PETER STARODUB - PALOS VERDES PENINSULA HIGH SCHOOL

Transcription

1 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 1 UNIT 2-2: CH. 5 GASES READ P ASSIGNMENTS: #1 P. 7 #1-12 Pressure Problems #2 P. 14 #1-17 Gas Law Problems #3 P. 17 #1-12 Gas Density, Molar Mass, Stoichiometry #4 P. 20 #1-6 Graham s Law #5 P. 22 #1-4 Partial Pressure Problems #6 P. 24 #1-10 KMT and Real Gases BASIC DEFINITIONS: Avogadro s hypothesis Barometer Compressibility Dalton s Law of Partial Pressures Diffusion Effusion Gas constant Ideal gas law Mole fraction (X) Partial pressure Pressure Root-mean-square (rms) speed Standard atmosphere (atm) Standard molar volume Standard temperature and pressure (STP) torr Van der Waals equation Equal volumes of gases under the same conditions of temperature and pressure have equal numbers of particles. (All gases do the same thing under the same conditions.) An apparatus used to measure atmospheric pressure. The change in volume with change in pressure. The total pressure of a mixture of gases is the sum of the pressures of the components of the mixture. The gradual mixing of the molecules of two or more substances by random molecular motion. The movement of gas molecules through a membrane or other porous barrier by random molecular motion. The proportionality constant in the ideal gas law. A law that relates pressure, volume, number of moles, and temperature for an ideal gas. PV = nrt The ratio of the number of moles of one substance to the total number of moles in a mixture of substances. The pressure exerted by one gas in a mixture of gases. The force exerted on an object divided by the area over which the force is exerted. The square root of the average of the squares of the speeds of the molecules in a sample. A unit of pressure: 1 atm = 760 mm Hg The volume occupied by 1 mol of gas at standard temperature and pressure; 22.1 L A temperature of 0 C and a pressure of exactly 1 atm. A unit of pressure equivalent to one millimeter of mercury A mathematical expression that describes the behavior of non-ideal gases.

2 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 2 General properties of gases and the basic gas laws Matter exists as a solid, a liquid, or a gas. Atoms and molecules in gases have the lowest density of all the states of matter and the weakest intermolecular forces. Gases expand to fill the space available to them. They take the shape of their container and are evenly distributed within it. They mix completely and uniformly with other gases when confined in the same space, providing no chemical reaction occurs. Expansion. Gases expand indefinitely to fill the space available to them. Indefinite shape. Gases take the shape of their container. Compressibility. Gases are the most compressible of the states of matter. They expand and contract easily with changes in pressure. Solids and liquids do not. Mixing. Two or more gases will mix evenly and completely when confined to the same container (air) Low density. D = V m. gases have much lower densities than liquids and solids. They are about 1/1000 th those of liquids and solids. o Density of water = 1 g/ml, density of air = g/ml. o Know the elements that exist as gases under normal temperature and pressure. (25 C. and 1 atmosphere pressure. Atmosphere is a unit of pressure.) o The state of a substance depends on its temperature and pressure. (Butane lighter liquid under pressure; it is a gas when released to the atmosphere) Gases exert pressure. INTRODUCTION TO AIR PRESSURE (ATMOSPHERIC PRESSURE) AND THE PRESSURE OF GASES Air exerts pressure on us all the time due to a column of air extending all the way to the upper atmosphere. It pushes on us from all directions all the time. These pushes equalize each other so we are unaware of them. Gas pressure is the result of simultaneous collisions of billions of gas particles on an object. When no gas particles are present, there is an empty space. There are no gas molecules to collide no gas molecules, no collisions, no pressure. This empty space is called a vacuum. Air exerts pressure because gravity holds air molecules in the earth s atmosphere. Atmospheric pressure results from the collisions of gas molecules with objects. (An inflated car tire). It decreases with an increase in elevation. A gas is a substance that is in the gaseous state at ordinary temperature and pressure. A vapor is the gaseous form of any substance that is a liquid or solid at normal temperatures and pressure. Water in the gas state is called water vapor. PRESSURE OF A GAS To describe the gaseous state, only 4 quantities are needed: 1. The quantity of gas, n (in moles), 2. The temperature of the gas, T (in kelvins). (Remember, K = C + 273) 3. The volume of gas, V (in liters), 4. The pressure of the gas P. Pressure is measured in: atmospheres (atm), mm of mercury (mm Hg), (1 mm Hg = 1 torr) kilopascals (kpa). The pressure of a gas is the force per unit area. A gas, such as our atmosphere exerts a pressure on every surface it contacts, no matter what the direction of contact. The atoms and molecules of the gases in the atmosphere, like all other matter, are subject to Earth s gravitational pull. Therefore, the atmosphere is much denser near the surface of Earth than at high altitudes. The denser the air, the greater the pressure it exerts. Atmospheric pressure is the pressure exerted by Earth s atmosphere. The value of atmospheric pressure depends on location, temperature, and weather conditions.

3 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 3 HOW ATMOSPHERIC PRESSURE IS MEASURED Atmospheric pressure is measured using a barometer. THE SIMPLE (TORICELLI) BAROMETER A simple barometer consists of a long glass tube, close at one end and filled with mercury. If the tube is carefully inverted in a dish of mercury so that no air enters the tube some mercury will flow out of the tube into the dish creating a vacuum at the top. The weight of the mercury remaining in the tube is supported by atmospheric pressure acting on the surface of the mercury in the dish. At sea level, the pressure of the atmosphere will support a column of mercury 760 mm high. This is called STANDARD ATMOSPHERIC PRESSURE. The pressure exerted by the mercury column is balanced by the pressure at the bottom of the column of air above the dish a column of gas that extends to the top of the atmosphere. Other atmospheric pressure units are torr, and kilopascals. On the top of Mt. Everest (6 miles high) the air exerts enough pressure to support a column of mercury only 253 mm high. h = 760 mm at sea level pool of Hg RELATIONSHIP OF PRESSURE UNITS: STANDARD ATMOSPHERIC PRESSURE = 1 atm = 760 mm Hg = 760 torr = kpa = 14.7 lb/in 2 (psi) Any liquid can be used in a barometer. The height of the column depends on the density of the liquid. If it were water, the column would be almost 34 feet high! WOW!! By using mercury in the barometer, a barometer is a useful practical size. Barometers today are called ANEROID BAROMETERS. In these devices atmospheric pressure is related to the number of collisions of air molecules with a sensitive metal diaphragm. The diaphragm controls the movement of a pointer that gives the pressure reading. DO EM IF YOU NEED EM PRESSURE UNIT CONVERSIONS WORKSHEET Use the factor-label method for the unit conversions. 1. The atmospheric pressure in San Francisco on a certain day was 732 mm Hg. What was the pressure in kpa? (97.6 kpa) 2. The pressure inside a plane before pressurization is 688 mm Hg. What is this pressure in atmospheres? (0.905) 3. Convert a pressure of 645 mm Hg into its value in (a) atmospheres (b) kilopascals. 4. Change the following temperatures from Celsius to kelvin: (a) 20.5 C = K (Treat 273 as a constant with infinite sig figs. For this course) (b) 272 C = 545 K (c) 273 C (d) 273 C (e) 48.1 C 5. Convert to Celsius degrees (a) 0 K (b) 273 K (c) K (d) K

