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Unit 1 (formerly Module 2) Gases and Their Applications

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Lesson 2-1 About Gases 2

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Gas is one of the three main states of matter Gas is one of the three main states of matter Gas particles may be atoms or molecules, depending on the type of substance (ie, element or compound) Gas particles may be atoms or molecules, depending on the type of substance (ie, element or compound) Gas particles have much more space between them than liquids or solids. Gas particles have much more space between them than liquids or solids. Gases are said to be an expanded form of matter, solids and liquids are condensed forms of matter. Gases are said to be an expanded form of matter, solids and liquids are condensed forms of matter. Gas is one of the three main states of matter Gas is one of the three main states of matter Gas particles may be atoms or molecules, depending on the type of substance (ie, element or compound) Gas particles may be atoms or molecules, depending on the type of substance (ie, element or compound) Gas particles have much more space between them than liquids or solids. Gas particles have much more space between them than liquids or solids. Gases are said to be an expanded form of matter, solids and liquids are condensed forms of matter. Gases are said to be an expanded form of matter, solids and liquids are condensed forms of matter. 3R

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General Properties of a Gas Gases do have mass (although it is sometimes difficult to measure). Gases do have mass (although it is sometimes difficult to measure). Gases have no definite volume, Gases have no definite volume, Gases have no definite shape. Gases have no definite shape. Gases are compressible, meaning they can be squeezed into smaller containers, or can expand to fill larger containers. Gases are compressible, meaning they can be squeezed into smaller containers, or can expand to fill larger containers. –Because gases compress, the density of gases can only be compared under specific conditions. 4

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Some Important Gases Oxygen (O 2 ): Oxygen (O 2 ): clear, breathable, supports combustion. Ozone (O 3 ): Ozone (O 3 ): poisonous, unstable form of oxygen Nitrogen (N 2 ): Nitrogen (N 2 ): clear, low activity, most abundant gas in the Earths atmosphere. Hydrogen (H 2 ): Hydrogen (H 2 ): clear, lighter than air, flammable/explosive Carbon dioxide (CO 2 ): Carbon dioxide (CO 2 ): clear, but turns limewater cloudy. Does not support respiration but low toxicity. Heavier than air. Largely responsible for the greenhouse effect (global warming) Sulphur dioxide (SO 2 ): Sulphur dioxide (SO 2 ): smelly gas. When it combines with oxygen and water vapour it can form H 2 SO 4, responsible for acid rain. 5

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Some Important Gases Carbon monoxide (CO): Carbon monoxide (CO): clear, colourless, but very toxic. It destroys the ability of blood to carry oxygen. About the same density as air. Ammonia (NH 3 ): Ammonia (NH 3 ): toxic, strong smell, refrigerant. Very soluble in water, forms a basic solution called ammonia- water (NH 4 OH) which is found in some cleaners. Freon ® or CFC: Freon ® or CFC: Non-toxic refrigerant used in air- conditioners & freezers. Freon may catalyze ozone breakdown. The original Freon formula is now banned, but low chlorine versions are still in use. Methane (CH 4 ): Methane (CH 4 ): flammable gas, slightly lighter than air, produced by decomposition. Found in natural gas. Methane is also a greenhouse gas. Helium (He): Helium (He): inert, lighter than air. Used in balloons and in divers breathing mixtures. 6

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Acetylene (C 2 H 2 ): Acetylene (C 2 H 2 ): AKA ethene, it is used as a fuel in welding, lanterns and other devices. Propane (C 3 H 8 ): Propane (C 3 H 8 ): used as a fuel in barbecues, stoves, lanterns and other devices. Radon (Rn): Radon (Rn): A noble gas that is usually radioactive. It is heavier than air, and sometimes found in poorly ventilated basements. Neon (Ne) and Xenon (Xe): Neon (Ne) and Xenon (Xe): Noble gases found in fluorescent light tubes, and as insulators inside windows. They glow more brightly than other gases when electrons pass through them. Neon is slightly lighter than air, Xenon is quite a bit heavier. Compressed Air (78% N 2, 21% O 2 ): ials. Compressed Air (78% N 2, 21% O 2 ): Not actually a pure gas, but a gas mixture that acts much like a pure gas. It is used by scuba divers (at shallow depths), and to run pneumatic tools, and for producing foam materials. 7

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Fun Gases (of no real importance) Nitrous Oxide (N 2 O) Nitrous Oxide (N 2 O) –AKA: Laughing gas, Happy gas, Nitro, NOS –Once used as an anaesthetic in dentist offices, this sweet-smelling gas reduces pain sensitivity and causes euphoric sensations. It is an excellent oxidizer, reigniting a glowing splint much like oxygen would. It is used in racing where it is injected into the carburetor to temporarily increase an engines horsepower. Sulfur Hexafluoride Sulfur Hexafluoride –One of the densest gases in common use. Fun with Sulfur hexafluoride Fun with Sulfur hexafluorideFun with Sulfur hexafluoride8

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Match the gas with the problem it causes GasProblem GasProblem Carbon DioxideOzone layer depletion Carbon DioxideOzone layer depletion CFCsGlobal Warming CFCsGlobal Warming MethaneToxic poisoning MethaneToxic poisoning Carbon monoxideNoxious smell Carbon monoxideNoxious smell Sulfur dioxideAcid Rain Sulfur dioxideAcid Rain Next slide: Summary 9

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Some Gases Classified by Relative Density Low Density gasesNeutral Density GasesHigh Density gases lighter than air<25 g / mol similar to air 29±4 g / mol Denser than air (>34 g / mol ) Testable Property*: Balloon will float in air Balloon drops slowly through air Balloon drops quickly through air Examples: Hydrogen (H 2 )2 Helium (He) 4 Methane (CH 4 )16 Ammonia (NH 3 )17 Neon (Ne)20 H ydrogen F luoride (HF) 21 Examples: Cyanide (HCN) 27 Acetylene (C 2 H 4 )28 Nitrogen (N 2 ) 28 C arbon monoxide 28 Ethane (C 2 H 6 )30 Oxygen (O 2 )32 Examples: Fluorine (F 2 )38 Argon (Ar)40 Carbon dioxide (CO 2 )44 Propane (C 3 H 8 )44 Butane (C 4 H 10 )58 S ulphur H exafluoride (SF 6 )146 *balloon test: Fill a large, lightweight balloon with the gas, then release it from a height of about 1.8 m in a room with still air. If the gas is lighter than air the balloon will float upwards. If it is close to air, the balloon will fall very slowly. If the gas is heavier than air, the balloon will fall quickly.

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Some Gases Classified by Chemical Properties Combustible gases (combustion /explosion) Reactive- oxidizing Gases (support combustion) Non-Reactive gases Testable property: Burning splint produces pop Testable property: Glowing splint reignites, burning splint grows brighter Testable property: Burning splint is extinguished, glowing splint is dimmed Other properties: Useful as fuels Other properties: Cause metals and some other materials to corrode or oxidize. Can improve combustion. Other properties: Can be used to preserve foods by slowing oxidation Examples: Hydrogen (H 2 ) Methane (CH 4 ) Propane (C 3 H 8 ) Acetylene (C 2 H 4 ) Examples: Oxygen (O 2 ) Fluorine (F 2 ) Chlorine (Cl 2 ) Nitrous Oxide (NO 2 ) Examples: Carbon dioxide (CO 2 ) Nitrogen (N 2 ) Argon (Ar) Helium (He)

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Textbook Assignments Read Chapter 1: pp. 37 to 50 Read Chapter 1: pp. 37 to 50 Do the exercises on pages 51 and 52 Do the exercises on pages 51 and 52 –Questions # 1 to 22 12

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Summary: Know the properties of gases Know the features of some important gases, esp: Oxygen Hydrogen Carbon dioxide Know the environmental problems associated with some gases, eg. Carbon dioxide CFCs Sulfur dioxide 13

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Chapter 2 The Kinetic Theory Moving, moving, moving, Keep those atoms moving... 14

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Kinetic Theory Overview: The kinetic theory of gases (AKA. kinetic- molecular theory) tries to explain the behavior of gases, and to a lesser extent liquids and solids, based on the concept of moving particles or molecules.

