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Topic 2.1 · Unit 2

Kinetic particle model of matter

How the arrangement, separation and motion of particles explain solids, liquids and gases, gas pressure, Brownian motion and the kelvin scale of temperature.

In this topic

  1. 2.1.1States of matter
  2. 2.1.2Particle model
  3. 2.1.3Gases and the absolute scale of temperature

Key points

2.1.1 States of matter

  • The three states of matter are solid, liquid and gas.
  • A solid has a fixed shape and a fixed volume. It is very hard to compress (squash).
  • A liquid has a fixed volume, but no fixed shape. It flows and takes the shape of its container. It is very hard to compress.
  • A gas has no fixed shape and no fixed volume. It spreads out to fill its container. It is easy to compress.
State Shape Volume Can it flow? Can it be compressed?
solid fixed fixed no no (very hard)
liquid takes the shape of the container fixed yes no (very hard)
gas fills the container fills the container yes yes (easily)
  • The names of the changes of state:
    • melting: solid → liquid
    • solidification (freezing): liquid → solid
    • boiling or evaporation: liquid → gas
    • condensation: gas → liquid
  • A change directly between solid and gas is not needed for this syllabus.

2.1.2 Particle model

  • All matter is made of tiny particles (atoms, molecules or ions). The kinetic particle model says that these particles are always moving.
  • Solid: the particles are very close together. They are arranged in a regular pattern. They vibrate about fixed positions.
  • Liquid: the particles are close together, but not in a regular pattern. They move around and slide past each other.
  • Gas: the particles are far apart, with no pattern. They move quickly in random directions. They travel in straight lines between collisions.
  • To draw simple particle diagrams, use circles of the same size for the particles:
    • solid: circles touching, in neat rows
    • liquid: circles mostly touching, in an irregular arrangement, with a few small gaps
    • gas: a few circles, far apart, spread randomly over the space
  • When the temperature rises, the particles move faster.
  • When the temperature falls, the particles move more slowly.
  • There is a lowest possible temperature. It is −273 °C, called absolute zero. At absolute zero, the particles have the least kinetic energy they can have.
  • The properties of a solid, liquid or gas depend on three things: the forces between its particles, the distances between them, and how the particles move. Here, particles can be atoms, molecules, ions or electrons. Extended
  • In a solid, the forces of attraction between particles are strong and the particles are very close. The forces hold each particle in a fixed position. So a solid keeps its shape and cannot be compressed. Extended
  • In a liquid, the particles are still close, and the forces are strong enough to keep them close. So the volume is fixed. But the particles move fast enough to slide past each other. So a liquid flows. Extended
  • In a gas, the particles are far apart and the forces between them are very weak, except during collisions. The particles move freely and quickly. So a gas fills its container and is easy to compress. Extended
  • Gas pressure comes from the motion of the gas particles. The particles collide with the walls of the container and bounce off.
  • Each collision pushes on the wall. A very large number of collisions every second gives a steady push, which we measure as pressure.
  • More collisions each second, or harder collisions, give a higher pressure.
  • When a gas particle hits a surface and bounces back, it exerts a force on the surface. Extended
  • The total force from all the collisions, divided by the area of the surface, is the pressure. So gas pressure is a force per unit area (p = F / A, see 1.8). Extended
  • Microscopic particles are particles big enough to see with a microscope, such as smoke particles in air or pollen grains in water. A suspension is a liquid or gas with such particles spread through it.
  • Microscopic particles in a suspension move in a random, zig-zag way. This is called Brownian motion.
  • Brownian motion is evidence for the kinetic particle model. It shows that the particles of the gas or liquid are moving.
  • Why it happens: the particles of the gas or liquid are moving fast in random directions. They collide with the microscopic particle from all sides.
  • At any moment, the collisions on one side are not balanced by the collisions on the other side. So the microscopic particle is pushed in one direction. A moment later it is pushed in another direction. This gives the random, zig-zag motion.
  • Example: in a smoke cell, smoke particles in air are seen through a microscope. They look like bright specks of light that jiggle about randomly.
  • The air or water molecules are light and move fast. A microscopic particle is much bigger and heavier. Many collisions with these light, fast molecules move it. Extended
  • Use the words carefully. Atoms and molecules are far too small to see with the light microscope used in this experiment. The things we see moving are the microscopic particles (smoke or pollen), not the molecules. Extended

2.1.3 Gases and the absolute scale of temperature

  • These two points are for a fixed mass of gas, which means no gas gets in or out.
  • Temperature rises, volume stays constant: the particles move faster. They hit the walls more often and harder. So the pressure increases.
  • Volume decreases, temperature stays constant: the particles move at the same speeds as before. But they are closer together, so they hit each part of the wall more often. So the pressure increases.
  • The opposite changes (cooling, or a larger volume) make the pressure decrease.
  • The kelvin (K) scale is the absolute scale of temperature. It starts at absolute zero: 0 K = −273 °C.
  • To convert: T (in K) = θ (in °C) + 273. To go from kelvin to degrees Celsius, subtract 273.
  • So 0 °C = 273 K, and 100 °C = 373 K.
  • A temperature change of 1 K is the same as a change of 1 °C.
  • Write temperatures on this scale as “300 K”, not “300 °K”.
  • For a fixed mass of gas at constant temperature, pressure × volume stays the same: pV = constant. Extended
  • So for a starting state 1 and a final state 2: p1V1 = p2V2. If the volume halves, the pressure doubles. Extended
  • A graph of p against V is a curve. The pressure falls as the volume rises, but the line never reaches either axis. Every point on the curve has the same value of p × V. Extended
  • A graph of p against 1/V is a straight line through the origin. This shows that p is inversely proportional to V. Extended