4 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 4 MEASURING PRESSURE OF GASES (OTHER THAN ATMOSPHERIC PRESSURE) The instrument used to measure pressure of gases other than air is called a manometer. A manometer will measure the pressure of a gas in a container, like propane in the barbeque. There are many types of manometers and there are two of them in your textbook. I will only discuss and expect you to know how an OPEN-END MANOMETER works. An open-end manometer is made up of a U-tube that has mercury in it. If both sides of the U-tube are open to the air, the levels of the mercury on both sides will be the same (atmospheric pressure of 760 mm Hg pushing on each side). SEE FIGURE 1 BELOW. To make this device measure the pressure of a gas, a flask with a gas under pressure will be added to one side of the U-tube (left side in figure 2 and 3 below). A valve will be opened that will allow the gas to go into the tube on the left side. The mercury will rise in the side that has less pressure on it (think of a teeter-totter; in Americanized see-saw). ASSIGNMENT: Here are the three possibilities in determining the pressure of a gas. In each case, consider the atmospheric pressure to be standard atmospheric pressure. Determine the pressure of each gas. Write down the relationship in symbols first as is shown in #1 below.

5 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 5 DO EM IF YOU NEED EM PRESSURE OF A GAS WORKSHEET 1. In the figure to the right: (a) If the atmospheric pressure were to increase, in which direction would the mercury move in the open arm? (b) If the atmospheric pressure were to change so that the levels of mercury were the same in both arms of the manometer, how would the pressure in the container change? 2. What causes atmospheric pressure (explain fully)? 3. Draw a sketch showing what a mercury manometer would look like when it is hooked up to a flask containing a gas sample at 90 kpa on a day when the atmospheric pressure is 100 kpa. Label the arrows you use to show the pressure at various points in the manometer. Write the pressure at each arrow. air pressure 4. In a simple barometer, how does the height of a column of mercury at sea level compare with the height on a mountain top? 5. An open-end manometer, similar to the one in the diagram above, is attached to a container of gas that is exerting a pressure of kpa. (a) When the valve is opened, will the mercury in the open arm of the U-tube move up or down? (b) After the mercury in the U-tube stops moving, what will be the difference in height of the mercury levels in the arms of the tube? (24 mm) STANDARD TEMPERATURE AND PRESSURE (S.T.P.) Standard temperature is 0 C and standard pressure is 1 atmosphere. These conditions are referred to as STP. MOLAR VOLUME (Gases only) Molar volume is the volume occupied by 1 mole of a gaseous substance. It applies to gases only. Molar volumes vary from substance to substance for solids and liquids therefore we do not study the molar volumes of solids and liquids. IT IS IMPORTANT TO NOTE THAT MOLAR VOLUMES ARE IDENTICAL FOR ALL GASES. It doesn t matter what the gas is; equal moles of any gas at the same temperature and pressure occupy equal volumes. OR Equal volumes of any gas at the same temperature and pressure have the same number of moles. For example, if 2 moles of CO 2 at STP occupies 44.8 liters of volume, then 2 moles of O 2, or H 2, or N 2 O 4 (g) will occupy the same volume: 44.8 liters (at the same temperature). AT STP, 1 MOLE OF ANY GAS OCCUPIES A VOLUME OF 22.4 LITERS L is known as the molar volume of a gas. Therefore, 22.4 L of any gas at STP contains x particles of that gas. STP means standard temperature of 0 C and a pressure of 1 atmosphere (atm). At sea level, a column of air above you will exert a pressure of 1 atmosphere due to the weight of the column of air due to gravity L of one gas does not have the same mass as 22.4 L of another gas because 1 mole of a gas (22.4 L) has a mass equal to the molar mass. 1 mole of O 2 gas occupies 22.4 L at STP (molar volume) has a mass of g (molar mass), and contains x molecules of O 2. 1 mole of He gas occupies 22.4 L at STP, has a mass of 4.00 grams, and contains x He atoms. 1 mole of NH 3 (g) occupies 22.4 L at STP, has a mass of g, and contains x NH 3 molecules. AVOGADRO S HYPOTHESIS: EQUAL VOLUMES OF DIFFERENT GASES AT THE SAME TEMPERATURE AND PRESSURE CONTAIN AN EQUAL NUMBER OF MOLES THEREFORE EQUAL NUMBERS OF PARTICLES. In other words, all gases do the same thing!! It doesn t matter what the gas is. They all exert the same pressure at the same temperature if they occupy the same volume and contain the same number of moles.

6 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 6 EQUAL MOLES OF ANY GAS AT THE SAME TEMPERATURE EXERT THE SAME PRESSURE IF THEY ARE IN THE SAME CONTAINER OR CONTAINERS WITH EQUAL VOLUMES. Suppose there is 1 mole of N 2 in a rigid steel container and it exerts a pressure of 4 atm. If there was 1 mole of CO 2 in the same container at the same temperature, then the CO 2 would also exert a pressure of 4 atm. EQUAL MOLES EXERT EQUAL PRESSURES AT THE SAME TEMP AND PRESSURE All gases do the same thing regardless of what gas it is. 1 mole of any gas under these conditions will exert the same pressure. If the number of moles of N 2 was doubled from 1 to 2, then the pressure exerted by the N 2 gas would double. By doubling the number of moles of any gas, the pressure will double If you had a container with 5 times as many moles of CO 2 then there is N 2, then the pressure exerted by the CO 2 gas would be 5 times that of the N 2. There is an important relationship between the pressures of gases and their number of moles. EQUAL MOLES OF GASES EXERT EQUAL PRESSURES. 5 MOLES OF A GAS WILL EXERT 5 TIMES THE PRESSURE OF 1 MOLE OF ANY OTHER GAS. COMPARISON OF MOLES OF A GAS TO RATIOS OF THEIR PRESSURES gas moles Temp. Volume (rigid steel container) pressure exerted moles CO moles N 2 2 presssure CO pressure N o 2 2 Comparison of ratios N C 1.0 L 2 atm CO C 1.0 L 4 atm = atm 2 atm = 2 The ratio of the moles of 1 gas is equal to ratio of the pressures. THE RATIO OF THE PRESSURES IS EQUAL TO THE RATIO OF THE MOLES OF GAS. You could put this into formula form but it is not necessary. n1 P Formula: = 1 (can be derived from the Combined Gas Law; just like the other gas laws) n2 P2 DO EM IF YOU NEED EM MOLAR VOLUME PRACTICE QUESTIONS 1. (a) Determine the volume in liters of moles of SO 2 gas at STP. (13.4) (b) What would the volume be if the gas were N 2 O 5 gas? 2. (a) How many molecules are in a 6.00 L balloon at STP filled with carbon dioxide? (1.61 x ) (b) Would your answer change if the gas were carbon monoxide? Explain your answer. 3. How many molecules are there in 58.3 grams of ammonia gas at STP? (2.06 x ) 4. What is the volume (at STP) of moles of hydrogen gas? (0.652 L) 5. How many moles of gas are in 572 liters of nitrogen gas at STP? (25.5) 6. What is the volume occupied by 3.3 x 10-3 grams of carbon dioxide at STP? (1.7 x 10 3 ) 7. What is the mass of L of N 2 (g) at STP? (0.306) 8. A sample of HCl gas at STP has a mass of 25.5 grams. What is the volume occupied by this mass of HCl? (15.7) 9. What is the volume at STP of 6.50 moles of sulfur dioxide gas? (146) 10. What is the mass of 44.8 liters of hydrogen bromide gas at STP? (162) 11. If we measure the densities of helium and neon gas at STP, we obtain values of g/l and g/l respectively. What is the volume occupied by exactly one mole of each of these noble gases at STP

