Unit 10: Gas Laws Name: Monday Tuesday Wednesday Thursday Friday February 8 Stoichiometry Test Review 9 Stoichiometry Test 10 Review for Cumulative Retest 11 Cumulative Re-Test 12 Pressure & Kinetic Theory of Gases 15 Combined Gas Law Soda can activity HW: p.8 16 Boyle s, Charles, and Avogadro s Law- HW: pp.14 15 17 Chem Think Gas Laws Tutorial- Computer Lab- 18 Gas Laws Lab/Activity Begin working on Study Guide- pgs. 24-28 Study for Quiz on Friday HW: p.4 Bring an empty soda can to class monday 19 Quiz Dalton s Law of Partial Pressures HW: Pg. 17 Study Guide- pgs. 24-28 22 Ideal Gas Law HW: p.20 Study Guide- pgs. 24-28 23 Stoichiometry with Gas Laws HW: p.23 and study guide (pp.24-28) 24 Review for Test Study Guide Due TODAY!! 25 Gas Laws Test 26 Class Period: Test Date: February 25th 1
Pressure 1. What is the definition of pressure? 2. What causes pressure? 3. Which shoes create the most pressure? How does changing the area of contact affect the amount of pressure exerted by an object? 4. What are the units used to measure pressure? 5. How do I convert between units of pressure? atm = mmhg = kpa = psi 6. How many kilopascals are equivalent to 880 mmhg? 7. Calculate the number of pounds per square inch (psi) that are in 2.60atm. Temperature ALWAYS use absolute temperature (Kelvin) when working with gases. Conversion: K = C + 273 Practice problems: 32 C = K How much is 75 C in Kelvin? 2
The Behavior of Gases and the Kinetic Theory Kinetic refers to. The energy an object has, because of its motion, is called The Kinetic theory states that the tiny particles in all forms of matter are in. Watch the video segment (Kinetic Molecular Theory in the video Standard Deviants School Chemistry: Molecular Geometry) on Discovery Education and fill in the missing information http://app.discoveryeducation.com/search?ntt=standard+deviants+gas Basic assumptions of the kinetic theory as it applies to gases are: 1. A gas is composed of particles, usually molecules or atoms that are from one another in comparison with their own dimensions. Particles are relatively far apart from one another and between them is. 2. Gas molecules are in. They travel in straight paths (unless they collide with a wall of a container) and move independently of each other. 3. The molecules exert no force on each other or on the container until they with each other or with the walls of the container. 4. The average kinetic energy of the molecules of a gas is proportional to the. 5. Every time a molecule collides with the wall, it exerts a on it which we call. Applying this knowledge we know Gases fill their containers regardless of the and of the containers. Because there is so much space between particles, gases are. Because gases are, they are used in automobile and other safety devices designed to the of an impact. All are perfectly. This means that during collisions kinetic energy is transferred without loss from one particle to another, and total kinetic energy remains. 3
The average speed of oxygen molecules in air at 20 o C is 1700 km/h. At these high speeds, the odor molecules from a hot pizza in Washington, D.C., should reach Mexico City in about 106 minutes. Why doesn t this actually happen? Questions: A. What happens when a closed container is inflated? B. A gas inside a bicycle tire exerts a pressure of 35 pounds per square inch (psi). How much air must be pumped into the tire to produce a pressure of 70 psi? ** The relationship between amount of gas and pressure is proportional, assuming the volume & temperature stay the same. C. What happens to pressure when a closed container is deflated? (Note: Gas particles move from region of higher pressure to lower pressure until equilibrium is reached.) HOMEWORK Day 1 - Practice Problems on Pressure & Temperature Conversions Show all work! Record your answer with the correct number of significant figures and units! 1. Calculate the pressure of 1.3atm in mmhg. 2. Convert 56kPa to psi. 3. How many atmospheres are equivalent to 230kPa? 4. What is 560K on the Celsius scale? 5. Water boils at 100 o C. What is the boiling point of water in Kelvin? 4
COMBINED GAS LAW The Combined Gas Law helps us explain what happens to gases as the pressure, temperature, and volume changes in respect to moles of a substance. Letter or Number Variable Name Unit Conversions P V 5
Letter or Number Variable Name Unit Conversions n* T 1 2 *NOTE: If n is not given in a problem, assume it to be 1 mole. Temperature must be in. Guided Practice: Remember: STP = atm and K or C 1. A hot air balloon has a volume of 7500L at 270K and a pressure of 1.2 atm. What will be the volume of the balloon if the pressure changed to 0.90atm and the temperature decreases to 230K? Givens and Unknowns: Equation: P 1 = V 1 = n 1 = T 1 = P 2 = V 2 = unknown n 2 = T 2 = Substitute & Solve: 6