Model

Particles in solids, liquids and gases: compare the arrangement, separation and motion of the particles in each state. Then change the temperature and the volume of the gas and watch the pressure.

3D modelParticles in solids, liquids and gases
Particles in solids, liquids and gasesOpen full screen: Particles in solids, liquids and gases

Equations

  • Kelvin and Celsius

    T (in K) = θ (in °C) + 273

    T = temperature in kelvin (K); θ = temperature in degrees Celsius (°C)

  • Gas at constant temperatureExtended

    pV = constant

    p = pressure of the gas (Pa); V = volume of the gas (m3); true for a fixed mass of gas at constant temperature, so p1V1 = p2V2

Kelvin and Celsius

Convert 27 °C to kelvin. Then convert 350 K to degrees Celsius.

  • T = θ + 273
  • T = 27 + 273
  • T = 300 K
  • For the second part, rearrange: θ = T − 273
  • θ = 350 − 273
  • θ = 77 °C
  • A gas warms from 27 °C to 77 °C. Its temperature rise is 50 °C, which is also 50 K.

Gas at constant temperature Extended

A syringe holds 60 cm3 of air at a pressure of 100 kPa. The end is sealed. The plunger is pushed in slowly until the volume is 40 cm3. The temperature does not change. Find the new pressure.

  • Given: p1 = 100 kPa, V1 = 60 cm3, V2 = 40 cm3
  • Fixed mass of gas at constant temperature, so p1V1 = p2V2
  • 100 × 60 = p2 × 40
  • p2 = 6000 ÷ 40
  • p2 = 150 kPa
  • Both volumes are in cm3, so there is no need to convert them to m3. The units cancel.

A gas has a volume of 3.0 m3 at a pressure of 200 kPa. At constant temperature, its pressure falls to 150 kPa. Find its new volume.

  • Given: p1 = 200 kPa, V1 = 3.0 m3, p2 = 150 kPa
  • V2 = p1V1 ÷ p2
  • V2 = 200 × 3.0 ÷ 150
  • V2 = 4.0 m3
  • Check: the pressure went down, so the volume went up.

Common mistakes

  • Students write that the particles in a solid do not move. / The mark scheme wants: the particles vibrate about fixed positions.
  • Students write that gas pressure rises because the particles collide with each other more. / The mark scheme wants collisions with the walls of the container: more often, and (if the temperature rises) harder.
  • Students write that the volume decreases, so the particles move faster. / The mark scheme wants: at constant temperature the particles move at the same speed; they hit the walls more often because there is less space.
  • Students subtract 273 to change °C into kelvin. / The mark scheme wants: add 273 to change °C into K; subtract 273 to change K into °C.
  • Students write that Brownian motion shows the air molecules moving. / The mark scheme wants: we see the microscopic particles (for example smoke) moving; they are hit by air molecules, which are too small to see with the microscope. Extended
  • Students use pV = constant when the temperature changes. / The mark scheme wants the conditions: a fixed mass of gas at constant temperature. Extended

Exam tips

  • Describe the particles in a state with three ideas: arrangement (pattern or no pattern), separation (close or far apart) and motion (vibrate, slide past each other, or move fast and randomly). Each idea is usually worth a mark.
  • Draw particle diagrams with circles of the same size. Make solid particles touch in rows. Make gas particles far apart.
  • Explain a pressure change in steps: what happens to the speed of the particles → how often and how hard they hit the walls → what happens to the pressure.
  • Explain Brownian motion with these words: random, collisions, uneven (more hits on one side), fast-moving molecules.
  • Calculate with pV = constant: write p1V1 = p2V2, substitute, then check that the answer makes sense (smaller volume → larger pressure). Extended
  • Sketch the p–V graph as a smooth curve that gets closer to each axis but never touches it. Do not draw a straight line. Extended
  • A typical 1-mark answer: “Absolute zero is −273 °C, the temperature at which the particles have the least kinetic energy.”
  • A typical 2-mark answer to “Why does the pressure in a tyre rise on a hot day? Assume the volume of the tyre stays the same.”: “The air particles move faster (1). They hit the walls of the tyre more often and with more force (1).”
  • A typical 3-mark answer to “Explain the motion of smoke particles in a smoke cell”: “The air molecules move fast and randomly (1). They collide with the smoke particles (1). More collisions on one side than the other push the smoke particle in a random direction (1).”