7 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 7 DO ASSIGNMENT #1 PRESSURE PROBLEMS P. 7 #1-12 ASSIGNMENT #1 PRESSURE PROBLEMS 1. Use the properties of gases to explain the following observations. Each can be explained in about 2 or 3 sentences. (a) Aerosol cans will explode if heated. (b) You can drink through a soda straw. (c) A thin-walled can will collapse when the air inside is removed by a vacuum pump. 2. Do the following unit conversions: (a) 725 mm Hg to kilopascals (b) 1.87 atm to mm Hg 3. Freon-12 (CF 2 Cl 2 ) is commonly used as the refrigerant in central home air conditions. The system is initially charged to a pressure of 4.8 atm. Express this pressure in each of the following units: (4.9 x 10 5, 3.6 x 10 3, 71 and one answer twice) (a) mm Hg (b) torr (c) Pa (d) psi The following two questions deal with 2 different manometers, one is a sealed-tube manometer and the other is an open-tube manometer. Read the questions carefully. 4. A sealed-tube manometer (as shown to the right) can be used to measure pressures below atmospheric pressure. The tube above the mercury is evacuated. When there is a vacuum in the flask, the mercury levels in both arms of the U-tube are equal. If a gaseous sample is introduced into the flask, the mercury levels are different. The difference h is a measure of the pressure of the gas inside the flask. If h is equal to 6.5 cm. calculate the pressure in the flask in mmhg, torr, pascals, and atmospheres. (answers in order: 65, 65, 8.7 x 10 3, 0.086) 5. A diagram for an open-end or open-tube manometer is shown to the right. If the flask is open to the atmosphere, the mercury levels are equal. For each of the two situations (a and b below) where a gas is contained in the flask, calculate the pressure in the flask in torr, atmospheres, and pascals. (answers not in order: 975, 1.28, 0.845, 642, 8.56 x 10 4, 1.30 x 10 5 ) (c) Calculate the pressures in the flask in parts a and b (in torr) if the atmospheric pressure is 635 torr. (517, 850) 6. What is the relationship between atmospheric pressure and altitude? 7. The density of a gaseous compound of carbon and oxygen is g/l at STP. Determine the molar mass of the compound. (43.99) 8. What is the molar mass of a gas that has a volume of liters and a mass of grams at STP? (32.05 g/mole) 9. Calculate the density (in g/l) of hydrogen gas at STP. (9.02 x 10 2 g/l) 10. Find the mass of 1 molecule of aspirin, C 9 H 8 O 4 (in grams). ( x ) 11. The density of a gaseous element at STP is 5.86 g/l. Determine the molar mass of the element and identify it. (xenon) 12. How many molecules of carbon dioxide gas are there in a volume 11.2 liters of gas at STP? (3.01 x )

8 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 8 REAL VS. IDEAL GASES: THE GAS LAWS We will explore various gas laws that deal with and predict the behavior of gases. To describe the gaseous state, only 4 quantities are needed: The quantity of gas, n (in moles), The temperature of the gas, T (in kelvins), The volume of gas, V (in liters), The pressure of the gas, P (in atm, kpa, or mm Hg). In using the gas laws, we will assume that we are dealing with IDEAL GASES. Ideal gases don t really exist. There is no such thing as an ideal gas, only real gases. Real gases can, however act as an ideal gas under the right conditions. Consider these fundamental properties of gases: As the pressure of a gas increases, the volume decreases (as P, V ). As the temperature of a gas increases, the volume increases (as T, V ). An ideal gas is one that will follow these relationships and gas laws under all conditions of pressure and temperature. A real gas does not work this way. The reason any gas is not an ideal gas is because you cannot study gases at very low temperatures and high pressures. GASES ARE IDEAL ONLY AT HIGH TEMPERATURES AND LOW PRESSURES. AT LOW TEMPERATURES AND HIGH PRESSURES, ALL GASES BECOME LIQUIDS SO YOU CANNOT STUDY THEM AS GASES ANY MORE. Also, as you increase pressure, the volume of an ideal gas would eventually become zero. This is impossible because the gas cannot be compressed to zero volume. (Law of Conservation of Mass) IMPORTANT HINTS IN WORKING WITH GAS LAWS Temperatures are ALWAYS in Kelvin. Kelvin = C Treat 273 as a constant that has infinite sig. figs. Cancel all units. In all problems, isolate and identify each quantity with symbols (pressure P, volume V, moles n). Get rid of the words! Gases will change conditions so use subscripts to indicate those conditions: 1 for initial conditions and 2 for final conditions (P 1 = 3 atm, and P 2 = 6 atm). When a condition such as temperature is held constant, it has no effect on the gas. When a condition is constant, it is not a variable in the study of the gas. You will be learning many new formulas in this section. When you use a formula, write it down, manipulate the formulas to the form required, substitute numbers with units, and solve. ALL WORK MUST BE SHOWN TO OBTAIN FULL CREDIT. If you try to substitute in your head while remembering the formula, you will make mistakes. Do these problems the way I tell you to do them. To solve problems using the formulas for the gas laws, rearrange the formula first, then plug in the numbers with units. In this way, the units will cancel. THE GAS LAWS 5 different gas laws: 1. Boyle s Law: (relationship of pressure and volume; temperature constant) 2. Charles Law: (relationship of volume and temperature; pressure constant) 3. Gay-Lussac s Law: (relationship of pressure and temperature; volume constant) 4. Combined Gas Law: combines the above three laws. 5. Ideal Gas Law: (when moles are involved). Gas Laws 1 through 4 inclusive are used when conditions of pressure, temperature, and/or volume change. Gas Law #5 is to solve for one variable when conditions of a gas are not changing.

