Ch.5 - Gases

Tro - Chemistry: A Molecular Approach 4th Edition

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Tro 4th Edition

Ch.5 - Gases

Problem 91

Chapter 5, Problem 91

Which postulate of the kinetic molecular theory breaks down under conditions of high pressure? Explain.

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Identify the postulates of the kinetic molecular theory, which include: 1) Gas particles are in constant, random motion. 2) The volume of the gas particles is negligible compared to the volume of the container. 3) Gas particles exert no forces on each other; they neither attract nor repel each other. 4) Collisions between gas particles and with the walls of the container are perfectly elastic. 5) The average kinetic energy of gas particles is proportional to the temperature in Kelvin.

Recognize that under high pressure, the volume of the gas particles becomes significant compared to the volume of the container.

Understand that at high pressure, gas particles are much closer together, which means the assumption that gas particles exert no forces on each other (postulate 3) breaks down.

Explain that under these conditions, intermolecular forces become significant, leading to deviations from ideal gas behavior.

Conclude that the postulate stating that gas particles exert no forces on each other is the one that breaks down under high pressure conditions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Kinetic Molecular Theory

The Kinetic Molecular Theory (KMT) describes the behavior of gases in terms of particles in constant motion. It posits that gas particles are small, have negligible volume, and experience elastic collisions. This theory helps explain gas properties such as pressure, temperature, and volume, providing a framework for understanding gas behavior under various conditions.

Ideal Gas Behavior

Ideal gas behavior refers to the assumption that gas particles do not interact with each other and occupy no volume. This behavior is described by the Ideal Gas Law (PV=nRT), which holds true under low pressure and high temperature. However, deviations from ideal behavior occur at high pressures, where particle volume and intermolecular forces become significant.

High Pressure Effects

Under high pressure, the assumptions of the Kinetic Molecular Theory begin to break down because gas particles are forced closer together, leading to significant intermolecular forces and a noticeable volume of the particles themselves. This results in deviations from the Ideal Gas Law, as real gases do not behave ideally under such conditions, affecting their pressure, volume, and temperature relationships.

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Textbook Question

Use the van der Waals equation and the ideal gas equation to calculate the volume of 1.000 mol of neon at a pressure of 500.0 atm and a temperature of 355.0 K. Explain why the two values are different. (Hint: One way to solve the van der Waals equation for V is to use successive approximations. Use the ideal gas law to get a preliminary estimate for V.)

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Textbook Question

The graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T₁ and T₂). Which temperature is greater? Explain.

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Textbook Question

Use the van der Waals equation and the ideal gas equation to calculate the pressure exerted by 1.000 mol of Cl₂ in a volume of 5.000 L at a temperature of 273.0 K. Explain why the two values are different.

A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the second gas.

A sample of N₂O effuses from a container in 42 seconds. How long will it take the same amount of gaseous I₂ to effuse from the same container under identical conditions?

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