Theme B — The Particulate Nature of Matter
B.3.5 Kinetic Theory of Gases — IB Physics HL Revision Notes & Topical Questions
5 min read 11 parts Lesson 29 of 53 1 quiz
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Lesson summary
B.3.5 Kinetic Theory of Gases — IB PHYSICS SL notes: State the assumptions of the kinetic model of an ideal gas and use it to explain gas pressure and the gas laws.Kinetic theory — a modelled system that approximates the behaviour of real gases as atoms or molecules moving random…
- Elastic collisions
- Straight lines
- Force on the wall
- Faster molecules
- Mean square speed
- Definition
Part 1 of 9The aim of the model
Kinetic theory
- Kinetic theory a modelled system that approximates the behaviour of real gases as atoms or molecules moving randomly at high speeds.
Link
- Link it connects microscopic properties to macroscopic properties (pressure and volume).
- (mass and speed of particles)
Method
- Method apply Newton's laws to the particles and average over them.
Part 2 of 9Assumptions
1
A gas consists of many identical molecules, all with the same mass, in a container.
2
The volume of the molecules is negligible compared with the volume of the container, so they are point particles.
3
The molecules are in continuous random motion at high speeds.
4
The molecules obey Newton's laws of motion.
5
The molecules collide elastically with each other and with the walls.
6
There are no intermolecular forces except during collisions.
7
The time of a collision is negligible compared with the time between collisions.
8
External forces such as gravity are ignored.
9
The number of molecules is very large, so the average behaviour is considered.
10
Each particle exerts a force on the wall it collides with, and the average of these forces gives a uniform gas pressure.
Part 3 of 9Why the assumptions matter
Elastic collisions
- Elastic collisions otherwise the gas would lose energy and its temperature would fall.
No forces
- No forces the internal energy is entirely kinetic.
Straight lines
- Straight lines between collisions the molecules move at constant velocity.
Part 4 of 9Explaining pressure
Rebound
- Rebound for a molecule of mass m rebounding elastically, the velocity component perpendicular to the wall reverses and the momentum change is 2mvx.
Force on the wall
- Force on the wall by Newton's third law the wall receives an equal and opposite impulse.
Averaging
- Averaging billions of collisions per second give a constant force, and the pressure is the average force per unit area.
Faster molecules
- Faster molecules a larger momentum change per collision and more collisions per second, so a higher pressure.
Part 5 of 9Explaining the gas laws
| Law | Explanation |
|---|---|
| Boyle's law (constant T) | The average speed is the same; if the volume halves, molecules reach a wall twice as often and the pressure doubles |
| Pressure law (constant V) | Raising T raises the average kinetic energy, so molecules hit harder and more often and P rises in proportion to T |
| Charles's law (constant P) | When T rises, the volume must grow until the collision rate falls enough to keep the pressure constant |
Part 6 of 9Result of the model
Equation
- Equation p = ⅓ρ⟨c2⟩, or pV = ⅓Nm⟨c2⟩.
- ρ is the density of the gas in kg m−3.
- N is the number of molecules and m the mass of one molecule.
- ⟨c2⟩ is the mean square speed in m2 s−2.
Mean square speed
- Mean square speed the 'mean square' is an average over all molecules.
Part 7 of 9Root-mean-square speed
1Definition
- Definition crms = √⟨c2⟩, found by squaring each speed, averaging, and taking the root.
2Compared with the mean speed
- Compared with the mean speed it is slightly larger, because squaring emphasises large values.
3Result
- Result crms = √(3RT/M) = √(3kBT/m).
4Lighter molecules
- Lighter molecules they are faster at the same temperature; hydrogen is about four times faster than oxygen.
5Speed distribution
- Speed distribution a skewed curve with a single peak and a long tail;
- raising T moves the peak right and flattens it, with the area unchanged.
6Atmospheres
- Atmospheres light molecules are the most easily lost from a planet.
Part 8 of 9Real and ideal gases
1Real gases
- Real gases they do not always obey the ideal gas equation, because the assumptions may fail.
2Ideal approximation is good
- Ideal approximation is good at low pressure, low density and a temperature well above the boiling point.
3High pressure and density
- High pressure and density molecules are close, attractive forces act and their volume is not negligible.
4Low temperature
- Low temperature the gas can become a liquid.
5Further limit
- Further limit real molecules can rotate and vibrate and store energy that does not appear in the pressure.
6Success of the model
- Success of the model it explains pressure and temperature in terms of mechanics.
Part 9 of 9More from the specification
1Kinetic energy across gas moles
- Kinetic energy across gas moles calculating kinetic energy per mole of ideal gas particles provides a thermodynamic means to determine absolute temperature.
2Mole
- Mole an amount of substance containing 6.02 times 10 to the 23 particles, and molar mass links mass to amount
3Kinetic theory
- Kinetic theory pressure arises from molecular collisions with walls, and temperature is proportional to mean kinetic energy
4Ideal gas equation
- Ideal gas equation pV equals nRT, which can be rearranged for any quantity such as amount of argon or helium
5Final state
- Final state combined gas laws relate initial and final pressure, volume and temperature for a fixed amount
6Helium
- Product of the fusion of hydrogen in stars.
7Boltzmann constant
- K = R/NA, the gas constant per molecule
8Avogadro constant
- The number of particles per mole, 6.02 × 10²³ mol⁻¹
9Thermodynamic temperature
- The absolute temperature in kelvin.
10N = nNA
What the symbols mean: N = number of particles · n = amount (mol) · NA = Avogadro constant (6.02 × 1023 mol−1)
Key terms
| Term | Meaning |
|---|---|
| Kinetic theory of gases | Model explaining gas properties by random motion of many particles |
| Mean square speed | Average of the squares of the molecular speeds, ⟨c2⟩ |
| R.m.s. speed | Square root of the mean square speed |
| Elastic collision | Collision in which kinetic energy is conserved |
| Point particle | Particle whose size is negligible |
| Speed distribution | Graph of the number of molecules against speed |
Avoid these mistakes
1
Saying all molecules have the same speed — they have a wide range of speeds.
2
Thinking collisions with the walls lose energy — they are elastic.
3
Using the square of the mean speed instead of the mean square speed — use ⟨c2⟩.
4
Saying the model works at all conditions — it fails at high pressure and low temperature.
5
Thinking heavier molecules move faster — at the same T they are slower.
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