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The Kinetic Theory of Gases (AKA: The Kinetic Molecular Theory) The Kinetic Theory of Gases tries to explain the similar behaviours of different gases based on the movement of the particles that compose them. Kinetic refers to motion. The idea is that gas particles* are in constant motion. * For simplicity, I usually call the gas particles molecules, although in truth, they could include atoms or ions. 2.1 Page 54 16

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The Particle Model Not in text The Kinetic Theory is part of the Particle Model of matter, which includes the following concepts: –All matter is composed of particles (ions, atoms or molecules) which are extremely small and have a varying space between them, depending on their state or phase. –Particles of matter may attract or repel each other, and the force of attraction or repulsion depends on the distance that separates them. –Particles of matter are always moving R

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Kinetic Molecular Theory And Temperature The absolute temperature of a gas (Kelvins) is directly proportional to the average kinetic energy of its molecules. –In other words, when it is cold, molecules move slowly and have lower kinetic energy. –When the temperature increases, molecules speed up and have more kinetic energy!18

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Particle Motion and Phases of Matter Recall that: In solids, the particles (molecules) are moving relatively slowly. They have low kinetic energy In liquids, molecules move faster. They have higher kinetic energy. In gases, the particles move fastest, and have high kinetic energy. But, as we will find out later: Heavy particles moving slowly can have the same kinetic energy as light particles moving faster Page R

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Kinetic Theory Model of States Solid Particles vibrate but dont flow. Strong molecular attractions keep them in place. Liquid Particles vibrate, move and flow, but cohesion (molecular attraction) keeps them close together. Gas Particles move freely through container. The wide spacing means molecular attraction is negligible. 20

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Kinetic Motion of Particles Particles (ie. Molecules) can have 3 types of motion, giving them kinetic energy –Vibrational kinetic energy ( vibrating ) –Rotational kinetic energy ( tumbling ) –Translational kinetic energy ( moving )2.1.1 Page 55 21

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Kinetic Theory and Solids & Liquids When it is cold, molecules move slowly In solids, they move so slowly that they are held in place and just vibrate (only vibrational energy) In liquids they move a bit faster, and can tumble and flow, but they dont escape from the attraction of other molecules (more rotational energy, along with a little bit of vibration & translation ) In gases they move so fast that they go everywhere in their container (more translational energy, with a little bit of rotation & vibration ) Page 56 22

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Plasma, the Fourth State (extension material) When strongly heated, or exposed to high voltage or radiation, gas atoms may lose some of their electrons. As they capture new electrons, the atoms emit lightthey glow. This glowing, gas-like substance is called plasma 23

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Kinetic Theory and the Ideal Gas As scientists tried to understand how gas particles relate to the properties of gases, they saw mathematical relationships that very closely, but not perfectly, described the behaviour of many gases. They have developed theories and mathematical laws that describe a hypothetical gas, called ideal gas Page 61 24

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To make the physical laws (derived from kinetic equations from physics) work, they had to make five assumptions about how molecules work. Four of these are listed on page 61 of your textbook The fifth one is not Page 61 25

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Kinetic Theory Hypotheses about an Ideal Gas 1.The particles of an ideal gas are infinitely small, so the size is negligible compared to the volume of the container holding the gas. 2.The particles of an ideal gas are in constant motion, and move in straight lines (until they collide with other particles) 3.The particles of an ideal gas do not exert any attraction or repulsion on each other. 4.The average kinetic energy of the particles is proportional to the absolute temperature Page 61 26

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No Gas is Ideal Some of the assumptions on the previous page are clearly not true. Molecules do have a size (albeit very tiny) Particles do exert forces on each other (slightly) As a result, there is no such thing as a perfectly ideal gas However, the assumptions are very good approximations of the real particle properties. Real gases behave in a manner very close to ideal gas, in fact so close that we can usually assume them to be ideal for the purposes of calculations. 27

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Other Imaginary Features of Ideal Gas Anideal gas would obey the gas laws at all conditions of temperature and pressureAn ideal gas would obey the gas laws at all conditions of temperature and pressure An ideal gas would never condense into a liquid, nor freeze into a solid.An ideal gas would never condense into a liquid, nor freeze into a solid. At absolute zero an ideal gas would occupy no space at allAt absolute zero an ideal gas would occupy no space at all Page 61 28

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Please Notice: Not all molecules move at exactly the same speed. The kinetic theory is based on averages of a great many molecules. –Even if the molecules are identical and at a uniform temperature, a FEW will be faster than the average, and a FEW will be slower. –If there are two different types of molecules, the heavier ones will be slower than the light ones – ON THE AVERAGE! – but there can still be variations. That means SOME heavy molecules may be moving as fast as the slowest of the light ones. Temperature is based on the average (mean) kinetic energy of sextillions of individual molecules. 29

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SlowSlowmolecules The range of kinetic energies can be represented as a sort of bell curve. Maxwells Velocity Distribution Curve. Increasing kinetic energy Average kinetic energy Increasing # molecules Most molecules mode mean Averagemolecules The mean & mode can help establish average molecules FastMolecules 30

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So, Given two different gases at the same temperature… What is the same about them? The AVERAGE kinetic energy is the same. Not the velocity of individual molecules Not the mass of individual molecules. In fact, the lighter molecules will move faster E k = mv 2 kinetic energy of molecules 2 So, kinetic energy depends on both the speed (v) and on the mass (m) of the molecules. 31

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Distribution of Particles Around Average Kinetic Energies. Kinetic Energy of molecules Kinetic Energy of molecules (proportional to velocity of molecules) Number of molecules Number of molecules Average kinetic energy of molecules Average kinetic energy of warmer molecules Fasterthan average molecules Slowerthan 32 Average kinetic energy of colder molecules

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Kinetic Theory Trivia The average speed of oxygen molecules at 20°C is 1656km/h. At that speed an oxygen molecule could travel from Montreal to Vancouver in three hours…If it travelled in a straight line. Each air molecule has about (ten billion) collisions per second 10 billion collisions every second means they bounce around a lot! The number of oxygen molecules in a classroom is about: –thats more than there are stars in the universe! The average distance air molecules travel between collisions is about 60nm. – m is about the width of a virus. 33

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Videos Kinetic Molecular Basketball – Average Kinetic Energies –http://www.youtube.com/watch?v=UNn_trajMFo&NR=1http://www.youtube.com/watch?v=UNn_trajMFo&NR=1 Thermo-chemistry lecture on kinetics 34

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Assignments Read pages 53 to 61 Do Page 62 # 1-11

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Chapter 2.2 Behaviors of Gases –Compressibility –Expansion –Diffusion and Effusion –Grahams Law

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Compressibility: –Because the distances between particles in a gas is relatively large, gases can be squeezed into a smaller volume. –Compressibility makes it possible to store large amounts of a gas compressed into small tanks Expansion: –Gases will expand to fill any container they occupy, due to the random motion of the molecules.

