Models kinetic molecular theory

We now have enough information to turn our qualitative ideas about a gas into a quantitative model that can be used to make numerical predictions. The kinetic model ( kinetic molecular theory, KMT) of a gas is based on four assumptions (Fig. 4.23) ... 

Ideal gas model Kinetic molecular theory Section 4.3... 

The concept of corresponding states was based on kinetic molecular theory, which describes molecules as discrete, rapidly moving particles that together constitute a fluid or soHd. Therefore, the theory of corresponding states was a macroscopic concept based on empirical observations. In 1939, the theory of corresponding states was derived from an inverse sixth power molecular potential model (74). Four basic assumptions were made (/) classical statistical mechanics apply, (2) the molecules must be spherical either by actual shape or by virtue of rapid and free rotation, (3) the intramolecular vibrations are considered identical for molecules in either the gas or Hquid phases, and (4) the potential energy of a coUection of molecules is a function of only the various intermolecular distances. 

The kinetic-molecular theory (KMT) represents the properties of gases by modeling the gas particles themselves at the microscopic level. The KMT assumes that ... 

While studying gases in this chapter you will consider four main physical properties—volume, pressure, temperature, and amount—and their interrelationships. These relationships, commonly called gas laws, show up quite often on the AP exam, so you will spend quite a bit of time working problems in this chapter. But before we start looking at the gas laws, let s look at the Kinetic Molecular Theory of Gases, the extremely useful model that scientists use to represent the gaseous state. 

The Kinetic Molecular Theory attempts to represent the properties of gases by modeling... 

We can understand how atmospheric pressure is just the weight of the atmosphere pushing down on the Earth s surface, but how can we apply the basic definition of pressure to a confined gas To expand our concept of pressure and provide a basic framework for understanding the behavior of gases, we use a simple model for a confined gas. This model is known as the kinetic molecular theory. The kinetic molecular theory states ... 

Kinetic Molecular Theory model that defines an ideal gas and assumes the average kinetic energy of gas molecules is directly proportional to the absolute temperature... 

It is not difficult to propose and develop a model for the gaseous state of insoluble monolayers. The arguments parallel those developed in kinetic molecular theory for three-dimensional gases and lead to equally appealing results. The problem, however, is that many assumptions of the model are far less plausible for monolayers than for bulk gases. To see this, a brief review of the derivation seems necessary. 

Thus far, we ve concentrated on describing the behavior of gases rather than on understanding the reasons for that behavior. Actually, the reasons are straightforward and were explained more than a century ago using a model called the kinetic-molecular theory. The kinetic-molecular theory is based on the following assumptions ... 

The behavior of gases can be accounted for using a model called the kinetic-molecular theory, a group of five postulates ... 

As you teach yourself about gases in this unit, develop a mental picture of how the molecules of a gas behave. The model for the action of gas molecules in a confined space is called kinetic molecular theory. Because kinetic means moving, the theory describes how molecules behave as a result of their motion. The speed of molecules is related to their temperature, in that the hotter they are, the faster they move. In an enclosed space, molecules randomly strike each other and collide with the walls of the container as they travel (Figure 6.1). 

An example of this type of model is the kinetic molecular theory, a simple model that attempts to explain the properties of an ideal gas. This model is based on speculations about the behavior of the individual gas particles (atoms or molecules). The postulates of the kinetic molecular theory can be stated as follows ... 

The agreement between the ideal gas law and the kinetic molecular theory gives us confidence in the validity of the model. The characteristics we have assumed for ideal gas particles must agree, at least under certain conditions, with their actual behavior. 

We have seen that the postulates of the kinetic molecular theory, combined with the appropriate physical principles, produce an equation that successfully fits the experimentally observed properties of gases as they approach ideal behavior. Two phenomena involving gases provide further tests of this model. 

We have seen that a very simple model, the kinetic molecular theory, by making some rather drastic assumptions (no interparticle interactions and zero volume for the gas particles), successfully explains ideal behavior. However, it is important that we examine real gas behavior to see how it differs from that predicted by the ideal gas law and to determine what modifications of the kinetic molecular theory are needed to explain the observed behavior. Since a model is an approximation and will inevitably fail, we must be ready to learn from such failures. In fact, we often learn more about nature from the failures of our models than from their successes. 

