Chapter 11 Gases 2006 Prentice Hall CHAPTER OUTLINE

Chapter 11 Gases 2006, Prentice Hall

CHAPTER OUTLINE § § § § § Properties of Gases Pressure & Its Measurement The Gas Laws Vapor Pressure & Boiling Point Combined Gas Law Avogadro’s Law STP & Molar Volume Ideal Gas Law Partial Pressures 2

PROPERTIES OF GASES q Gases occupy are the much least dense greater and space mostthan mobile the of same three amount phases of liquid of matter. or solid. q This Particles is because of matter the gas in the particles gas phase are spaced apart far apart from one another andand are move therefore rapidly compressible. and collide with each other often. q Solid or liquid particles are spaced much closer and cannot be compressed. 3

PROPERTIES OF GASES q Gases are characterized by four properties. q These are: 1. Pressure (P) 2. Volume (V) 3. Temperature (T) 4. Amount (n) 4

KINETIC-MOLECULAR THEORY q The Scientists KMT use consists the kinetic-molecular of several postulates: theory (KMT) to describe the behavior of gases. 1. Gases consist of small particles (atoms or molecules) that move randomly with rapid velocities. 2. Gas particles have little attraction for one another. Therefore attractive forces between gas molecules can be ignored. 3. The distance between the particles is large compared to their size. Therefore the volume occupied by gas molecules is small compared to the volume of the gas. 5

KINETIC-MOLECULAR THEORY 4. Gas particles move in straight lines and collide with each other and the container frequently. The force of collision of the gas particles with the walls of the container causes pressure. 5. The average kinetic energy of gas molecules is directly proportional to the absolute temperature (Kelvin). Animation 6

Kinetic Molecular Theory Tro's Introductory Chemistry, Chapter 7

PRESSURE & ITS MEASUREMENT q Pressure is the result of collision of gas particles with the sides of the container. Pressure is defined as the force per unit area. q Pressure is measured in units of atmosphere (atm) or mm. Hg or torr. The SI unit of pressure is pascal (Pa) or kilopascal (k. Pa). 1 atm = 760 mm. Hg = 101. 325 k. Pa 1 mm. Hg = 1 torr 8

Common Units of Pressure Unit Average Air Pressure at Sea Level 101, 325 pascal (Pa) kilopascal (k. Pa) 101. 325 atmosphere (atm) 1 (exactly) millimeters of mercury (mm. Hg) inches of mercury (in. Hg) torr (torr) 760 (exactly) 29. 92 760 (exactly) pounds per square inch (psi, lbs. /in 2) Tro's Introductory Chemistry, Chapter 14. 7 9

PRESSURE & ITS MEASUREMENT q Atmospheric pressure can be measured with the use of a barometer. q Mercury is used in a barometer due to its high density. q At sea level, the mercury stands at 760 mm above its base. 10

Atmospheric Pressure & Altitude • the higher up in the atmosphere you go, the lower the atmospheric pressure is around you üat the surface the atmospheric pressure is 14. 7 psi, but at 10, 000 ft is is only 10. 0 psi • rapid changes in atmospheric pressure may cause your ears to “pop” due to an imbalance in pressure on either side of your ear drum Tro's Introductory Chemistry, Chapter 11

Pressure Imbalance in Ear If there is a difference in pressure across the eardrum membrane, the membrane will be pushed out – what we commonly call a “popped eardrum. ” Tro's Introductory Chemistry, Chapter 12

Example 1: The atmospheric pressure at Walnut, CA is 740. mm. Hg. Calculate this pressure in torr and atm. 1 mm. Hg = 1 torr 740. mm. Hg = 740. torr 740. mm. Hg 1 760 = 0. 974 atm 13

Example 2: The barometer at a location reads 1. 12 atm. Calculate the pressure in mm. Hg and torr. 1. 12 atm 760 1 = 851 mm. Hg = 1 torr 851 mm. Hg = 851 torr 14

PRESSURE & MOLES OF A GAS q The pressure of a gas is directly proportional to the number of particles (moles) present. The greater the moles of the gas, the greater the pressure 15