9 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 9 BOYLE S LAW This law illustrates the relationship between the pressure and volume of a gas when temperature is held constant. Boyle s Law: At a constant temperature, the volume of a fixed amount of a gas is inversely proportional to its pressure. P 1 V 1 = P 2 V 2 The product of the initial pressure P 1, and the initial volume V 1 will be equal to the product of the new pressure P 2 and the new volume V 2. Ex. 1: A gas is collected in a 242-cm 3 container. The pressure of the gas in the container is measured and determined to be 87.6 kpa. What is the volume of this gas at standard temperature and pressure? (209) Ex. 2: Here s a problem to show you how to line up the data so that your units cancel. 216 ml of a gas is collected at a temperature of 73 C. What is the volume of the gas if the pressure changes to 86.7 kpa from 2.20 atm? (555)

10 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 10 CHARLES LAW: This law illustrates the relationship between volume and temperature, as pressure is held constant. When a gas is heated, it expands. An inflated balloon immersed in a pan of boiling water will increase in size and may even burst. Charles Law: At a constant pressure, the volume of a fixed amount of gas is directly proportional to its Kelvin temperature. = V 1 is the volume of the gas at a temperature T 1 and V 2 is the volume of the gas at a second temperature T 2. Volume (L) Temperature Ex. 1: A balloon inflated in an air-conditioned room at 27 C has a volume of 4.00 liters. It is heated to a temperature of 57 C. What is the new volume of the balloon if the pressure remains constant? (4.40) Ex. 2: Carbon dioxide produced by yeast in bread dough causes the dough to rise, even before baking. During baking, the carbon dioxide expands. Predict the final volume of liters of carbon dioxide in bread dough that is heated from 25 C to 98 C. (0.124 )

11 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 11 GAY-LUSSAC S LAW This law illustrates the relationship between pressure and temperature with volume held constant. If a gas is contained in a vessel that cannot expand such as a steel cylinder or an automobile tire, as the temperature is increased the pressure will increase. GAY-LUSSAC S LAW: At constant volume, the pressure of a fixed mass of any gas is directly proportional to its Kelvin temperature. = Where P 1 and P 2 represent the pressure of the gas at the temperatures T 1 and T 2. You must use Kelvin temperatures. Ex 1: A steel cylinder with a volume of 450 ml contains a gas at a pressure of 520 kpa at 25 C. If the cylinder is heated to 410. C, what will the new pressure be? (1200 kpa) Ex. 2: A glass vessel that can only withstand a maximum internal pressure of 225 kpa is filled with gas at 21 C and 100. kpa and then heated. At what temperature (in C) would the vessel burst? (389) THE COMBINED GAS LAW In each of the 3 gas laws discussed above, one of the variables (pressure, volume, or temperature) was held constant. In practice, we often find that all three variables change. For example, when a weather balloon is released, the temperature, volume, and pressure of the gas inside the balloon all change as the balloon ascends into the atmosphere. We can calculate the new value of any one of the three variables, provided that the new values of the other two are known by using the combined gas law. It is a combination of Boyle s, Charles, and Gay-Lussac s Law. Each of these laws can be derived from the Combined Gas Law by eliminating the variable that is held constant. NOTE: n = moles and can be entered into the Combined Gas Law as well. You probably didn t have moles in this law in Honors Chemistry. Combined Gas Law: = Ex. 1: An 11.2-L sample of gas is determined to contain 0.50 mol of N 2. At the same temperature and pressure, how many moles of gas would there be in a 20.0-L sample?? (0.89) Ex. 2: A weather balloon with a volume of 55.0 L is filled with hydrogen gas at a pressure of 98.5 kpa and a temperature of 13 C. When the balloon is released, it rises to the stratosphere where the temperature is 48 C and the pressure is 19.7 kpa. What is the volume of the balloon under these conditions? (216)

12 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 12 DO EM IF YOU NEED EM COMBINED GAS LAW PROBLEMS 1. A sample of gas has a volume of 152 cm 3 when its temperature is 18 C. If its temperature is increased to 32 C, what will its volume become, assuming the pressure remains constant throughout? (159) 2. A gas confined in a rigid container exerts a pressure of 33.5 kpa at a temperature of 17.0 C. what will the pressure of this gas be if it is cooled to a temperature of 23.0 C? (28.9) 3. If a gas is confined in a rigid container and then heated, what will happen to the pressure exerted by the gas? 4. Show how Charles Law can be derived from the combined gas law. 5. A gas has a volume of 844 ml at a pressure of 98.5 kpa. Correct this volume to standard atmospheric conditions. 6. A container with an initial volume of 1.00 liters is occupied by a gas at a pressure of 1.5 atm at 25 C. By changing the volume, the pressure of the gas increases to 6.0 atm as the temperature is raised to 100. C. What is the new volume? (0.31 L) 7. A cylinder of compressed oxygen gas has a volume of 30.0 liters and 100. atm pressure at 27 C. The cylinder is cooled until the pressure is 5.0 atm. What is the new temperature of the gas in the cylinder (in C)? ( 258) 8. Assume that you place some octane in the cylinder of an automobile engine. The cylinder has a volume of 250. cm 3, and the pressure of gaseous octane is 3.50 atm in the hot engine (250 C). What would be the pressure in the cylinder if you lower the temperature of the automobile engine to room temperature (25 C) and change the volume of the cylinder to 500. cm 3? (0.997) THE IDEAL GAS LAW You used the combined gas law (including Boyle s, Charles and Gay-Lussac s) in problems that involved changing conditions of P, V and T. An ideal gas is a hypothetical gas whose pressure-volume-temperature behavior can be completely accounted for by the ideal gas equation. Although there is no such thing in nature as an ideal gas, discrepancies in the behavior of real gases over reasonable temperature and pressure ranges do not significantly affect calculations. Thus we can safely use the ideal gas equation to solve many gas problems. The ideal gas law has great importance in the study of gases. It does not contain information that is characteristic of any particular gas. Rather, it is a generalization applicable to most gases, at pressures up to about 10 atm, and at temperatures above 0 C. An ideal gas is one whose behavior agrees with that predicted by the ideal gas law. Although ideal gases do not exist, as long as we avoid low temperatures and high pressures, most gases behave as if they were ideal. The ideal gas law is used when a gas is under fixed conditions and you are trying to find the P, V, T, or n (number of moles) of the gas. IDEAL GAS LAW: PV = nrt where P = pressure (in atm) V = volume (in L) n = moles T = temperature (Kelvin) R = Ideal Gas constant = Ex. 1: If you have a 150. L tank of gaseous nitrogen and the gas exerts a pressure of 41.8 mmhg at 25 C, how many moles of nitrogen are in the tank? (0.337)

