Unit 8 Kinetic Theory of Gases Chapter 13-14
This tutorial is designed to help students understand scientific measurements. Objectives for this unit appear on the next slide. Each objective is linked to its description. Select the number at the front of the slide to go directly to its description. Throughout the tutorial, key words will be defined. Select the word to see its definition.
Objectives 4 Define kinetic theory of gases including collisions 5 Define pressure, including atmospheric pressure, vapor pressure, pressure differentials, and how a barometer works 6 Describe boiling points, including normal boiling points, using vapor pressure graphs, explaining the difference between boiling and evaporation, and how intermolecular forces and molecular weight determine evaporation rates 7 Define and use data based on the triple point phase diagram 8 Define and know the variables of the Gas Laws, including Boyle s Law, Charles Law, Gay-Lussac s Law, and the combined gas law 9 State Avogadro s Principle 10 Use the ideal gas law to solve problems and know the variables of the ideal gas law 11 State and use Dalton s Law of Partial Pressures 12 State and use Graham s Law of effusion and define diffusion
4 The Kinetic Theory Particles at the molecular level have been described previously. It has been stated that these particles are in a constant state of motion and are attracted to each other through intermolecular forces. The kinetic theory as described on the next slide is specific to gases.
Kinetic Theory of Gases There are five parts to the kinetic theory of gases. 1. Gases will fill the entire volume allowed. This means that is 10 oxygen molecules are released in a classroom, they will arrange themselves equally throughout that space. If the same 10 were released in a gymnasium, they will do the same.
Kinetic Theory of Gases 2. Gases can be compressed. The volume a gas holds can be increased or decreased. 3. The motion of gases is random. Gas molecules will travel in straight lines until they run into an object. 4. Gas molecules have elastic collision. When gas molecules collide, there is no loss in kinetic energy.
Kinetic Theory of Gases 5. The kinetic energy of a gas molecule is measured by temperature. As the temperature increases, gas molecules move faster, and as the temperature decreases, gas molecules move slower.
Kinetic Theory of Gases A quick recap: 1. Gases fill the entire volume allowed. 2. Gases can be compressed. 3. The motion of a gas is random. 4. Gases have elastic collisions. 5. The kinetic energy of gases is measured with temperature. The link below is for a simulator that demonstrates some of these ideas. http://phet.colorado.edu/en/simulation/gas-properties
5 Pressure Pressure is a measure of force per unit surface area. For instance, assume you are standing. You are exerting a force on the floor. The surface area is the size of both of your feet. If you stand on only one foot, the force would be the same but the surface area is halved so the pressure doubles. When referring to gases, pressure is the measure of the force exerted when two gas particles collide.
Air Pressure and Vapor Pressure The molecules that make of the air around you are constantly colliding with each other and the objects in the room (including you). These collisions make up air pressure. Vapor pressure is the pressure exerted by the air on a liquid.
Measuring pressure Atmospheric pressure is determined using an instrument known as a barometer. The barometer is filled with mercury because of its density. As atmospheric pressure pushes down on the mercury, it forces the mercury up the column. Atmospheric pressure is measured by the distance the mercury is displaced. Atmospheric Pressure Mercury 760 mm
Pressure The barometer was invented by a scientist by the name of Torricelli. Pressure is often given with units of mm Hg but the torr is used as well. To make the numbers easier to work with, atmospheric pressure was set equal to 1 atm (atmosphere)
Units of Pressure There are several units for pressure and all are used. Therefore the following values are equal to atmospheric pressure: 1 atm = 101.325 kpa (kilopascals) 101,325 Pa (Pascals) 760 mm Hg 760 torr
6 Temperature vs. Heat The last part of the kinetic theory mentioned temperature. Temperature is often confused with heat but the two are quite different. Temperature is a measure of the average kinetic energy of molecules. Heat is the measure of the total kinetic energy of molecules.
Temperature vs. Heat All molecules are in a state of motion. The motion is measured by kinetic energy. However, not all molecules are moving at the same speed and thus do not have the same kinetic energy. The average is taken to determine the speed of the majority of the molecules. The total is determined for a purpose that will be discussed in Unit 9.
Temperature The average kinetic energy is reported in three different scales. Fahrenheit Celsius Kelvin ( F) ( C) (K) Each scale is used by certain individuals about the world. The scientific community prefers Celsius or Kelvin.
