3.1.1a Density of materials

Density: how much mass is packed into a volume

Definition

Density

Density is the mass per unit volume of a material.

Density tells you how much mass is contained in a given volume of a material.
A material has a high density if a given volume of it has a large mass.
A material has a low density if the same volume has a smaller mass.
For two objects of the same volume, the one with the greater mass has the greater density.
For two objects of the same mass, the one with the smaller volume has the greater density.
Density is given the symbol $ρ\rho$ , the Greek letter “rho”.

Key Idea

Density is a property of the material, not of the size of the object. A large, heavy object can still have a low density if its volume is large, because density compares mass with volume rather than looking at either on its own.

The density equation

Density is calculated from mass and volume using the equation $ρ=mV\rho = \dfrac{m}{V}$ , which in words is $density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}$ .
Density, $ρ\rho$ , is measured in kilograms per metre cubed, $kg/m3\text{kg/m}^3$ .
Mass, $m$ , is measured in kilograms, $kg\text{kg}$ .
Volume, $V$ , is measured in metres cubed, $m3\text{m}^3$ .
The unit follows straight from the equation: dividing kilograms by metres cubed gives $kg/m3\text{kg/m}^3$ .
In the lab you will often measure grams and centimetres cubed, giving $g/cm3\text{g/cm}^3$ ; to convert, multiply by 1000, so $kg/m31\ \text{g/cm}^3 = 1000\ \text{kg/m}^3$ .

Example

A solid block has a mass of $kg12\ \text{kg}$ and a volume of $m30.004\ \text{m}^3$ . Calculate its density.

State the equation:

\rho = \frac{m}{V}

Substitute the values:

\rho = \frac{12}{0.004} = 3000\ \text{kg/m}^3

The density of the material is $kg/m33000\ \text{kg/m}^3$ .

Common Mistake

Do not confuse density with mass: mass tells you how much matter there is, while density compares that mass with the volume.
Do not assume a large or heavy object must be dense, as its mass may just be spread over a large volume.
Do not turn the equation upside down: it is always mass divided by volume, never volume divided by mass.

Exam technique

Show the equation, the substitution, the answer and the unit, as each can earn a mark.
Before you calculate, check the mass is in $kg\text{kg}$ and the volume in $m3\text{m}^3$ , so the density comes out in $kg/m3\text{kg/m}^3$ .

Self review

What does density mean?
Write the density equation in words and in symbols.
What does the symbol $ρ\rho$ represent?
State the standard units of mass, volume and density.
Two objects have the same volume; which one has the greater density?
Why is the unit of density $kg/m3\text{kg/m}^3$ ?

3.1.1b The particle model, states of matter and measuring density (required practical)

The particle model: how solids, liquids and gases differ

Definition

Particle model

The particle model represents a material as tiny particles, such as atoms or molecules, and is used to explain the three states of matter and the differences in their densities.

In a solid, the particles are packed closely together, usually in a regular pattern.
These particles vibrate about fixed positions but cannot move past one another, so a solid keeps a fixed shape and volume.
In a liquid, the particles are still close together but arranged randomly.
These particles can move past one another, so a liquid flows and takes the shape of its container while keeping the same volume.
In a gas, the particles are far apart and arranged randomly.
These particles move quickly in all directions and spread out to fill their container, so a gas has no fixed shape or volume.

Diagram showing the particle arrangement in solids, liquids, and gases. Particles in a solid are in a regular, close-packed pattern; in a liquid, they are close but random; in a gas, they are far apart and random. Arrows show that increasing temperature leads to increased molecular motion.

Key Idea

To draw simple particle diagrams:

solid: circles touching in a regular, ordered pattern;
liquid: circles touching but in a random arrangement;
gas: a few circles spread far apart and randomly placed.

The circles model the particles; they do not show their real size, shape or spacing.

Explaining density with the particle model

Definition

Density

Density is the mass per unit volume of a material, $ρ=mV\rho = \dfrac{m}{V}$ .

In solids and liquids the particles are close together, so a large number of particles, and therefore a large mass, is packed into each cubic metre, giving a high density.
In a gas the particles are far apart, so far fewer particles, and much less mass, occupy each cubic metre, giving a much lower density.
When a substance melts or boils, the number of particles does not change, but they spread further apart, so the density usually falls.

