0625 · 2.1Kinetic particle model of matter

Particle arrangements and states

0:00A sealed syringe contains air, but its plunger can still move inwards. The air takes up less space, and pushing becomes harder. The same syringe filled with water is much harder to compress. These everyday differences make sense when we look at how particles are arranged and how they move. In this video, we will connect the properties of solids, liquids and gases to their particles. We will explain temperature, gas pressure and the irregular movement called Brownian motion.

0:25Then we will use the absolute temperature scale and calculate how gas pressure changes with volume. The aim is to understand what each equation describes. We need two familiar ideas before starting. Kinetic energy is the energy an object has because of its motion. Pressure is force per unit area, so pressure equals force divided by area. The particle model connects these ideas by describing matter as particles that move and interact with one another.

0:52Start with properties that we can observe without seeing any particles. A solid has a fixed shape and a fixed volume. A liquid has a fixed volume but takes the shape of the part of its container that it occupies. A gas has neither a fixed shape nor a fixed volume and fills its container. Solids and liquids are difficult to compress. Their volumes hardly decrease when pressure increases. Gases are much easier to compress.

1:17These differences depend mainly on particle separation and freedom of movement. Our particle diagrams use circles to represent particles, rather than showing their actual appearance or size. In a solid, particles are close together and have a regular arrangement in the simple model. They vibrate about fixed positions rather than travelling freely through the solid. Forces between the particles hold them around those positions. This explains why a solid maintains its shape, even though its particles are moving.

1:45In a liquid, the particles are still close together, but their arrangement is irregular. They move around and slide past one another. This allows a liquid to flow and take the shape of its container. Because the particles remain close together, the liquid keeps approximately the same volume and is difficult to compress. Gas particles are widely separated and arranged randomly. They move rapidly in random directions, changing direction when they collide with other particles or surfaces.

2:11Their freedom of movement allows a gas to fill its container. The large spaces between particles also allow the gas to be compressed. Compression does not mean squeezing individual gas particles into smaller particles. It mainly means reducing the spaces between them. That is why a gas can undergo a large decrease in volume. Solids and liquids already have closely packed particles, leaving much less space that can be reduced.

2:34For the Supplement content studied at Extended level, connect these properties explicitly to forces, distances and motion. In solids, strong forces keep particles vibrating about fixed positions. In liquids, attractions keep particles close while allowing movement past one another. In gases, particles are far apart and attractions have little effect on their motion between collisions. The word particle is a general term in this model. Depending on the material, the particles involved may be atoms, molecules, ions or electrons.

3:05You are not expected to explain detailed structures here. The important point is that particle arrangement, separation, motion and forces affect the properties of matter. We can now name the changes between states. Melting changes a solid into a liquid, while freezing changes a liquid into a solid. Vaporisation changes a liquid into a gas and can happen through boiling or evaporation. Condensation changes a gas into a liquid. Ice melting into water and water freezing into ice are familiar examples.

3:34Water becoming water vapour is a liquid changing into a gas. Water vapour condensing forms liquid droplets, such as those on a cold window. The state changes, but the particles do not become a different substance. A common mistake is describing gas particles as larger than liquid particles. A particle diagram should show greater separation in the gas, not larger circles. Another mistake is drawing liquid particles almost as far apart as gas particles.

4:01Liquid particles remain close together, despite being able to move past one another.

Temperature and kelvin scale

4:06Temperature is connected to particle motion. As temperature increases, the average kinetic energy of particles increases. In a solid, this means more vigorous vibration about fixed positions. In a gas, the particles move faster on average. Individual particles do not all have the same speed. The word average matters because particles have a range of kinetic energies. A higher temperature does not mean every particle moves at one identical speed.

4:33It means the average kinetic energy is greater. Also, a solid that appears motionless still contains particles that are vibrating. There is a lowest possible temperature, called absolute zero. For this syllabus, its value is minus two hundred and seventy-three degrees Celsius. At absolute zero, particles have their least kinetic energy. Use that description rather than saying particles disappear or that all particle motion must stop. The kelvin scale starts at absolute zero, rather than at the freezing point of water.

5:03A temperature change of one kelvin has the same size as a change of one degree Celsius. The two scales therefore differ by a fixed offset. Temperature in kelvin equals temperature in degrees Celsius plus two hundred and seventy-three. For a first worked calculation, convert twenty-seven degrees Celsius into kelvin. We add two hundred and seventy-three because the kelvin zero lies that far below the Celsius zero. 27 + 273 = 300.

5:30The temperature is therefore three hundred kelvin, with no degree sign in the unit. Now convert two hundred and fifty kelvin into degrees Celsius. We reverse the conversion by subtracting two hundred and seventy-three. 250 − 273 equals minus twenty-three. The answer is minus twenty-three degrees Celsius, so a positive kelvin temperature can correspond to a negative Celsius temperature.

Explaining Brownian motion

5:55The particle model also explains an observation called Brownian motion. This is the random motion of microscopic particles in a suspension. A suspension contains small particles dispersed in a gas or liquid. Smoke particles suspended in air can be observed moving irregularly when viewed with suitable microscope equipment. The visible smoke particles are not the individual air molecules. Each smoke particle is much larger and contains many atoms or molecules.

6:20The air molecules are too small to see in this observation. Their effects become visible because they repeatedly collide with the larger smoke particles. Air molecules move rapidly in random directions and strike a smoke particle from different sides. At any instant, these collisions are not perfectly balanced. The resultant force moves the smoke particle in one direction. As the imbalance changes, its direction changes again, producing an irregular, unpredictable path.

