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# 13.1: Kinetic-Molecular Theory and Gases

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## Lesson Objectives

• State the main points of the kinetic molecular theory, and describe how it relates to the properties of an ideal gas.
• Define pressure and describe how gases exert pressure.
• Understand the barometer and how it measures atmospheric pressure. Convert between units of gas pressure.
• Relate temperature to average kinetic energy.

## Lesson Vocabulary

• absolute zero
• atmospheric pressure
• barometer
• gas pressure
• ideal gas
• kinetic-molecular theory
• pascal
• pressure

### Recalling Prior Knowledge

• How are gases different from solids and liquids in terms of the arrangement of the particles?
• What are kinetic energy and temperature?
• What is the Kelvin temperature scale?

Matter commonly exists in three forms or states: solid, liquid, or gas. In earlier chapters, you learned about the study of matter at the atomic and molecular level. In this chapter, we will be concerned with the macroscopic properties of matter. In other words, we will study the properties and behavior of large quantities of matter. This lesson focuses on a general conception of matter called the kinetic-molecular theory, with special attention focused on its application to gases.

Start this section out with a funny review of the phases of matter at http://video.pbs.org/video/2175892485

You can also review the phases of matter by working a puzzle at http://education.jlab.org/sciencecrossword/matter_01.html.

Review what phases look like on the molecular level at http://www.youtube.com/watch?v=yXAu_1DXN7o.

You can also review phases of matter by watching a video lecture at http://www.khanacademy.org/science/chemistry/states-of-matter/v/states-of-matter.

There is also a follow-up of the above video lecture at http://www.khanacademy.org/science/chemistry/states-of-matter/v/states-of-matter-follow-up.

Another great review of the phases of matter is provided by NASA at http://www.grc.nasa.gov/WWW/k-12/airplane/state.html.

## The Kinetic-Molecular Theory

The kinetic-molecular theory is a theory that explains the states of matter and is based on the idea that matter is composed of tiny particles that are always in motion. The theory helps explain observable properties and behaviors of solids, liquids, and gases. However, the theory is most easily understood as it applies to gases, and it is with gases that we will begin our detailed study. The theory applies specifically to a model of a gas called an ideal gas. An ideal gas is an imaginary gas whose behavior perfectly fits all the assumptions of the kinetic-molecular theory. In reality, gases are not ideal, but are very close to being so under most everyday conditions.

The kinetic-molecular theory as it applies to gases has five basic assumptions.

1. Gases consist of very large numbers of tiny spherical particles that are far apart from one another compared to their size. The particles of a gas may be either atoms or molecules. The distance between the particles of a gas is much, much greater than the distances between the particles of a liquid or a solid. Most of the volume of a gas, therefore, is composed of the empty space between the particles. In fact, the volume of the particles themselves is considered to be insignificant compared to the volume of the empty space.
2. Gas particles are in constant rapid motion in random directions. The fast motion of gas particles gives them a relatively large amount of kinetic energy. Recall that kinetic energy is the energy that an object possesses because of its motion. The particles of a gas move in a straight line until they collide with another particle or with one of the walls of their container (Figure below).
3. Collisions between gas particles and between particles and the container walls are elastic collisions. An elastic collision is one in which there is no overall loss of kinetic energy. Kinetic energy may be transferred from one particle to another during an elastic collision, but there is no change in the total energy of the colliding particles.
4. There are no forces of attraction or repulsion between gas particles. Attractive forces are responsible for particles of a real gas condensing together to form a liquid. It is assumed that the particles of an ideal gas have no such attractive forces. The motion of each particle is completely independent of the motion of all other particles.
5. The average kinetic energy of gas particles is dependent upon the temperature of the gas. As the temperature of a gas is increased, its component particles begin to move faster, resulting in an increase in their kinetic energies. Not all particles in a given sample have the same speed, so the sample will contain particles with a range of different kinetic energies. However, the average kinetic energy of the particles in a sample is proportional to its temperature.

Gas particles move in a random, linear fashion according to the kinetic-molecular theory. The space between particles is very large compared to the size of the particles.

Watch what happens when the average kinetic energy of water decreases at http://www.youtube.com/watch?v=uTsC6k0ZzH4.

Watch an animation of the kinetic energy of a gas at http://www.dlt.ncssm.edu/core/Chapter11-Thermochemistry/Chapter11-Animations/KineticEnergy-Gas.html.

Watch an animation of the kinetic energy of a liquid at http://www.dlt.ncssm.edu/core/Chapter11-Thermochemistry/Chapter11-Animations/KineticEnergy-Liquid.html.

Watch an animation of the kinetic energy of a solid at http://www.dlt.ncssm.edu/core/Chapter11-Thermochemistry/Chapter11-Animations/KineticEnergy-Solid.html.

NASA provides a lot of information on the kinetic molecular theory and activities you can do at home at http://www.grc.nasa.gov/WWW/k-12/airplane/kinth.html.

## Gas Pressure

Pressure is defined as the force per unit area on a surface.