Common Mistake

Do not say that the particles in a gas have “no mass” or that they disappear. The particles still have the same mass; a gas has a lower density only because the same particles are spread out over a much larger volume.

Practical

Investigation: measuring the density of solids and liquids

Aim: to measure the density of a regularly shaped solid, an irregularly shaped solid and a liquid.
Apparatus: a $cm30\ \text{cm}$ ruler marked in millimetres, a digital balance, a displacement (eureka) can, a selection of measuring cylinders, a beaker of water, a regular solid such as a metal cuboid, an irregular solid such as a small stone or metal object, a liquid such as a sugar solution, and paper towels.

Part 1 — a regularly shaped solid

Measure the mass of the object with the balance and record it.
Use the ruler to measure the length, width and height, reading each scale at eye level.
Calculate the volume from the dimensions using $\text{length} \times \text{width} \times \text{height}$ .
Calculate the density using $ρ=mV\rho = \dfrac{m}{V}$ .

Part 2 — an irregularly shaped solid (displacement)

Measure the mass of the object with the balance.
Fill the displacement can until water just runs from the spout, then wait until the dripping stops.
Place an empty measuring cylinder under the spout.
Lower the object gently into the can, on a thread, until it is fully submerged.
Collect all the water pushed out of the spout in the measuring cylinder.
Read the volume of displaced water at eye level; this volume equals the volume of the object.
Calculate the density using $ρ=mV\rho = \dfrac{m}{V}$ , then refill the can before repeating for another object.

Part 3 — a liquid

Measure the mass of an empty measuring cylinder.
Pour in a known volume of the liquid, reading the volume at the bottom of the meniscus at eye level.
Measure the mass of the measuring cylinder and liquid together.
Subtract the empty-cylinder mass to find the mass of the liquid alone.
Calculate the density using $ρ=mV\rho = \dfrac{m}{V}$ .

Worked result

A metal cuboid has a mass of $g216\ \text{g}$ and measures $cm6.0\ \text{cm} \times 3.0\ \text{cm} \times 2.0\ \text{cm}$ .
Volume: $\times 3.0 \times 2.0 = 36\ \text{cm}^3$ .
Density: $g/cm3\rho = \dfrac{216}{36} = 6.0\ \text{g/cm}^3$ .

Accuracy and safety

Make sure the object is fully submerged, and dry it before weighing, or the readings will be wrong.
Wait until the can has stopped dripping before you start, or the measured volume will be too large.
Masses in grams with volumes in $cm3\text{cm}^3$ give a density in $g/cm3\text{g/cm}^3$ ; multiply by 1000 to convert to $kg/m3\text{kg/m}^3$ .
Wipe up any spilt water straight away so that no one slips.
For an irregular object, never try to work out the volume from measured dimensions; use displacement.

Self review

Describe the arrangement and movement of the particles in a solid, a liquid and a gas.
Why do gases have much lower densities than solids and liquids?
What does the density equation tell you to measure?
How do you find the volume of a regularly shaped solid, and of an irregularly shaped one?
Why must you wait for the displacement can to stop dripping before lowering in the object?

3.1.1a Density of materials

Density: how much mass is packed into a volume

Definition

Density

Density is the mass per unit volume of a material.

Density tells you how much mass is contained in a given volume of a material.
A material has a high density if a given volume of it has a large mass.
A material has a low density if the same volume has a smaller mass.
For two objects of the same volume, the one with the greater mass has the greater density.
For two objects of the same mass, the one with the smaller volume has the greater density.
Density is given the symbol $ρ\rho$ , the Greek letter “rho”.