6:47For Supplement, be especially careful with the names of the objects involved. Small molecules that move very quickly hit the larger microscopic particles. These collisions push the larger particles around. The visible particle is the object being knocked around, not the invisible molecule causing a collision. This distinction is essential when explaining a microscope observation. Brownian motion is evidence for the kinetic particle model of matter. The random movement of visible particles supports the idea that invisible gas or liquid particles are moving continually.

7:17Similar motion can occur for particles suspended in a liquid. Do not explain it as the smoke particle deliberately moving or moving under its own power.

Particle model of gas pressure

7:26Now connect particle motion to gas pressure. Gas particles repeatedly collide with the walls of their container. Each collision exerts a force on the wall. The combined effect of many collisions produces the pressure of the gas, even though individual collisions occur at different places and times. For Supplement, describe this explicitly as force per unit area. Pressure is the total force exerted on a surface divided by its area.

7:51More frequent collisions can increase the total force on the wall. More forceful collisions can also increase that force, producing a greater pressure on the same area. First consider a fixed mass of gas heated at constant volume. Fixed mass means no gas enters or leaves, while constant volume means the container does not expand. The particles gain average kinetic energy and move faster. They collide with the walls more frequently and more forcefully, so the pressure increases.

8:18Cooling the same gas at constant volume has the opposite effect. Its particles have less average kinetic energy and move more slowly. Wall collisions are less frequent and less forceful, so pressure decreases. The explanation concerns motion and collisions, not particles becoming larger when heated or smaller when cooled. Now decrease the volume of a fixed mass of gas while keeping its temperature constant. The average particle speed remains unchanged because the temperature stays the same.

8:46Particles travel shorter distances between encounters with the walls, increasing the frequency of wall collisions. The greater force per unit area means the pressure increases. Increasing the volume at constant temperature produces the opposite result. The same particles occupy a larger space and collide with the walls less frequently per unit area. The pressure therefore decreases. Always identify what is held constant, because heating a gas and compressing it involve different changes in particle behaviour.

Boyle’s law calculations and graphs

9:14The next relationship is Supplement content for Extended students. For a fixed mass of gas at constant temperature, pressure multiplied by volume is constant. This relationship is often called Boyle’s law. Pressure is inversely proportional to volume. If the volume decreases by some factor, the pressure increases by the same factor. Compare two states of the same gas under these conditions. Initial pressure multiplied by initial volume equals final pressure multiplied by final volume.

9:43Halving the volume therefore doubles the pressure. The equation works because the product stays unchanged, not because pressure and volume each stay unchanged. Consider a gas with an initial pressure of one hundred kilopascals and a volume of sixty cubic centimetres. It is compressed to twenty cubic centimetres without changing its temperature or mass. We need its final pressure. The volume becomes three times smaller, so we expect the pressure to become three times greater.

10:10First calculate the constant product by multiplying one hundred by sixty, giving six thousand. Next divide six thousand by the final volume of twenty. This gives a final pressure of three hundred kilopascals. The result agrees with our prediction, and using the same volume units throughout makes the calculation consistent. For another example, a gas initially has a pressure of two hundred kilopascals and a volume of thirty cubic centimetres.

10:37Its pressure falls to seventy-five kilopascals at constant temperature. The lower pressure tells us that the final volume should be larger. We again use the unchanged pressure multiplied by volume. Multiply two hundred by thirty to obtain six thousand. Divide six thousand by seventy-five to find the final volume. The result is eighty cubic centimetres. This is larger than the initial volume, which agrees with the expected effect of decreasing pressure.

11:02The graph of pressure against volume is a curve that slopes downwards and becomes less steep, not a straight line. At small volumes, pressure is high, while at larger volumes, pressure is lower. Doubling the volume halves the pressure wherever you start on the curve. This is why the curve never reaches either axis. An alternative graph plots pressure against one divided by volume. This produces a straight line through the origin.

11:26Pressure is directly proportional to one divided by volume because pressure multiplied by volume is constant. Both graphs describe the same relationship for a fixed mass of gas at constant temperature.

Exam explanations and recap

11:37In an examination, the command word describe asks you to state what happens or what is observed. Explain asks you to give the physical reasons. For example, a question might ask you to explain why pressure rises when a sealed, rigid container of gas is heated. Build a chain from temperature to motion, collisions, force and pressure. The particles gain average kinetic energy and move faster. They collide with the container walls more frequently.

12:03Each collision exerts a greater force on average. The total force per unit area increases, so the pressure increases. Another question might ask you to explain the random movement of a smoke particle suspended in air. Fast-moving air molecules collide with the smoke particle. The collisions are uneven, producing a resultant force whose direction changes randomly. This causes the smoke particle to move irregularly. Watch for three errors when using the gas equation.

12:30The mass must remain fixed, so a leaking container does not meet the stated conditions. The temperature must remain constant, so heating during compression changes the situation. Pressure and volume are inversely related, rather than both increasing together. Let us bring the model together. Solids have closely packed particles vibrating about fixed positions, while liquid particles remain close but can move past one another. Gas particles are widely separated and move rapidly in random directions.

12:59These differences explain shape, volume, flow and compressibility. Higher temperature means greater average particle kinetic energy, while absolute zero is the lowest possible temperature. Brownian motion reveals the effects of invisible moving molecules through collisions with larger microscopic particles. Gas pressure comes from collisions exerting force per unit area. At constant temperature and fixed mass, pressure multiplied by volume remains constant.