13 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 13 DO EM IF YOU NEED EM IDEAL GAS LAW PROBLEMS **In solving Ideal Gas Law problems, use the value of R given above using pressure units of atm. If pressure is given to you in kpa or mm Hg, change them to atm in the problem. Do it as one step in the factor label method. 1. What is the pressure exerted by 4.50 moles of gas in a 198 L container at a temperature of 8 C? (0.524) 2. What volume would be occupied by 3.22 moles of gas at a temperature of 35 C and a pressure of 93.2 kpa? (88.5) 3. How many moles of gas can be contained in a 1.4 L flask at 32 C and 93.5 kpa? (0.052) 4. A certain sample of gas occupies a volume of 20.0 L at a temperature of 21 C and a pressure of 94.2 kpa. (a) How many moles are there in the sample? (0.771) (b) If the temperature is increased to 85 C and the volume is changed to 35.0 L, what is the pressure? (0.647) 5. What pressure is exerted by moles of gas contained in a 9.22 L vessel at 16 C? (1.60) DO ASSIGNMENT #2 GAS LAW PROBLEMS P. 14 #1-17

14 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 14 ASSIGNMENT #2 GAS LAW PROBLEMS 1. A particular balloon is designed by its manufacturer to be inflated to a volume of no more than 2.5 L. If the balloon is filled with 2.0 L of helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is only 500. mm Hg, will the balloon burst? (Assume temperature is constant.) (3.0) 2. As temperature decreases, at constant pressure, at what point will a gas cease to obey Charles Law? 3. A sample of oxygen gas has a volume of 205 cm 3 when its temperature is 22.0 C and its pressure is 30.8 kpa. What volume will the gas occupy at STP? (57.7) 4. A rigid metal container contains hydrogen gas. The volume of the container is 2.0 liters. If 10.0 moles of the gas exert a pressure of 6.00 atm at 28 C, how many moles of gas would have to be released at 28 C so the pressure in the tank is 2.00 atm? (3.33 is a partial answer) 5. Suppose that 2 quantities A and B are related to each other by inverse proportion. If the value of A becomes 5 times greater than it was, what will happen to the value of B? 6. Imagine that you live in a small cabin with an interior volume of 150. m 3. On a cold morning the indoor temperature is 10. C but by afternoon the sun has warmed the cabin air to 18 C. Because air expands (to maintain a constant pressure) as the temperature increases, and because the cabin is not sealed, some of the air has leaked out of the cabin. How many cubic meters of air have been forced out of the cabin by the sun s warming? How many liters? (154, 1.54 x 10 5 ) 7. A 12.5-liter bulb contains a gas at 3.6 atm pressure. If it is connected to an empty 3.6-Liter bulb. What is the new pressure of the gas? (2.8) 8. What temperature in C is a gas if 2.31 moles of it occupy 61.0 L at a pressure of 94.6 kpa? (27) 9. When can the Ideal Gas Law not be used? 10. When a rigid hollow sphere containing 680. L of helium gas is heated from 300 K to 600 K, the pressure of the gas increases to 18.0 atm. How many moles of helium does the sphere contain? (249) 11. A 2.50 L container is filled with sulfur dioxide gas at a pressure of kpa at a temperature of 27 C. Calculate the mass of sulfur dioxide gas in the container. (7.70) 12. Find the volume of 1.00 g of water in the gas phase at its boiling point (100 C) and standard pressure. (1.68) 13. Consider the following chemical equation: 2 NO 2 (g) N 2 O 4 (g) If 25.0 ml of NO 2 gas is completely converted to N 2 O 4 gas under the same conditions, what volume will the N 2 O 4 occupy? (12.5) 14. What volume is occupied by 2.0 g of He at 25 C and a pressure of 775 mmhg? (12) 15. A hot-air balloon is filled with air to a volume of 4.00 x 10 3 m 3 at 745 torr and 21 C. The air in the balloon is then heated to 62 C, causing the balloon to expand to a volume of 4.20 x 10 3 m 3. What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.) (0.921/1) 16. A compressed gas cylinder contains 1.00 x 10 3 g of argon gas. The pressure inside the cylinder is psi (pounds per square inch) at a temperature of 18 C. How much gas remains in the cylinder if the pressure is decreased to 650. psi at a temperature of 26 C? (309) 17. Consider two separate gas containers at the following conditions (see table to the right). How is the pressure in container B related to the pressure in container A? (twice) Container A Contents: SO 2 (g) Pressure = P A Moles of gas = 1.0 mol Volume = 1.0 L Temperature = 7 C Container B Contents: Unknown gas Pressure = P B Moles of gas = 2.0 mol Volume = 2.0 L Temperature = 287 C

15 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 15 GAS STOICHIOMETRY According to Avogadro s Law, equal volumes of all gases at the same temperature and pressure contain the same number of moles. Because of this, the coefficients in a balanced equation apply to molecules, moles, and volume units as shown below. The volume units can be in L, ml, or any volume units. In the reaction to produce ammonia NH 3 : 3 H 2 (g) + N 2 (g) 2 NH 3 (g) 3 molecules 1 molecule 2 molecules 3 moles 1 mole 2 moles 3 volumes 1 volume 2 volumes (liters) (liters) (liters) Therefore, 3 L of H 2 combines with 1 L N 2 to produce 2 L of NH 3 ; the same relationship as moles. You don t have to change volume to moles in stoichiometry problems. Use volume units just like you use moles. ** This works only if both substances are in the gas phase. It cannot be used if one of the substances is either a solid or a liquid. Gas Stoichiometry Ex. 1: Calculate the mass in grams of hydrogen chloride produced when 5.6 L of molecular hydrogen measured at STP react with an excess of molecular chorine gas. (18) DO THIS ONE!! Ex. 2:The discovery of oxygen resulted from the decomposition of mercury (II) oxide. 2 HgO(s) 2 Hg(s) + O 2 (g) (a) What volume of oxygen will be produced by the decomposition of 25.2 grams of the oxide if the gas produced is measured at 20. C and 2.30 atm? (0.608) (b) How many grams of mercury (II) oxide must be decomposed to yield 10.8 L of O 2 at 1 atm and 298 K? (191)

16 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 16 MOLAR MASS OF A GAS A very important use of the ideal gas law is in the calculation of the molar mass (molecular weight) of a gas from its measured density. By using the ideal gas law, a formula for the density and also the molar mass of a gas can be derived to give the formula below. Memorize these 2 formulas together. Ideal Gas Law Formula: Formula for molar mass and density PV = nrt PMM = drt ex. 1: The density of a gas was measured at 1.50 atm and 27 C and found to be 1.95 g/l. Calculate the molar mass of the gas. (32.0 g/mol) Method 1 (using the formula) d = 1.95 L g P = 1.50 atm T = 27 C = 300.K MM =? PMM = drt drt MM = P 1.95 g L atm ( )( )(300.K) = L mole K 1.50 atm = 32.0 g/mole Method 2 (using PV = nrt) Memorizing the formulas above is unnecessary!! Remember: when finding molar mass, you are being asked to find the unit g/mole. d = 1.95 L g P = 1.50 atm T = 27 C = 300.K g =? mole g = mole 1.95 g mol PV = nrt PV n = RT (1.50 atm)(1 L) = L atm ( )(300.K) mol K = mol The density of 1.95 indicates a mass of 1.95 g in a volume of exactly 1 L; therefore m = 1.95 g V = 1 L = 32.0 g/mole DO ASSIGNMENT #3 P. 17 #1-12 GAS DENSITY, MOLAR MASS, AND REACTION STOICHIOMETRY

