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1.1.2 Kinetic particle theory of gases

Kinetic particle theory

Definition

Kinetic particle theory

The theory that all matter is made of tiny particles in constant motion, whose energy and forces of attraction explain the properties of solids, liquids and gases.

Definition

Kinetic energy

The energy that a particle has because it is moving.

Definition

Forces of attraction

The forces that pull neighbouring particles towards one another and hold them together in a solid or a liquid.

  1. Kinetic particle theory explains the behaviour of solids, liquids and gases using two ideas: the particles are always moving, and there are forces of attraction between neighbouring particles.
  2. A moving particle has kinetic energy, and the faster it moves the more kinetic energy it has.
  3. The temperature of a substance is a measure of the average kinetic energy of its particles, so a higher temperature means that the particles are moving faster on average.
  4. The forces of attraction are strongest in a solid, weaker in a liquid and very weak in a gas, because the particles are furthest apart in a gas.
  5. When a substance is heated, energy is transferred to its particles and is used in one of two ways.
    1. The energy can increase the kinetic energy of the particles, so they move faster and the temperature rises.
    2. The energy can overcome the forces of attraction between the particles, so they move further apart and the substance changes state while the temperature stays constant.
  6. When a substance is cooled, energy is transferred from its particles to the surroundings, so the particles slow down or are pulled closer together by the forces of attraction.
  7. The stronger the forces of attraction between the particles of a substance, the more energy is needed to separate them, so the higher its melting point and boiling point.

Explaining changes of state

  1. Melting
    1. As a solid is heated, its particles gain kinetic energy and vibrate more strongly about their fixed positions, so the temperature rises.
    2. At the melting point, the particles have enough energy to overcome some of the forces of attraction that hold them in fixed positions.
    3. The particles can then slide past one another, so the regular arrangement breaks down and a liquid forms.
    4. Energy must keep being taken in from the surroundings until all the solid has melted.
  2. Boiling
    1. As a liquid is heated, its particles gain kinetic energy and move faster, so the temperature rises.
    2. At the boiling point, particles throughout the liquid have enough energy to overcome the remaining forces of attraction between them.
    3. The particles separate and move far apart as a gas, forming bubbles of gas inside the liquid.
    4. Boiling needs far more energy than melting, because the particles must be separated completely rather than only freed from fixed positions.
  3. Evaporation
    1. The particles in a liquid do not all move at the same speed, so at any moment some of them have much more kinetic energy than the average.
    2. A particle at the surface that has enough kinetic energy can overcome the attractions of its neighbours and escape as a gas, even below the boiling point.
    3. The particles that escape are the most energetic ones, so the average kinetic energy of the particles left behind falls and the liquid cools down.
    4. This is why sweat evaporating from your skin cools you down on a hot day.
  4. Freezing
    1. As a liquid cools, its particles lose kinetic energy and move more slowly, so the temperature falls.
    2. At the freezing point, the forces of attraction pull the slow-moving particles into fixed positions in a regular arrangement.
    3. Energy is released to the surroundings as the particles settle into place, and this keeps the temperature constant until all the liquid has frozen.
  5. Condensation
    1. As a gas cools, its particles lose kinetic energy and move more slowly.
    2. When the particles are moving slowly enough, the forces of attraction pull them close together and the gas becomes a liquid.
    3. Energy is released to the surroundings while the gas condenses.
Common Mistake
  • Do not say that the particles themselves melt, expand or get bigger, because only their energy, movement and separation change.
  • Do not say that a change of state breaks the particles apart, because the particles stay whole and only the forces of attraction between them are overcome.

Heating and cooling curves

Definition

Heating curve

A graph of temperature against time for a substance that is heated at a steady rate.

Definition

Cooling curve

A graph of temperature against time for a substance that is losing thermal energy to its surroundings.

Definition

Freezing point

The temperature at which a liquid changes into a solid, which is the same temperature as the melting point for a pure substance.