Key Idea

The density equation

Density is calculated from mass and volume using the equation $ρ=mV\rho = \dfrac{m}{V}$ , which in words is $density=massvolume\text{density} = \dfrac{\text{mass}}{\text{volume}}$ .
Density, $ρ\rho$ , is measured in kilograms per metre cubed, $kg/m3\text{kg/m}^3$ .
Mass, $m$ , is measured in kilograms, $kg\text{kg}$ .
Volume, $V$ , is measured in metres cubed, $m3\text{m}^3$ .
The unit follows straight from the equation: dividing kilograms by metres cubed gives $kg/m3\text{kg/m}^3$ .
In the lab you will often measure grams and centimetres cubed, giving $g/cm3\text{g/cm}^3$ ; to convert, multiply by 1000, so $kg/m31\ \text{g/cm}^3 = 1000\ \text{kg/m}^3$ .

Example

A solid block has a mass of $kg12\ \text{kg}$ and a volume of $m30.004\ \text{m}^3$ . Calculate its density.

State the equation:

\rho = \frac{m}{V}

Substitute the values:

\rho = \frac{12}{0.004} = 3000\ \text{kg/m}^3

The density of the material is $kg/m33000\ \text{kg/m}^3$ .

Common Mistake

Do not confuse density with mass: mass tells you how much matter there is, while density compares that mass with the volume.
Do not assume a large or heavy object must be dense, as its mass may just be spread over a large volume.
Do not turn the equation upside down: it is always mass divided by volume, never volume divided by mass.

Exam technique

Show the equation, the substitution, the answer and the unit, as each can earn a mark.
Before you calculate, check the mass is in $kg\text{kg}$ and the volume in $m3\text{m}^3$ , so the density comes out in $kg/m3\text{kg/m}^3$ .

Self review

What does density mean?
Write the density equation in words and in symbols.
What does the symbol $ρ\rho$ represent?
State the standard units of mass, volume and density.
Two objects have the same volume; which one has the greater density?
Why is the unit of density $kg/m3\text{kg/m}^3$ ?

3.1.1b The particle model, states of matter and measuring density (required practical)

The particle model: how solids, liquids and gases differ

Definition

Particle model

In a solid, the particles are packed closely together, usually in a regular pattern.
These particles vibrate about fixed positions but cannot move past one another, so a solid keeps a fixed shape and volume.
In a liquid, the particles are still close together but arranged randomly.
These particles can move past one another, so a liquid flows and takes the shape of its container while keeping the same volume.
In a gas, the particles are far apart and arranged randomly.
These particles move quickly in all directions and spread out to fill their container, so a gas has no fixed shape or volume.

Key Idea

To draw simple particle diagrams:

solid: circles touching in a regular, ordered pattern;
liquid: circles touching but in a random arrangement;
gas: a few circles spread far apart and randomly placed.

The circles model the particles; they do not show their real size, shape or spacing.

Explaining density with the particle model

Definition

Density

Density is the mass per unit volume of a material, $ρ=mV\rho = \dfrac{m}{V}$ .

In solids and liquids the particles are close together, so a large number of particles, and therefore a large mass, is packed into each cubic metre, giving a high density.
In a gas the particles are far apart, so far fewer particles, and much less mass, occupy each cubic metre, giving a much lower density.
When a substance melts or boils, the number of particles does not change, but they spread further apart, so the density usually falls.

Common Mistake

Do not say that the particles in a gas have “no mass” or that they disappear. The particles still have the same mass; a gas has a lower density only because the same particles are spread out over a much larger volume.

Practical

Investigation: measuring the density of solids and liquids

Aim: to measure the density of a regularly shaped solid, an irregularly shaped solid and a liquid.
Apparatus: a $cm30\ \text{cm}$ ruler marked in millimetres, a digital balance, a displacement (eureka) can, a selection of measuring cylinders, a beaker of water, a regular solid such as a metal cuboid, an irregular solid such as a small stone or metal object, a liquid such as a sugar solution, and paper towels.

Part 1 — a regularly shaped solid

Measure the mass of the object with the balance and record it.
Use the ruler to measure the length, width and height, reading each scale at eye level.
Calculate the volume from the dimensions using $\text{length} \times \text{width} \times \text{height}$ .
Calculate the density using $ρ=mV\rho = \dfrac{m}{V}$ .

