Matter and Its Three States – States and Changes of State of Matter (Senior 1 Chemistry) | Ganzaa

States and Changes of State of Matter

Lessons

Senior 1 · Chemistry

States and Changes of State of Matter

5 lessons

Lesson 1 of 5

Matter and Its Three States

25 min

Why does one stone float?

Drop a lump of the dark volcanic stone used for walls in Musanze into a bucket of water and it sinks at once. Drop in a piece of pumice, the light grey volcanic stone sold for scrubbing feet, and it floats. Both are rock. Both are matter. The difference is not how heavy each lump is, but how much mass is packed into each cubic centimetre: its density.

Definition

Matter: anything that has mass and takes up space. Matter exists in three common states: solid, liquid and gas.

Definition

Mass and volume: mass ( $m$ ) is the amount of matter in an object, measured in grams (g) or kilograms (kg); volume ( $V$ ) is the space it takes up, measured in $\mathrm{cm^3}$ or $\mathrm{dm^3}$ .

Experiment: the density of a stone

Weigh a small, dry stone on a balance and record its mass (Figure 1.1, step 1).
Pour water into a 100 cm³ measuring cylinder up to about the 50 cm³ mark and read the volume exactly, with your eye level with the bottom of the meniscus (step 2).
Tie a thread round the stone and lower it gently into the water until it is covered. Read the new volume (step 3).
The rise in the water level is the volume of the stone.

Figure 1.1: Finding the volume of an irregular solid by displacement of water.

Warning

Safety and accuracy. Lower the stone on a thread; a stone dropped into a glass cylinder can crack or break it. Choose a stone that fits easily and does not float or dissolve. Wipe up spilled water at once so nobody slips.

Density

The density of a substance is its mass per unit volume:

$\rho = \frac{m}{V}$

where $\rho$ (the Greek letter "rho") is the density, $m$ the mass and $V$ the volume. With mass in grams and volume in cubic centimetres, density is in grams per cubic centimetre, $\mathrm{g\,cm^{-3}}$ . The same formula can be rearranged to give $m = \rho V$ or $V = \frac{m}{\rho}$ .

Definition

Density: the mass of one unit of volume of a substance, $\rho = \frac{m}{V}$ , in $\mathrm{g\,cm^{-3}}$ . Example: pure water has a density of $1.00\,\mathrm{g\,cm^{-3}}$ : every cubic centimetre has a mass of 1.00 g.

Worked example

Problem. Use the results in Figure 1.1 to find the density of the stone. Will it float in water?

Solution.

Volume of the stone $V = 75\,\mathrm{cm^3} - 50\,\mathrm{cm^3} = 25\,\mathrm{cm^3}$ .
Density $\rho = \frac{m}{V} = \frac{65.0\,\mathrm{g}}{25\,\mathrm{cm^3}} = 2.6\,\mathrm{g\,cm^{-3}}$ .
Compare with water: $2.6\,\mathrm{g\,cm^{-3}} > 1.00\,\mathrm{g\,cm^{-3}}$ .

Answer: $2.6\,\mathrm{g\,cm^{-3}}$ . It is denser than water, so it sinks.

Worked example

Problem. Ethanol has a density of $0.79\,\mathrm{g\,cm^{-3}}$ . What is the mass of $250\,\mathrm{cm^3}$ of ethanol?

Solution. Rearrange the formula: $m = \rho V = 0.79\,\mathrm{g\,cm^{-3}} \times 250\,\mathrm{cm^3} = 197.5\,\mathrm{g}$

Answer: about 198 g, less than the 250 g that the same volume of water would weigh.

Table 1.1: Densities of some substances

Substance	State at room temperature	Density in $\mathrm{g\,cm^{-3}}$
Air	gas	0.0012
Ethanol	liquid	0.79
Cooking oil	liquid	about 0.92
Ice	solid	0.92
Water	liquid	1.00
Aluminium	solid	2.70
Iron	solid	7.87
Gold	solid	19.3

Tip

Anything less dense than a liquid floats on it; anything denser sinks. That is why cooking oil floats on water in a sauce pan, and why ice floats on a drink.

The three states of matter

Each state has its own properties, which you can observe without any special equipment (Table 1.2). The reason for the differences lies in the particles that make up matter (Figure 1.2), which you will study in the next lesson.