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2.2.3 Diffusion Diffusion is the tendency for molecules to move from areas of high concentration to areas of lower concentration, until the concentration is uniform. They do this because of the random motion of the molecules. Diffusion is the tendency for molecules to move from areas of high concentration to areas of lower concentration, until the concentration is uniform. They do this because of the random motion of the molecules. Effusion is the same process, but with the molecules passing through a small hole or barrier Effusion is the same process, but with the molecules passing through a small hole or barrier Next slide: 38

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Rate of Diffusion or Effusion It has long been known that lighter molecules tend to diffuse faster than heavy ones, since their average velocity is higher, but how much faster? It has long been known that lighter molecules tend to diffuse faster than heavy ones, since their average velocity is higher, but how much faster? 39 heavy particle heavy particle light particle light particle

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Grahams Law Thomas Graham (c. 1840) studied effusion (a type of diffusion through a small hole) and proposed the following law: Thomas Graham (c. 1840) studied effusion (a type of diffusion through a small hole) and proposed the following law: The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. In other words, light gas particles will diffuse faster than heavy gas molecules, and there is a math formula to calculate how much faster. In other words, light gas particles will diffuse faster than heavy gas molecules, and there is a math formula to calculate how much faster. Next slide: Example 40 Where: v 1 = rate of gas 1 v 2 = rate of gas 2 M 1 = molar mass of gas1 M 2 =molar mass of gas 2 Internet demo of effusion Internet demo of effusion Internet demo of effusion Internet demo of effusion

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Grahams Law Version #1, based on Effusion Rate The relationship between the rate of effusion or diffusion and the molar masses is: Where: v 1 is the rate of diffusion of gas 1, in any appropriate rate units* v 2 is the rate of diffusion of gas 2, in the same units as gas 1 M 1 is the molar mass of gas 1 M 2 is the molar mass of gas 2 *Rate units must be an amount over a time for effusion (eg: mL/s or L/min), or a distance over a time for diffusion (eg: cm/min or mm/s) Note: See the inversion of the 1 and 2 in the 2 nd ratio!

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Thomas Graham ( ) Graham derived his law by treating gases as ideal, and applying the kinetic energy formula to them. E k = ½ mv 2 All gases have the same kinetic energy at the same temperature, Therefore, mv 2 for the first gas = mv 2 for the second gas: m 1 v 1 2 = m 2 v 2 2. A bit of algebra then gave him his famous law. And in my spare time I invented dialysis, which has saved the lives of thousands of kidney patients

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Grahams Law Version #2, Based on Effusion Time Sometimes its easier to measure the time it takes for a gas to effuse completely, rather than the rate. Grahams law can be changed for this, but the relationship between time and molar mass is direct as the square root: Where: t 1 is the time it takes for the first gas to effuse completely. t 2 is the time it takes for an equal volume of the 2 nd gas to effuse M 1 is the molar mass of the first gas M 2 is the molar mass of the second gas. Note: In this variant law, the relationship is not inverted!

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Example of Grahams Law: How much faster does He diffuse than N 2 ? Nitrogen (N 2 ) has a molar mass of 28.0 g/mol Nitrogen (N 2 ) has a molar mass of 28.0 g/mol Helium (He) has a molar mass of 4.0 g/mol Helium (He) has a molar mass of 4.0 g/mol The difference between their diffusion rates is: The difference between their diffusion rates is: Notice the reversal of order! Notice the reversal of order! So helium diffuses 2.6 times faster than nitrogen So helium diffuses 2.6 times faster than nitrogen M N 2 =2x14.0=28 g/mol Next slide: 2.3 Pressure of Gases M He =1x4.0=4 g/mol 44

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Assignments Read pages 63 to 67 Read pages 63 to 67 Do Questions 1 to 10 on page 68 Do Questions 1 to 10 on page 68

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Chapter 2.3 Pressure of Gases –What is Pressure –Atmospheric Pressure –Measuring Pressure 100 km < kPa 40 km 1 kPa 20 km 6 kPa 10 km 25 kPa 5 km 55 kPa 5 km 55 kPa 0 km 101 kPa 0 km 101 kPa Mt Everest 31 kPa 46 Highest Jet 4 kPa Edge of Space X15 (1963) Spaceship 1 (2006) Outer Space (immeasurable) Mr. Smith

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Pressure Pressure is the force exerted by a gas on a surface. The surface that we measure the pressure on is usually the inside of the gass container. Pressure and the Kinetic Theory Gas pressure is caused by billions of particles moving randomly, and striking the sides of the container. Pressure Formula: Pressure = force divided by area 47

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Atmospheric Pressure This is the force of a 100 km high column of air pushing down on us. Standard atmospheric pressure is 1.00 atm (atmosphere), or kPa (kilopascals), or 760 Torr (mmHg), or 14.7 psi (pounds per square inch) Pressure varies with: Altitude. (lower at high altitude) Weather conditions. (lower on cloudy days) 48

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Pressure conversions Example 1: convert 540 mmHg to kilopascals =72.0 kPa Example 2: convert 155 kPa to atmospheres =1.53 atm SP 1.00 atm 760 mmHg 760 Torr kPa 14.7 psi 1013 mB 29.9 inHg M u l t i p l y Divide

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Measuring Pressure Barometer: measures atmospheric pressure. –Two types: Mercury Barometer Aneroid Barometer Manometer: measures pressure in a container (AKA. Pressure guage) Dial Type: Similar to an aneroid barometer U-Tube: Similar to a mercury barometer Piston type: used in tire guage 50

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A tube at least 800 mm long is filled with mercury (the densest liquid) and inverted over a dish that contains mercury. The mercury column will fall until the air pressure can support the mercury. On a sunny day at sea level, the air pressure will support a column of mercury 760 mm high. The column will rise and fall slightly as the weather changes. Mercury barometers are very accurate, but have lost popularity due to the toxicity of mercury. the Mercury Barometer51

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The Aneroid Barometer In an aneroid barometer, a chamber containing a partial vacuum will expand and contract in response to changes in air pressure A system of levers and springs converts this into the movement of a dial.

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Manometers work much like barometers, but instead of measuring atmospheric pressure, they measure the pressure difference between the inside and outside of a container. Like barometers they come in mercury and aneroid types. There is also a cheaper piston type used in tire gauges, but not in science. U-tube manometer Pressure gauge U-tube manometer Pressure gauge (mercury manometer) (aneroid) You Tube manometer You Tube manometer You Tube manometer You Tube manometer Manometers (Pressure Gauges) Tire gauge (piston manometer)

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Reading U-tube manometers When reading a mercury U- tube manometer, you measure the difference in the heights of the two columns of mercury. If the tube is closed then the height (h) is the gas pressure in mmHg. P (mmHg) =h (mmHg) If the tube is open and h is positive (the pressure you are measuring is greater than the atmosphere) then you must add atmospheric pressure in mmHg. P gas(mmHg) = P atm(mmHg) +h (mm) Must be in mmHg, not cm or kPa! Atm. pressure After you finish, you can convert your answer to kPa, or atm. Or whatever.

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Manometer Examples on a day when the air pressure is 763mmHg (101.7 kPa) Closed tube: P gas(mm Hg) =h (mm Hg) P gas = h = 4 cm = 40 mm Hg P gas = Open: P gas(mmHg) =P atm(mmHg) +h (mmHg) P gas = mm Hg =823 mm Hg P gas = Open: P gas(mmHg) =P atm(mmHg) -h (mmHg) P gas = mm Hg =703 mm Hg P gas = 6 cm Higher 6 cm Lower 4 cm 6 9 h= 4 cm

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Assignments Read pages 69 to 73. Do Page 74, Questions 1 to 4.