2. The volume of a gas at STP is 22.4L. At 12 o C, the volume of the balloon changes to 55.0L. What is the new pressure? Givens and Unknowns: Equation: P 1 = V 1 = n 1 = T 1 = P 2 = V 2 = = n 2 = T 2 = Substitute & Solve: 7
Homework - Combined Gas Law Practice 1. A 5.00 L air sample at 170 K has a pressure of 107 kpa. What is the new pressure if the temperature is raised to 548 K and the volume expands to 7.00L? 2. A gas at 880mmHg and 298K occupies a container with an initial volume of 1.00 L. The pressure increases to 1980mmHg as the temperature rises to 398K. What will be the new volume? 3. The volume in a gas filled balloon is 30.0 L at 40 C and 3.6 atm of pressure. What volume will the balloon occupy at STP? 4. A container has an initial volume of 4.5 L, a pressure of 450 kpa and is at a temperature of 15 o C. If the container is expanded to 6.5 L while the pressure is decreased to 125 kpa, find the resulting temperature. 8
Soda Can Activity OBJECTIVES Students will demonstrate the effects of air pressure. Students will demonstrate that as a gas is heated it expands and as it cools it will contract. MATERIALS an empty aluminum soft-drink can a 1000 ml beaker a pair of beaker tongs hot plate PROCEDURE 1. Fill the large beaker with ice cold water. 2. Put 15 20 milliliters of water into the empty soft-drink can. 3. Heat the can on the hot plate at the highest setting. When the water boils, a cloud of condensed vapor will escape from the opening in the can. Allow the water to boil for about two minutes. Do not let all of the water evaporate. 4. Using the beaker tongs, grasp the can and quickly invert it and dip it into the water in the pan. Be careful of the hot water! 5. Record your observation. 6. Clean up your lab station. OBSERVATION CONCLUSION Explain why the can was crushed (discuss the relationships between pressure, volume, and temperature). Why did you have to heat the can up in order for the can to be crushed? 9
Boyle s Law and Charles Law The Effect of Changing Size of Container Boyle s Law WHAT IF temperature and moles do not change and we just look at the relationship between pressure and volume. Our equation would look like this: P 1 V 1 = P 2 V 2 Boyle s Law Boyle s Law states that at a constant temperature, the volume of a gas is inversely proportional to the pressure exerted by that gas. Examples: a. If a gas is compressed from 2L to 1L, the pressure will by a factor of 2. b. If a gas is expanded from 1L to 3L, the pressures will by a factor of 3. c. Gases cool when they expand and heat when they compress. Why? Thus, if you forget to wear your suit in space, you will!!! Example Problems 1. The pressure of a 3.5L balloon was determined to be 1.5atm. Assuming that the temperature remained constant, what would be the volume of the balloon if the pressure was decreased to 0.45atm? 2. At 45 o C, a certain container of gas has the volume of 580mL and a pressure of 980mmHg. What would be the new volume of the gas at 250 mmhg and 45 o C? 10
The Effect of Temperature changes on Volume Charles s Law As the gas inside a balloon, the average KE of molecules. With fewer and less collisions, the gas molecules move together and occupy a volume than they previously did. The, assuming no change in the amount of gas and pressure. Charles Law V1 T 1 V T 2 2 Charles law states: At a constant pressure, the of a gas is directly to the in Kelvin. GUIDED PRACTICE: Temperature must be in. 1. The temperature of a 0.65L sample of carbon dioxide gas is 580K. If the pressure remains constant, what is the new volume of the gas if the temperature increases to 1300K? 2. A balloon has a volume of 5.6L at a temperature of 98 o C. If the volume of balloon increases to 9.5L, what will be the temperature of the gas in Celsius? Assume that the pressure remains constant. 11
Avogadro s Law Avogadro's Law (Avogadro's theory; Avogadro's hypothesis) is a principle stated in 1811 by the Italian chemist Amedeo Avogadro (1776-1856) that "equal volumes of gases at the same temperature and pressure contain the same number of molecules regardless of their chemical nature and physical properties". This number (Avogadro's number) is 6.02 X 10 23. It is the number of molecules of any gas present in a volume of 22.4 L and is the same for the lightest gas (hydrogen) as for a heavy gas such as carbon dioxide or bromine. Or to put it another way, "the principle that equal volumes of all gases at the same temperature and pressure contain the same number of molecules. Thus, the molar volume of all ideal gases, at 0 C and a pressure of 1 atm., is 22.4 liters" V 1 = V 2 V = the volume of the gas n 1 n 2 n = the amount of substance, in moles, of the gas Example #1: 5.00 L of a gas is known to contain 0.965 mol. If the amount of gas is increased to 1.80 mol, what new volume will result (at an unchanged temperature and pressure)? Example #2: A cylinder with a movable piston contains.005 mol of helium, He, at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many moles of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? (The temperature was held constant.) 12
