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Module 1: Basic Concepts - Kinetics
Contents-
Animation #1:
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Effect of Temperature on Molecular Velocity
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Animation #2:
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Gas Volume Change with Temperature
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Animation #3:
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Gas Volume Change with Pressure
Objective
- Explain how gas volume depends on temperature and pressure.
Gases are composed of a large number of molecules, which are moving rapidly within the volume they occupy. The molecules themselves are small compared to the volume of space as indicated in Figure 1 (Motion of gas molecules). Collisions occur frequently between these molecules.
For the purposes of air pollution-related work, we can assume that these molecular collisions are "elastic." This simply means that there are no molecule-to-molecule chemical interactions during the collisions. In a sense, the molecules behave like miniature billiard balls during collisions. Momentum is transferred from one to another depending on the mass and the velocities of the molecules.
The velocities of the molecules depend on the temperature. When the temperature is increased, the velocities of the molecules moving in the occupied space increase. Conversely, when the temperature is lowered, the velocities of the molecules moving in the occupied space decrease.
As the gas cools or heats up, an equilibrium condition is re-established rather quickly due to the rapid speed of the gas molecules and the number of molecule-to-molecule collisions that occur. The kinetic energy is transferred back and forth between molecules until it is uniform. At equilibrium, momentum continues to be transferred between molecules, but the overall kinetic energy of the gas molecules (and their velocities) remains constant.
 Animation #1 
This animation,
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At temperatures approaching absolute zero (the coldest temperature possible), the velocities of the gas molecules are extremely small. As the gas temperature increases from absolute zero, the average speed of the molecules increases at a rate that is indicated by Equation 1.
- Where:
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c = average speed of molecules
- R = Universal gas constant
- T = absolute temperature
- M = molecular weight
- R = Universal gas constant
Note: This equation is based on classical kinetic theory. More accurate (and complex) theories indicate that the motion of the molecules does not cease entirely at absolute zero.
The average velocity of molecules is directly related to the square root of the absolute temperature. If the absolute temperature increases by a factor of 2, the average velocity of the gas molecules increases by a factor of 1.414.
The average speeds calculated using Eq. 1 are quite fast as indicated by the data for several gases shown in Table 1.
To put these molecular velocities into perspective, note that carbon dioxide's velocity of 362.5 m/sec at 273°K (0°C) is equivalent to approximately 811 mi/hr. Obviously, the molecules are moving rapidly, and this means that there are many molecule-to-molecule collisions and molecule-to-container wall collisions occurring every second. During each collision, momentum is transferred from one molecule to another. Momentum is also transferred back and forth from the molecules on the surfaces of the container that surround the gas volume.
As energy is being added or subtracted from the gas, an equilibrium condition is reestablished relatively quickly due to the rapidity of the movement of gas molecules and the number of molecule-to-molecule collisions which are occurring. The energy can be transferred back and forth until it is uniform throughout the gas. At equilibrium, there continues to be momentum transfer among the molecules, but the overall total kinetic energy of the gas molecules (and their velocities) remains constant.
Volume Change With Temperature
As the temperature increases, the forces exerted by all of the molecules on the walls of their container (i.e. pressure) increase. If the gas is contained in an expandable container such as that shown in
Figure 2 (Gas volume change with temperature), the rise in temperature will cause the gas volume to increase. As an amount of gas is heated, the same number of molecules are present. However, there is more space between the molecules.
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Animation #2
This animation,
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Note: Animations require a Netscape 4.7 or Internet Explorer 4.01 or higher browser and a Shockwave Flash plug-in (Netscape browsers) or Shockwave Flash ActiveX Control (Internet Explorer browsers). Shockwave Flash plug-in/ActiveX Control (version 3.0 minimum) can be obtained at the
Macromedia
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If you heat any gas and measure its volume at different temperatures while maintaining the same pressure, you will get a relationship similar to that shown in Table 2 (volume increases with temperature).
Figure 3 (Proportional relationship between volume and temperature), shows that the gas volume occupied by a given number of molecules is directly proportional to the absolute temperature. This relationship is shown below:
Volume Change with Pressure
All gases exert a pressure on the surfaces of their container. This pressure is the result of the momentum transferred from the molecules in the gas as they strike molecules in the container. If the space occupied by the gas is compressed due to an outside force (such as the piston shown in the
Figure 4), the pressure increases.
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Animation #3
This animation,
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Note: Animations require a Netscape 4.7 or Internet Explorer 4.01 or higher browser and a Shockwave Flash plug-in (Netscape browsers) or Shockwave Flash ActiveX Control (Internet Explorer browsers). Shockwave Flash plug-in/ActiveX Control (version 3.0 minimum) can be obtained at the
Macromedia
web site. Before downloading or installing any software or plug-ins, please refer to your organization's network/computer policies or check with your system administrator.
If you apply increasing pressure to any gas and measure its volume at different points, you will get a relationship similar to that shown in Table 3 (volume decreases with pressure).
Figure 5 (Inverse relationship between volume and pressure) shows the inverse relationship between the volume of the gas and its pressure.
Practice Problems
Kinetics
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Instructions:
- Complete the Practice Problems before proceeding to the next lesson. Click on the button below.