OCR Specification focus:
‘Use a simple kinetic model to explain the macroscopic properties of solids, liquids and gases.’
The simple kinetic model of matter explains the observable properties of solids, liquids, and gases by describing how the motion and energy of their particles differ.
The Particle Model of Matter
The simple kinetic model is based on the assumption that all matter is made up of tiny particles (atoms or molecules) that are in constant motion. These particles interact through forces of attraction and repulsion, and their behaviour determines the macroscopic (large-scale) properties such as shape, volume, and pressure.
Key Assumptions of the Kinetic Model
Matter is composed of a large number of small particles.
The particles are in continuous random motion.
Collisions between particles, and with the walls of a container, are perfectly elastic (no net loss of kinetic energy).
The volume of the particles themselves is negligible compared to the space between them (especially in gases).
The average kinetic energy of particles depends only on the temperature of the system.
These assumptions allow us to link microscopic particle motion to macroscopic properties such as pressure and temperature.
Solids, Liquids, and Gases in the Kinetic Model
The kinetic model provides a unified framework for describing the three main states of matter, focusing on particle spacing, ordering, and motion.
Diagram comparing particle arrangements in a solid (ordered lattice with vibrations), liquid (close-packed but disordered, particles sliding past each other), and gas (widely spaced, random motion). This visual supports how microscopic structure determines shape, volume, and flow. Labels are minimal and appropriate for OCR A-level coverage. Source.
Solids
Particles are closely packed in a regular, ordered lattice structure.
Strong intermolecular forces hold the particles in fixed positions.
Particles vibrate about fixed points but do not move freely.
Solids have a definite shape and fixed volume.
The energy of particles in a solid is mostly potential energy, associated with the strong attractive forces between them. Increasing temperature increases vibrational kinetic energy, leading eventually to melting when the structure breaks down.
Liquids
Particles are close together, but the arrangement is irregular.
Intermolecular forces are weaker than in solids, allowing particles to move past one another.
Liquids have a definite volume but no fixed shape, taking the shape of their container.
Motion is random and fluid, with frequent collisions between particles.
The balance between kinetic and potential energy in liquids explains their ability to flow and their viscosity, which depends on the strength of intermolecular attractions.
Gases
Particles are widely spaced and move freely and rapidly in all directions.
Intermolecular forces are negligible except during collisions.
Gases have no fixed shape or volume and expand to fill their container.
The motion of particles is random and highly energetic.
Because the particles are so far apart, the kinetic energy of gas molecules dominates over their potential energy. The macroscopic pressure exerted by a gas results from collisions of particles with the walls of the container.
A single gas molecule strikes a rigid wall; the normal component of momentum reverses, exerting a force on the wall. Many such collisions per unit area produce the pressure we measure. The arrows clarify velocity before/after collision and the force direction. Source.
Pressure and the Kinetic Model
The pressure of a gas can be explained by the collisions of gas particles with container walls.
EQUATION
—-----------------------------------------------------------------
Pressure of an Ideal Gas (pV = nRT)
p = Pressure (Pa)
V = Volume (m³)
n = Number of moles
R = Gas constant (8.31 J mol⁻¹ K⁻¹)
T = Absolute temperature (K)
—-----------------------------------------------------------------
This ideal gas equation is derived from kinetic theory and links microscopic particle motion to measurable macroscopic quantities. It assumes ideal conditions where intermolecular forces are negligible and collisions are perfectly elastic.
A useful kinetic interpretation also relates average molecular kinetic energy to temperature:
EQUATION
—-----------------------------------------------------------------
Average Kinetic Energy per Molecule (Ek = 3/2 kT)
Ek = Average kinetic energy (J)
k = Boltzmann constant (1.38 × 10⁻²³ J K⁻¹)
T = Absolute temperature (K)
—-----------------------------------------------------------------
This relationship shows that the temperature of a substance is directly proportional to the average kinetic energy of its particles.
Microscopic Explanation of Macroscopic Properties
Density
Density differences between solids, liquids, and gases can be explained by particle spacing:
Solids: particles are close together → high density.
Liquids: slightly less tightly packed → moderate density.
Gases: particles are far apart → low density.
Diffusion
Diffusion is the spreading of particles from regions of high concentration to low concentration due to their random motion.
Diffusion: The net movement of particles from an area of higher concentration to an area of lower concentration as a result of random motion.
Diffusion is faster in gases than in liquids because gas particles move more rapidly and have larger mean free paths.
Pressure–Temperature Relationship
As the temperature of a gas increases, the average kinetic energy of particles rises. This results in:
More frequent and forceful collisions with the container walls.
A higher pressure, if the volume remains constant.
This behaviour is summarised by Gay-Lussac’s law, one of the gas laws derived from kinetic theory.
