Questions: Kinetic Molecular Theory and Gas Behavior

Question 1

A sealed container holds equal moles of helium (atomic mass 4) and xenon (atomic mass 131) at the same temperature. Which statement correctly describes their molecular motion?

• A. Helium atoms have more kinetic energy than xenon atoms, because lighter particles move faster
• B. Helium atoms move faster than xenon atoms, but both have the same average kinetic energy
• C. Xenon atoms move faster than helium atoms, because heavier particles carry more momentum per collision
• D. Helium and xenon atoms move at identical speeds because they share the same temperature

Answer: (B)

At the same temperature, all gas molecules have the same average kinetic energy (KE_avg = 3/2 kT depends only on T). Since KE = ½mv², equal kinetic energy with smaller mass means greater velocity — helium atoms must move much faster than xenon atoms. This is why lighter gases effuse and diffuse more rapidly (Graham's law). Option D is the common misconception: same temperature means same average KE, not same speed.

Question 2

A gas sample's actual pressure is significantly lower than what the ideal gas law predicts. Under which conditions is this deviation most likely, and what causes it?

• A. High temperature and low pressure — particles move too fast for the ideal approximation to hold
• B. Low temperature and high pressure — intermolecular attractions reduce wall collision force, and particle volume matters at high density
• C. High temperature and high pressure — the gas becomes too energetic for ideal behavior
• D. Low temperature and low pressure — the gas is near condensation and the model collapses entirely

Answer: (B)

Real gases deviate below ideal predictions when intermolecular attractions are significant (low temperature — slow particles) AND when particle volume matters (high pressure — crowded particles). At low temperature, particles move slowly enough that van der Waals attractions briefly pull them toward each other, reducing the force of wall collisions and lowering observed pressure below ideal prediction. At high pressure, the actual volume of the molecules reduces available empty space beyond what the ideal model assumes.

Question 3

According to kinetic molecular theory, doubling the absolute temperature of a gas at constant volume doubles its average kinetic energy and increases its pressure.

• T. True
• F. False

Answer: True

KE_avg = (3/2)kT, so average kinetic energy is directly proportional to absolute temperature (in Kelvin). Doubling T doubles KE_avg. Faster-moving particles hit the container walls harder and more frequently, increasing pressure. This is why Gay-Lussac's law (P ∝ T at constant volume) follows directly from KMT.

Question 4

Kinetic molecular theory predicts that most molecules in a gas sample at a given temperature move at exactly the same speed.

• T. True
• F. False

Answer: False

KMT predicts that the average kinetic energy is proportional to temperature, but individual molecules have a distribution of speeds — the Maxwell-Boltzmann distribution. At any moment, some molecules are moving much faster and others much slower than the average. The theory specifies the statistical average, not a uniform speed for every particle. This distribution of speeds is actually experimentally verified and explains phenomena like evaporation (faster-than-average surface molecules escape).

Question 5

According to kinetic molecular theory, why does decreasing the volume of a gas at constant temperature increase its pressure?

Model answer: Pressure arises from gas molecules colliding with the container walls. When volume decreases at constant temperature, the same number of particles (moving at the same average speed) are confined to a smaller space. They collide with the walls more frequently per unit time per unit area — more collisions per second means higher pressure. Temperature is unchanged, so the force of each collision is unchanged; it's the frequency of collisions that increases. This is precisely Boyle's law explained at the molecular level.

This question tests whether students understand pressure as a statistical outcome of molecular collisions, not a property of the gas itself. Many students think of pressure as something a gas 'has' abstractly, but KMT grounds it in the mechanics of particle-wall collisions. Reducing volume reduces the average distance a particle travels between wall hits, increasing collision frequency and therefore pressure.