BOYLE’S LAW q At Theconstant relationship temperature, of pressure the and volume of a in fixed amount gases is called of gas Boyle’s is inversely Law. proportional to its pressure. As pressure Pressure and increases, volume of athe volume gas areof the gas decreases inversely proportional 16

BOYLE’S LAW q Boyle’s Law can be mathematically expressed as P 1 x V 1 = P 2 x V 2 P and V under initial condition P and V under final condition 17

Example 1: A sample of gas has a volume of 12 -L and a pressure of 4500 mm. Hg. What is the volume of the gas when the Pressure pressure is reduced to 750 mm. Hg? Volume decreases P 1= 4500 mm. Hg increases P 1 x V 1 = P 2 x V 2 P 2= 750 mm. Hg V 1 = 12 L V 2 = ? ? ? V 2 = 72 L 18

Example 2: A sample of hydrogen gas occupies 4. 0 L at 650 mm. Hg. What volume would it occupy at 2. 0 atm? Pressure P 1= 650 mm. Hg Volume Pincreases = 2. 0 atm = 1520 mm. Hg 2 decreases P 1 x V 1 = P 2 x V 2 P 2= 2. 0 atm V 1 = 4. 0 L V 2 = ? ? ? Pressures must be in the same. V 2 = 1. 7 L unit 19

CHARLES’S LAW q At Theconstant relationship pressure, of temperature the volumeand of a volume fixed in amount gases is called of gas Charles’ is directly. Law. proportional to its absolute temperature. Temperature and As temperature volume of a gas increases, the are directly volume of the proportional gas increases 20

CHARLES’S LAW q Charles’ Law can be mathematically expressed as V and T under T must be in initial units of K condition V and T under final condition 21

Example 1: A 2. 0 -L sample of a gas is cooled from 298 K to 278 K, at constant pressure. What is the new volume of the gas? Temperature Volume decreases V 1 = 2. 0 L V 2 = ? ? ? T 1 = 298 K T 2 = 278 K V 2 = 1. 9 L 22

Example 2: If 20. 0 L of oxygen is cooled from 100ºC to 0ºC, what is the new volume? Temperature s must be in + 273 = 373 Volume Temperature T = 100ºC K V 1 = 20. 0 L 1 K decreases V 2 = ? ? ? T 2= 0ºC + 273 = 273 K T 1 = 100ºC T 2 = 0ºC V 2 = 14. 6 L 23

GAY-LUSSAC’S LAW q q The At constant relationship volume, of temperature the pressureand of apressure fixed in amount gases is ofcalled gas is Gay-Lussac’s directly proportional Law. to its absolute temperature. As temperature Temperature and increases, the pressure of a gas pressure of the are directly gas increases proportional 24

GAY-LUSSAC’S LAW q Gay-Lussac’s Law can be mathematically expressed as P and T under initial T must be in condition units of K P and T under final condition 25

Example 1: An aerosol spray can has a pressure of 4. 0 atm at 25 C. What pressure will the can have if it is placed in a fire Temperatures and reaches temperature of 400 C ? must be in K P 1 = 4. 0 atm P 2 = ? ? ? T 1 = 25ºC T 1= 25ºC + 273 = 298 K T 2= 400ºC + 273 = 673 K T 2 = 400ºC 26

Example 1: An aerosol spray can has a pressure of 4. 0 atm at 25 C. What pressure will the can have if it is placed in a fire Temperature and reaches temperature of 400 C ? Pressure increases P 1 = 4. 0 atm P 2 = ? ? ? T 1 = 298 K T 2 = 673 K P 2 = 9. 0 atm 27

Example 2: A cylinder of gas with a volume of 15. 0 -L and a pressure of 965 mm. Hg is stored at a temperature of 55 C. To what temperature must the cylinder be cooled to reach a Pressure Temperature pressure of 850 decreases mm. Hg? decreases P 1 = 965 mm. Hg T 1= 55ºC + 273 = 328 K P 2 = 850 mm. Hg T 1 = 55ºC T 2 = ? ? ? TT 22==289 16ºC K 28

VAPOR PRESSURE & BOILING POINT q In an open container, liquid molecules at the surface that possess sufficient energy, can break away from the surface and become gas particles or vapor. q In a closed container, these gas particles can accumulate and create pressure called vapor pressure. q Vapor pressure is defined as the pressure above a liquid at a given temperature. Vapor pressure varies with each liquid and increases with temperature. 29