Temperature The Celsius scale was designed to have the boiling point of water be 100 C while the freezing point of water would be 0 C. The Kelvin scale was designed using the same increments as Celsius but instead placed zero at absolute zero.
Temperature It is important to be able to convert from one scale to another so the following equations were determined: F = C 9 5 + 32 C=( F 32) x 5 9 K = 273.15 + C
Boiling Points Boiling is the process of taking a liquid to the gaseous state. This process occurs by adding heat to the liquid. However, there are additional factors that can affect the boiling point. These include intermolecular forces and vapor pressure.
Intermolecular Forces When heat is added to a liquid, the particles in that liquid gain kinetic energy. Gaining kinetic energy means that they are moving faster. It is the intermolecular forces that hold the molecules close together. With enough kinetic energy, a molecule can overcome the intermolecular forces and break free. The stronger the intermolecular force, the more kinetic energy will be required to break free.
Boiling versus Evaporation It also depends on where the heat is added as to how easy it will be to overcome the intermolecular force. Both boiling and evaporation are ways to bring a liquid to a gas but each can occur at different temperatures.
Evaporation When considering evaporation, the heat comes from a source above the liquid. This means the particles on the top of the liquid gain kinetic energy (shown in red) Once they gain enough energy, they can break free of the intermolecular forces. Heat Notice, it is only the top that increases kinetic energy while the rest of the molecules remain the same. This is why the temperature of the liquid does not have to greatly increase during evaporation.
Boiling In comparison to evaporation, boiling adds heat to the bottom of the liquid. Since the bottom particles have to work their way to the top, it is more difficult to overcome the intermolecular forces. In order to overcome the intermolecular forces, all particles will need to gain kinetic energy. Because all particles must gain energy, the temperature increases. This is also why boiling proceeds faster than evaporation.
Vapor Pressure The other factor effecting the boiling point is vapor pressure. Vapor pressure is the pressure from the atmosphere above a liquid. The gas particles above a liquid can prevent molecules that have enough energy to break free from the intermolecular forces from becoming a gas. The image on the next slide illustrates this idea.
Vapor Pressure Gas Particles The particle escapes but transfers its energy to a gas particle. The particle falls back to the liquid.
Vapor Pressure If there were less particles above the liquid, it would be easier to boil. The boiling point at one atmosphere is considered to be the normal boiling point. A vapor pressure diagram can help determine the boiling point.
Pressure (atm) Vapor Pressure Diagrams Vapor pressure diagrams show the relationship between vapor pressure and the boiling point. The red line below represents the normal boiling point. Notice, it is easier to boiling if there is a smaller vapor pressure. This liquid would boil at 62 C if the pressure of 0.18 atm. The normal boiling point is 101 C at 1 atm. Vapor Pressure Diagram 1.00 0.80 0.60 0.40 0.20 0.00 0 20 40 60 80 100 120 Temperature (C)
Standard Temperature and Pressure (STP) For the purposes of scientific consistency, a select temperature and pressure were selected. This way, all experiments could be repeated at the same atmospheric conditions. STP is 1 atm of pressure and 0 C.
7 Triple Point Diagrams The vapor pressure diagram shows a portion of a larger diagram known as the triple point diagram. This diagram represents the three types of matter and their relationships to pressure and temperature. The following slide shows a possible triple point diagram. There are six phase changes that occur as you cross each line form one phase to the next. The triple point is denoted with a blue dot.
Pressure (atm) Triple Point Diagram 1.20 Critical Point 1.00 Solid Liquid 0.80 Melting 0.60 Freezing Vaporization 0.40 Condensation Sublimation 0.20 0.00 Deposition Gas Triple Pt. 0 20 40 60 80 100 120 Temperature (C)
Triple Point Diagrams The triple point indicates a point where all three phases are present at the same time. It only occurs at one temperature and pressure for each substance. The critical point is also marked. The critical point indicates where the kinetic theory does not accurately describe the properties of this chemical.
8 Gas Laws Temperature, pressure, and volume have a distinct affect on gases. It was determined that these three variables have distinct relationships. These relationships are known as the gas laws.