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Chapter 2.4 The Simple Gas Laws –Boyles LawRelates volume & pressure –Charles LawRelates volume & temperature –Gay-Lussacs LawRelates pressure & temperature –Avogadros LawRelates to the number of moles Other Simple Laws that are a Gas: –Coles Law Relates thinly sliced cabbage to vinegar –Murphys LawAnything that can go wrong will. –Clarkes LawsRelates possible and impossible 57

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Clarkes Laws of the impossible* Clarkes 1 st Law: If an elderly and respected science teacher (like me) tells you that something is possible, he is probably right. If he tells you something is impossible, hes almost certainly wrong. Clarkes 1 st Law: If an elderly and respected science teacher (like me) tells you that something is possible, he is probably right. If he tells you something is impossible, hes almost certainly wrong. Clarkes 2 nd Law: The only way to find the limits to what is possible is to go beyond them. Clarkes 2 nd Law: The only way to find the limits to what is possible is to go beyond them. Clarkes 3 rd Law: Any sufficiently advanced technology is indistinguishable from magic. Clarkes 3 rd Law: Any sufficiently advanced technology is indistinguishable from magic. *these are slightly paraphrased, I quote them from memory. They were developed by science fiction writer Arthur C. Clarke

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Lesson Boyles Law Robert Boyle (1662) Lesson Boyles Law Robert Boyle (1662) For a given mass of gas at a constant temperature, the volume varies inversely with pressure. For a given mass of gas at a constant temperature, the volume varies inversely with pressure. For Pressure and Volume Next slide: Air in Syringe 59

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Robert Boyle B orn: 25 January 1627 Lismore, County Waterford, Ireland Died 31 December 1691 (aged 64) London, England B orn: 25 January 1627 Lismore, County Waterford, Ireland Died 31 December 1691 (aged 64) London, England Fields: Physics, chemistry; Known for Boyle's Law. Considered to be the founder of modern chemistry Fields: Physics, chemistry; Known for Boyle's Law. Considered to be the founder of modern chemistry Influences: Robert Carew, Galileo Galilei, Otto von Guericke, Francis Bacon Influences: Robert Carew, Galileo Galilei, Otto von Guericke, Francis Bacon Influenced: Dalton, Lavoisier, Charles, Gay-Lussack, Avogadro. Influenced: Dalton, Lavoisier, Charles, Gay-Lussack, Avogadro. Notable awards: Fellow of the Royal Society Notable awards: Fellow of the Royal Society 60

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Pressure Gas pressure is the force placed on the sides of a container by the gas it holds Gas pressure is the force placed on the sides of a container by the gas it holds Pressure is caused by the collision of trillions of gas particles against the sides of the container Pressure is caused by the collision of trillions of gas particles against the sides of the container Pressure can be measured many ways Pressure can be measured many ways Standard Pressure Atmospheres (atm)1 atm Kilopascals (kPa)or(N/m 2 )101.3 kPa = N/m 2 Millibars (mB)1013 mB Torr (torr)or mm mercury760 torr = 760 mmHg Centimetres of mercury76 cmHg Inches of mercury (inHg)29.9 inHg(USA only) Pounds per sq. in (psi)14.7 psi(USA only) 61

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Example of Boyles Law: Air trapped in a syringe If some air is left in a syringe, and the needle removed and sealed, you can measure the amount of force needed to compress the gas to a smaller volume. Next slide: Inside syringe 62

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Inside the syringe… The harder you press, the smaller the volume of air becomes. Increasing the pressure makes the volume smaller! The harder you press, the smaller the volume of air becomes. Increasing the pressure makes the volume smaller! The original pressure was low, the volume was large. The new pressure is higher, so the volume is small. The original pressure was low, the volume was large. The new pressure is higher, so the volume is small. Click Here for an internet demo using psi (pounds per square inch) instead of kilopascals (1kPa=0.145psi) Click Here for an internet demo using psi (pounds per square inch) instead of kilopascals (1kPa=0.145psi)Here Next slide: PV low low high high 63

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This means that: As the volume of a contained gas decreases, the pressure increases As the volume of a contained gas decreases, the pressure increases As the volume of a contained gas increases, the pressure decreases As the volume of a contained gas increases, the pressure decreases This assumes that: This assumes that: no more gas enters or leaves the container, and no more gas enters or leaves the container, and that the temperature remains constant. that the temperature remains constant. The mathematical formula for this is given on the next slide The mathematical formula for this is given on the next slide As the volume of a contained gas decreases, the pressure increases As the volume of a contained gas increases, the pressure decreases This assumes that: n no more gas enters or leaves the container, and that the temperature remains constant. The mathematical formula for this is given on the next slide Next slide: Example 64

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Boyles Law Relating Pressure and Volume of a Contained Gas By changing the shape of a gas container, such as a piston cylinder, you can compress or expand the gas. This will change the pressure as follows : Where: P 1 is the pressure* of the gas before the container changes shape. P 2 is the pressure after, in the same units as P 1. V 1 is the volume of the gas before the container changes, in L or mL V 2 is the volume of the gas after, in the same units as V 1 *appropriate pressure units include: kPa, mmHg, atm. Usable, but inappropriate units include psi, inHg.

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Example 1 You have 30 mL of air in a syringe at 100 kPa. If you squeeze the syringe so that the air occupies only 10 mL, what will the pressure inside the syringe be? You have 30 mL of air in a syringe at 100 kPa. If you squeeze the syringe so that the air occupies only 10 mL, what will the pressure inside the syringe be? P 1 × V 1 = P 2 × V 2, so.. P 1 × V 1 = P 2 × V 2, so kPa × 30 mL = ? kPa × 10 mL 100 kPa × 30 mL = ? kPa × 10 mL 3000 mL·kPa ÷ 10 mL = 300 kPa 3000 mL·kPa ÷ 10 mL = 300 kPa The pressure inside the syringe will be 300 kPa The pressure inside the syringe will be 300 kPa Next slide: Graph of Boyles Law 66

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Graph of Boyles Law The Pressure-Volume Relationship Pressure (kPa) Pressure (kPa) Volume (L) Volume (L) Boyles Law produces an inverse relationship graph. 100 x 8 = x 4 = x 2 = x 1 = 800 P(kpa) x V(L) Next slide: Real Life Data 300 x 2.66 = x 1.6 = x 1.33 = x 1.14 =

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Example 2: Real Life Data In an experiment Mr. Taylor and Tracy put weights onto a syringe of air. At the beginning, Mr. Taylor calculated the equivalent of 4 kgf of atmospheric pressure were exerted on the syringe. 0+4= 4kg : 29 mL (116) 2+4= 6kg : 20 mL (120) 4+4=8kg : 15 mL (120) 6+4=10kg: 12 mL (120) 8+4=12kg: 10.5 mL (126) Next slide: Boyles Law Experiment or skip to: Lesson 2.3 Charles Law: Lesson 2.3 Charles LawLesson 2.3 Charles Law 68

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Summary: Boyles law The volume of a gas is inversely proportional to its pressure Formula: P 1 V 1 =P 2 V 2 Graph: Boyles law is usually represented by an inverse relationship graph (a curve) Volume (L) Volume (L) Pressure (kPa) Pressure (kPa) P 1 V 1 =P 2 V 2 69

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Assignments on Boyles Law Read pages 75 to 79 Do questions 1 to 10 on page 97

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Boyles Law Lab Activity We will use the weight of a column of mercury to compress and expand air (a gas) sealed in a glass tube. Read the handout for details of the procedure. (Note: You may shorten the procedure section in your report by including and referring to this handout as part of a complete sentence.) You should still write all other report sections (purpose, materials, diagram, observations etc.) in full, as normal. Read, Dont Write

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#1. Horizontal #2 Open end up #3 Open end down Diagram of Boyles Law Apparatus

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Collecting Data You will need to find the length of the mercury column with the tube held horizontal: You also need this atmospheric information: (a) Position of rightside of mercury___ mm (b) Position of left of mercury column___ mm (c) Height of mercury column (a) – (b)(c) mm (d) todays temperature * ___ °C (e) todays barometric pressure (blackboard) (e) mmHg *used to calibrate the barometer, not used in calculations

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Collecting Data (continued) (f) Position of left side of columnmm (g) Position of closuremm (h) volume of gas (f) – (g) (h) Mm Data set 2 - Open End Up: (i) Position of bottom of columnmm (j) Position of closure should be same as (g) mm (k) volume of gas (i) – (j) (k) mm Data set 1 - Horizontal Tube:

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Collecting Data (continued) Data set 3 - Open End Down: l) Position of Top of columnmm m) Position of closure should be same as (g) mm n) volume of gas (l) – (m) mm This concludes the collection of data, now we must process it and calculate the PV (pressure x volume) values at each of the three conditions.