17 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 17 ASSIGNMENT #3 GAS DENSITY, MOLAR MASS, AND REACTION STOICHIOMETRY 1. Sodium azide decomposes according to the equation. 2 NaN 3 (s) 2 Na(s) + 3 N 2 (g) What volume of N 2 at 1.1 atm and 50 C will be produced by the decomposition of 5.0 g of NaN 3? (2.8 L) 2. Assume that you take 355 L of H 2 gas at 25 C and 542 mmhg and combine it with excess N 2 gas. What is the theoretical yield (in moles) of NH 3 gas? (6.87) 3. Consider the reaction of 20.0 g calcium oxide with carbon dioxide CaO(s) + CO 2 (g) CaCO 3 (s) If you have 5.5 L of CO 2 at 7.50 atm and 22 C, will you have enough carbon dioxide to react with all the CaO? (Support your answer with full calculations.) 4. A gas consisting of only carbon and hydrogen has an empirical formula of CH 2. The gas has a density of 1.65 g/l at 27 C and 734 torr. Determine the molar mass and molecular formula of the gas. (42.1 g/mol C 3 H 6 ) 5. A student adds 4.00 g of dry ice (solid CO 2 ) to an empty balloon. What will be the volume of the balloon at STP after all the dry ice sublimes (converts to gaseous CO 2 )? (2.04) 6. The method used by Joseph Priestley to obtain oxygen made use of the thermal decomposition of mercuric oxide: 2 HgO(s) heat 2 Hg(l) + O 2 (g) What volume of oxygen gas, measured at 30. C and 725 torr can be produced from the complete decomposition of 4.10 g mercuric oxide? (0.247) 7. Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide NaN 3 to decompose explosively according to the following reaction: 2 NaN 3 (s) 2 Na(s) + 3 N 2 (g) What mass of NaN 3 (s) must be reacted in order to inflate an air bag to 70.0 L at STP? (135) 8. Urea H 2 NCONH 2 is used extensively as a nitrogen source in fertilizers. It is produced commercially from the reaction of ammonia and carbon dioxide: heat pressure 2 NH 3 (g) + CO 2 (g) H 2 NCONH 2 (s) + H 2 O(g) Ammonia gas at 223 C and 90. atm flows into a reactor at a rate of 500. L/min. What mass of urea is produced per minute by this reaction assuming 100% yield? (3.3 x 10 4 ) 9. Methanol, CH 3 OH, can be produced by the following reaction: CO(g) + 2 H 2 (g) CH 3 OH(g) Hydrogen at STP flows into a reactor at a rate of 16.0 L/min. carbon monoxide at STP flows into the reactor at a rate of 25.0 L/min. If 5.30 g of methanol is produced per minute, what is the percent yield of the reaction? (46.5) 10. A compound has the empirical formula CHCl. A 256-mL flask at 373 K and 750. torr, contains g of the gaseous compound. Give the molecular formula. (C 2 H 2 Cl 2 ) 11. Calculate the density of ammonia gas at 27 C and 635 torr. (0.578) 12. Suppose you are given two flasks at the same temperature, one of volume exactly 2 L and the other of exact volume 3 L. The 2-L flask contains 4.8 g of gas, and the gas pressure is X atm. The 3-L flask contains 0.36 g of gas and the gas pressure is 0.1X. (a) Do the two gases have the same molar mass? (b) If not, which contains the gas of higher molar mass?

18 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 18 DALTON S LAW OF PARTIAL PRESSURE Molecules of a gas do not attract or repel one another. Because there is no attraction, the pressure exerted by one type of molecule is unaffected by the presence of another gas. This leads to Dalton s Law of Partial Pressure that states: IN A MIXTURE OF GASES, THE TOTAL PRESSURE OF A MIXTURE OF GASES IS EQUAL TO THE SUM OF THE PRESSURES THAT EACH GAS WOULD EXERT IF IT WERE PRESENT ALONE. For example: suppose that you have 1 L of oxygen at a pressure of 200 kpa and 1L of nitrogen also at 150 kpa. You now transfer one of the gases into the container occupied by the other. You will find that the total pressure is now 350 kpa. Each gas is occupying the same volume of 1L (although they are mixed). Each gas is therefore exerting its original pressure. Within the single volume of 1L, the two pressures combine to produce a total of 350 kpa PTOTAL = P1 + P2 + P3 +.+ PN. Where P 1, P 2, P N are partial pressures. FINDING THE PARTIAL PRESSURE WHEN MOLES OF EACH GAS IS GIVEN Partial pressure refers to the pressure of each individual gas in the mixture. When you are given the amount (in moles) of each gas in the mixture, you are able to find the mole fraction (χ) of each gas. Once you have the mole fraction of each gas and you know the total pressure, you can find the partial pressure of each gas by the formula below: P 1 = Χ P T where P i = partial pressure of gas 1 Χ = mole fraction of gas 1 P T = total pressure of all gases mole fraction (X) = Ex. 1: Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium if the partial pressures of the gases are: P oxygen = 150 mm Hg, P nitrogen = 350 mm Hg, P helium = 200 mm Hg. Ex. 2: Air contains oxygen, nitrogen, carbon dioxide and trace amounts of other gases. At a pressure of 1 atm, what is the partial pressure of oxygen if the partial pressure of nitrogen is mm Hg, carbon dioxide 0.3 mm Hg, and the pressure of other gases = 7.1 mm Hg?

