Collisions of Gas Particles with the Container Walls

In the analysis of the kinetic molecular model that led to the ideal gas equation, we assumed that the pressure a gas exerts is caused by the collisions of its particles with the walls of its container. In this section we will consider the details of that phenomenon. 

How is ZA expected to depend on the average velocity of the gas particles For example, if we double the average velocity, we double the number of wall impacts, so ZA should double. Thus ZA depends directly on wavg  

Similarly, ZA depends directly on A, the area of the wall under consideration. That is, if we double the area being considered, we will double the number of impacts per second that occur within that section of the wall. Thus Za A. 

Likewise, if the number of particles in the container is doubled, the impacts with the wall will double. For a general case, we need to consider not the absolute number of particles but the number of particles per unit volume (the number density of particles), which can be represented by N/V, the number of particles N divided by the volume V (in m3). Thus ZA is expected to depend directly on N/V. That is, ZA N/V. 

Note that the units for ZA expected from this relationship are 

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

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. 

The attraction of the gas particles for each other tends to lessen the pressure of the gas since the attraction slightly reduces the force of the collisions of the gas particles with the container walls. The amount of attraction depends on the concentration of gas particles and the magnitude of the intermolecular force of the particles. The greater the intermolecular forces of the gas, the higher the attraction is, and the less the real pressure. Van der Waals compensated for the attractive force by the term P + an2/V2, where a is a constant for individual gases. The greater the attractive force between the molecules, the larger the value of a. 

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. 

Pressure is defined as force per unit area. The pressure exerted by a gas comes from the forces exerted by collisions of gas molecules with the walls of the container. Since the mass of the walls of the container is much larger than the mass of each particle, the assumption of elastic collisions implies that the velocity component perpendicular to the wall is exactly reversed, and the other two components are unaffected as discussed in Section 7.1. 

The increase in the number of gas particles in the container leads to an increase in the number of collisions with the walls per unit time. This leads to an increase in the force per unit area-that is, to an increase in gas pressure. 

The left-hand cylinder in the figure contains a certain volume of gas at a certain pressure. (Pressure is the collision of the gas particles with the inside walls of the container.) When the volume is decreased, the same number of... 

Origin of pressure (Figure 5.14). From postulates 1 and 2, each gas particle (point of mass) colliding with the container walls (and bottom of piston) exerts a force. Countless collisions over the inner surface of the container result in a pressure. The greater the number of particles, the more frequently they collide with the container, and so the greater the pressure. 

When gas A is mixed with flas B, P,ota = Pa + Pb the numbers of collisions of particles of each gas s. with the container walls are in proportion to the amount (mol) of that gas. 

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. 

Louis Gay-Lussac continued the ballooning exploits initiated by Charles, ascending to over 20,000 feet in a hydrogen balloon in the early 1800s. Gay-Lussac s law defines the relationship between the pressure and temperature of an ideal gas. If the temperature of the air in the syringe increases while keeping the volume constant, the gas particles speed up and make more collisions with the inside walls of the syringe barrel. As we have seen, an increase frequency in the number of collisions of the gas particles with a container s wall translates into an increase in pressure. Gay-Lussac s law says that pressure is directly... 

With all other quantities held constant increasing the number of gas particles increases the pressure. These added particles are at the same temperature as the other particles so they donT hit the container any harder. Because there are more particles though they hit the walls of the container more often. More collisions with the container mean a higher pressure. Removing gas particles decreases the pressure because there are fewer collisions with the walls of the container. 

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. 

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. 

Pressure is caused by molecular collisions with the container walls. At constant temperature, a gas exerts greater pressure as its volume is compressed, which increases the concentration of particles and the number of collisions for each instant. The relationship between the pressure applied to a gas and its volume is related in Boyle s law. 

Pressure is a direct result of collisions between gas particles and the walls of their container. An increase in temperature increases collision frequency and energy, so raising the temperature should also raise the pressure if the volume is not changed. Joseph Gay-Lussac (1778-1850) found that a direct proportion exists between kelvin temperature and pressure, as illustrated in Figure 13.3. Gay-Lussac s law states that the pressure of a fixed amount of gas varies directly with the kelvin temperature when the volume remains constant. It can be expressed mathematically as follows. 

Figure 13.3 When the cylinder is heated, the kinetic energy of the particles increases, increasing both the frequency and energy of the collisions with the container wall. The volume of the cylinder is fixed, so the pressure exerted by the gas increases. 

Disruptive forces completely overcome cohesive forces between particles in the gaseous or vapor state. As a result, the particles of a gas move essentially independently of one another in a totally random way (see Figure 6.3C). Under ordinary pressure, the particles are relatively far apart except when they collide with each other. Between collisions with each other or with the container walls, gas particles travel in straight lines. The particle velocities and resultant collision frequencies are quite high for gases, as shown in h Table 6.2. 

Figure 4.4 An ideal gas particle collides with the waUs of the container without losing energy. The energy of the particle is the same before (Ej), during (E2), and after (Ej) the collision with the container wall Ej = Ej = Ej. 

All gas properties relate in some way to the kinetic character. Specifically, particle motion explains why gases fill their containers. Also, pressure results from the large numbers of particle collisions with the container walls. 3. Gas molecules move independently of each other in all directions. Therefore, they exert pressure on the container walls, including the top, uniformly in all directions. Liquid and solid pressures are the result of gravity, so they exert a downward pressure on the bottom of the container. Liquid particles can move amongst themselves, so they also exert horizontal pressures against the walls of their container. Solid particles lack this freedom of horizontal movement, so they exert no horizontal pressure on the walls of a container. 

You can understand Dalton s law in terms of the kinetic-molecular theory. Each of the rapidly moving particles of gases in a mixture has an equal chance to collide with the container walls. Therefore, each gas exerts a pressure independent of that exerted hy the other gases present. The total pressure is the result of the total number of collisions per unit of wall area in a given time. 

Boyle s law follows from the idea that pressure results from the collisions of the gas particles with the walls of their container. If the volume of a gas sample is decreased, the same number of gas particles is crowded into a smaller volume, resulting in more collisions with the walls and therefore an increase in the pressure (Figure 5.8 ). 

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