams per cubic centimetre? Answer with a number.
Ready to practise?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.