- Describe how a gas is able to be compressed.
- Identify three factors that affect gas pressure. Describe the effects according to the kinetic-molecular theory.
Check Your Understanding
Recalling Prior Knowledge
- What is the kinetic-molecular theory as it pertains to gases?
- What is responsible for a gas exerting pressure?
- How is temperature defined?
The behavior of gases is relatively easy to describe because of the large space that exists between the particles. Because there is so much space between particles, intermolecular forces can largely be ignored, which vastly simplifies any analysis of the motion exhibited by individual particles. In this lesson, we will begin our study of the effect that volume, temperature, and amount has on the pressure of an enclosed gas.
Scuba diving is a form of underwater diving in which a diver carries his own breathing gas, usually in the form of a tank of compressed air. The pressure in most commonly used scuba tanks ranges from 200 to 300 atmospheres. Gases are unlike other states of matter in that a gas expands to fill the shape and volume of its container. For this reason, gases can also be compressed so that a relatively large amount of gas can be forced into a small container. If the air in a typical scuba tank were transferred to a container at the standard pressure of 1 atm, the volume of that container would need to be about 2500 liters (Figure below).
Scuba divers carry all of their breathable air on their backs in tanks. The air is compressed so that a large amount of air can fit in a relatively small volume.
Compressibility is a measure of how much a given volume of matter decreases when placed under pressure. As discussed in the chapter States of Matter, the kinetic-molecular explains why gases are more compressible than either liquids or solids. Gases are compressible because most of the volume of a gas is composed of the large amounts of empty space between the gas particles. At room temperature and standard pressure, the average distance between gas molecules is about ten times the diameter of the molecules themselves. When a gas is compressed, as when the scuba tank is being filled, the gas particles are forced closer together.
Factors Affecting Gas Pressure
Recall from the kinetic-molecular theory that gas particles move randomly and in straight lines until they elastically collide with either other gas particles or with one of the walls of their container. It is these collisions with the walls of the container that define the pressure of the gas. Four variables are used to describe the condition of a gas. They are pressure (P), volume (V), temperature (T), and the amount of the gas, as measured by the number of moles of gas particles (n). We will examine separately how the volume, temperature, and amount of gas each affect the pressure of an enclosed gas sample.
Amount of Gas
The pressure of the air in a basketball has to be adjusted so that the ball bounces to the correct height (Figure below). Before a game, the officials check the ball by dropping it from shoulder height and seeing how far back up it bounces. What would the official do if the ball did not bounce up as far as it is supposed to? What would he do if it bounced too high?
There must be just the right amount of air in a basketball so that it will bounce up to the height that players are used to and will not adversely affect the game.
The pressure inside a container is dependent on the amount of gas inside the container. If the basketball does not bounce high enough, the official could remedy the situation by using a hand pump and adding more air to the ball. Conversely, if it bounces too high, he could let some air out of the ball. Figure below is an illustration of what happens when air is added to a rigid container. A rigid container is one that is incapable of expanding or contracting. A steel canister is an example of a rigid container.
When gas is pumped into a closed rigid container, the pressure increases. If the number of gas particles is doubled, the pressure doubles.
The canister on the left contains a gas at a certain pressure. The attached air pump is then used to double the amount of gas in the canister. Since the canister cannot expand, the increased number of air molecules will strike the inside walls of the canister twice as frequently as they did before. The result is that the pressure inside the canister doubles. As you might imagine, if more and more air is continually added to a rigid container, it may eventually burst. Reducing the number of molecules in a rigid container has the opposite effect, and the pressure decreases.
The air in a fully inflated car tire is at a higher pressure than the air outside the tire. What happens if you press on the tiny valve stem of the tire (Figure below)? You hear the distinctive hissing noise as the air rushes out of the tire. A gas will move from an area of higher pressure to an area of lower pressure until the pressures are equal. If you continue to press on that valve stem, the tire will eventually go flat.
Don’t press on the valve stem of a tire unless you want the air in the tire to escape!
Pressure is also affected by the volume of the container. If the volume of a container is decreased, the gas molecules have less space in which to move around. As a result, they will strike the walls of the container more often, resulting in an increase in pressure.
Figure below shows a cylinder of gas whose volume is controlled by an adjustable piston. On the left, the piston is pulled mostly out and the gauge reads a certain pressure. On the right, the piston has been pushed down so that the volume available to the sample of gas has been cut in half. As a result, the pressure of the gas doubles. Increasing the volume of the container would have the opposite effect - the pressure of the gas would decrease.
When the volume of an enclosed container of gas is reduced by pushing in an adjustable piston, the gas pressure increases. More specifically, if the volume is cut in half, the pressure doubles.
It would be very inadvisable to place a can of soup over a campfire without venting the can. As the can heats up, it may explode. The kinetic-molecular theory explains why. The air inside the rigid can of soup is given more kinetic energy by the heat coming from the campfire. The added kinetic energy causes the air molecules to move faster, so they impact the container walls more frequently and with more force. The increase in pressure inside may eventually exceed the strength of the can, causing it to explode. An additional factor is that the heated soup will have a higher vapor pressure (more water molecules escaping into the gas phase), adding more gas molecules and therefore more pressure to the inside of the can.
Figure below shows a cylinder of gas on the left that is at room temperature (300 K). On the right, the cylinder has been heated until the Kelvin temperature has doubled to 600 K. The kinetic energy of the gas molecules increases, so collisions with the walls of the container are now more forceful than they were before. As a result, the pressure of the gas doubles. Decreasing the temperature would have the opposite effect, and the pressure of an enclosed gas would decrease.
An increase in the temperature of an enclosed gas causes the pressure to increase. If the Kelvin temperature is doubled, the pressure doubles.
- Gases are compressible because of the large amounts of empty space between the particles.
- The condition of a gas sample can be described by four variables: pressure, volume, temperature, and amount of gas. The pressure of an enclosed gas will increase if the amount of gas is increased, the volume is decreased, or the temperature is increased.
Lesson Review Questions
- Why are gases easy to compress? Why are solids and liquids difficult to compress?
- Compare the characteristics of a rigid container and a flexible container. Explain how each type of container would respond if more gas is added to it.
- The amount of gas in a rigid container is tripled. What happens to the gas pressure?
- The volume of a rigid container is reduced to one fourth of its original size. What happens to the pressure of the gas inside?
- The Kelvin temperature of the gas in a rigid container is increased by a factor of 10. How does the pressure inside the container change?
- Explain what happens to a basketball if it is taken outside and used on a cold winter day.
- A student places a small amount of water in an empty aluminum can and heats it until the water is boiling. Then she quickly turns the can upside down and plunges it into a cold water bath. The can immediately collapses inwards. Describe this experiment according to the kinetic-molecular theory.
- Explain the noise that occurs when a vacuum-packed item such as a can of potato chips is opened.
- Liquid nitrogen is an extremely cold liquid (77 K) used for storage purposes. What would happen to an inflated balloon placed in a container of liquid nitrogen for several minutes? What would happen when the balloon was removed?
Further Reading / Supplemental Links
Points to Consider
The relationships between pressure, volume, temperature, and amount of gas can be treated mathematically in a set of equations called the gas laws.
- How many gas laws must there be if each law includes the relationship between two of the variables?
- Can a single gas law relate all of the variables to one another?