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Calculations Barometric pressure Item (e) Column Height Item (c) Pressure P Volume V PV PxV Horizontal (e)(c)(e)(h) Open End Up (e)(c)(e)+(c)(k) Open End Down (e)(c)(e)- (c)(n) Since we are using analogues for pressure & volume, the units dont matter.

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Conclusion and Discussion According to Boyles law, the PV values should all be identical. In the real world they will not be identical, but they should be very close. Analyze your results. While doing this you should find the percentage similarity between your largest and smallest result (smallest over largest x 100%). This can help you conclude if your results have supported Boyles Law or not. Discuss sources of error, and explain if they were significant in your results. Discuss the meaning of Boyles law as it relates to this activity.

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Answers to Boyles Law Sheet L of a gas at standard temperature and pressure (101 kPa) is compressed to 473 mL. What is the new pressure of the gas? formula P 1 V 1 =P 2 V 2 Known P 1 = 101 kPa V 1 = 1.00x10 3 mL P 2 = unknown V 2 = 473 mL 101kPa 1000 mL = P 2 kPa 473 mL P 2 = kPamL = kPa 473 mL Answer: the pressure will be about 214 kilopascals 1 mark

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2.In a thermonuclear device the pressure of L of gas reaches 4.0x10 8 kPa. When the bomb casing explodes, the gas is released into the atmosphere where it reaches a pressure of 1.00x10 2 kPa. What is the volume of the gas after the explosion? Known P 1 = 4.0x10 8 kPa V 1 = L P 2 = 1x10 2 kPa V 2 =unknown formula P 1 V 1 =P 2 V 2 4.0x10 8 kPa 0.050L = 1x10 2 kPa V 2 L V 2 = 4x kPaL = 2.00x10 5 L 1x10 2 kPa Answer: there will be 2.00x10 5 (or L) of gas Answer: there will be 2.00x10 5 Litres (or L) of gas 1 mark

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3.synthetic diamonds can be manufactured at pressures of 6.00x10 4 atm. If we took 2.00L of gas at 1.00 atm and compressed it to 6.00x10 4 atm, what would the volume be? Known P 1 = 1.00 atm V 1 = 2.00 L P 2 = 6.0x10 4 atm V 2 = unknown Formula P 1 V 1 =P 2 V = V 2 V 2 = 2.00 ÷ 6.0x10 4 V 2 = 3.33 x10 -5 L 1 mark or P 1 =1.01x10 2 kPa, P 2 =6.06x10 6 kPa. The volume would be 3.33x10 -5 Litres 1 mark

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4.Divers get the bends if they come up too fast because gas in their blood expands, forming bubbles in their blood. If a diver has L of gas in his blood at a depth of 50m where the pressure is 5.00x10 3 kPa, then rises to the surface where the pressure is 1.00x10 2 kPa, what will the volume of gas in his blood be? Do you think this will harm the diver? Known P 1 =5.00x10 3 kPa V 1 = L P 2 = 1.00x10 2 kPa V 2 = Unknown Formula P 1 V 1 =P 2 V 2 5.0x10 3 kPa L = 1x10 2 kPa V 2 L V 2 = 5x kPaL = 2.50 L 1x10 2 kPa The sudden appearance of 2½ litres of gas in the divers bloodstream could be quite deadly. 1 mark

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Lesson Charles Law The Relationship between Temperature and Volume. Volume varies directly with Temperature Next slide: Jacques Charles 83

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Jacques Charles (1787) The volume of a fixed mass of gas is directly proportional to its temperature (in kelvins) if the pressure on the gas is kept constant This assumes that the container can expand, so that the pressure of the gas will not rise. Next slide: The Mathematical formula for this law Born: November 12, 1746 ( ) Beaugency, Orléanais Died: April 7, 1823 ( ) (aged 76), Paris Nationality: France Fields: physics, mathematics, hot air ballooning Institutions: Conservatoire des Arts et Métiers

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Charles Law Relating Volume and Temperature of a Gas If you place a gas in an expandable container, such as a piston or balloon, as you heat the gas its volume will increase, as you cool it the volume will decrease. Where: T 1 is Temperature of the gas before it is heated, in kelvins. T 2 is Temperature of the gas after it is heated, in kelvins V 1 is the volume of the gas before it was heated, in L or mL V 2 is the volume of the gas after it was heated, in the same units.

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Charles Law Evidence Charles used cylinders and pistons to study and graph the expansion of gases in response to heat. See the next two slides for diagrams of his apparatus and graphs. Lord Kelvin (William Thompson) used one of Charles graphs to discover the value of absolute zero. Next slide: Diagram of Cylinder & Piston 86

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Charles Law ExamplePiston Cylinder Trapped Gas Next slide: Graph of Charles Law Click Here for a simulated internet experiment Here 87

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Graph of Charles Law 0°C 100°C 200°C 150°C 50°C 250°C 1L 2L 3L 4L 5L 6L -250°C -200°C -150°C -100°C -50°C °C Expansion of an Ideal Gas Expansion of most real gases 273°C Next slide: Example Liquid state Solid state condensation freeze Charles discovered the direct relationship Lord Kelvin traced it back to absolute zero.

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Example If 2 Litres of gas at 27°C are heated in a cylinder, and the piston is allowed to rise so that pressure is kept constant, how much space will the gas take up at 327°C? If 2 Litres of gas at 27°C are heated in a cylinder, and the piston is allowed to rise so that pressure is kept constant, how much space will the gas take up at 327°C? Convert temperatures to kelvins: 27°C =300k, 327°C = 600k Convert temperatures to kelvins: 27°C =300k, 327°C = 600k Use Charles Law: (see below) Use Charles Law: (see below) Answer: 4 Litres Answer: 4 Litres Next slide: Lesson 2.4 Gay Lussacs Law

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Standard Temperature & Pressure (STP) Since the volume of a gas can change with pressure and temperature, gases must be compared at a specific temperature and pressure. The long-standing standard for comparing gases is called Standard Temperature and Pressure (STP) Standard Temperature =0°C = 273 K Standard Pressure =101.3 kPa

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Ambient Temperature Some chemists prefer to compare gases at 25°C rather than 0°C. At zero it is freezing, a temperature difficult to maintain inside the lab. This alternate set of conditions is known as Standard Ambient Temperature and Pressure (SATP). Although not widely used, you should be aware of it, and always watch carefully in case a question uses AMBIENT temperature instead of STANDARD temperature. Ambient Temperature = 25°C = 298 K Standard Pressure = kPa (SATP)

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Comparison Standard and Ambient Conditions Standard Temperature & Pressure (STP) Ambient Temperature & Pressure (SATP) Pressure kPa Temperature °C 0 °C25 °C Temperature K K K Molar Volume 22.4 L/mol24.5 L/mol

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Summary: Charles law The volume of a gas is directly proportional to its temperature Formula: Graph: Charles law is usually represented by a direct relationship graph (straight line) Video1 Absolute zero 0°C=273K Temp Temp Volume (L) Volume (L)

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Charles Law Worksheet 1. The temperature inside my fridge is about 4˚C, If I place a balloon in my fridge that initially has a temperature of 22˚C and a volume of 0.50 litres, what will be the volume of the balloon when it is fully cooled? (for simplicity, we will assume the pressure in the balloon remains the same) Data: T 1 =22˚C T 2 =4˚C V 1 =0.50 L To find: V 2 = unknown Temperatures must be converted to kelvin =295K=277K So: V 2 =V 1 x T 2 ÷ T 1 V 2 =0.5L x 277K 295K V 2 =0.469 L The balloon will have a volume of 0.47 litres multiply divide 94

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2.A man heats a balloon in the oven. If the balloon has an initial volume of 0.40 L and a temperature of 20.0°C, what will the volume of the balloon be if he heats it to 250°C. 95 Data V 1 = 0.40L T 1 = 20°C T 2 = 250°C V 2 = ? Convert temperatures to kelvin = 293K, =523k =293 K =523 K Use Charles Law 0.40L x 523 K ÷ 293 K = L L Answer: The balloons volume will be 0.71 litres

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3. On hot days you may have noticed that potato chip bags seem to inflate. If I have a 250 mL bag at a temperature of 19.0°C and I leave it in my car at a temperature of 60.0°C, what will the new volume of the bag be? Answer: The bag will have a volume of 285mL Data: V 1 =250 mL T 1 = 19.0°C T 2 =60.0°C V 2 = ? Convert temperatures to kelvin = 292K, =333K =292 K =333 K Use Charles Law 250mL x 333 K ÷ 292 K = mL mL

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4. The volume of air in my lungs will be 2.35 litres Be sure to show your known information Change the temperature to Kelvins and show them. Show the formula you used and your calculations State the answer clearly The temperature is K, which corresponds to C. A jacket or sweater would be appropriate clothing for this weather. Although only the answers are shown here, in order to get full marks you need to show all steps of the solution!

