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FCS Physics and Chemistry

Behavior of Gases
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Gases are one of the most pervasive aspects of our environment on the Earth. We continually exist with constant exposure to gases of all forms.
   The steam formed in the air during a hot shower is a gas. The Helium used to fill a birthday balloon is a gas. The oxygen in the air is an essential gas for life.
 A windy day or a still day is a result of the difference in pressure of gases in two different locations. A fresh breeze on a mountain peak is a study in basic gas laws.  

To fully understand the world around us requires that we have a good understanding of the behavior of gases. The description of gases and their behavior can be approached from several perspectives. The Gas Laws are a mathematical interpretation of the behavior of gases. However, before understanding the mathematics of gases, a chemist must have an understanding of the conceptual description of gases. That is the purpose of the Kinetic Molecular Theory.

The Kinetic Molecular Theory Postulates

The experimental observations about the behavior of gases discussed so far can be explained with a simple theoretical model known as the kinetic molecular theory. This theory is based on the following postulates, or assumptions.

  1. Gases are composed of a large number of particles that behave like hard, spherical objects in a state of constant, random motion.
  2. These particles move in a straight line until they collide with another particle or the walls of the container.
  3. These particles are much smaller than the distance between particles. Most of the volume of a gas is therefore empty space.
  4. There is no force of attraction between gas particles or between the particles and the walls of the container.
  5. Collisions between gas particles or collisions with the walls of the container are perfectly elastic. None of the energy of a gas particle is lost when it collides with another particle or with the walls of the container.
  6. The average kinetic energy of a collection of gas particles depends on the temperature of the gas and nothing else.

The assumptions behind the kinetic molecular theory can be illustrated with the apparatus shown in the figure below, which consists of a glass plate surrounded by walls mounted on top of three vibrating motors. A handful of steel ball bearings are placed on top of the glass plate to represent the gas particles.

graphic

When the motors are turned on, the glass plate vibrates, which makes the ball bearings move in a constant, random fashion (postulate 1). Each ball moves in a straight line until it collides with another ball or with the walls of the container (postulate 2). Although collisions are frequent, the average distance between the ball bearings is much larger than the diameter of the balls (postulate 3). There is no force of attraction between the individual ball bearings or between the ball bearings and the walls of the container (postulate 4).

The collisions that occur in this apparatus are very different from those that occur when a rubber ball is dropped on the floor. Collisions between the rubber ball and the floor are inelastic, as shown in the figure below. A portion of the energy of the ball is lost each time it hits the floor, until it eventually rolls to a stop. In this apparatus, the collisions are perfectly elastic. The balls have just as much energy after a collision as before (postulate 5).

Any object in motion has a kinetic energy that is defined as one-half of the product of its mass times its velocity squared.

KE = 1/2 mv2

At any time, some of the ball bearings on this apparatus are moving faster than others, but the system can be described by an average kinetic energy. When we increase the "temperature" of the system by increasing the voltage to the motors, we find that the average kinetic energy of the ball bearings increases (postulate 6).


How the Kinetic Molecular Theory Explains the Gas Laws

The kinetic molecular theory can be used to explain each of the experimentally determined gas laws.

The Link Between P and n

The pressure of a gas results from collisions between the gas particles and the walls of the container. Each time a gas particle hits the wall, it exerts a force on the wall. An increase in the number of gas particles in the container increases the frequency of collisions with the walls and therefore the pressure of the gas.

Amontons' Law (PT)

The last postulate of the kinetic molecular theory states that the average kinetic energy of a gas particle depends only on the temperature of the gas. Thus, the average kinetic energy of the gas particles increases as the gas becomes warmer. Because the mass of these particles is constant, their kinetic energy can only increase if the average velocity of the particles increases. The faster these particles are moving when they hit the wall, the greater the force they exert on the wall. Since the force per collision becomes larger as the temperature increases, the pressure of the gas must increase as well.

Boyle's Law (P = 1/v)

Gases can be compressed because most of the volume of a gas is empty space. If we compress a gas without changing its temperature, the average kinetic energy of the gas particles stays the same. There is no change in the speed with which the particles move, but the container is smaller. Thus, the particles travel from one end of the container to the other in a shorter period of time. This means that they hit the walls more often. Any increase in the frequency of collisions with the walls must lead to an increase in the pressure of the gas. Thus, the pressure of a gas becomes larger as the volume of the gas becomes smaller.