$\mathrm{Pressure=\dfrac{force}{area}}$

When a person stands on the floor, his feet exert pressure on the surface. That pressure is related to both the mass of the person and the surface area of his feet. If the person were holding a heavy object, the pressure would increase because of a greater force. Alternatively, if the person stands on his toes, the pressure also increases because of a decrease in the surface area.

Gas molecules also exert pressure. Earth’s atmosphere exerts pressure because gravity acts on the huge number of gas particles contained in the atmosphere, holding it in place. Pressure is also exerted by small samples of gas, such as the outward pressure exerted by the gas inside a balloon. Gas pressure is the pressure that results from collisions of gas particles with an object. Inside the balloon, the gas particles collide with the balloon’s inner walls. It is those collisions which keep the balloon inflated. If the gas particles were to suddenly stop moving, the balloon would instantly deflate. Figure below is an illustration of gas particles exerting pressure inside a container.

NASA provides a diagram and a thorough explanation of pressure at http://www.grc.nasa.gov/WWW/k-12/airplane/pressure.html.

You can perform an inquiry experiment to determine the relationship between compression and state of matter. You must download a program from the Concord Consortium. This is a very useful program because it contains lots of chemistry experiments for you to do. The instructions to this activity can be found at https://docs.google.com/open?id=0B_ZuEGrhVEfMMkNmT2tvUWRyUzQ.

### Measuring Pressure

Atmospheric pressure is the pressure exerted by the gas particles in Earth’s atmosphere as those particles collide with objects. A barometer is an instrument used to measure atmospheric pressure. A traditional mercury barometer consists of an evacuated tube immersed in a container of mercury (Figure below (A)). Air molecules from the atmosphere push down on the outer surface of the mercury, but because the inside of the tube is a vacuum, there is no corresponding downward push on the mercury in the tube. As a result, the mercury rises inside the tube. The height to which the mercury rises is dependent on the external air pressure.

(A) A barometer measures atmospheric pressure as the height of a column of mercury. (B) A more modern aneroid barometer can be read by looking at the position of a dial. Barometers are frequently used by meteorologists to help them predict upcoming weather patterns.

At sea level, a mercury column will rise a distance of 760 mm. This atmospheric pressure is reported as 760 mmHg (millimeters of mercury). At higher altitudes, the atmospheric pressure is lower, so the column of mercury will not rise as high. For example, on the summit of Mt. Everest (at an elevation of 8848 m), the air pressure is 253 mmHg. Atmospheric pressure is also slightly dependent on weather conditions.

A more convenient barometer, called an aneroid barometer, measures pressure by the expansion and contraction of a small spring within an evacuated metal capsule. Figure above (B) shows an aneroid barometer.

A device similar to a barometer is used to measure the pressure of an enclosed gas sample (Figure below). The pressure of the gas in the bulb is determined by the difference in the height of mercury between the two arms of the U-tube.

A manometer is used to measure the pressure of an enclosed gas sample. The difference in height (Δh) between the two arms of the U-tube indicates the gas pressure.

An excellent interactive animation to help you understand atmospheric pressure can be found at http://www.dlt.ncssm.edu/core/Chapter7-Gas_Laws/Chapter7-Animations/AtmosphericPressure.html.

You can see a barometer made in a chemistry lab at http://www.youtube.com/watch?v=GgBE8_SyQCU!

### Units of Gas Pressure

As seen above, a barometer measures gas pressure by the height of the column of mercury. One unit of gas pressure is the millimeter of mercury (mmHg). An equivalent unit to the mmHg is called the torr, in honor of the inventor of the barometer, Evangelista Torricelli. The pascal (Pa) is the standard unit of pressure. A pascal is a very small amount of pressure, so a more useful unit for everyday gas pressures is the kilopascal (kPa). A kilopascal is equal to 1000 pascals. Another commonly used unit of pressure is the atmosphere (atm). Standard atmospheric pressure is called 1 atm of pressure and is equal to 760 mmHg and 101.3 kPa.

1 atm = 760 mmHg = 760 torr = 101.3 kPa

It is important to be able to convert between different units of pressure. To do so, we will use the equivalent standard pressures shown above.

Sample Problem 13.1: Pressure Unit Conversions

The atmospheric pressure in a mountainous location is measured to be 613 mmHg. What is this pressure in atm and in kPa?

Step 1: List the known quantities and plan the problem.

Known

• given: 613 mmHg
• 1 atm = 760 mmHg
• 101.3 kPa = 760 mmHg

Unknown

• pressure = ? atm
• pressure = ? kPa

Use conversion factors from the equivalent pressure units to convert from mmHg to atm and from mmHg to kPa.

Step 2: Solve.

$\mathrm{613 \ mmHg \times \dfrac{1 \ atm}{760 \ mmHg}=0.807 \ atm}$
$\mathrm{613 \ mmHg \times \dfrac{101.3 \ kPa}{760 \ mmHg}=81.7 \ kPa}$

The air pressure is about 80% of the standard atmospheric pressure at sea level. The standard pressure of 760 mmHg can be considered to have three significant figures.

Practice Problem
1. Convert the pressure of 535 kPa to mmHg and to atm.