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Charles Law Assignments Read pages 80 to 84 Do questions 11 to 21 on pages 97 and 98

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Gay-Lussacs Law For Temperature-Pressure changes. Pressure varies directly with Temperature Lesson Next slide: 99

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Joseph Gay-Lussac (1802) The pressure of a gas is directly proportional to the temperature (in kelvins) if the volume is kept constant. Next slide: Born 6 December 1778 Saint-Léonard-de-Noblat Died 9 May Saint-Léonard-de-Noblat Nationality: French Fields: Chemistry Known for Gay-Lussac's law Gay-Lussac's lawGay-Lussac's law

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Gay-Lussacs Law Relating Pressure and Temperature of a Gas Where: P 1 is the pressure* of the gas before the temperature change. P 2 is the pressure after the temperature change, in the same units. T 1 is the temperature of the gas before it changes, in kelvins. T 2 is the temperature of the gas after it changes, in kelvins. *appropriate pressure units include: kPa, mmHg, atm.

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Gay-Lussacs Law As the gas in a sealed container that cannot expand is heated, the pressure increases. As the gas in a sealed container that cannot expand is heated, the pressure increases. For calculations, you must use Kelvin temperatures: For calculations, you must use Kelvin temperatures: K=°C+273 K=°C+273 pressure

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Example A sealed can contains 310 mL of air at room temperature (20°C) and an internal pressure of 100 kPa. If the can is heated to 606 °C what will the internal pressure be? A sealed can contains 310 mL of air at room temperature (20°C) and an internal pressure of 100 kPa. If the can is heated to 606 °C what will the internal pressure be? multiply x = ÷ 293 x = 300 Next slide: T vs P graph Data: P 1 = 100kPa V 1 =310 mL T 1 =20˚C P 2 =unknown T 2 =606˚C ˚Celsius must be converted to kelvins 20˚C = 293 K 606˚C = 879 K Answer: the pressure will be 300 kPa Remove irrelevant fact =293K =879K divide Formula:

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Temperature & Pressure Graph The graph of temperature in Kelvin vs. pressure in kilopascals is a straight line. Like the temperature vs. volume graph, it can be used to find the value of absolute zero. The graph of temperature in Kelvin vs. pressure in kilopascals is a straight line. Like the temperature vs. volume graph, it can be used to find the value of absolute zero

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Graph of Pressure-Temperature Relationship (Gay-Lussacs Law) Temperature (K) Temperature (K) Pressure (kPa) Pressure (kPa) 273K Next slide:

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Summary: Gay-Lussacs law The pressure of a gas is directly proportional to its temperature Formula: Graph: Gay-Lussacs law is usually represented by an direct relationship graph (straight line) Absolute zero 0°C=273K Temp Temp Pressure Pressure

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Assignment on Gay-Lussacs Law Read pages 85 to 87 Answer questions #22 to 30 on page 98

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Avogadros Law For amount of gas. The volume of a gas is directly related to the number of moles of gas Lesson Next slide: Lorenzo Romano Amedeo Carlo Avogadro di Quaregna

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Lorenzo Romano Amedeo Carlo Avogadro di Quaregna Equal volumes of gas at the same temperature and pressure contain the same number of moles of particles. Amedeo Avogadro Born: August 9, 1776 Turin, Italy Died: July 9, 1856 Field: Physics University of Turin Known for Avogadros hypothesis, Avogadros number.

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You already know most of the facts that relate to Avogadros Law: You already know most of the facts that relate to Avogadros Law: –That a mole contains a certain number of particles (6.02 x ) –That a mole of gas at standard temperature and pressure will occupy 22.4 Litres (24.5 at SATP) The only new thing here, is how changing the amount of gas present will affect pressure or volume. The only new thing here, is how changing the amount of gas present will affect pressure or volume. –Increasing the amount of gas present will increase the volume of a gas (if it can expand), –Increasing the amount of gas present will increase the pressure of a gas (if it is unable to expand). 110

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Its mostly common sense… If you pump more gas into a balloon, and allow it to expand freely, the volume of the balloon will increase. If you pump more gas into a balloon, and allow it to expand freely, the volume of the balloon will increase. If you pump more gas into a container that cant expand, then the pressure inside the container will increase. If you pump more gas into a container that cant expand, then the pressure inside the container will increase. 111

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Avogadros Laws Relating Moles of Gas to Volume or Pressure or Where:V 1 = volume before, in appropriate volume units. V 2 = volume after, in the same volume units P 1 =pressure before, in appropriate pressure units. P 2 =pressure after, in the same pressure units. n 1 = #moles before n 2 = #moles after 112

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Assignments on Avogadros Law Read pages 92 to 96 Do Questions 31 to 36 on page

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Lesson 2.5 The General Gas Law and the Ideal Gas Law Next slide: 114

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The Combined or General Gas Law The general (or combined) gas law replaces the four simple gas laws. It puts together: Boyles Law Charles Law Gay-Lussacs Law Avogadros Law Advantages of the Combined Gas Law: It is easier to remember one law than four. It can handle changing more than one variable at a time (eg. Changing both temperature and pressure) 115 = General Gas Law

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The General Gas Law Relating all the Simple Laws Together Where: P 1 P 2 are the pressure of the gas before and after changes. V 1, V 2 are the volume of the gas before and after changes. T 1 T 2 are the temperatures, in kelvins n 1, n 2 is the number of moles of the gas.

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The neat thing about the General gas law is that it can replace the three original gas laws. Just cross out or cover the parts that dont change, and you have the other laws: Most of the time, the number of moles stays the same, so you can remove moles from the equation. If the temperature is constant, then you have Boyles law. If, instead, pressure remains constant, you have Charles Law And finally, if the volume stays constant, then you have Gay- Lussacs Law 117

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The Ideal Gas Law The Ideal Gas Law is derived from the General Gas Law in several mathematical steps. First, start with the general gas law, including P, V, T, and the amount of gas in moles (n). Next slide:

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Remember Standard Temperature & Pressure (STP) Standard Temperature is 0°C or more to the point, 273K = 25°C = 298K) Standard Temperature is 0°C or more to the point, 273K = 25°C = 298K) Standard Pressure is kPa (one atmospheric pressure at sea level) Standard Pressure is kPa (one atmospheric pressure at sea level) At STP one mole of an ideal gas occupies exactly 22.4 Litres = 24.5 L) At STP one mole of an ideal gas occupies exactly 22.4 Litres = 24.5 L)

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The Ideal Gas Law: Calculating the Ideal Gas Constant. We are going to calculate a new constant by substituting in values for P 2, V 2, T 2 and n 2 We are going to calculate a new constant by substituting in values for P 2, V 2, T 2 and n 2 At STP we know all the conditions of the gas. At STP we know all the conditions of the gas. Substitute and solve to give us a constant Substitute and solve to give us a constant Next slide: R-- The Ideal Gas Constant

