Collisions of Gas Particles

One of the statements that define the kinetic theory of gases is that the gas particles are constantly colliding with each other, and during the course of these collisions, the overall energy is conserved. The kinetic theory of gases allows us to understand some of the characteristics of these collisions. In order to understand these characteristics, we need to define some parameters of the gas particles themselves. 

Unless otherwise noted, all art on this page is Cengage Learning 2014. 

V = 0 if distance between centers is greater than 2r (that is, no interaction occurs) 

Exact distances between colliding particles may be long or short (on the atomic scale), but let us assume that there is some average distance a particle travels between collisions. We call this average the mean free path (because it is the average—or mean—distance that the particle is free and not colliding with any other particle) 

FIG U RE 19.6 In the hard-sphere model of gas particles, each particle is defined as having an impenetrable radius r. Two times r, or the diameter d, is a parameter that will be used in understanding the behavior of gas particles. 

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Just like the walls in a squash court, against which squash balls continually bounce, the walls of the gas container experience a force each time a gas particle collides with them. From Newton s laws of motion, the force acting on the wall due to this incessant collision of gas particles is equal and opposite to the force applied to it. If it were not so, then the gas particles would not bounce following a collision, but instead would go through the wall. 

Boyle s law describes the relationship between the volume and the pressure of a gas when the temperature and amount are constant. If you have a container like the one shown in Figure 8.3 and you decrease the volume of the container, the pressure of the gas increases because the number of collisions of gas particles with the container s inside walls increases. 

All gas particles have some volume. All gas particles have some degree of interparticle attraction or repulsion. No collision of gas particles is perfectly elastic. But imperfection is no reason to remain unemployed or lonely. Neither is it a reason to abandon the kinetic molecular theory of ideal gases. In this chapter, you re introduced to a wide variety of applications of kinetic theory, which come in the form of the so-called gas laws. ... 

Gas particles in constant motion collide with each other and with the walls of their container. The kinetic-molecular theory states that the pressure exerted by a gas is a result of collisions of the molecules against the walls of the container, as shown in Figure 7. The kinetic-molecular theory considers collisions of gas particles to be perfectly elastic that is, energy is completely transferred during collisions. The total energy of the system, however, remains constant. 

A lighted match can instantly ignite the gas in a Bunsen burner, but it usually cannot cause a large piece of wood to catch fire. The wood tends simply to scorch. Explain the difference in terms of collisions of gas particles. 

To understand gas pressure, picture a typical gas in a closed container. Each time a gas particle collides with and ricochets off one of the walls of its container, it exerts a force against the wall. The sum of the forces of these ongoing collisions of gas particles against all the container s interior walls creates a continuous pressure upon those walls. Pressure is force divided by area. 

Gases exert pressure on their containers. Pressure is a force per unit area resulting from collisions of gas particles with the walls of their container. 

One of the assumptions of the kinetic molecular theory is that the volume of a gas particle is negligible. If this were the case, the ratio of the number of collisions of gas particles with the walls of the container compared to the number of collisions a given gas particle experiences with other gas particles should be quite high. Determine the volume of a cube (in L) filled with helium such that the ratio of the number of collisions of helium atoms with the container walls to the number of inter-molecular collisions for a given helium atom is 1 quin-tillion (1 quintillion = 1.00 X 10 ). The atomic radius of helium is 3.2 X 10 m. 

Collisions of Gas Particles with the Container Walls 167 Intermolecular Collisions 169 Real Gases 171... 

Fig. IS. The collisions of gas particles with a sphere, which are taken into account in the expansion of the force on the sphere in powers of the inverse Knudsen number, (a) Collisions that are responsible for the free molecular flow force (b, c, d) dynamical events that contribute to the K correction to this value (d) represents a process where the second gas particle does not hit the sphere, but would have, had the second collision not taken place (e) represents one of the type of events that contribute to order log K .

A prediction of kinetic molecular theory— which we already encountered in explaining how straws work—is the very existence of pressure. Pressure is the result of the constant collisions between the atoms or molecules in a gas and the surfaces around them. Because of pressure, we can drink from straws, inflate basketballs, and move air into and out of our lungs. Variation in pressure in Earth s atmosphere creates wind, and changes in pressure help predict weather. Pressure is all aroimd us and even inside us. The pressure exerted by a gas sample is defined as tiie force per unit area that results from the collisions of gas particles with surrounding surfaces. 

Pressure Pressure is the force per xmit area that results from the collision of gas particles with surfaces. The SI unit of pressure is the pascal, but pressure is often expressed in other xmits such as atmospheres, millimeters of mercury, torr, poxmds per square inch, and inches of mercury. Pressure Pressure is a fundamental property of a gas. It allows tires to be inflated and makes it possible to drink from straws. 

The inverse of the collision rate, 1/z, is the average time between collisions of gas particles. Calculate the average time between collisions of an Xe atom in 1.00 mol of Xe at STP. 

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