What is the Kinetic Theory of Gases?
The kinetic theory explains how gas molecules move at random, colliding constantly. Temperature reflects their average kinetic energy; pressure comes from collisions with container walls — simple but powerful.
Gas molecules move randomly at high speed, colliding elastically with walls and each other. Pressure = force from wall collisions; temperature ∝ average kinetic energy (KE_avg = 3/2 kT per molecule).
- •Gas molecules are tiny points (negligible volume)
- •Molecules move randomly at high speeds
- •Collisions are perfectly elastic (no energy loss)
- •No forces between molecules except during collisions
- •Temperature ∝ average kinetic energy
- •Pressure ∝ molecular collisions
- •Volume ∝ number of molecules (Avogadro's law)
- •P ∝ T at constant V (Gay-Lussac's law)
- •Speed increases with temperature: v_rms = √(3RT/M)
- •Different gases mix randomly (diffusion/effusion)
Step-by-step worked examples
At 300 K, find the root-mean-square (rms) speed of N₂ molecules.
v_rms = √(3RT/M) M(N₂) = 0.028 kg/mol, R = 8.314 J/(mol·K) v_rms = √(3×8.314×300/0.028) v_rms = √(2,678,500) ≈ 517 m/s
A gas at 300 K is heated to 600 K at constant volume. How does pressure change?
At constant V and n: P/T = constant (Gay-Lussac's law) P₂/P₁ = T₂/T₁ = 600/300 = 2 Pressure doubles.
Compare average kinetic energies of He and O₂ at the same temperature.
KE_avg = 3/2 kT (depends only on T, NOT on mass) At same T: both have identical average KE. (But v_rms of He is higher due to lower mass.)
Flashcards
Quick quiz
Q1.In kinetic theory, gas molecules have:
Q2.At constant volume and amount, doubling T does what to P?
Q3.Do all gases have the same average kinetic energy at 25°C?
Q4.Why do faster molecules at higher T exert more pressure?
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Common mistakes
Heavier molecules move faster at the same temperature. — Correct: Lighter molecules move faster; at same T all have same average KE.
Pressure depends on the volume of gas molecules. — Correct: Kinetic theory assumes negligible molecular volume — only collisions matter.
Ideal gas has attractive forces between molecules. — Correct: Ideal gas has NO forces except elastic collisions.
Temperature is independent of molecular speed. — Correct: Temperature is directly proportional to average kinetic energy (and speed).
FAQ
What are the five postulates of kinetic theory?
(1) Gas is point molecules, (2) random high-speed motion, (3) elastic collisions, (4) no intermolecular forces (except collisions), (5) T ∝ KE.
How does kinetic theory explain Boyle's law (PV=nRT)?
P ∝ collision frequency; compress gas (↑V) → more frequent collisions → higher P. Linear relationship.
Why does gas expand when heated?
Higher T → faster molecules → more energetic collisions → molecules push walls outward.
What is the relationship between pressure and molecular speed?
P ∝ m·n·v², where m is mass, n is number density, v is speed. Faster molecules → higher pressure.