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The Ideal Gas Constant is the proportionality constant that makes the ideal gas law work The Ideal Gas Constant has the symbol R The Ideal Gas Constant has the symbol R R=8.31 L· kPa / K·mol The Ideal Gas constant is 8.31 litre- kilopascals per kelvin-mole. The Ideal Gas constant is 8.31 litre- kilopascals per kelvin-mole. Next slide: Ideal Gas Formula

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So, if So, if Then, by a bit of algebra: P 1 V 1 =n 1 RT 1 Then, by a bit of algebra: P 1 V 1 =n 1 RT 1 Since we are only using one set of subscripts here, we might as well remove them: PV=nRT Since we are only using one set of subscripts here, we might as well remove them: PV=nRT

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The Ideal Gas Law Relating Conditions to the Ideal Gas Constant Where: P=Pressure, in kPa V=Volume, in Litres n= number of moles, in mol R= Ideal Gas constant, 8.31 L kPa / K mol T = Temperature, in kelvins

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The Ideal gas law is best to use when you dont need a before and after situation. The Ideal gas law is best to use when you dont need a before and after situation. Just one set of data (one volume, one pressure, one temperature, one amount of gas) Just one set of data (one volume, one pressure, one temperature, one amount of gas) If you know three of the data, you can find the missing one. If you know three of the data, you can find the missing one.

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Sample Problem 8.0 g of oxygen gas is at a pressure of 2.0x10 2 kPa (ie: 200 Kpa w. 2 sig fig) and a temperature of 15°C. How many litres of oxygen are there? Formula: PV = nRT 8.0 g of oxygen gas is at a pressure of 2.0x10 2 kPa (ie: 200 Kpa w. 2 sig fig) and a temperature of 15°C. How many litres of oxygen are there? Formula: PV = nRT Variables: P=200 kPa Variables: P=200 kPa V=? (our unknown)= x V=? (our unknown)= x n= 8.0 g ÷ 32 g/mol =0.25 mol n= 8.0 g ÷ 32 g/mol =0.25 mol R=8.31 L·kPa/K·mol (ideal gas constant) R=8.31 L·kPa/K·mol (ideal gas constant) T= 15°C = 288K T= 15°C = 288K 200 x = (0.25)(8.31)(288), therefore 200 x = (0.25)(8.31)(288), therefore x = (0.25)(8.31)(288) ÷ 200=2.99 L x = (0.25)(8.31)(288) ÷ 200=2.99 L There are 3.0 L of oxygen (rounded to 2 S.D.) There are 3.0 L of oxygen (rounded to 2 S.D.)

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Sample problem 8.0 g of oxygen gas is at a pressure of 2.0x102 kPa (ie: 200KPa) and a temperature of 15°C. How many litres of oxygen are there? (assume 2 significant digits) 8.0 g of oxygen gas is at a pressure of 2.0x102 kPa (ie: 200KPa) and a temperature of 15°C. How many litres of oxygen are there? (assume 2 significant digits) Data: P=200 kPa V=unknown = X n= not given R=8.31 L·kPa/K·mol T= 15°C = 288K --- m (O 2 ) = 8g M (O 2 ) = 32.0 g/mol 0.25 mol Temperature has been converted to kelvins Calculate the value of n using the mole formula: 200 x = (0.25)(8.31)(288), therefore x= (0.25)(8.31)(288) ÷ 200=2.99 L There are 3.0 L of oxygen (rounded to 2 S.D.)

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Sample Problem 8.0 g of oxygen gas is at a pressure of 2.0x10 2 kPa (ie: 200KPa) and a temperature of 15°C. How many litres of oxygen are there? (give answer to 2 significant digits) Data: P = 200 kPa R = 8.31 L·kPa/K·mol T = = 288K m(O 2 )= 8.0 g M(O 2 )= 32.0 g/mol n = To find: V Formula: Work: Next slide: Ideal vs. Real

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Ideal vs. Real Gases The gas laws were worked out by assuming that gases are ideal, that is, that they obey the gas laws at all temperatures and pressures. In reality gases will condense or solidify at low temperatures and/or high pressures, at which point they stop behaving like gases. Also, attraction forces between molecules may cause a gas behavior to vary slightly from ideal. A gas is ideal if its particles are extremely small (true for most gases), the distance between particles is relatively large (true for most gases near room temperature) and there are no forces of attraction between the particles (not always true) At the temperatures where a substance is a gas, it follows the gas laws closely, but not always perfectly. For our calculations, unless we are told otherwise, we will assume that a gas is behaving ideally. The results will be accurate enough for our purposes! Next slide: Summary

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Testing if a gas is ideal If you know all the important properties of a gas (its volume, pressure, temperature in kelvin, and the number of moles) substitute them into the ideal gas law, but dont put in the value of R. Instead, calculate to see if the value of R is close to 8.31, if so, the gas is ideal, or very nearly so. If the calculated value of R is quite different from 8.31 then the gas is far from ideal. If you know all the important properties of a gas (its volume, pressure, temperature in kelvin, and the number of moles) substitute them into the ideal gas law, but dont put in the value of R. Instead, calculate to see if the value of R is close to 8.31, if so, the gas is ideal, or very nearly so. If the calculated value of R is quite different from 8.31 then the gas is far from ideal.

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Example A sample of gas contains 1 mole of particles and occupies 25L., its pressure 100 kPa is and its temperature is 27°C. Is the gas ideal? A sample of gas contains 1 mole of particles and occupies 25L., its pressure 100 kPa is and its temperature is 27°C. Is the gas ideal? Convert to kelvins: 27°C+273=300K Convert to kelvins: 27°C+273=300K PV=nRT(ideal gas law formula) PV=nRT(ideal gas law formula) 100kPa 25L=1mol R 300K, so… 100kPa 25L=1mol R 300K, so… R=100kPa 25L÷(300K 1mol) R=100kPa 25L÷(300K 1mol) R=8.33 kPa L / K mol expected value: 8.31 kPa L / K mol R=8.33 kPa L / K mol expected value: 8.31 kPa L / K mol So the gas is not ideal, but it is fairly close to an ideal gas, So the gas is not ideal, but it is fairly close to an ideal gas, It varies from ideal by only 0.24% It varies from ideal by only 0.24%

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Gas Laws Overview When using gas laws, remember that temperatures are given in Kelvins (K) –Based on absolute zero: –273°C The three original gas laws can be combined, and also merged with Avogadros mole concept to give us the Combined Gas Law. Rearranging the Combined Gas Law and doing a bit of algebra produces the Ideal Gas Law. Substituting in the STP conditions we can find the Ideal Gas Constant. Ideal gases are gases that obey the gas laws at all temperatures and pressures. In reality, no gas is perfectly ideal, but most are very close.

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Gas Laws: Summary Simple gas laws –Boyles Law: –Charles Law: –Gay-Lussacs Law: –Combined gas law: –Ideal gas law: –The ideal gas constant: R=8.31 L kpa/K mol

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Video Simple gas laws

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Assignments on the Simple Gas Laws Finish Exercises p. 99 #37 to 52

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Extra Assignments Old text References: –Textbook Chapter 10: pp. 221 to 240 –Student Study Guide pp. 2-4 to 2-11 Old Textbook: page 241 # 25 to 30 –Do these in your assignments folder. Extra practice: Study guide: pp 2.12 to 2.17 # 1 to 22 –There is an answer key in the back for these –Do these on your own as review

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Exercise Answers 14)The pressure will double, since there is twice as much gas occupying the same space. (I answered this using logic and Avagadros hypothesis rather than math. It stands to reason that twice as much gas in the same space will increase the pressure.) 15)The pressure will be four times as high, since the volume is one quarter what it was before: P 1 V 1 = P 2 V 2 so… P 1 V 1 = 4P 1 x ¼V 1 (again, although you can do it with math, logic works better) 16)The pressure will be one third as great as it was before, since there is three times the volume: P 1 V 1 = P 2 V 2, so = 1 / 3 P 1 x 3V 1

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17)The gas cannot expand, so it exerts force on its container. As the temperature increases, the gas particles move faster, hitting the container sides more frequently and with more force. This causes greater pressure. You can also explain this using Gay-Lussacs law; P 1 /T 1 = P 2 /T 2 18)Make sure you use the KELVIN temperatures. The formula is P 1 /T 1 = P 2 /T 2 or 300 kpa/300K = x kPa/100K, so the pressure will be 100 kPa 19)An ideal gas obeys the gas laws at all temperatures and pressures (no real gas is perfectly ideal. More ideal properties will be discussed in the next section).