VAPOR PRESSURE & BOILING POINT q Listed below is the vapor pressure of water at various temperatures. 30

VAPOR PRESSURE & BOILING POINT q A liquid reaches its boiling point when its vapor pressure becomes equal to the external pressure (atmospheric pressure). q For example, at sea level, water reaches its boiling point at 100 C since its vapor pressure is 760 mm. Hg at this temperature. 31

VAPOR PRESSURE & BOILING POINT q At higher altitudes, where atmospheric pressure is lower, water reaches boiling point at temperatures lower than 100 C. q For example, in Denver, where atmospheric pressure is 630 mm. Hg, water boils at 95 C, since its vapor pressure is 630 mm. Hg at this temperature. 32

COMBINED GAS LAW q This All pressure-volume-temperature law is useful for studying the effect relationships of changes can be combined in two variables. into a single relationship called the combined gas law. Initial condition Final condition 33

COMBINED GAS LAW q The individual gas laws studied previously are embodied in the combined gas law. Charles’s Law Boyle’s Gay-Lussac’s Law 34

Example 1: A 25. 0 -m. L sample of gas has a pressure of 4. 00 atm at a temperature of 10 C. What is the volume of the gas at a pressure of 1. 00 atm and a temperature of 18 C? P 1= 4. 00 atm V 1= 25. 0 m. L T 1= 283 K P 2= 1. 00 atm V 2= ? ? ? T 2 = 291 K Both pressure and temp. change Must use V 2 =combined 103 m. L gas law 35

AVOGADRO’S LAW q At Theconstant relationship temperature of molesand andpressure, volume inthe gases volume is calledof. Avogadro’s a fixed amount Law. of gas is directly proportional to the number of moles. As number of Number of moles increases, and thevolumeof ofa gasgas areincreases directly the proportional 36

Avogadro’s Law Tro's Introductory Chemistry, Chapter 37

AVOGADRO’S LAW q As a result of Avogadro’s Law, equal volumes of different gases at the same temp. and pressure contain equal number of moles (molecules). 2 Tanks of gas of equal volume at the same T & P contain the same number of molecules 38

AVOGADRO’S LAW q Avogadro’s Law also allows chemists to relate volumes and moles of a gas in a chemical reaction. This relationship is For example: 2 H 2 (g) only valid for gaseous substances (g) 2 H O + 1 O 2 2 (g) 2 molecules 1 molecule 2 molecules 2 moles 1 mole 2 moles 2 Liters 1 Liter 2 Liters 39

Example 1: A sample of helium gas with a mass of 18. 0 g occupies 1. 6 Liters at a particular temperature and pressure. What Same Temp. mass of oxygen would occupy 1. 6 L at the same temperature and pressure? & Pressure mol of He = 4. 50 mol of O 2 = mol of He = 4. 50 mol mass of O 2 = 144 g 40

Example 2: How many Liters of NH 3 can be produced from reaction of 1. 8 L of H 2 with excess N 2, as shown below? N 2 (g) + 3 H 2 (g) 2 NH 3 (g) 1. 8 L H 2 2 3 = 1. 2 L NH 3 41

STP & MOLAR VOLUME q To better understand the factors that affect gas behavior, a set of standard conditions have been chosen for use, and are referred to as Standard Temperature and Pressure (STP). STP = 0ºC (273 K) 1 atm (760 mm. Hg) 42

STP & MOLAR VOLUME q At STP conditions, one mole of any gas is observed to occupy a volume of 22. 4 L. V = 22. 4 L Molar Volume at STP 43

Example 1: If 2. 00 L of a gas at STP has a mass of 3. 23 g, what is the molar mass of the gas? mol of gas = Molar mass = volume at STP 1 22. 4 = 0. 0893 mol = 36. 2 g/mol 44

Example 2: A sample of gas has a volume of 2. 50 L at 730 mm. Hg and 20 C. What is the volume of this gas at STP? P 1= 730 mm. Hg V 1= 2. 50 L T 1= 293 K P 2= 760 mm. Hg V 2= ? ? ? T 2 = 273 K V 2 = 2. 24 L 45

