Kinetic Molecular Theory, Gas Behavior, and Effusion Flashcards

Vocabulary flashcards covering Kinetic Molecular Theory postulates, Graham's Law of effusion, gas molecular speeds, and real versus ideal gas behavior.

Kinetic Molecular Theory Postulate on Intermolecular Forces

The core assumption of KMT stating that ideal gas particles exert no attractive or repulsive forces on one another, enabling gases to expand indefinitely and fill any container they occupy.

Average Kinetic Energy ($KE$)

The measure of kinetic energy calculated as $KE = \frac{3}{2}RT$, which depends solely on absolute temperature in Kelvin and is directly proportional to it regardless of gas identity.

Root-Mean-Square Speed ($u_{\text{rms}}$)

The average molecular speed determined by $u_{\text{rms}} = \sqrt{\frac{3RT}{M}}$, where at a given temperature, a gas with a lower molar mass (such as $\text{He}$ at $4\,g/mol$) has a higher speed than a gas with a higher molar mass (such as $\text{CO}_2$ at $44\,g/mol$).

Graham's Law of Effusion

The physical law stating that the rate of effusion of a gas is inversely proportional to the square root of its molar mass ($\text{Rate} \propto \frac{1}{\sqrt{M}}$).

Uranium Hexafluoride ($\text{UF}_6$)

A compound used in gaseous diffusion during the Manhattan Project because fluorine has only one stable isotope, ensuring molecular weight differences arise solely from uranium isotopes.

Cascade System for Uranium Enrichment

A massive system consisting of thousands of sequential stages needed for gaseous diffusion because the minute mass difference between $^{235}\text{UF}_6$ and $^{238}\text{UF}_6$ produces only a tiny enrichment factor per stage.

Elastic Collision

A collision involving gas particles where there is no net loss of total kinetic energy when particles collide with each other or with the container walls.

Macroscopic Gas Pressure

The pressure exerted by a gas on container walls, generated microscopically by the continuous, cumulative transfer of momentum when gas molecules undergo elastic collisions with the walls.

Particle Volume Postulate Breakdown

The breakdown in ideal gas behavior occurring under high pressures when the volume of the actual gas particles becomes significant relative to the total container volume.

Gas Particle Trajectory

The path taken by gas particles between collisions, moving in random, straight lines rather than curved trajectories.

Effusion Comparison: Methyl Mercaptan vs. Uranium Hexafluoride

Methyl mercaptan ($\text{CH}_3\text{SH}$, $48\,g/mol$) effuses significantly faster than uranium hexafluoride ($\text{UF}_6$, $352\,g/mol$) because its molar mass is much smaller.

Equal Kinetic Energy Principle

Under identical temperature and pressure conditions, light gases (like helium) and heavy gases (like xenon) possess the exact same average kinetic energy.