Density Dive

Density Dive

Density is how much mass is packed into a given amount of space. It is what people are reaching for when they say something is "heavy for its size". It also settles the old trick question. A kilogram of lead and a kilogram of feathers have exactly the same mass; what differs is the volume they take up, and that difference is density. Two sets of units are used: g/cm³ for laboratory-sized objects and kg/m³ for larger ones. Behind all of it sits the particle model: how tightly the particles are packed.

Density = mass ÷ volume

The equation, with its symbol: density = mass ÷ volume, written ρ = m ÷ V (ρ is the Greek letter rho) It rearranges the way any three-quantity equation does, and both rearrangements get examined: • mass = density × volume, for finding how much a known volume of something weighs. • volume = mass ÷ density, for finding how much space a known mass occupies. Watch the units. Mass in grams with volume in cm³ gives g/cm³; mass in kilograms with volume in m³ gives kg/m³. Mixing them is the commonest way to be out by a factor of a thousand.

Work out the density

A metal block has a mass of 60 g and a volume of 20 cm³. What is its density, in g/cm³?

Find the mass

A liquid has a density of 0.8 g/cm³. What is the mass of 250 cm³ of it, in grams?

The particle model

Everything is made of particles, and the three states differ only in how those particles are arranged and how much energy they have. The particles themselves are identical in all three, which is the point most often missed:

Which box is the gas?

These three boxes show particles in the three states of matter. Tap the box showing a GAS.

The kettle paradox

Boil a kettle dry and the steam that leaves has the same total mass as the water that was in it. Yet steam has a far lower density than water. How can both of those be true at once?

• The same mass now occupies a far larger volume, because the particles have spread apart, and density is mass divided by volume
• The particles become lighter when the water boils
• Some of the particles are lost during boiling
• The particles swell up and become larger

What the particles do

Measuring density

Mass is easy: put it on a balance. Volume is where the method has to change with the shape of the object. A regular solid can be measured with a ruler. A cube of side 2 cm has a volume of 2 × 2 × 2 = 8 cm³, and no water is needed. An irregular solid defeats a ruler entirely, so you use displacement. The object is lowered into water, and because it cannot be in the same place as the water, it pushes an equal volume of water out of the way. The rise in the water level is the volume of the object, and that is the whole idea rather than a trick of the apparatus. Then density = mass ÷ volume as usual, whichever way the volume was found.

Order the method

Put the steps for finding the density of an irregular solid by displacement into order.

• Weigh the solid on a balance to find its mass
• Part-fill a measuring cylinder with water and read the volume
• Lower the solid in carefully and read the new, higher volume
• Subtract to find the rise, which is the volume of the solid
• Divide the mass by that volume to get the density

Physical or chemical?

Changes of state are physical changes, and knowing what that means is what makes the mass-conservation point explicable rather than something to memorise:

Changes of state

Select ALL THREE statements that are TRUE of a change of state.

• The total mass is unchanged, because no particles are created or destroyed
• The density changes, because the same particles now occupy a different volume
• It can usually be reversed by heating or cooling
• A new substance is formed
• The particles themselves grow larger
• Mass is lost when a liquid boils away

From the dimensions

A cube of metal has sides of 2 cm and a mass of 48 g. What is its density, in g/cm³?

The dive rules

Density is mass divided by _____, and it rearranges so that mass = density × volume. In a gas the particles are far apart, so the same mass fills a much larger space and the density is _____. For an irregular solid the volume is found by _____, where the rise in the water level is the volume of the object. A change of state is a _____ change, so no new substance is made and the total mass is unchanged.