## Kinetic Energy and Temperature

As stated in the kinetic-molecular theory, the temperature of a substance is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the speeds at which the particles are moving. This is observed as an increase in the temperature of the substance.

### Average Kinetic Energy

At any given temperature, not all of the particles in a sample of matter have the same kinetic energy. Instead, the particles display a wide range of kinetic energies. Most of the particles have a kinetic energy near the middle of the range. However, some of the particles have kinetic energies a great deal lower or a great deal higher than the average (Figure below).

A distribution of molecular kinetic energies as a function of temperature. The blue curve is for a low temperature, while the red curve is for a high temperature.

The blue curve in Figure above is for a sample of matter at a relatively low temperature, while the red curve is for a sample at a relatively high temperature. In both cases, most of the particles have intermediate kinetic energies, close to the average. Notice that as temperature increases, the range of kinetic energies increases and the distribution curve “flattens out.”

At a given temperature, the particles of any substance have the same average kinetic energy. At room temperature, the molecules in a sample of liquid water have the same average kinetic energy as the molecules in a sample of oxygen gas or the ions in a sample of sodium chloride.

You can see an exciting demonstration of the relationship between kinetic energy and temperature by watching a piece of nitrocellulose ignite from the compression of air at http://www.youtube.com/watch?v=jsQlfxdZ9ys.

You can visualize the motion of gas molecules indirectly by watching glass beads move in mercury gas at http://www.youtube.com/watch?v=26dAsmFWz24.

### Absolute Zero

As a sample of matter is continually cooled, the average kinetic energy of its particles decreases. Eventually, one would expect the particles to stop moving completely. Absolute zero is the temperature at which the motion of particles theoretically ceases. Absolute zero has never been attained in the laboratory, but temperatures on the order of 1 × 10−10 K have been achieved. The Kelvin temperature scale is based on this theoretical limit, so absolute zero is equal to 0 K. The Kelvin temperature of a substance is directly proportional to the average kinetic energy of the particles of the substance. For example, the particles in a sample of hydrogen gas at 200 K have twice the average kinetic energy as the particles in a hydrogen sample at 100 K.

Helium gas liquefies at 4 K or four degrees above absolute zero. Liquid helium is used as a coolant for large superconducting magnets and must be stored in insulated metal canisters. Pictured here is a large liquid helium container used to cool the magnet of a particle accelerator.

You can view a simulation of the molecular motion of gas molecules as heat is added at http://www.dlt.ncssm.edu/core/Chapter11-Thermochemistry/Chapter11-Animations/KineticEnergy-Gas.html.

## Lesson Summary

• The kinetic-molecular theory describes all matter, but it is especially useful for explaining the behavior of gases. Gas particles are assumed to occupy an insignificant volume compared to the space between particles. Particles undergo random linear motion and collide elastically with one another and with their container.
• Gas pressure results from the collisions of gas particles with an object. Pressure is measured with a barometer or a manometer. Conversions between pressure units can be performed by using dimensional analysis.
• The temperature of a substance in Kelvin is directly proportional to the average kinetic energy of the particles in that substance.

## Lesson Review Questions

### Reviewing Concepts

1. How are gases different from liquids and solids in terms of the distance between the particles?
2. Which of the following are behaviors of a gas that can be explained by the kinetic-molecular theory?
1. Gases are compressible.
2. Gases exert pressure.
3. All particles of a gas sample move at the same speed.
4. Gas particles can exchange kinetic energy when they collide.
5. Gas particles move in a curved-line path.
3. What is an elastic collision?
4. List several common units of gas pressure.
5. How high does a column of mercury rise when inverted in a dish of mercury at sea level? Why do you suppose that mercury is used to measure atmospheric pressure rather than water?
6. Would it be more or less difficult to drink water through a straw on the summit of Mt. Everest than it would be at sea level? Explain.
7. How does the average kinetic energy of an air sample near a campfire compare to air that is far away from it?

### Problems

1. Perform the indicated conversions for the following pressure measurements.
1. 1.721 atm to mmHg
2. 559 torr to kPa
3. 91.1 kPa to atm
4. 2320 mmHg to atm
2. A manometer is attached to an enclosed gas sample as in Figure above. The mercury rises 20 mm higher on the side of the U-tube that is open to the air. The atmospheric pressure is 752 mmHg. What is the pressure of the gas sample in the bulb?
3. A sample of neon gas is at −25°C. What would be its Celsius temperature when the average kinetic energy of the particles is tripled?
4. The density of water is approximately 1/14th that of mercury. If the atmospheric pressure at a certain location is 750. mmHg, to what height (in m) would a column of water rise?

A document to guide you through this simulation with questions can be found at https://docs.google.com/open?id=0B_ZuEGrhVEfMZW5TcTc4aDI0RXc.

## Points to Consider

The particles of a liquid are much closer together than the particles of a gas, resulting in far different behaviors for liquids as compared to gases.

• How does the kinetic energy of the particles in a liquid relate to the rate of evaporation of the liquid?
• How is the boiling point of a liquid defined?

Aug 02, 2012

Sep 09, 2014