Kinetic-Molecular Theory: Gas Laws, Molecular Speeds, and Effusion

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What is the kinetic-molecular theory (KMT)?

A microscopic model explaining gas behavior through assumptions about particle motion, size, collisions, and energy.

What does the KMT assume about particle forces and collisions?

Particles exert no attractive or repulsive forces, and collisions are elastic, with no kinetic energy lost.

How does the KMT explain Boyle’s law?

At constant temperature and amount, reducing gas volume increases wall collisions per unit area and raises pressure.

How is average kinetic energy per mole related to temperature?

It equals $\frac{3}{2}RT$, where $T$ is kelvin temperature and $R$ is the gas constant.

What does Graham’s law relate?

At the same temperature, two gases’ effusion-rate ratio is the square root of the inverse ratio of their molar masses.

Quiz questions

1. What does a Maxwell-Boltzmann distribution show for a gas?Answer: The relative number of particles moving at each speed.
2. Which equation gives the root-mean-square speed of a gas with molar mass $M$ at temperature $T$?Answer: $u_{\mathrm{rms}}=\sqrt{\frac{3RT}{M}}$
3. At the same kelvin temperature, how do the average kinetic energies of different ideal gases compare?Answer: They are equal, regardless of the gases’ identities.
4. What is effusion?Answer: The escape of gas particles through a small opening.
5. At the same temperature, gas A has molar mass $M_A$ and gas B has molar mass $M_B$. Which expression gives their effusion-rate ratio?Answer: $\frac{\text{rate}_A}{\text{rate}_B}=\sqrt{\frac{M_B}{M_A}}$