19 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 19 THE COLLECTION OF GASES OVER WATER In the laboratory preparation of gases that are lighter than air such as hydrogen and oxygen, the gas is usually collected by the displacement of water. This process is useful for collecting many gases but the gas must be practically insoluble in water. When the collection is finished, water vapor is Table: Pressure of Water Vapor at Various Temperatures present in the container along with the gas collected. The pressure in the container actually is the sum of the partial pressures of the gas and the water vapor. (Dalton s Law of Partial Pressures.) We know that each of the gases exerts the same pressure it would if it were present alone in the container. Therefore, if we subtract the value for water vapor pressure from the total pressure, the result will be the pressure of the collected gas alone (the dry gas). The vapor pressure of water at various temperatures has been measured and is contained in a table of Vapor Pressures of Water at various temperatures. Temperature ( C) Water Vapor Pressure (mm Hg) In all types of gases law problems you have been doing so far, you have been dealing with DRY GASES only. You will now have to watch out for gases that are collected over water. If they are, you must subtract the vapor pressure of water to get the pressure of the dry gas alone. You will recognize these gas problems because they will indicate that the gas has been collected over water or collected by water displacement. Vapor pressure changes with a change of temperature. Ex. 1: A quantity of gas is collected over water at 10 C. The pressure of gas over the water was found to be 675 mmhg. (a) What is the pressure of the collected dry gas only? (**Use the vapor pressure of water table). (b) What volume would the dry gas occupy at standard pressure if originally collected in a 353-cm 3 vessel? (309) Ex. 2: ml of oxygen is collected over water at 23 C and 748 mm Hg. Calculate the volume of the oxygen gas at 10. C and 700. mm Hg. The vapor pressure of water at 23 C is 21.1 mm Hg) (496 ml) DO ASSIGNMENT #4 P. 20 #1-6 PARTIAL PRESSURE PROBLEMS

20 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 20 ASSIGNMENT #4 PARTIAL PRESSURE PROBLEMS 1. A mixture of 1.00 g of H 2 and 1.00 g of He is placed in a 1.00-L container at 27 C. Calculate the partial pressure of each gas and the total pressure. (M.F.: 0.333, 0.667) 2. Consider the flasks diagramed at the right. What are the final partial pressures of H 2 and N 2 after the stopcock between the two flasks is opened? What is the total pressure in torr? (317, 50.7, 368) 3. At 0 C a 1.0-L flask contains 5.0 x 10 2 mol of N 2, 1.5 x 10 2 mg O 2, and 5.0 x molecules of NH 3. What is the partial pressure of each gas, and what is the total pressure in the flask?(1.4, 1.1, 0.18, 0.10) 4. Helium is collected over water at 25 C and 1.00 atm total pressure. What total volume of gas must be collected to obtain g of helium? (At 25 C the vapor pressure of water is 23.8 torr.) (3.69) 5. The oxides of Group 2A metals (symbolized by M here) react with carbon dioxide according to the following reaction: MO(s) + CO 2 (g) MCO 3 (s) A 2.85-g sample containing only MgO and CuO is placed in a 3.00-L container. The container is filled with CO 2 to a pressure of 740. torr at 20. C. After the reaction has gone to completion, the pressure inside the flask is 390. torr at 20. C. What is the mass percent of MgO in the mixture? Assume that only the MgO reacts with CO 2. (81.4) 6. Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. The reaction is: Zn(s) + 2 HCl(aq) ZnCl 2 (aq) + H 2 (g) Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose 240. ml of hydrogen gas is collected at 30. C and has a total pressure of atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at 30 C.) (0.990 atm, g) THE MEANING OF TEMPERATURE The exact relationship between temperature and average kinetic energy of gas molecules is K.E. avg = RT where: R = T = Kelvin temperature This is a very important relationship. It summarizes the meaning of the Kelvin temperature of a gas. The kelvin temperature is an index of the random motions of the particles of a gas, with higher temperature meaning greater motion and therefore greater kinetic energy. THEREFORE, THE AVERAGE KINETIC ENERGY OF DIFFERENT GASES IS THE SAME AT THE SAME TEMPERATURE. THE AVERAGE KINETIC ENERGY OF A GAS DEPENDS ONLY ON THE TEMPERATURE! You would think that heavier molecules would have more energy because of their larger mass. The relationship in the formula is true because the lighter molecules move faster and the heavier molecules move slower therefore they have the same average kinetic energy. IN THE AP EXAM YOU WILL NEVER BE ASKED A CALCULATION QUESTION REGARDING KINETIC ENERY. JUST KNOW THAT THE AVERAGE KINETIC ENERGY OF ALL GAS MOLECULES IS THE SAME AND DEPENDS ONLY ON TEMPERATURE.

21 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 21 SPEED OF MOLECULES How fast does a molecule move on the average at any temperature T? One way to estimate molecular speed is to calculate the rootmean-square (rms) speed (u rms ) which is an average molecular speed. The heavier a gas is, the slower the molecules move. As the Kelvin temperature increases, all molecules of any gas increase their root-mean-speed. The rms of a molecule can be determined using the following formula: ROOT-MEAN-SPEED: u rms = 3RT MM J where R = ideal gas constant = K mole T = temp. in Kelvin MM = molar mass (in kg/mole) The unit of root-mean-speed that you will end up with is m/s. In using this formula, you must also know this relationship: 1 Joule (J) = 1 kg m Ex. 1: Place the following gases in order of increasing average molecular speed at 25 C: CO, SF 6, H 2 S, Cl 2, HI. s 2 2 Ex.2: Calculate the root-mean-square speed of the nitrogen molecule in m/s at 25 C. (515 m/s) NOTE: The speed of different gas molecules is not the same. The speed of a gas molecule is dependent on molar mass and temperature. However, the average kinetic energy of all gas molecules is the same and is dependent only on the temperature. Lighter molecules move faster and heavier molecules move slower so that the average kinetic energy of all gas molecules is the same.

22 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 22 EFFUSION, DIFFUSION AND GRAHAM S LAW Because gas molecules are in rapid motion, one gas can mix with another. Gases move from where there is a high concentration to where there is a low concentration. The ability of a gas to move from one place to another is called diffusion. Diffusion is usually a slow process. The rate of diffusion is the rate of mixing gases. Effusion is the term used to describe the passage of a gas through a tiny opening in a membrane (air passing through the pores of a balloon). The rate of effusion measures the speed at which a gas is transferred through a membrane. Different gases travel at different rates because heavier gases move slower than light gases. The heavier the gas, the slower it moves. Ammonia molar mass of 17 g/mole moves faster than does hydrogen chloride HCl at 36.5 g/mole. Graham s Law of Effusion: Graham developed a law that states that the effusion rate of a gas is inversely proportional to the square root of its molar mass. His law compares the velocity or speed of 2 molecules and the formula yields a ratio of how fast one molecule is compared to another. GRAHAM S LAW OF EFFUSION: The rates of effusion of gases at the same temperature and pressure are inversely proportional to the square roots of their molar masses. r r 1 2 = u 1 = 2 u2 MM 1 MM where MM = molar mass u = root mean speed (or just speed) r = rate of effusion Ex. 1: The rate of diffusion of an unknown gas is four times faster than the rate of oxygen gas. Calculate the molar mass of the unknown gas and identify it. (hydrogen) Ex. 2: Calculate the ratio of the effusion rates of N 2 and O 2,, that is: rn 2 /ro 2. (1.069) DO ASSIGNMENT #5 GRAHAM S LAW P. 22 #1-4 ASMT #5 GRAHAM S LAW PROBLEMS 1. What is the ratio of the rates of effusion of hydrogen gas to ethane gas, C 2 H 6? (3.86/1) 2. If a molecule of neon gas travels at an average of 400. m/s at a given temperature, estimate the average speed of a molecule of butane gas C 4 H 10 at the same temperature. (235 m/s) 3. At a certain temperature and pressure, chlorine molecules have an average velocity of m/s. What is the average velocity of sulfur dioxide molecules under the same conditions? ( m/s) 4. The diffusion rate of an unknown gas is measured and found to be ml/min. under identical experimental conditions, the diffusion rate of O 2 is found to be ml/min. If the choices are CH 4, CO, NO, CO 2, and NO 2, what is the identity of the unknown gas? (NO)

