What Is Density?

Introduction

Is a kilogram of iron heavier than a kilogram of feathers? No — they have the same mass. But the iron fits in your hand, while the feathers fill a large sack. The difference is density : how much mass is packed into a given volume. Density explains why stones sink, why oil floats on water and why hot-air balloons rise. It is one of the most useful properties in chemistry.

Core explanation

Definition. Density is the mass of a substance per unit volume:

density = mass ÷ volume

A substance with a high density has a lot of mass packed into each cubic centimetre; a substance with a low density has little.

Units. In the laboratory, mass is usually measured in grams and volume in cm³, so density is given in g/cm³ (grams per cubic centimetre). The SI unit is kg/m³ . Because 1 g/cm³ = 1000 kg/m³, water's density can be written as 1.00 g/cm³ or 1000 kg/m³. For liquids, g/mL is the same as g/cm³.

Typical densities (at room temperature, g/cm³):

Substance Density --- --- Air 0.0012 Cork about 0.24 Ethanol 0.79 Water 1.00 Aluminium 2.70 Iron 7.87 Copper 8.96 Lead 11.3 Gold 19.3

Same volume, different mass. A 1 cm³ cube of aluminium has a mass of 2.70 g, while a 1 cm³ cube of gold has a mass of 19.3 g. Gold is about seven times as dense. Equal volumes of different substances almost always have different masses.

Density is a characteristic property. For a pure substance at a given temperature and pressure, density is the same whether you have a tiny chip or a huge block. A small gold ring and a large gold bar have the same density — the bar has more mass and more volume in the same ratio. This makes density useful for identifying substances (page 49).

What controls density? Two things: how heavy the individual particles are, and how closely they are packed. Gold atoms are heavy and closely packed, so gold is very dense. Gas particles are far apart, so gases have very low densities.

Formulae

density (ρ) = mass (m) ÷ volume (V). Units: g/cm³ or kg/m³. The Greek letter ρ (rho) is the usual symbol for density.

Step-by-step reasoning

To compare the densities of two blocks of the same size:

1. Check that the volumes are equal. 2. Weigh both blocks. 3. The block with the greater mass has the greater density, because it packs more mass into the same volume. 4. To get numbers, divide each mass by its volume.

Visual explanation

Picture two boxes of the same size. One contains ten tightly packed marbles; the other contains the same ten marbles spread out, with room for many more. Or picture two boxes packed equally tightly, one with glass marbles and one with steel ball bearings of the same size. Both pictures show the two routes to high density: heavier particles, or particles packed more closely.

Real-world analogy

Think of a crowded train carriage at rush hour compared with the same carriage late at night. The carriage (volume) is the same size, but at rush hour it holds many more people (mass). The rush-hour carriage has a higher "density" of passengers.

Real-world example

Aircraft are built mainly from aluminium alloys and carbon-fibre composites rather than steel. Aluminium is about one-third as dense as steel, so parts of the same size have about one-third of the mass, which saves huge amounts of fuel over the life of the aircraft.

Why?

Why is the density of a substance the same for a small or large sample? If you double the size of a sample, you double both its mass and its volume. Dividing mass by volume gives the same answer, so density does not depend on the amount — it depends only on what the substance is and its conditions.

Common misconception

"Heavy objects are dense and light objects are not." A large wooden log is heavy but has a low density and floats; a small iron nail is light but dense and sinks. Density compares mass with volume; mass alone does not tell you the density.

Worked example

Question: A 10.0 cm³ block has a mass of 27.0 g. What is its density, and which metal in the table could it be?

Reasoning: density = mass ÷ volume = 27.0 ÷ 10.0 = 2.70 g/cm³. This matches aluminium.

Answer: 2.70 g/cm³; aluminium.

Quick check

1. Which is denser: 1 cm³ of copper (8.96 g) or 1 cm³ of iron (7.87 g)? Answer: Copper, because the same volume has a greater mass.

Exam focus

Learn the equation density = mass ÷ volume and the units g/cm³ and kg/m³. Examiners like "a kilogram of feathers versus a kilogram of lead" questions: the masses are equal, but lead has the higher density and so a much smaller volume.

Advanced insight

Densities of solids and liquids change only slightly with temperature and pressure, but gas densities change a lot. The densest element at room conditions is osmium (about 22.6 g/cm³); the least dense solids are aerogels, which are more than 99% air and can have densities below 0.01 g/cm³.

Summary

Density is mass per unit volume, ρ = m ÷ V, measured in g/cm³ or kg/m³ (1 g/cm³ = 1000 kg/m³). It depends on the mass of the particles and how closely they are packed. For a pure substance it is the same for any sample size, making it a characteristic property. Equal volumes of different substances usually have different masses.

Practice questions

1. State the equation for density and give its laboratory unit. Answer: Density = mass ÷ volume, measured in g/cm³. 2. Convert the density of iron, 7.87 g/cm³, into kg/m³. Answer: 7.87 × 1000 = 7870 kg/m³. 3. A small piece and a large piece are cut from the same copper bar. How do their densities compare? Explain. Answer: They are equal, because mass and volume increase in the same proportion, so mass ÷ volume stays the same. 4. Which has the larger volume, 1 kg of cork or 1 kg of lead? Explain. Answer: 1 kg of cork, because cork has a much lower density, so the same mass occupies much more space.