Speed molecules following collisions

Molecules in a gas move in straight lines only for rather short distances before they are deflected by collisions and change direction (Fig. 9.22). Because each molecule follows a zigzag course, they take more time to travel a particular net distance from their starting points than they would if there were no collisions. This fact helps explain why diffusion is slow in gases. Recall that at room temperature the speed of a molecule is on the... 

Because speed is distance traveled divided by the time taken for the journey, the r.m.s. speed c, which we can loosely think of as the average speed, is the average length of the flight of a molecule between collisions (that is, the mean free path, X) divided by the time of flight (1/z). It follows that the mean free path and the collision frequency are related by... 

Several closures have been proposed to calculate the collision density for molecules in gas mixtures [109] (pp. 52-55). To derive these expressions for the collision density one generally perform an analysis of the particle-particle interactions in an imaginary container [80, 109, 135], called the conceptual collision cylinder in kinetic theory, as outlined in Sect. 2.4.2.5. A fundamental assumption in this concept is that the rate of molecular collisions in a gas depends upon the size, number density, and average speed of the molecules. Following Maxwell [95] each type of molecules are considered hard spheres, resembling billiard balls, having diameter dg, mass ntg and number density These hard spheres exert no forces on... 

At room temperature, the average speed of a nitrogen molecule is found to be about one-quarter mile per second. In one second, however, the nitrogen molecule has collided with many other molecules, so its motion follows a zig-zag path. Although the average distance between molecules is small, the molecule passes by many other molecules without hitting them, so the distance it travels between collisions is about fifteen times the average distance between the molecules (at room pressure and temperature). 

Consider the simple situation illustrated in Figure 2.6. Here a single, hard-sphere molecule of A is moving through a gas composed of identical, stationary, hard-sphere B molecules. The speed of A is c, and in its path through the matrix of B molecules, A will follow a randomly directed course determined by collisions with B. Collisions are defined to occur when the distance between centers is smaller than ... 

To understand heat conduction, diffusion, viscosity and chemical kinetics the mechanistic view of molecule motion is of fundamental importance. The fundamental quantity is the mean-free path, i. e. the distance of a molecule between two collisions with any other molecule. The number of collisions between a molecule and a wall was shown in Chapter 4.1.1.2 to be z = CNQvdtl6. Similarly, we can calculate the number of collisions between molecules from a geometric view. We denote that all molecules have the mean speed v and their mean relative speed with respect to the colliding molecule is g. When two molecules collide, the distance between their centers is d in the case of identical molecules, d corresponds to the effective diameter of the molecule. Hence, this molecule will collide in the time dt with any molecule centre that lies in a cylinder of a diameter 2d with the area Jid and length gdt (it follows that the volume is Jtd gdt). The area where d is the molecule (particle) diameter is also called collisional cross section a. This is a measure of the area (centered on the centre of the mass of one of the particles) through which the particles cannot pass each other without colliding. Hence, the number of collisions is z = c n gdt. A more correct derivation, taking into account the motion of all other molecules with a Maxwell distribution (see below), leads to the same expression for z but with a factor of V2. We have to consider the relative speed, which is the vector difference between the velocities of two objects A and B (here for A relative to B) ... 

SECTION 10.8 It follows from Idnetic-molecular theory that the rate at which a gas undergoes effusion (escapes through a tiny hole) is inversely proportional to the square root of its molar mass (Graham law). The diffusion of one gas through the space occupied by a second gas is another phenomenon related to the speeds at which molecules move. Because molecules undergo frequent collisions with one another, the mean fiee path—the mean distance traveled between collisions- -is short. Collisions between molecules limit the rate at which a gas molecule can diffuse. 

The temperature of a 5.00-L container of N2 gas is increased from 20 °C to 250 °C. If the volume is held constant, predict qualitatively how this change affects the following (a) the average kinetic energy of the molecules (b) the root-mean-square speed of the molecules (c) the strength of the impact of an average molecule with the container waHs (d) the total number of collisions of molecules with walls per second. 

This reaction involves three molecules as reactants. It is clear that if this reaction occurred in a single step, it would imply that the three molecules (reagents) meet (or are very close to each other) at the same time to give rise to a reaction that is followed by the simultaneous transfer of two electrons. This situation is thought to be unlikely. Indeed the probabihty of collision of three gas molecules can be calculated through the kinetic theory of gases and is very low, certainly well below the number of molecules that react per second, which can be obtained from the reaction speed that readily becomes explosive. We therefore prefer a path that is a... 

On collision, each molecule performs a zigzag path. If one rectifies the molecnle s path one can assert that in the unit of time, the molecule describes the cylinder volnme with a height equal to the speed of the molecule o and with a cross-section ncP. The collision will take place with those molecules whose centers lie inside this cylinder. We shall consider that all molecules are at rest except those, which we follow up. Then the number of collisions in a unit of time v will make... 

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