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2: Gases

Last updated

Apr 13, 2022
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- 1.S: The Basics (Summary)
- 2.1: The Empirical Gas Laws

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Gases comprise a very important type of system that can be modeled using thermodynamics. This is true because gas samples can be described by very simple equations of state, such as the ideal gas law. In this chapter, both macroscopic and microscopic descriptions of gases will be used to demonstrate some of the important tools of thermodynamics.

2.1: The Empirical Gas Laws
The page describes the empirical gas laws, which are relationships describing the behavior of gas samples based on observation. Boyle's Law explains the inverse relationship between pressure and volume at constant temperature. Charles' Law states that volume is proportional to temperature at constant pressure. Gay-Lussac's Law relates pressure to temperature. These laws combine into the Combined Gas Law.
2.2: The Ideal Gas Law
The ideal gas law combines empirical laws into a single expression, predicting the existence of a universal gas constant. The constants can be expressed in various units. The law is based on empirical data representing "limiting ideal behavior," with deviations explained by conditions for ideal behavior. The kinetic molecular theory of gases suggests the form of the ideal gas law and the gas law constant.
2.3: The Kinetic Molecular Theory of Gases
The gas laws were derived from empirical observations. Connecting them to fundamental properties of the gas particles is subject of great interest. The Kinetic Molecular Theory is one such approach. In its modern form, the Kinetic Molecular Theory of gasses is based on five basic postulates.
2.4: Kinetic Energy
This page discusses the calculation of kinetic energy using expressions for molecular speeds, derived from the Kinetic Molecular Theory. It highlights that average kinetic energy in a gas depends on temperature, while molecular speed varies with mass. The relationship between kinetic energy, speed, and the ideal gas law is also explained, demonstrating consistency with the ideal gas law using the root-mean-square speed.
2.5: Graham’s Law of Effusion
The page discusses the kinetic molecular theory and its implications on effusion and diffusion of gases, using the example of gas effusion from a balloon. The rate of effusion is inversely related to the square root of molecular weight. This concept is further explored through the Knudsen Cell Experiment, where gas effusion through an orifice is used to measure vapor pressure, with the mass of effused gas proportional to vapor pressure.
2.6: Collisions with Other Molecules
The page discusses the importance of understanding molecular collisions in gas-phase experiments, specifically molecular beams. It explains how to predict collision frequency by considering molecules as spheres and outlines the concept of a "collision cylinder." Relevant formulas are provided for calculating the number of collisions, frequency of collisions, and mean free path, taking into account factors like pressure, temperature, and molecular size.
2.7: Real Gases
This page discusses the deviations from ideal gas behavior and introduces the van der Waals equation, which provides corrections for these deviations by considering intermolecular interactions and molecular size. It presents the van der Waals constants for different gases and mentions other equations of state like Redlich-Kwong and Dieterici that account for temperature dependence. The Virial Equation is introduced as another way to account for deviations from ideal behavior.
2.E: Gases (Exercises)
Exercises for Chapter 2 "Gases" in Fleming's Physical Chemistry Textmap.
2.S: Gases (Summary)
The chapter focuses on the empirical and ideal gas laws, kinetic molecular theory, and deviations from ideal gas behavior through models like van der Waals. It aims to equip readers with the ability to perform calculations related to these theories, understand molecular speed distributions, and derive expressions for gas behavior. Key concepts include diffusion, effusion, critical points, and the principle of corresponding states.

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