Example #3: 13
Homework Boyle s, Charles, and Avogadro s Laws Practice First, identify which gas law you need to use to solve the problem and then solve for the unknown. Be sure to show all work. For every problem, report your answer with the correct number of significant figures and the correct units! Remember, temperature must be in KELVINS!!! 1. Gas law: A sample of carbon dioxide occupies a volume of 3.5 L at 125 kpa. What pressure would the gas exert if the volume were decreased to 2.00 L? Assume that the temperature remains constant. 14
2. Gas law: A 6.0 L sample at 25 C and 2.00 atm of pressure contains 0.5 moles of a gas. If an additional 0.25 moles of gas at the same pressure and temperature are added, what is the final total volume of the gas? 3. Gas law: When 250 ml of O 2 is heated, there is now 310 ml O 2 at 273K. What is the original temperature in o C? 4. Gas law: Your Valentine s Day balloon has a maximum volume of 5.5 L. Your balloon originally has a volume of 5.2 L at 288K. When you walk into your Chemistry classroom, you realize that they have finally fixed the heat. The temperature in there is now 320K. Should you worry that your balloon will pop? Support your answer with calculations! 5. Gas law: The pressure on anesthetic gas changes from 15.0 atm to 6.0 atm. If the original volume was 12.0 L, what will be the new volume of the anesthetic gas after the pressure has been decreased? 6. Gas law: You have 2.00 L of dry H 2 at STP. How many moles is this? 15
Dalton s Gas Law of Partial Pressures Partial pressure of a gas in a mixture of gases is the pressure which that gas would exert if it were the only gas present in the container. Dalton's Law of Partial Pressures states that the total pressure in a gas mixture is the sum of the partial pressures of each individual gas. P total = P gas a + P gas b + P gas c + etc Dalton's Law of Partial Pressures assumes each gas in the mixture is behaving like an ideal gas. P total = P gas a + P gas b = + Example Problems 1. Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (P oxygen) at 101.3kPa if the partial pressures of nitrogen, carbon dioxide, and other gases are 79.10kPa, 0.040kPa, and 0.94kPa, respectively. 2. A mixture of gases contains oxygen, nitrogen, and helium. The partial pressure of oxygen is 2.1atm. The partial pressure of nitrogen in 0.21atm, and the partial pressure of helium is 7.80atm. Determine the total pressure of this mixture. 16
Homework for Dalton s Gas Law of Partial Pressures For each problem, calculate the pressure using correct units. Box final answer. SHOW ALL WORK!! 1. Oxygen gas from the decomposition of potassium chlorate, KClO 3, was collected by water displacement. 2 KClO 3 2 KCl + 3 O 2 What is the partial pressure of oxygen collected if the barometric pressure (total) was 731.0 torr and the vapor pressure of water at 20.0 C was 17.5 torr? P 1 = P total = P 2 = 2. A sample of nitrogen gas was collected over water at a temperature of 23.0 C. What is the partial pressure of nitrogen if the atmospheric pressure (total) was 785 mmhg and the vapor pressure of water was 21.1 mmhg? P 1 = P total = P 2 = 3. At high altitudes, pilots have to supplement their supply of oxygen. In this mixture, there are oxygen and nitrogen gases. If nitrogen s partial pressure is 250mmHg, calculate the partial pressure of oxygen if the total pressure is 710mmHg. 4. Saturn s atmosphere is composed of hydrogen and helium. If the partial pressures of the gases are 25.0atm and 1.2atm, respectively, what is the total pressure? 17