  1. A heating curve is drawn by heating a substance at a steady rate and plotting its temperature on the vertical axis against time on the horizontal axis.
  2. A cooling curve is drawn in the same way while the substance cools.
  3. Each curve is made of two kinds of section.
    1. A sloping section shows that only one state is present and that the temperature of that state is changing.
    2. A horizontal section, called a plateau, shows that two states are present together and that the substance is changing state at a constant temperature.
  4. Reading a heating curve that starts with a solid
    1. In the first sloping section, only solid is present, and its particles vibrate more strongly as the temperature rises.
    2. At the first plateau, the solid is melting, so solid and liquid are both present and the temperature stays at the melting point.
    3. The temperature stays constant because the energy supplied overcomes forces of attraction instead of increasing the kinetic energy of the particles.
    4. In the second sloping section, only liquid is present, and its particles move faster as the temperature rises.
    5. At the second plateau, the liquid is boiling, so liquid and gas are both present and the temperature stays at the boiling point.
    6. The boiling plateau is longer than the melting plateau, because more energy is needed to separate the particles completely than to free them from fixed positions.
    7. In the final sloping section, only gas is present, and its particles move faster as the temperature rises.
  5. Reading a cooling curve that starts with a gas
    1. In the first sloping section, only gas is present, and its particles slow down as the temperature falls.
    2. At the first plateau, the gas is condensing, so gas and liquid are both present.
    3. In the second sloping section, only liquid is present, and it cools.
    4. At the second plateau, the liquid is freezing, so liquid and solid are both present and the temperature stays at the freezing point.
    5. The temperature stays constant during each plateau because energy is released as the forces of attraction pull the particles together, and this replaces the energy lost to the surroundings.
    6. In the final sloping section, only solid is present, and it cools.
  6. The melting plateau on a heating curve and the freezing plateau on a cooling curve occur at the same temperature for the same substance.
  7. The boiling plateau on a heating curve and the condensing plateau on a cooling curve also occur at the same temperature.

Heating curve graph of temperature versus heat added for water, showing solid, liquid, and gas states with horizontal plateaus at 0 °C for melting and freezing, and at 100 °C for boiling and condensation.

Example

Interpreting a cooling curve

  • Liquid X is cooled from 120 ∘C120\,^{\circ}\text{C}120∘C and its temperature is recorded every minute.
  • The temperature falls from 120 ∘C120\,^{\circ}\text{C}120∘C to 80 ∘C80\,^{\circ}\text{C}80∘C during the first 4 min4\ \text{min}4 min, so only liquid X is present and its particles are slowing down.
  • The temperature stays at 80 ∘C80\,^{\circ}\text{C}80∘C from 4 min4\ \text{min}4 min to 11 min11\ \text{min}11 min, so this plateau shows X freezing, with liquid and solid present together.
  • The freezing point of X is therefore 80 ∘C80\,^{\circ}\text{C}80∘C, which is also its melting point.
  • After 11 min11\ \text{min}11 min the temperature falls again, so all of X has become solid and the solid is cooling.
  • Room temperature, 25 ∘C25\,^{\circ}\text{C}25∘C, is below the melting point of X, so X is a solid at room temperature.
Practical

Obtaining a cooling curve

  • Aim: to record the temperature of a molten substance as it cools and freezes, and to use the cooling curve to find its freezing point.
  • Apparatus: a boiling tube about one third full of stearic acid, a 250 cm3250\ \text{cm}^3250 cm3 beaker of hot water at about 90 ∘C90\,^{\circ}\text{C}90∘C, a thermometer reading from −10 ∘C-10\,^{\circ}\text{C}−10∘C to 110 ∘C110\,^{\circ}\text{C}110∘C in 1 ∘C1\,^{\circ}\text{C}1∘C divisions, a clamp stand, a stopwatch and eye protection.
  • Method:
    • Stand the boiling tube in the beaker of hot water until all of the stearic acid has melted into a clear liquid.
    • Put the thermometer into the molten stearic acid and leave it until the temperature reaches about 85 ∘C85\,^{\circ}\text{C}85∘C.
    • Lift the boiling tube out of the water, dry the outside and clamp it upright in the air, away from draughts.
    • Start the stopwatch and record the temperature every 30 s30\ \text{s}30 s, reading the thermometer at eye level to the nearest 0.5 ∘C0.5\,^{\circ}\text{C}0.5∘C.
    • Stir gently with the thermometer while the stearic acid is still liquid, and stop stirring as soon as solid begins to form.
    • Note the time when solid first appears and the time when the stearic acid has become completely solid.
    • Continue recording until the temperature has fallen to about 50 ∘C50\,^{\circ}\text{C}50∘C.
    • Plot a graph of temperature / ∘C^{\circ}\text{C}∘C against time / min and join the points with a smooth curve.
  • Results: the temperature falls steadily at first, stays almost constant at about 69 ∘C69\,^{\circ}\text{C}69∘C for several minutes while the stearic acid freezes, and then falls again once all of it is solid.
  • Conclusion: the temperature of the plateau is the freezing point of stearic acid, which is also its melting point.
  • Sources of error: draughts change the rate of cooling, and a thermometer bulb that is not fully covered by the stearic acid gives readings that are too low.
  • Safety: wear eye protection, take care with the hot water and the hot molten stearic acid, and do not try to pull the thermometer out of the solid stearic acid, because it can snap.