Pressure (atm) Boyle s Law Boyle s Law describes the relationship between pressure and volume. The relationship is inverse which means as one increases, the Boyle's Law other decreases. 1 The equation for Boyle s Law is: 0.5 P 1 V 1 =P 2 V 2 0 0 2 4 6 8 10 12 Volume (L)
Volume (L) Charles Law Charles Law describes the relationship between temperature and volume. The relationship is direct which means as one increases, the Charles' Law 14 other increases. 12 The equation for 10 8 Charles Law is: 6 V 1 T 1 =V 2 T 2 4 2 0 250 270 290 310 330 350 Temperature (K)
Pressure (atm) Gay-Lussac s Law Gay-Lussac s Law describes the relationship between pressure and temperature. The relationship is direct which means as one increases, the Gay-Lussac's Law 1.4 other increases. 1.2 1 The equation for 0.8 Gay-Lussac s Law is: 0.6 P 1 T 1 =P 2 T 2 0.4 0.2 0 250 270 290 310 330 350 Temperature (K)
Gas Laws The three gas laws described require certain units to be used. Volume = liters Temperature = Kelvin Pressure = kpa or atm The three can also be combined.
Combined Gas Law As that all three variables can be difficult to hold constant, the three gas laws can be combined to create the combined gas law. P 1 V 1 T 1 = P 2V 2 T 2
Gas Law Recap Gas Law Boyle s Charles Gay- Lussac s Combined Equation P 1 V 1 =P 2 V 2 V 1 T 1 = V 2 T 2 P 1 T 1 = P 2 T 2 P 1 V 1 T 1 = P 2V 2 T 2 Relationship Inverse Direct Direct Constant Temperature Pressure Volume Nothing
9 Avogadro s Principle Up to this point, we have examined gases under the assumption that we always held the same number of moles in the container. This is not always the case. Just as a relationship was determined between pressure, volume, and temperature, a relationship was determined between the number of moles and volume.
Avogadro s Principle According to Avogradro s Principle, if the number of moles increase, the volume also must increase assuming constant temperature and pressure. V 1 n 1 = V 2 n 2 n = moles
Avogadro s Principle Using this principle, it was determined that at STP (standard temperature and pressure), one mole of a gas would always take up the same volume. At 0 C and 1 atm, 1 mole will take up 22.4 liters.
10 Ideal Gas Law With the inclusion of the mole into the relationships of gases, it could be added to the combined gas law as well. PV T = k V n = k K represents a constant PV nt = k
Ideal Gas Law Upon further analysis, it was determined that the constant could be calculated and was the same for each container. Assume STP conditions: 1 Mole 22.4 Liters 273.15 K 1 atm PV nt = k 1 atm x 22.4 L 1 mole x 273.15 K = k k = 0.0821 atm x L mole x K
Ideal Gas Law The constant was changed to R and requires specific units to be used. There are two commonly used values for atm x L kpa x L R: 0.0821 or 8.314 mole x K mole x K Required Units: Volume: Liters Amount: moles Temperature: Kelvin Pressure: atm or kpa
Ideal Gas Law The equation for the Ideal Gas Law is: PV=nRT The value of R is chosen based on the units on the pressure.
11 Dalton s Law of Partial Pressures When gases were discussed in Unit 10, it was mentioned that pressure was measured with the collisions gas particles underwent. The total pressure is a sum of all of those collisions. Therefore, Dalton s Law states that the pressure of each gas can be added to determine the total pressure.
Dalton s Law of Partial Pressures Though Dalton s Law seems fairly basic, it is extremely useful when collecting a gas. When most experiments are performed, the gases produced are allowed to escape. However, if it is the gas that needs to be analyzed, the gas most be collected. The collection of this gas is typically done over water.
Collecting a Gas over Water Collecting a gas over water requires a sealed container with a tube into a tank of water. In the tank of water, an inverted tube is filled with water. As the reaction progresses, the gas produced follows the tube into the water chamber and up the inverted tube.
Dalton s Law Dalton s Law comes into play because a small amount of water with change to a gas in the container. Therefore, the gas collected and water vapor combine to give the pressure. That pressure is equal to the atmospheric pressure outside of the tube. Therefore, the following equation applies: P atmosphere = P gas + P water
12 Effusion and Diffusion Graham s Law of Effusion states that at the same temperature, a heavier molecule will move slower than a lighter molecule. Recall that temperature is the average kinetic energy of a molecule. Kinetic energy is calculated by taking the mass times the velocity squared (KE=mv 2 ) The relationship between speed and mass is inverse. Diffusion is the dispersion of molecules from areas of high concentration to areas of low concentration.
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Definitions-Select the word to return to the tutorial Absolute zero the temperature at which molecules no longer move. Intermolecular Forces forces that hold molecules together. These include hydrogen bonding, dipole forces, and London forces