Ideal Gas Law An ideal gas is one that follows the gas laws at. Such a gas would have to conform precisely to the assumptions of. As you probably suspect, there is for which this is true. An ideal gas exist. Nevertheless, at many conditions of temperature and pressure, behave very much like an ideal gas. An important behavior of real gases that differs from that of a hypothetical ideal gas is that real gases can be and sometimes by cooling and by applying pressure. Ideal gasses cannot be. For example, when water vapor is cooled below 100 o C at standard atmospheric pressure, it condenses to a liquid. The behavior of other real gases is similar, although lower temperature and greater pressures may be required. ****Gases behave ideally at. If we look at one side of the Combined Gas Law: P V n T and solve it for one mole at STP, you would get a constant (symbolized as R). (101.3 kpa)(22.4 L) = 8.31 (L. kpa)/(k. mol) (1 mole)(273 K) We call this the ideal gas constant (R): If pressure is measured in: kpa atm mmhg torr The ideal gas constant (R) is: 8.31 (L. kpa)/(k. mol) 0.0821 (L. atm)/(k. mol) 62.4 (L. mmhg)/(k. mol) 62.4 (L. torr)/(k. mol) SO Label the variables: P : V: n: R: T: 18
GUIDED PRACTICE: 1. Calculate the number of moles of oxygen in a 12.5 L tank containing 250 atm, measured at 22 o C. Givens and Unknowns: Equation: PV = nrt Substitute & Solve: P = V = n = R = T = 2. If 4.5 g methane gas (CH 4) is introduced into an evacuated 2.00 L container at 35 o C, what is the pressure in the container, in atm? Givens and Unknowns: Equation: PV = nrt Substitute & Solve: P = V = n = R = T = 3. A balloon is filled with 0.34 moles of pure nitrogen. If the balloon is at 37 o C and is under pressure of 100 kpa, calculate the volume of the balloon. Givens and Unknowns: P = Equation: PV = nrt Substitute & Solve: V = n = R = T = 19
Homework for Ideal Gas Law 1. 16 L of carbon dioxide is at a temperature of 45º C and a pressure of 85 kpa. Calculate the number of moles of gas present. 2. The pressure inside a balloon filled with 168 g of nitrogen (N 2) is 95 kpa with a temperature of 15º C. Calculate the volume of the balloon. 3. 76 L of compressed oxygen is at a temperature of 330 K. If there are 7.3 mols of oxygen in the container, calculate the pressure (in atm) inside the container. 4. What mass of carbon dioxide will occupy 5.5 L at 5.0 C and 0.74 atm? 5. If a cave has a volume of 5.4 x 10 6 L of air at a pressure of 140 kpa and it is determined that there are 3.0 x 10 5 mols of CO 2 present, calculate the temperature inside the cave. 20
Ideal Gas Law and Stoichiometry of Gases Ideal Gas Law and Stoichiometric Problems In industry and in the laboratory, many important chemical reactions involve gases. A common laboratory experiment that produces small amounts of hydrogen gas involves the reaction of an active metal with a strong acid. This reaction can be represented by the general equation: M (s) + HA (aq) MA (aq) + H 2 (g) where "M" represents the metal, "HA" the acid, and "MA" the salt formed between the metal and the anion of the acid. It is important to be able to perform stoichiometric calculations for gas reactions. Stoichiometric calculations involving gases are identical to those involving solids and liquids with one important exception. For chemical reactions involving only solids and/or liquids, the amounts of reactants and products are usually expressed in grams; however, for chemical reactions involving gases, the amounts of gaseous reactants are usually expressed in liters. To perform a stoichiometric calculation, the number of liters of a gas reactant must first be converted to moles using the ideal gas law. For stoichiometric calculations in which the number of moles of gas products has been calculated, the volume can be calculated using the ideal gas law. Example 1: 3.00 liters of nitrogen (N 2) gas is reacted with excess hydrogen (H 2) gas to form ammonia (NH 3) gas at 304K and a pressure of 1.02 atm. How many liters of ammonia gas are formed? Step 1: Write the balanced chemical reaction. N 2 (g) + H 2 (g) NH 3 (g) Step 2: Convert liters of N 2 to moles of N 2. NOTE: Since the gas is not at STP, you must convert using the Ideal Gas Law before you can do Stoichiometry!!! PV = nrt: Step 3: Convert moles of N 2 to moles of NH 3 using the mole ratio of the balanced chemical equation. Step 4: Convert moles of NH 3 to liters of NH 3 using the ideal gas law. PV = nrt: mole K 21
Example 2: Calculate the volume of hydrogen gas produced at 0.0 C and 1.00 atm of pressure by reacting 12.0 g of zinc metal with excess sulfuric acid. Step 1: Write the balanced chemical reaction. Step 2: Convert grams of zinc to moles of H 2 using the mole ratio from the balanced equation. Step 3: Convert moles of H 2 to liters of H 2 using the ideal gas law. PV = nrt Class Practice: 3. How many grams of calcium carbonate will be needed to form 4.29 liters of carbon dioxide? The following reaction takes place at a pressure of 1 atm and a temperature of 298K. CaCO 3(s) CO 2(g) + CaO(s) 22