The kinetic molecular theory of gases predicts that an increase in temperature increases molecular velocities and so increases the frequency of in-termolecular collisions. This agrees with the observation that reaction rates are greater at higher temperatures. Thus there is qualitative agreement between the collision model and experimental observations. However, it is found that the rate of reaction is much smaller than the calculated collision frequency in a given collection of gas particles. This must mean that only a small fraction of the collisions produces a reaction. Why ... 

Kinetic molecular theory a model that assumes that an ideal gas is composed of tiny particles (molecules) in constant motion. (5.6)... 

Although the kinetic-molecular theory was developed to explain the behavior of gases, the model can be applied to liquids and solids. When applying the kinetic-molecular theory to these states of matter, you must consider the forces of attraction between particles as well as their energy of motion. 

You can t understand gases without understanding the movement of gas particles. Remember from your study of the kinetic-molecular theory in Chapter 13 that gas particles behave differently than those of liquids and solids. The kinetic theory provides a model that is used to explain the properties of solids, liquids, and gases in terms of particles that are always in motion and the forces that exist between them. The kinetic theory assumes the following concepts about gases are true. 

To better understand the complex behavior of gases, scientists have theorized a model of an ideal gas. This model is called the kinetic molecular theory. In the kinetic molecular theory, an ideal gas lacks certain real gas characteristics. Ideal gas has the following four characteristics not shared by a real gas ... 

Until now our discussions have dealt with ideal behavior of gases. By this we mean that the identity of a gas does not affect how it behaves, and the same equations should work equally well for all gases. Under ordinary conditions most real gases do behave ideally their P and V are predicted by the ideal gas laws, so they do obey the postulates of the kinetic-molecular theory. According to the kinetic-molecular model, (1) all but a negligible volume of a gas sample is empty space, and (2) the molecules of ideal gases do not attract one another because they are so far apart relative to their own sizes. 

In 1905, Albert Einstein created a mathematical model of Brownian motion based on the impact of water molecules on suspended particles. Kinetic molecular theory could now be observed under the microscope. Einstein s more famous later work in physics on relativity may be applied to chemistry by correlating the energy change of a chemical reaction with extremely small changes in the total mass of reactants and products. 

The Kinetic Molecular Theory provides a simple model of the nature of matter. It has the following components ... 

The kinetic-molecular theory is primarily a mathematical model of a gas based on the following postulates ... 

The kinetic-molecular theory produces a model of a gas that explains the properties of real gases quite well. As temperatures get lower and pressures higher, the deviation of real gases from ideal behavior increases. Yet, the KMT describes gas behavior at the molecular level very well, and for that reason, it contributes to our understanding of gases. 

So far we have discussed observations of macroscopic samples of gas decreasing cylinder volume, increasing tank pressure, and so forth. This section presents the central model that explains macroscopic gas behavior at the level of individual particles the kinetic-molecular theory. The theory draws conclusions through mathematical derivations, but here our discussion will be largely qualitative. 

A fundamental principle of science is that simpler models are more useful than complex ones—as long as they explain the data. You can certainly appreciate the usefulness of the kinetic-molecular theory. With simple postulates, it explains the behavior of the ideal gases in terms of particles acting like infinitesimal billiard balls, moving at speeds governed by the absolute temperature, and experiencing only perfectly elastic collisions. 

Our experiences show us that when we make a change in a property of a gas, other properties change in a predictable way. In this chapter we will discuss relationships among the characteristics of gases such as pressure, volume, temperature, and amount of gas. These relationships were discovered by making observations as simple as seeing that a balloon expands when you blow into it, or that a sealed balloon will shrink if you put it into the freezer. But we also want to explain these observations. Why do gases behave the way they do To explain gas behavior we will propose a model called the kinetic molecular theory. 

The kinetic molecular theory (KMT) is a model based on the properties of individual gas components that explains the relationship of P, V, T, and n for an ideal gas. 

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