Charles' Law (V T)

The average kinetic energy of the particles in a gas is proportional to the temperature of the gas. Because the mass of these particles is constant, the particles must move faster as the gas becomes warmer. If they move faster, the particles will exert a greater force on the container each time they hit the walls, which leads to an increase in the pressure of the gas. If the walls of the container are flexible, it will expand until the pressure of the gas once more balances the pressure of the atmosphere. The volume of the gas therefore becomes larger as the temperature of the gas increases.

Avogadro's Hypothesis (V N)

As the number of gas particles increases, the frequency of collisions with the walls of the container must increase. This, in turn, leads to an increase in the pressure of the gas. Flexible containers, such as a balloon, will expand until the pressure of the gas inside the balloon once again balances the pressure of the gas outside. Thus, the volume of the gas is proportional to the number of gas particles.

 

Ideal vs. Real Gases

Kinetic Molecular Theory explains the behavior of what is called "Ideal Gases"; real gases behavior only like real gases under two conditions

1. AT HIGH TEPERATURES gas particles do not attract each other, however, at extremely low temperatures they do in some cases.  For example, O combines with a free oxygen atom in the atmosphere to make O3 (ozone)

2. At LOW PRESSURES gas particle volume does not matter becuase their is a great deal of distance seperating them and most likely they will not combine.  At high pressure, the gas particle volume is important and becomes a factor.

 

Combined Gas Law Equation
 
The relationship among pressure, temperature and volume can be mathematically represented by an equation known as the combined gas law.  You need to be able to solve this equation for any of the variables involved; simply plugging in numbers and doing the math in your head will not help you on the Regents exam.
 
 
 

cgl.jpeg

When using this equation, you must remember:
 
  • Units of pressure and temperature must be the same
  • Temperature must be in kelvin

 

Practice Problems: see bottom of page for answers
 

1.  The volume of the lungs is measured by the volume of air inhaled or exhaled.  If the volume of the lungs is 2.400 L during exhalation and the pressure is 101.70 KPa, and the pressure during inhalation is 101.01 KPa, what is the volume of the lungs during inhalation? 

2.  The total volume of a soda can is 415 mL.  Of this 415 mL, there is 60.0 mL of headspace for the CO2 gas put in to carbonate the beverage.  If a volume of 100.0mL of gas at standard pressure is added to the can, what is the pressure in the can when it has been sealed?

3.  It is hard to begin inflating a balloon.  A pressure of 800.0 Kpa is required to initially inflate the balloon 225.0 mL.  What is the final pressure when the balloon has reached it's capacity of 1.2 L?

4.  If a piston compresses the air in the cylinder to 1/8 it's total volume and the volume is 930 cm3  at STP, what is the pressure after the gas is compressed? 

5.  If a scuba tank that has a capacity of 10.0 dm3  is filled with air to 500.0 KPa, what will be the volume of the air at 702.6 KPa? 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Gas Law Solutions

 

1.  The volume of the lungs is measured by the volume of air inhaled or exhaled.  If the volume of the lungs is 2.400 L during exhalation and the pressure is 101.70 KPa, and the pressure during inhalation is 101.01 KPa, what is the volume of the lungs during inhalation? 

    V2 = [V1][P1]          V2 = [2.400L][101.70KPa]  =  2.412L
                   [P2]                                 [101.01KPa]

2.  The total volume of a soda can is 415 mL.  Of this 415 mL, there is 60.0 mL of headspace for the CO2 gas put in to carbonate the beverage.  If a volume of 100.0 mL of gas at standard pressure is added to the can, what is the pressure in the can when it has been sealed?

    P2 = [V1][P1]          P2 = [100.0 mL][101.3KPa]  =  169 KPa
            [V2]                         [60.0 mL]

3.  It is hard to begin inflating a balloon.  A pressure of 800.0 Kpa is required to initially inflate the balloon 225.0 mL.  What is the final pressure when the balloon has reached it's capacity of 1.2 L?

     P2 = [V1][P1]          P2 = [0.225L][800.0 KPa]  =  150 KPa
             [V2]                         [1.2 L]

4.  If a piston compresses the air in the cylinder to 1/8 it's total volume and the volume is 930 cm3  at STP, what is the pressure after the gas is compressed? 

      P2 = [V1][P1]          V2 = [930cm3 ][101.3 KPa]  =  810 KPa
              [V2]                         [930/8cm3]

5.  If a scuba tank that has a capacity of 10.0 dm3  is filled with air to 500.0 KPa, what will be the volume of the air at 702.6 KPa? 

     V2 = [V1][P1]          V2 = [10.0 dm3][500.0KPa]  =  7.11 dm3
                    [P2]                                    [702.6KPa]

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