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.

Short answer

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).

Kinetic Theory Postulates

The Five Postulates

•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

Key Predictions (validated by experiments)

•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:

Correct answer: B. Assumption 1: molecules are point-like, negligible volume vs. container.

Q2.At constant volume and amount, doubling T does what to P?

Correct answer: B. Gay-Lussac: P/T = const → P₂ = P₁(T₂/T₁) = P₁(2).

Q3.Do all gases have the same average kinetic energy at 25°C?

Correct answer: B. KE_avg = 3/2 kT — same T → same KE, regardless of mass or type.

Q4.Why do faster molecules at higher T exert more pressure?

Correct answer: B. Faster molecules hit walls more often and harder.

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Common mistakes

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Heavier molecules move faster at the same temperature. — Correct: Lighter molecules move faster; at same T all have same average KE.

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Pressure depends on the volume of gas molecules. — Correct: Kinetic theory assumes negligible molecular volume — only collisions matter.

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Ideal gas has attractive forces between molecules. — Correct: Ideal gas has NO forces except elastic collisions.

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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.