IMAT Chemistry · States of Matter and Gas Laws

Solids, Liquids, Gases and the Kinetic Model

Matter is made of particles in constant motion; how close they are and how freely they move decides the state, and their average kinetic energy is set by the absolute temperature.

All States of Matter and Gas Laws notes

Why this matters

The 2023 ministry paper asked why a kilogram of ice takes up more room than a kilogram of liquid water. The 2018 and 2021 papers asked how the kinetic energy of molecules changes when the temperature changes.

Concept 1 of 3: The three states of matter in the particle model

Every substance is made of tiny particles (atoms, molecules or ions) that never stop moving. Forces of attraction pull them together; their motion pulls them apart. In a solid the attractions win, in a gas the motion wins, and a liquid sits in between.

Definition

The kinetic model (kinetic theory) of matter says:

All matter is made of particles that are always moving.
In a solid the particles are packed closely in fixed positions and vibrate about those positions.
In a liquid the particles are still close together but can slide past one another, so a liquid flows.
In a gas the particles are far apart and move fast and randomly in straight lines between collisions.
Heating a substance gives its particles more kinetic energy; this is what eventually overcomes the attractions and changes the state.

State	Arrangement and spacing	Motion of particles	Shape and volume	Compressible?
Solid	Close together, usually in a regular pattern	Vibrate about fixed positions	Fixed shape and fixed volume	Almost not at all
Liquid	Close together, no regular pattern	Move around and slide past one another	Takes the shape of the container, fixed volume	Almost not at all
Gas	Far apart, random	Fast, random, straight lines between collisions	Fills the whole container	Very easily

A gas at room conditions is mostly empty space: the gaps between molecules are about ten times the size of the molecules.

Practice this conceptself-check · 3 quick reps

Particles in a solid still move

Particles in a solid are not still. They vibrate about fixed positions, and they vibrate more as the solid gets hotter. Options saying the particles of a solid have no kinetic energy are wrong.

Concept 2 of 3: Absolute temperature and the average kinetic energy of particles

Temperature is a measure of how fast the particles are moving on average. The Celsius scale puts its zero at the melting point of ice, which is an arbitrary choice. The kelvin scale puts its zero where the particle motion would be at its minimum, so on that scale the average kinetic energy is directly proportional to the number.

Definition

The kelvin (K) is the SI unit of temperature. Absolute zero, 0 K, is $-273.15\ ^\circ\text{C}$ .
A temperature step of 1 K is the same size as a step of 1 °C, so only the zero point differs.
The average kinetic energy of the particles is directly proportional to the absolute temperature. Doubling the kelvin temperature doubles it; doubling the Celsius temperature does not.
At the same temperature, all gases have the same average kinetic energy per molecule. Heavier molecules therefore move more slowly.
For a gas, the average kinetic energy per molecule is $\tfrac{3}{2}k_B T$ , where $k_B$ is the Boltzmann constant.

Kelvin from Celsius, and kinetic energy

T\,(\text{K}) = \theta\,({}^{\circ}\text{C}) + 273.15 \qquad \bar{E}_k \propto T

$T$ absolute temperature, in K
$\theta$ temperature in degrees Celsius (IMAT often uses 273 instead of 273.15)
$\bar{E}_k$ average kinetic energy of the particles

Worked example

A sample of argon is at

-73\ ^\circ\text{C}

. To what Celsius temperature must it be heated so that the average kinetic energy of its atoms becomes 1.5 times larger?

Practice this conceptself-check · 4 quick reps

Only kelvin temperatures can be used in ratios

Going from 20 °C to 40 °C does not double the kinetic energy: in kelvin it is 293 K to 313 K, a rise of under 7%. Any calculation where the answer depends on a ratio of temperatures must use kelvin.

At the same temperature, heavier molecules are slower, not more energetic

All gases at the same temperature have the same average kinetic energy per molecule. Since

E_k = \tfrac{1}{2}mv^2

, the heavier molecules move more slowly.

Concept 3 of 3: Water is unusual: ice is less dense than liquid water

For most substances the solid is the most tightly packed state. Water is different because of hydrogen bonding. In ice every molecule is held by hydrogen bonds in an open, cage-like lattice with a lot of empty space. When ice melts, part of that lattice collapses and the molecules crowd closer together.

Definition

Ice is less dense than liquid water: about 0.92 g/cm³ against about 1.00 g/cm³. So the same mass of ice has a larger volume (about 9% more), and ice floats.
The reason is the open hexagonal lattice of hydrogen-bonded molecules in ice: the particles are further apart in ice than in the liquid.
Liquid water is densest at about 4 °C. Below 4 °C it expands again as it cools.
Ice and water at 0 °C have the same average kinetic energy (same temperature). The energy taken in on melting goes into breaking hydrogen bonds, not into speeding the molecules up.
Consequences: ponds freeze from the top down, water in a sealed bottle or a pipe can burst it on freezing, and higher pressure slightly lowers the melting point of ice.

Property	Ice at 0 °C	Liquid water at 0 °C
Density	About 0.92 g/cm³	About 1.00 g/cm³
Volume of 1 kg	About 1.09 L	About 1.00 L
Arrangement	Open lattice held by hydrogen bonds; molecules further apart	Some hydrogen bonds broken; molecules packed closer
Average kinetic energy	Same as the liquid at 0 °C	Same as the ice at 0 °C

Water is one of very few substances whose solid floats on its own liquid.

Practice this conceptself-check · 3 quick reps

The solid is not always the densest state

For most substances the solid is denser than the liquid, but water is the exception: ice is less dense than liquid water because its molecules are further apart. The explanation is the spacing of the molecules, not their kinetic energy.

Summary — formulas & gotchas at a glance

A revision cheat-sheet for the formulas and gotchas above. Click any concept name to jump back to its full explanation.

Formulas (1)

Absolute temperature and the average kinetic energy of particles
Kelvin from Celsius, and kinetic energy
$T\,(\text{K}) = \theta\,({}^{\circ}\text{C}) + 273.15 \qquad \bar{E}_k \propto T$

Reference tables (2)

The three states of matter in the particle model3 rows

State	Arrangement and spacing	Motion of particles	Shape and volume	Compressible?
Solid	Close together, usually in a regular pattern	Vibrate about fixed positions	Fixed shape and fixed volume	Almost not at all
Liquid	Close together, no regular pattern	Move around and slide past one another	Takes the shape of the container, fixed volume	Almost not at all
Gas	Far apart, random	Fast, random, straight lines between collisions	Fills the whole container	Very easily

A gas at room conditions is mostly empty space: the gaps between molecules are about ten times the size of the molecules.

Water is unusual: ice is less dense than liquid water4 rows

Property	Ice at 0 °C	Liquid water at 0 °C
Density	About 0.92 g/cm³	About 1.00 g/cm³
Volume of 1 kg	About 1.09 L	About 1.00 L
Arrangement	Open lattice held by hydrogen bonds; molecules further apart	Some hydrogen bonds broken; molecules packed closer
Average kinetic energy	Same as the liquid at 0 °C	Same as the ice at 0 °C

Water is one of very few substances whose solid floats on its own liquid.

Watch out for (4)

Particles in a solid still move
→ The three states of matter in the particle model
Only kelvin temperatures can be used in ratios
→ Absolute temperature and the average kinetic energy of particles
At the same temperature, heavier molecules are slower, not more energetic
→ Absolute temperature and the average kinetic energy of particles
The solid is not always the densest state
→ Water is unusual: ice is less dense than liquid water

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