Ideal and Stoichiometry Homework: 1. How many liters of water can be made from 55 grams of oxygen gas and an excess of hydrogen at a pressure of 12.4 atm and a temperature of 85 0 C? 2H 2(g) + O 2(g) 2H 2O (l) 2. If you burned a gallon of gas (C 8H 18) (approximately 4000 grams), how many liters of carbon dioxide would be produced at a temperature of 21.0 o C and a pressure of 1.00 atm? 2C 8H 18(l) + 25 O 2(g) 16 CO 2(g) + H 2O(g) 3. Using the same chemical equation as in #2, how many grams of water would be produced if 20.0 liters of oxygen were burned at a temperature of 263 o K and a pressure of 1.3 atm? 23
Gas Laws STUDY GUIDE Due: February 24 th Units of Measurement: For the following questions, use the following answer choices to indicate what each unit of measurement is used to measure. A. Pressure B. Volume C. Temperature 1. K 4. kpa 7. psi 2. atm 5. L 8. mmhg 3. ml 6. o C Kinetic Molecular Theory A crew was given steam cleaning equipment and asked to steam clean a Tank Car. The interior of the tank car was washed out & cleaned with steam. Then all the outlet valves were shut and the tank car was sealed. All the workers went home for the evening and when they returned, the picture below shows what they found. Explain why this happened using the behavior of gases to support your answer. Pressure Answer the following questions related to pressure. For any problems, show all work (using dimensional analysis) and report your answers with the proper number of units and significant figures. 1 atm = 760 mmhg = 101.3 kpa = 14.7 psi 9. In a sample of gas, what causes pressure? Answer in a complete sentence. 24
10. How many millimeters of mercury are in 4.5atm? 11. How many kilopascals are in 76.0 psi? Relationships among P, V, T and the Number of Gas Particles Answer the following questions in complete sentences. 12. If temperature is held constant, as the volume increases, the pressure for a given sample of gas will? Justify your answer on a molecular level. 13. How does increasing the number of gas particles affect the pressure of a gas? Justify your answer on a molecular level. 14. How does the kinetic energy of a gas change as temperature is increased? How does this affect the pressure? Gas Laws and Graphing 15. Define Boyle s, Charles, and Avogadro s Laws. Use the following graphs to answer the next 7 problems. 25
Pressure(kPa) Volume (L) Graph #1 :The Relationship between Volume and Pressure of a Gas 100 80 60 40 20 0 0 20 40 60 80 100 Volume (ml) Graph #2: The Relationship between Volume and Temperature of a Gas 100 50 0 0 20 40 60 Temperature (K) 16. Which graph represents Boyle s Law? 17. Which graph represents Charles s Law? 18. Which graph has the same shape as Avogadro s Law? 19. In Graph #1, what is the pressure on 20mL of gas? 20. In Graph #2, what is the volume when the temperature reaches 55K? 21. Which graph represents an inverse relationship? 22. Which graph represents a direct relationship? Sample Problems Show all work. Be sure to report your answers with the correct numbers of significant figures and the correct units. Also, write down the gas law used to solve each problem. 23. What is the volume of a sample of gas that contains 1.2mol at 780K and 1.3atm? Name of Gas Law used here: 26
24. A balloon is heated so that it will expand. Initially, the volume is 56mL at 45 o C. If the balloon is heated so that it expands to 130mL, what is the new temperature in the balloon in degrees Celsius? Name of Gas Law used here: 25. What is the new pressure if a 2.0L sample at 120kPa is reduced to 1.2L assuming that the temperature remains constant? Name of Gas Law used here: 26. Laughing gas is a mixture of dinitrogen monoxide and oxygen. If the total pressure is 1.2atm, what is the partial pressure of dinitrogen monoxide given that the partial pressure of oxygen is 0.45atm? Name of Gas Law used here: 27. The Kelvin temperature of a gas was originally doubled. If the initial pressure is 740mmHg, what would be the new pressure after the temperature was increased? Name of Gas Law used here: 27
28. A 3.45L sample of nitrogen gas is originally at STP. If the temperature is increased to 50 o C and the pressure is raised to 2.3atm, what is the new volume? Name of Gas Law used here: 29. What is the mass of carbon monoxide gas if 0.304L is kept at 0.45atm and 440K? Name of Gas Law used here: 30. A cylinder with a movable piston contains 0.500 moles of helium at room temperature. More helium was added to the cylinder and the volume was adjusted so that the gas pressure remained the same. How many moles of helium were added to the cylinder if the volume was changed from 2.00 L to 2.70 L? Name of Gas Law used here: 31. How many grams of AlCl 3 must decompose in order to produce 3.10 liters of Cl 2 at 50.0 C and 98.4 kpa? 2AlCl 3 2Al + 3Cl 2 28