IDEAL GAS LAW q Combining all the laws that describe the behavior of gases, one can obtain a useful relationship that relates the volume of a gas to the temperature, pressure and number of moles. Universal gas constant R = 0. 0821 L atm/mol K 46

IDEAL GAS LAW q This relationship is called the Ideal Gas Law, and commonly written as: P V = n R T Temp. in K Pressure in atm Volume in Liters Number of moles 47

Example 1: A sample of H 2 gas has a volume of 8. 56 L at a temp. of 0 C and pressure of 1. 5 atm. Calculate the moles of gas present. P = 1. 5 atm V = 8. 56 L T = 273 K n = ? ? ? R = 0. 0821 PV = n. RT = 0. 57 mol 48

Example 2: What volume does 40. 0 g of N 2 gas occupy at 10 C and 750 mm. Hg? Moles must be=calculated mol of N = 1. 43 mol P =750 mm. Hg 2 from mass V = ? ? ? T = 283 K n = not given m = 40. 0 g R = 0. 0821 P = 750 mm. Hg. Pressure must be converted to P = 0. 987 atm 49

Example 2: What volume does 40. 0 g of N 2 gas occupy at 10 C and 750 mm. Hg? P =0. 987 atm V = ? ? ? T = 283 K n = 1. 43 R = 0. 0821 V = 33. 7 L 50

Ideal vs. Real Gases • • Real gases often do not behave like ideal gases at high pressure or low temperature Ideal gas laws assume 1) no attractions between gas molecules 2) gas molecules do not take up space ü based on the Kinetic-Molecular Theory • at low temperatures and high pressures these assumptions are not valid Tro's Introductory Chemistry, Chapter 51

Ideal vs. Real Gases Tro's Introductory Chemistry, Chapter 52

PARTIAL PRESSURES q Many gas samples are mixture of gases. For example, the air we breathe is a mixture of mostly oxygen and nitrogen gases. q Since gas particles have no attractions towards one another, each gas in a mixture behaves as if it is present by itself, and is not affected by the other gases present in the mixture. q In a mixture, each gas exerts a pressure as if it was the only gas present in the container. This pressure is called partial pressure of the gas. 53

DALTON’S LAW q In a mixture, the sum of all the partial pressures of gases in the mixture is equal to the total pressure of the gas mixture. Ptotal = P 1 + P 2 + P 3 + ··· Total pressure of = Sum of the partial pressures a gas mixture of the gases in the mixture q This is called Dalton’s law of partial pressures. 54

PARTIAL PRESSURES + PHe = 2. 0 atm PAr = 4. 0 atm PTotal = ? ? ? PHe + PAr = 6. 0 atm Total pressure of a gas mixture is the sum of partial pressures of each gas in the mixture 55

PARTIAL PRESSURES q The partial pressure of each gas in a mixture is proportional to the amount (mol) of gas present in the mixture. q For example, in a mixture of gases consisting of 1 mole of nitrogen and 1 mol of hydrogen gas, the partial pressure of each gas is one-half of the total pressure in the container. 56

PARTIAL PRESSURES Twice as many moles of Ar compared to He + PHe = 2. 0 atm PPAr = 2 PHe Ar = 4. 0 atm PTotal = 6. 0 atm The partial pressure of each gas is proportional to the amount (mol) of the gas present in the mixture 57

Example 1: A scuba tank contains a mixture of oxygen and helium gases with total pressure of 7. 00 atm. If the partial pressure of oxygen in the tank is 1140 mm. Hg, what is the partial pressure of helium in the tank? Ptotal = Poxygen + Phelium Poxygen = 1140 mm. Hg x 1 atm = 1. 50 atm 760 mm. Hg Phelium ==7. 00 PTotalatm - P–oxygen 1. 50 atm = 5. 50 atm 58

Example 2: A mixture of gases contains 2. 0 mol of O 2 gas and 4. 0 mol of N 2 gas with total pressure of 3. 0 atm. What Twice as many is the partial pressure of each gas in the mixture? moles of N 2 compared to O 2 Ptotal = Poxygen + Pnitrogen = 2 Poxygen Pnitrogen = 2/3 (Ptotal ) = 2. 0 atm Poxygen = 1/3 (Ptotal ) = 1. 0 atm 59

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