Mass is a physical quantity that indicates the amount of matter present in an object. It is denoted by m and is generally expressed in grams (g) or kilograms (kg). These units can of course be converted if needed.
To measure it, a balance is used.
Be careful not to confuse mass and weight: Mass always remains the same, regardless of the planet you are on. Weight depends on the gravitational force exerted by that planet. Thus, an astronaut with a mass of 70 kg on Earth will still have 70 kg on the Moon… but will "weigh" much less there!
Key points
What is the unit of mass?
What instrument is used to measure mass?
Does your mass change if you go to Mars?
Volume
Volume is the space occupied by an object or a substance, whether it is a solid, a liquid or a gas. It is denoted by V and is expressed in litres (L), cubic metres (m³) or cubic centimetres (cm³).
For substances that cannot be poured
For solids with simple shapes (cube, sphere…), the volume can be calculated using geometric formulas. For solids with irregular shapes, it must be measured directly using the water displacement method. For gases, it can be measured using an adapted water displacement method: by collecting it in an inverted measuring cylinder filled with water (the gas takes the place of the water and pushes it out). It can also be measured by drawing the gas into a graduated syringe.
Key points
What are the common units of volume?
How do you measure the volume of a liquid?
How do you measure the volume of an irregular object like a stone?
How can you measure the volume of a gas?
Comparing masses at equal volume
Let us take cubes of the same volume but made of different materials. By placing them on a balance, we notice that they do not have the same mass: for equal volumes, some materials are heavier than others.
Example: a 1 cm³ cube of iron is much heavier than a 1 cm³ cube of wood, which is itself heavier than a 1 cm³ cube of foam.
Mass and volume: proportionality
For the same material, if we take twice as much volume, we get twice as much mass: mass is proportional to volume. Thus, for the same material, if the volume doubles, the mass also doubles. Similarly, if the mass triples, the volume also triples.
Volume of water
Mass
1 L
1000 g
2 L
2000 g
3 L
3000 g
For water: 1 L weighs 1000 g, so 2 L weigh 2000 g and 3 L weigh 3000 g.
Predicting the order of two liquids
This idea makes it possible to predict how two liquids that do not mix (immiscible) arrange themselves: for equal volumes, the "heaviest" liquid sinks to the bottom, while the lighter one stays on top.
Example: for equal volumes, oil is lighter than water; oil therefore floats on top of water.
Key points
For equal volumes, do two different materials have the same mass?
For the same material, what happens to the mass if the volume is doubled?
Between two immiscible liquids, which one settles at the bottom?
Density, the link between mass and volume
Density indicates how much mass a certain volume of a material contains. One could say that it is "heaviness per unit volume". For example, pure water has a density of 1000 g/L, which means that 1 litre of water has a mass of 1000 g (or 1 kg). For an equal volume, a heavier object therefore has a higher density.
This concept also explains why certain liquids layer on top of each other when they do not mix (they are said to be immiscible). The liquid with the lowest density always stays on top, and the one with the highest density sinks to the bottom. This is why oil floats on water, or why honey sinks below water.
This property is useful in cooking to create layered drinks or desserts, in chemistry to separate liquids by decantation, or in the environment to recover oil floating on the water surface after an oil spill.
Key points
What is density?
Why does oil float on water?
In what order do water (1000 g/L), oil (920 g/L) and honey (1400 g/L) layer?
Give a concrete example of using the difference in density.
Calculating and using density
Density is denoted by the Greek letter ρ (rho). The fundamental relationship is:
$$\rho = \frac{m}{V}$$
where: $ρ$ is the density, $m$ the mass of the object, $V$ its volume.
Units must be consistent: if the mass is in grams and the volume in litres, the density will be in g/L. If the mass is in kilograms and the volume in cubic metres, it will be in kg/m³.
Example: a sample of 150 g occupies a volume of 0.2 L. We apply the formula:
$$\rho = \frac{150}{0.2} = 750 \ \text{g/L}$$
This corresponds, for example, to the density of petrol.
Each substance has its own density, making it a kind of "identity card".
Table of Densities
Material
Density (g/cm³)
Density (kg/m³)
Behavior in water
Common use
Metals
Aluminium
2.70
2,700
Sinks
Cans, aircraft, utensils
Iron
7.87
7,870
Sinks
Construction, tools
Copper
8.96
8,960
Sinks
Electrical cables, plumbing
Lead
11.34
11,340
Sinks
Batteries, radiation shielding
Gold
19.30
19,300
Sinks
Jewelry, electronics
Liquids
Water
1.00
1,000
Reference
Drinking, cleaning, transport
Olive oil
0.92
920
Floats
Cooking, cosmetics
Petrol
0.75
750
Floats
Automotive fuel
Mercury
13.53
13,530
Sinks
Thermometers (historical)
Common solids
Pine wood
0.50
500
Floats
Construction, furniture
Oak wood
0.75
750
Floats
Furniture, barrel making
PET plastic
1.38
1,380
Sinks
Bottles, textiles
Glass
2.50
2,500
Sinks
Windows, containers
Concrete
2.40
2,400
Sinks
Construction, roads
Ice
0.92
920
Floats
Cooling, icebergs
Gases (at 20°C, 1 atm)
Air
0.00120
1.20
Rises in water
Breathing, atmosphere
Helium
0.00018
0.18
Rises in air
Balloons, diving
Carbon dioxide
0.00198
1.98
Sinks in air
Fizzy drinks, fire extinguishers
In the laboratory or in daily life, measuring the density of a material makes it possible to identify an unknown substance or to check its purity. For example, pure water at 4°C has a density of exactly 1000 g/L; if a different value is found, it means there are impurities (such as salt in seawater).
Key points
What is the formula for density?
Calculate the density of a 200 g sample occupying 0.25 L.
How can an unknown substance be identified using its density?
Why is the density of seawater higher than that of freshwater?
