Question

According to kinetic theory of gases (A) collisions are always elastic. (B) heavier molecules transfer more momentum to the wall of the container. (C) only a small number of molecules have very high velocity. (D) between collisions, the molecules move in straight lines with constant velocities.

Short answer

The correct statements according to the kinetic theory of gases are: (A) collisions are always elastic, (C) only a small number of molecules have very high velocity, and (D) between collisions, the molecules move in straight lines with constant velocities.

Step-by-step solution

Review Kinetic Theory Postulates

First, recall the key postulates of the kinetic molecular theory of gases: 1) Gas molecules are in constant, random motion. 2) The volume of the individual gas particles is negligible compared to the container's volume. 3) Gas particles exert no forces on each other; they neither attract nor repel each other. 4) All collisions between gas particles are perfectly elastic, meaning they conserve kinetic energy. 5) The average kinetic energy of gas particles is proportional to the gas temperature in kelvins.

Assess Option A

Since the kinetic theory states all collisions are elastic (see postulate 4), Option A is correct.

Assess Option B

The momentum transferred to the walls of the container depends on the velocity and mass of the molecules. Heavier molecules will transfer more momentum if their velocities are the same as lighter molecules. However, at a given temperature, heavier molecules have lower velocities than lighter ones, making this a more complex situation. Still, in a general sense without specifying temperature, Option B is reasonable.

Assess Option C

According to the distribution of molecular speeds in a gas (Maxwell-Boltzmann distribution), there is a variety of velocities among molecules, but only a few have extremely high velocities. Therefore, Option C is correct.

Assess Option D

According to the kinetic theory, molecules move in straight lines with constant speeds between collisions. This is due to the postulate that there are no intermolecular forces acting when they are not colliding. Thus, Option D is correct.

Key concepts

Elastic Collisions

In the context of the kinetic molecular theory of gases, an elastic collision is a fundamental concept. It refers to a situation where two molecules collide and bounce off each other without any loss of kinetic energy. This is akin to two perfectly smooth billiard balls hitting each other on a pool table.

This conservation of kinetic energy is crucial because it implies that the total energy within a closed system remains constant. The theory assumes that gases consist of many small particles moving in random directions, with collisions occurring frequently and, importantly, elastically. This allows us to predict behaviors of gases under various conditions, such as changes in temperature and pressure.

Momentum Transfer in Gases

When we consider momentum transfer in gases, we are analyzing the exchange of momentum between gas molecules and the walls of their container. Each time a gas molecule hits the wall, it transfers momentum to it. This transfer is the result of the mass and velocity of the molecule—the two factors that combine to define momentum.

• Mass of molecule: Heavier molecules carry more momentum and thus transfer more of it upon collision, provided the velocity is the same.
• Velocity of molecule: Faster-moving molecules will also transfer more momentum in a collision.

The cumulative effect of these countless collisions is what we observe as pressure exerted by the gas on the container walls.

Maxwell-Boltzmann Distribution

The Maxwell-Boltzmann distribution offers a statistical view of the molecular motion within gases. It describes the varying speeds of particles and shows that while many molecules might have moderate speeds, there will always be a few with very high or very low velocities.

The distribution takes the shape of a bell curve when plotted, displaying the probability of finding a molecule with a particular velocity. Factors like the temperature of the gas influence the spread and peak of this distribution. At higher temperatures, the curve flattens and broadens, indicating that molecules are likely to be moving faster on average, highlighting the direct relationship between temperature and molecular velocity.

Molecular Motion and Velocity

In gas behaviour, molecular motion and velocity are intertwined concepts. Particles in a gas move with a range of velocities, each traveling in straight lines until it experiences a collision, either with another molecule or with the container's wall. This pattern of movement is random and constant.

The kinetic molecular theory informs us that the average kinetic energy—and hence average velocity—of these particles is proportional to the temperature of the gas. Therefore, an increase in temperature leads to an increase in the average velocity of the gas molecules. Conversely, a decrease in temperature will reduce the average velocity. Understanding this relationship is vital for comprehending the macroscopic properties of gases—like pressure and volume—as well as the outcomes of temperature variations on these properties.