Temperature and the volume of a gas

Definition

Gas pressure

The force that a gas exerts on each unit area of the walls of its container.

  1. In a gas the particles are far apart and the forces of attraction between them are very weak, so the particles move freely in straight lines at high speed.
  2. The particles continually collide with the walls of the container, and each collision pushes on the walls.
  3. These collisions with the walls are what produce gas pressure.
  4. The pressure is greater when the particles hit the walls more often or with more force.
  5. Heating a gas at constant pressure
    1. Heating gives the gas particles more kinetic energy, so they move faster.
    2. The faster particles hit the walls more often and with more force.
    3. In a container that can change size, such as a balloon or a gas syringe, these collisions push the walls outwards and the gas expands.
    4. As the gas expands, the particles spread further apart and hit each part of the walls less often.
    5. The gas stops expanding when its pressure has fallen back to the pressure of the surroundings, so at a higher temperature the gas takes up a larger volume.
  6. Cooling a gas at constant pressure
    1. Cooling lowers the kinetic energy of the particles, so they move more slowly and hit the walls less often and with less force.
    2. The pressure of the surroundings is now greater than the gas pressure, so the walls are pushed inwards and the gas contracts to a smaller volume.
  7. If the container cannot change size, heating the gas raises its pressure instead of its volume, which is why an aerosol can must never be heated.

Pressure and the volume of a gas

  1. Increasing the pressure at constant temperature
    1. Pushing in the plunger of a sealed syringe squeezes the same number of particles into a smaller volume.
    2. The temperature does not change, so the particles keep the same average kinetic energy and the same average speed.
    3. The particles are now closer together, so they hit each part of the walls more often and the gas pressure rises.
    4. The plunger stops moving when the gas pressure has risen to match the pressure pushing on the plunger, so a higher pressure gives a smaller volume.
  2. Decreasing the pressure at constant temperature
    1. When the pressure on the gas is reduced, the collisions of the particles push the walls outwards and the gas expands.
    2. The particles spread further apart and hit each part of the walls less often, until the gas pressure falls to match the lower pressure outside.
    3. A lower pressure therefore gives a larger volume.
Common Mistake

Do not explain gas pressure using collisions between the particles themselves, because the pressure comes from the particles colliding with the walls of the container.

Exam technique

Explaining gas and state changes

  • Mention the particles in every explanation, because an answer about "the gas" alone does not use kinetic particle theory.
  • For a temperature change, link the temperature to the kinetic energy and speed of the particles, then to how often and how hard they hit the walls.
  • For a pressure change at constant temperature, state that the speed of the particles does not change and that they hit the walls more or less often because they are closer together or further apart.
  • At each plateau on a heating or cooling curve, name both states that are present and state that the energy is used to overcome forces of attraction or is released as they pull particles together.
Self review
  • State what happens to the average kinetic energy of the particles when the temperature of a substance rises.
  • Explain why the temperature of a substance stays constant while it is melting.
  • Name the two states present during the boiling plateau of a heating curve.
  • Explain why evaporation cools the liquid that is left behind.
  • Explain, in terms of particles, why heating a gas at constant pressure increases its volume.
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Revision notes for CIE IGCSE Chemistry 1.1.2 Kinetic particle theory of gases: explanations and worked examples.

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