Part 2 — an irregularly shaped solid (displacement)

Measure the mass of the object with the balance.
Fill the displacement can until water just runs from the spout, then wait until the dripping stops.
Place an empty measuring cylinder under the spout.
Lower the object gently into the can, on a thread, until it is fully submerged.
Collect all the water pushed out of the spout in the measuring cylinder.
Read the volume of displaced water at eye level; this volume equals the volume of the object.
Calculate the density using $ρ=mV\rho = \dfrac{m}{V}$ , then refill the can before repeating for another object.

Part 3 — a liquid

Measure the mass of an empty measuring cylinder.
Pour in a known volume of the liquid, reading the volume at the bottom of the meniscus at eye level.
Measure the mass of the measuring cylinder and liquid together.
Subtract the empty-cylinder mass to find the mass of the liquid alone.
Calculate the density using $ρ=mV\rho = \dfrac{m}{V}$ .

Worked result

A metal cuboid has a mass of $g216\ \text{g}$ and measures $cm6.0\ \text{cm} \times 3.0\ \text{cm} \times 2.0\ \text{cm}$ .
Volume: $\times 3.0 \times 2.0 = 36\ \text{cm}^3$ .
Density: $g/cm3\rho = \dfrac{216}{36} = 6.0\ \text{g/cm}^3$ .

Accuracy and safety

Make sure the object is fully submerged, and dry it before weighing, or the readings will be wrong.
Wait until the can has stopped dripping before you start, or the measured volume will be too large.
Masses in grams with volumes in $cm3\text{cm}^3$ give a density in $g/cm3\text{g/cm}^3$ ; multiply by 1000 to convert to $kg/m3\text{kg/m}^3$ .
Wipe up any spilt water straight away so that no one slips.
For an irregular object, never try to work out the volume from measured dimensions; use displacement.

Self review

Describe the arrangement and movement of the particles in a solid, a liquid and a gas.
Why do gases have much lower densities than solids and liquids?
What does the density equation tell you to measure?
How do you find the volume of a regularly shaped solid, and of an irregularly shaped one?
Why must you wait for the displacement can to stop dripping before lowering in the object?

3.1.1 Density of materials

3.1.1a Density of materials

Density: how much mass is packed into a volume

The density equation

3.1.1b The particle model, states of matter and measuring density (required practical)

The particle model: how solids, liquids and gases differ

Explaining density with the particle model

Investigation: measuring the density of solids and liquids

Part 1 — a regularly shaped solid

Part 2 — an irregularly shaped solid (displacement)

Part 3 — a liquid

Worked result

Accuracy and safety

Review 3.1.1 Density of materials by teaching Genie

Remember key concepts with flashcards

3.1.1 Density of materials

3.1.1a Density of materials

Density: how much mass is packed into a volume

The density equation

3.1.1b The particle model, states of matter and measuring density (required practical)

The particle model: how solids, liquids and gases differ

Explaining density with the particle model

Investigation: measuring the density of solids and liquids

Part 1 — a regularly shaped solid

Part 2 — an irregularly shaped solid (displacement)

Part 3 — a liquid

Worked result

Accuracy and safety

Review 3.1.1 Density of materials by teaching Genie

Remember key concepts with flashcards

3.1.1 Density of materials

3.1.1a Density of materials

Density: how much mass is packed into a volume

The density equation

3.1.1b The particle model, states of matter and measuring density (required practical)

The particle model: how solids, liquids and gases differ

Explaining density with the particle model

Investigation: measuring the density of solids and liquids

Part 1 — a regularly shaped solid

Part 2 — an irregularly shaped solid (displacement)

Part 3 — a liquid

Worked result

Accuracy and safety

Review 3.1.1 Density of materials by teaching Genie

Remember key concepts with flashcards

3.1.1 Density of materials Revision Guide

3.1.1 Density of materials

3.1.1a Density of materials

Density: how much mass is packed into a volume

The density equation

3.1.1b The particle model, states of matter and measuring density (required practical)

The particle model: how solids, liquids and gases differ

Explaining density with the particle model

Investigation: measuring the density of solids and liquids

Part 1 — a regularly shaped solid

Part 2 — an irregularly shaped solid (displacement)

Part 3 — a liquid

Worked result

Accuracy and safety

Review 3.1.1 Density of materials by teaching Genie

Remember key concepts with flashcards

3.1.1 Density of materials Revision Guide