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20) P CO 2 = 3.33 kPa, since all the partial pressures will add up to the total pressure ( =33.3) 21) Use Boyles law: P 1 V 1 =P 2 V 2, therefore 91.2kpa 4.0L=20.3kpa x L so therefore x =91.2x4÷20.3 the new volume is 17.9 L 22) Use Boyles law: P 1 V 1 =P 2 V 2,so x =100kPa 6L÷25.3kPa. The new volume will be 23.7L

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23) Use CharlesLaw: V 1 /T 1 =V 2 /T 2, convert the temperature from °C K, so -50°C 223K and 100 °C 373K so… 5L/223K = x /373K so… x =5 373÷223. The new volume will be about 8.36 L 24) Use Gay-Lussacks law: P 1 /T 1 =P 2 /T 2, dont forget to change 27°C 300K. So… 200kPa/300K=223kPa/ x. The new temperature will be 61.5°C (converted from 334.5K)

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ANSWERS 25)The combined gas laws: (this answer is straight from the lesson) 26) Convert the temperatures to kelvin, set up equation, leaving out n 1 and n 2 (moles dont change), cross multiply: Answer: The new pressure is kPa Multiply these together Then divide by these

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27) Data given:need to find: m=12g (O 2 ) M (O 2 ) P=52.7kPa V= x L R=8.31L kPa/K moln in mol T= 25°CT in kelvin Find the number of moles of O 2 : n=m/M M (O 2 ) =32 g/mol so: 12 g ÷ 32 g/mol = mol. Convert C K, 25°C+273=298K formula: PV=nRT so: 52.7 kPa x L =0.375 mol 8.31 LkPa/Kmol 298 K so: x = (0.375 mol 8.3 1LkPa 298 K ) __1_ K mol 52.7 kpa Answer: The volume will be about 17.6 L 32g/mol 0.375mol 298K

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#28-30, answers (with brief explanation) (see me at lunch if you need more explanation) 28) Litres at STP a)56 L b) 6.72 L c) 7.84 L (remember: each mole of 29) Answer: The pressure will be 1714 kPa (use the formula PV=nRT) 30) Answer: The volume will be 16.8 L (use the formula PV=nRT)

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Lesson 2.8 Daltons Law of partial pressures

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John Dalton Born 6 September 1766 Eaglesfield, Cumberland, England Died 27 July 1844 Manchester, England Notable students James Prescott Joule Known for Atomic Theory, Law of Multiple Proportions, Dalton's Law of Partial Pressures, Daltonism Influences John Gough Besides being the founder of modern atomic theory, John Dalton experimented on gases. He was the first to reasonably estimate the composition of the atmosphere at 21% oxygen, 79% Nitrogen

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Partial Pressure Many gases are mixtures, eg. Air is 78% nitrogen, 21% Oxygen, 1% other gases Each gas in a mixture contributes a partial pressure towards the total gas pressure. The total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of the individual gases in the mixture. 101.3 kPa (P air ) = 79.1 kPa (N 2 ) kPa (O 2 ) kPa(Other) Next slide:

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Kinetic Theory Connection Hypothesis 3 of the kinetic theory states that gas particles do not attract or repel each other. Dalton established that each type of gas in a mixture behaved independently of the other gases. The pressure of each gas contributes towards the total pressure of the mixture.

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Daltons Law The Law of Partial Pressures of Gases Where:P T is the total pressure of mixed gases P 1 is the pressure of the 1 st gas P 2 is the pressure of the 2 nd gas etc...

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Variant of Daltons Law (used for finding partial pressure of a gas in a mixture) Where: P A =Pressure of gas A n A = moles of gas A n T = total moles of all gases P T = Total Pressure of all gases

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Uses of Daltons Law In the 1960s NASA used the law of partial pressures to reduce the launch weight of their spacecraft. Instead of using air at 101 kPa, they used pure oxygen at 20kPa. Breathing low-pressure pure oxygen gave the astronauts just as much partial pressure of oxygen as in normal air. Lower pressure spacecraft reduced the chances of explosive decompression, and it also meant their spacecraft didnt have to be as strong or heavy as those of the Russians (who used normal air).. This is one of the main reasons the Americans beat the Russians to the moon. Story Dont copy

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Carelessness with pure oxygen, however, lead to the first major tragedy of the American space program… At 20 kPa, pure oxygen is very safe to handle, but at 101 kPa pure oxygen makes everything around it extremely flammable, and capable of burning five times faster than normal. hatch. On January 27, 1967, during a pre-launch training exercise, the spacecraft Apollo-1 caught fire. The fire spread instantly, and the crew died before they could open the hatch. Carelessness with pure oxygen, however, lead to the first major tragedy of the American space program… At 20 kPa, pure oxygen is very safe to handle, but at 101 kPa pure oxygen makes everything around it extremely flammable, and capable of burning five times faster than normal. hatch. On January 27, 1967, during a pre-launch training exercise, the spacecraft Apollo-1 caught fire. The fire spread instantly, and the crew died before they could open the hatch.

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Gus Grissom, Ed White, Roger Chaffee Crew of Apollo 1

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Exercises : Page 113 in new textbook, # 1 to 8 Extra practice (if you havent already started): Study guide: pp 2.12 to 2.17 # 1 to 22 –There is an answer key in the back for these –Do these on your own as review

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Summary: Daltons Law: The total pressure of a gas mixture is the sum of the partial pressures of each gas. P T = P 1 + P 2 + … Grahams Law: light molecules diffuse faster than heavy ones Avogadros hypothesis –A mole of gas occupies 22.4L at STP and contains 6.02x10 23 particles

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Summary of Kinetic Theory Hypotheses (re. Behaviour of gas molecules): 1. Gases are made of molecules moving randomly 2. Gas molecules are tiny with lots of space between. 3. They have elastic collisions (no lost energy). 4. Molecules dont attract or repel each other (much) Results: The kinetic energy of molecules is related to their temperature (hot molecules have more kinetic energy because they move faster) –Kinetic theory is based on averages of many molecules (graphed on the Maxwell distribution bell curve) –Pressure is caused by the collision of molecules with the sides of their containers. –Hotter gases and compressed gases have more collisions, therefore greater pressure.

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Energy of a particle: KE = ½ mV 2 Pressure is the result of particles colliding with the container walls. P = F /A Gases are made of particles Particles move randomly! Pressure

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Assigned Activities References: –Read Textbook pp Practice problems: –Textbook: p199 #1-3 –Student study guide: pp to 2-20 (practice problems are for self-correction) Assignments (to be collected in your folder): –Page 241: all questions from 25 to 34 –Handout #1: combined gas law #52-58 –Handout #2: gases & gas laws 5 questions (on the back.)

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Answers (sheet 1) 52: The volume of gas will be 36.5 L 53: The temperature will be 908K or 635C 54: The volume will be 250 mL or 0.25L 55: The pressure will be 251 kPa 56: The pressure will stay the same 57: The pressure will be 42.2 kPa 58: The volume will be 10.2 L

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Answers (sheet 2) 1: The volume is about 32.5 L 2: The mass is about 1.53 x g 3: The pressure is about kPa 4: The pressure will increase by 168 kPa (tricky: most students say 268kPa, but thats what it ends at, NOT how much it changes!) 5: The total pressure is about 172kPa

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The end of module 2

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