Table 1.2: Properties of the three states

Property	Solid	Liquid	Gas
Shape	fixed	takes the shape of its container	fills the whole container
Volume	fixed	fixed	not fixed: fills any container
Can it be squashed (compressed)?	hardly	hardly	easily
Does it flow?	no	yes	yes, in all directions
Density	usually high	usually high	very low
Examples	stone, ice, salt	water, milk, petrol	air, steam, methane

Figure 1.2: The arrangement of particles in the three states.

Definition

States of matter: the three forms in which a substance can exist: solid (fixed shape and volume), liquid (fixed volume, takes the shape of its container) and gas (no fixed shape or volume). Example: water exists as ice, liquid water and steam.

Density in Rwanda

A 20-litre jerrycan full of water has a mass of about 20 kg, because 1 cm³ of water has a mass of 1 g and 20 L is 20,000 cm³. Filled with petrol, the same jerrycan would be lighter, about 15 kg, because petrol is less dense. In Lake Kivu, the deep water contains more dissolved salts than the surface water, so it is denser and stays at the bottom instead of mixing upwards; that is one reason the dissolved gases stay trapped deep down.

Warning

Common mistake: saying that iron is "heavier" than wood. A large log is heavier than an iron nail! Iron is denser: any piece of iron has more mass than the same volume of wood.

FuseSchool: Density Of Different States (4 min). Watch how the spacing of the particles explains why gases have such low densities.

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Practice

Write the formula for density and give its unit when mass is in grams and volume in cubic centimetres.
A block of wood has a mass of 120 g and a volume of 200 cm³. Find its density. Does it float on water?
The water in a measuring cylinder rises from 40 cm³ to 52 cm³ when a key is lowered in. What is the volume of the key?
The key in question 3 has a mass of 102 g. Find its density and use Table 1.1 to suggest what metal it is made of.
Gold has a density of $19.3\,\mathrm{g\,cm^{-3}}$ . What is the mass of a 5.0 cm³ piece of gold?
Give two properties of a gas that are different from those of a liquid.
A trader says a 1 L bottle of cooking oil should weigh the same as a 1 L bottle of water. Is she right? Explain using densities.

Show answersHide answers

$\rho = \frac{m}{V}$ ; $\mathrm{g\,cm^{-3}}$ .
$\rho = \frac{120}{200} = 0.60\,\mathrm{g\,cm^{-3}}$ ; it is less dense than water, so it floats.
$52 - 40 = 12\,\mathrm{cm^3}$ .
$\rho = \frac{102}{12} = 8.5\,\mathrm{g\,cm^{-3}}$ : closest to iron (in fact brass or steel), not aluminium.
$m = \rho V = 19.3 \times 5.0 = 96.5\,\mathrm{g}$ .
Any two: a gas has no fixed volume; it can be compressed easily; it fills its whole container; it has a much lower density.
No. Oil (about $0.92\,\mathrm{g\,cm^{-3}}$ ) is less dense than water ( $1.00\,\mathrm{g\,cm^{-3}}$ ), so 1 L of oil has a mass of about 920 g, less than the 1000 g of 1 L of water.

Sources and credits

Chemistry 2e, 1.4: Measurements (density, its formula and units, and finding a volume by displacement of water) by Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson, OpenStax, via LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Chemistry 2e, 1.2: Phases and Classification of Matter (the properties of solids, liquids and gases) by Paul Flowers, Klaus Theopold, Richard Langley and William R. Robinson, OpenStax, via LibreTexts, licensed under CC BY 4.0. Adapted by Ganzaa.
Physical Sciences Grade 10, Chapter 3: States of matter and the kinetic molecular theory (the three states of matter) by Siyavula Education and volunteers, Siyavula, licensed under CC BY 3.0. Adapted by Ganzaa.
Image: Pumice Floating in Water.JPG by Outlookxp, via Wikimedia Commons, licensed under CC BY-SA 4.0.
Video: Density Of Different States, FuseSchool - Global Education, embedded from YouTube.
The diagrams, worked examples, Practice items and exercises were written and drawn by Ganzaa.

This lesson adapts CC BY-SA material and is shared under CC BY-SA 4.0.

1Why does one stone float?

2Experiment: the density of a stone

3Density

4The three states of matter

5Density in Rwanda

Why does one stone float?

Experiment: the density of a stone

Density

The three states of matter

Density in Rwanda