Question

List the five basic postulates of the kinetic-molecular theory. Which assumption is incorrect at very high pressures? Which one is incorrect at low temperatures? Which assumption is probably most nearly correct?

Short answer

Postulate 1 fails at high pressures; Postulate 2 fails at low temperatures. Postulate 5 is most correct.

Step-by-step solution

Understanding the Kinetic-Molecular Theory

The kinetic-molecular theory of gases provides a model that explains the behavior of gas particles. Let's explore its five basic postulates.

Postulate 1: Particle Volume is Negligible

Gas particles are considered to have mass but no volume. They are so small compared to the distances between them that we treat their volume as zero.

Postulate 2: No Intermolecular Forces

Gas particles do not exert any attractive or repulsive forces on each other, allowing them to move linearly until they collide with the container or other particles.

Postulate 3: Constant, Random Motion

Gas particles are in constant, random motion, colliding with each other and the walls of the container, resulting in the pressure exerted by the gas.

Postulate 4: Elastic Collisions

Collisions between gas particles and between particles and the container walls are perfectly elastic, meaning no energy is lost in the collisions.

Postulate 5: Average Kinetic Energy and Temperature

The average kinetic energy of gas particles is directly proportional to the absolute temperature of the gas, meaning higher temperatures result in higher kinetic energy.

Assumptions That Fail Under Certain Conditions

At very high pressures, the assumption that particle volume is negligible (Postulate 1) fails because particles are forced closer together, making their volume significant. At low temperatures, the assumption of no intermolecular forces (Postulate 2) is incorrect, as attractions between particles become significant.

Evaluating the Most Correct Assumption

Postulate 5, relating kinetic energy to temperature, is the most accurate because it applies well across a wide range of conditions, as long as interactions between particles and their real volumes are negligible.

Key concepts

Postulates of Kinetic-Molecular Theory

The kinetic-molecular theory is essential for understanding gas behavior. It is composed of five primary postulates that paint a picture of how gas particles interact and move.

• Particle Volume is Negligible: Gas particles are assumed to occupy no space. Their volumes are so small compared to the distances between them that they are considered virtually non-existent.
• No Intermolecular Forces: In this model, gas particles do not attract or repel each other. This allows them to move independently without being affected by nearby particles.
• Constant, Random Motion: Gas particles are always moving in a random, chaotic way, which contributes to the pressure of the gas as they collide frequently with container walls and each other.
• Elastic Collisions: When gas particles collide with each other or the walls of a container, they bounce back without losing any energy. This keeps the overall energy constant within the system.
• Average Kinetic Energy and Temperature: The average kinetic energy of gas particles is directly tied to the absolute temperature. As temperature increases, so does kinetic energy, driving faster particle motion.

Gas Particle Behavior

The behavior of gas particles can seem chaotic at first, but there is a method to their madness. These particles move continuously and randomly, leading to unique properties of gases.

• Gas particles are in perpetual motion, changing direction only when they hit something.
• This constant motion is what produces gas pressure, as particles bounce off the walls of their container.
• The lack of significant intermolecular forces in an ideal gas model means particles do not stick together, allowing them to move freely.

Understanding these behaviors helps in predicting how gases behave under different conditions, and why they fill their containers evenly.

Real Gases

Real gases differ from the idealized model presented by the kinetic-molecular theory. In the real world, some assumptions of this model fall short, especially under extreme conditions.

• At high pressures, gas particles are closer together and the volume of individual particles cannot be ignored. This makes gases deviate from ideal behavior.
• At low temperatures, gases do not behave ideally since intermolecular attractions then become more apparent. Gas particles may begin to form liquids as they slow down.
• Real gases are better described using adjustments to the ideal gas law, such as the Van der Waals equation, which accounts for particle volume and intermolecular forces.

These deviations help explain why gases like carbon dioxide sometimes liquify faster than expected.

Temperature and Kinetic Energy

A key aspect of the kinetic-molecular theory is the relationship between temperature and kinetic energy. Temperature provides a direct measure of the energy gas particles possess.

• Higher temperatures mean that gas particles have more energy, causing them to move quickly.
• This increased motion at higher temperatures results in frequent and robust collisions with container walls, thus increasing pressure.
• Absolute temperature, measured in Kelvin, is directly proportional to the average kinetic energy of the particles, linking thermodynamics to particle physics.

The understanding of this relationship allows scientists to predict how gases will react when heated or cooled.

Limitations of Kinetic-Molecular Theory

While the kinetic-molecular theory provides a strong framework for understanding gases, it has its limitations. It assumes conditions that don’t always match real-world scenarios.

• The theory neglects the volume of particles. At high pressures, this becomes a misleading assumption.
• It also assumes no attractive forces exist between particles, which is not true at low temperatures where such forces can cause gases to condense into liquids.
• Because the particles are assumed not to influence each other, scenarios dealing with real gases need corrective models like Van der Waals' to be accurately depicted.

These limitations highlight the need for adjustments and modifications when applying the theory to complex scientific problems.