The Kinetic-Molecular Theory A Model for Gas Behavior

A FIGURE 5.15 A Model for Gas Behavior In the kinetic molecular theory of gases, a gas sample is modeled as a collection of particles in constant straight-line motion. The size of each particle is negligibly small, and the particles collisions are elastic. 

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 ... 

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. 

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. 

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. 

The kinetic molecular theory of gases is a model that accounts for ideal gas behavior. This model assumes that a gas consists of tiny particles with negligible volumes, that there are no interactions among particles, and that the particles are in constant motion, colliding with the container walls to produce pressure. 

One of the most important procedures in science is correcting our models as we collect more data. We will understand more clearly how gases actually behave if we can figure out how to correct the simple model that explains the ideal gas law so that the new model fits the behavior we acmally observe for gases. So the question is How can we modify the assumptions of the kinetic molecular theory to fit the behavior of real gases The first person to do important work in this area was Johannes van der Waals (1837-1923), a physics professor at the University of Amsterdam who in 1910 received a Nobel Prize for his woik. To follow his analysis, we start with the ideal gas law,... 

In trying to account for the properties of gases, scientists have devised the kinetic molecular theory. The theory describes an ideal gas model by which we can visualize the nature of the gas by comparing it with a physical system we can either see or readily imagine. As always, chemists explain observable macroscopic phenomena in terms of particulate behavior. 

The behavior of gases is quite different from that of liquids and solids. Gas particles are far apart, whereas particles of both liquids and solids are held close together. A gas has no definite shape or volume and will completely fill any container. Because there are great distances between gas particles, a gas is less dense than a solid or liquid, and easy to compress. A model for the behavior of a gas, called the kinetic molecular theory of gases, helps us understand gas behavior. 

The simplest model for the behavior of gases is the kinetic molecular theory. In this theory, a gas is modeled as a collection of particles (either molecules or atoms, depending on the gas) in constant motion (Figure 5.15 ). A single particle... 

Kinetic energy is energy of motion. The kinetic energy of an object with mass m and velocity u is K.E. = mu. The kinetic-molecular theory of gases is a model for describing gas behavior. It is based on a set of assumptions and yields equations from which various properties of gases can be deduced. 

Thermodynamics deals with relations among bulk (macroscopic) properties of matter. Bulk matter, however, is comprised of atoms and molecules and, therefore, its properties must result from the nature and behavior of these microscopic particles. An explanation of a bulk property based on molecular behavior is a theory for the behavior. Today, we know that the behavior of atoms and molecules is described by quantum mechanics. However, theories for gas properties predate the development of quantum mechanics. An early model of gases found to be very successftd in explaining their equation of state at low pressures was the kinetic model of noninteracting particles, attributed to Bernoulli. In this model, the pressure exerted by n moles of gas confined to a container of volume V at temperature T is explained as due to the incessant collisions of the gas molecules with the walls of the container. Only the translational motion of gas particles contributes to the pressure, and for translational motion Newtonian mechanics is an excellent approximation to quantum mechanics. We will see that ideal gas behavior results when interactions between gas molecules are completely neglected. 

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