Phase Transitions
Changes of state — such as melting, boiling, or condensation — can be explained by changes in the energy and arrangement of particles.
When energy is supplied to a solid, vibrational motion increases until intermolecular forces are overcome, allowing particles to move more freely (melting).
In boiling, particles gain enough energy to escape attractive forces and move freely as gas molecules.
During these transitions, temperature remains constant, but internal energy increases due to the work done in overcoming forces.
Energy Distribution and Temperature
The kinetic model also supports the Maxwell–Boltzmann distribution, which describes how particle speeds are distributed at a given temperature.
Plot of Maxwell–Boltzmann speed distributions for several temperatures, showing the peak shift and broadening as T increases. This clarifies that higher temperature means a larger fraction of fast-moving molecules. The figure includes labelled axes and markers for characteristic speeds; these extra annotations extend beyond syllabus minimum but aid interpretation. Source.
Most particles have speeds near the most probable value, but some move much faster or slower. When temperature rises, the entire distribution shifts towards higher energies, meaning a greater fraction of particles have enough energy to overcome attractive forces and cause evaporation or chemical reactions.
Limitations of the Simple Kinetic Model
Although powerful, the simple kinetic model has limitations:
It treats particles as point masses with no volume.
It ignores intermolecular forces except during collisions.
It assumes collisions are perfectly elastic, which is not entirely true in real gases.
Real substances deviate from ideal behaviour at high pressures and low temperatures, where intermolecular forces become significant and the assumptions of the simple kinetic model break down. Nonetheless, the model provides an essential foundation for understanding thermal physics and the link between microscopic motion and macroscopic behaviour in matter.
FAQ
Temperature is a measure of the average kinetic energy of the particles in a substance. In the simple kinetic model, higher temperature means that particles move faster, increasing both their speed and energy of motion.
Because temperature reflects the mean kinetic energy, not all particles move at the same speed. The distribution of speeds broadens with rising temperature, meaning some molecules move much faster while others remain slow.
This microscopic interpretation links temperature directly to particle motion rather than simply how “hot” something feels.
Elastic collisions ensure that kinetic energy is conserved when molecules collide. This simplifies analysis because total energy remains constant, allowing predictions of gas pressure and temperature without accounting for energy loss.
In real gases, collisions are nearly elastic at low pressures and moderate temperatures, when intermolecular forces are weak. At high pressures or low temperatures, small deviations occur as some energy converts to potential energy during interactions.
The simple kinetic model assumes negligible intermolecular forces and particle volume. Real gases deviate when these assumptions fail.
Deviations occur when:
Pressure is high, so particles are close enough for their finite size to matter.
Temperature is low, so attractive forces slow molecules and reduce pressure compared to ideal predictions.
Such deviations are described by the Van der Waals equation, which introduces correction terms for molecular size and attraction.
At a fixed temperature, all gases have the same average kinetic energy, but lighter molecules move faster than heavier ones because Ek = ½mv².
Low-mass gases (e.g., helium, hydrogen) have higher root mean square speeds, leading to faster diffusion and effusion rates.
Heavier gases move more slowly, giving narrower Maxwell–Boltzmann distributions.
Thus, molecular mass determines the shape and spread of the speed distribution without affecting the total kinetic energy at a given temperature.
The model provides a molecular explanation for Boyle’s law. At constant temperature, when volume decreases, molecules collide more often with container walls, increasing pressure.
The assumptions that collisions are elastic and that molecules occupy negligible volume make this proportional relationship clear:
Smaller volume → more frequent collisions → higher pressure.
Larger volume → fewer collisions → lower pressure.
This microscopic view links measurable macroscopic behaviour to particle dynamics, reinforcing the predictive power of the ideal gas law.
Practice Questions
Question 1 (2 marks)
State two key assumptions of the simple kinetic model of a gas.
Mark scheme:
1 mark for each correct assumption (maximum 2 marks).
Accept any two of the following:
Gas consists of a large number of particles (atoms or molecules).
The particles are in constant random motion.
Collisions between particles (and with the walls of the container) are perfectly elastic.
The volume of the particles themselves is negligible compared to the total volume of the gas.
The average kinetic energy of the particles depends only on temperature.
Question 2 (5 marks)
Using the simple kinetic model, explain how the pressure of an ideal gas arises and how it changes with temperature at constant volume.
Mark scheme:
(1 mark) Gas molecules move in random directions with a range of speeds.
(1 mark) When molecules collide with the walls of the container, they exert a force due to the change in momentum on impact.
(1 mark) The total pressure is the result of many molecular collisions per unit area per second on the walls.
(1 mark) As temperature increases, the average kinetic energy of the molecules increases (Ek = 3/2 kT).
(1 mark) Increased molecular speeds cause more frequent and forceful collisions, producing a higher pressure at constant volume.