23 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 23 INTERESTING STUFF: Earth unlike Jupiter does not have a lot of hydrogen or helium in its atmosphere. Because Earth is smaller than Jupiter, Earth has a weaker gravitation attraction for the lighter molecules. To escape Earth s gravity, a molecule must possess an escape velocity equal to or greater than 11,000 m/s. Because the average speed of helium is considerably greater than that of molecular nitrogen or molecular oxygen, more helium atoms escape from Earth s atmosphere into outer space. Therefore, only a trace amount of helium is present in our atmosphere. Jupiter, with a mass about 320 times greater than that of Earth retains both heavy and light gases in its atmosphere. WOW THE KINETIC MOLECULAR THEORY Gas laws help us to predict the behavior of gases, but they do not explain what happens at the level of the molecules to cause the changes observed in the world, for example, why does a gas expand upon heating? The physical properties of gases can be explained in terms of the motion of individual molecules. This molecular movement is a form of energy, which is the capacity to produce change or to do work. Molecules have kinetic energy. The word kinetic means moving so kinetic energy is the type of energy expended by a moving object or the energy of motion. Generalizations about gas behavior can be made and are contained in the KINETIC MOLECULAR THEORY OF GASES which contains the following assumptions: 1. A gas is composed of very tiny molecules very widely separated. These molecules are separated from each other by distances far greater than their own dimensions. The molecules possess mass but have negligible volume. 2. The molecules are in rapid, random, straight-line motion. 3. The molecules collide frequently with each other and with the walls of the container but the collisions are perfectly elastic. This means that they do not lose any speed after a collision. 4. All gases at the same temperature and pressure have the same number of molecules per unit volume. For example, 22.4 L of any gas at STP contains one mole. 5. IMPORTANT: The average kinetic energy of all molecules is directly proportional to the temperature of the gas (only the temperature!) Any 2 gases at the same temperature will have the same average kinetic energy. As temperature increases, the kinetic energy increases. The absolute temperature (K) is a measure of the average kinetic energy of the molecules. In other words, the absolute temperature is an index of the random motion of the molecules the higher the temperature, the more energetic the molecules. The warmer the gas, the more energy the molecules have. Individual molecules may possess differing amounts of energy because a few may be a little faster or a little slower than all the others. Notice in the formula below, absolute temperature is the only variable on which the energy of the molecules depends. 3 The average kinetic energy of a molecule is given by: KE ave = RT KE depends only on temperature. 2 Average KE of all gas molecules is the same The speed of a gas molecule speed = u rms = 3 RT MM The speed of a gas molecule is dependent on temperature and molar mass. Gas molecules travel at different speed. Because hydrogen molecules are lighter than oxygen molecules, they move faster than hydrogen molecules (at the same temperature.) However, the energy of oxygen and hydrogen molecules is the same because they are at the same temperature. Therefore, for different gas molecules at the same temperature: The speed is different but the kinetic energy is the same. APPLICATION OF THE KINETIC MOLECULAR THEORY Ex. 1: Use the Kinetic Molecular Theory to explain the cause of gas pressure. Gas pressure is caused by collisions between molecules and the walls of their container. The frequency of collisions and how hard the molecules hit the walls determines how much pressure is exerted by the gas. If more molecules hit the wall, then the pressure is higher. If the molecules hit harder, then the pressure increases. Ex. 2: Use the Kinetic Molecular Theory to explain temperature. Absolute temperature is a measure of the average kinetic energy of the molecules. Higher temperatures are determined by more movement of the molecules hitting each other and creating friction. Friction causes heat. The higher the temperature, the more energetic the molecules. The more energetic the molecules the more often they will hit each other and therefore more heat will be produced thereby raising the temperature.

24 STARODUB CHEM. 2AP UNIT 2-2 CH. 5: Gases 24 DO ASSIGNMENT #6 P. 24 #1-10 KINETIC MOLEULAR THEORY AND REAL GASES ASSIGNMENT #6 KINETIC MOLECULAR THEORY AND REAL GASES 1. Calculate the average kinetic energy of N 2 molecules in a sample of N 2 gas at 273 K and 546 K. (3.40 x 10 3, 6.81 x 10 3 ) 2. Do all the molecules in a 1-mol sample of CH 4 (g) have the same velocity at 546 K? Explain your answer. 3. Consider a 1.0-L container of neon gas at STP. Will the average kinetic energy, average velocity, and frequency of collisions of gas molecules with the walls of the container increase, decrease, or remain the same under each of the following conditions? (a) The temperature is increased to 100 C. (b) The temperature is decreased to 50 C. (c) The volume is decreased to 0.5 L. (d) The number of moles of neon is doubled. 4. Consider separate 1.0-L gaseous samples of H 2, Xe, Cl 2 and O 2 all at STP. (a) Rank the gases in order of increasing average kinetic energy. (b) Rank the gases in order of increasing average velocity. (c) How can separate 1.0-L samples of O 2 and H 2 each have the same average velocity? 5. The rate of effusion of a particular gas was measured and found to be 24.0 ml/min. Under the same conditions, the rate of effusion of pure methane (CH 4 ) gas is 47.8 ml/min. What is the molar mass of the unknown gas? (63.7) 6. It took 4.5 min for 1.0 L of helium to effuse through a porous barrier. How long will it take for 1.0 L of Cl 2 gas to effuse under identical conditions? (19 min) 7. Use the Kinetic Molecular Theory to explain the following observations. (a) Aerosol cans will explode if heated. (b) You can drink through a soda straw. (c) A thin-walled can will collapse when the air inside is removed by a vacuum pump. (d) Manufacturers produce different types of tennis balls for high and low elevations. 8. Consider the three flasks in the diagram on the right. Assuming the connecting tubes have negligible volume, what is the partial pressure of each gas and the total pressure when all the stopcocks are opened? (Give your answer in torr.) (224.7, 45.0, 85.9, 93.8) 9. An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only times that of oxygen gas at the same temperature. What is the identity of the unknown gas? (I 2 ) 10. A sample of pure methane CH 4 is found to effuse through a porous barrier in 1.50 min. under the same conditions, an equal number of molecules of an unknown gas effuse through the barrier in 4.73 min. What is the molar mass of the unknown gas? (159)