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Unit 1 (formerly Module 2) Gases and Their Applications Lesson 2-1 About Gases 2 R 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 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. 3 General Properties of a Gas Gases do have mass (although it is sometimes difficult to measure). Gases have no definite volume, Gases have no definite shape. 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 Some Important Gases Oxygen (O2): clear, breathable, supports combustion. Ozone (O3): poisonous, unstable form of oxygen Nitrogen (N2): clear, low activity, most abundant gas in the Earth’s atmosphere. Hydrogen (H2): clear, lighter than air, flammable/explosive Carbon dioxide (CO2): 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 (SO2): smelly gas. When it combines with oxygen and water vapour it can form H2SO4, responsible for acid rain. 5 Some Important Gases Carbon monoxide (CO): clear, colourless, but very toxic. It destroys the ability of blood to carry oxygen. About the same density as air. Ammonia (NH3): toxic, strong smell, refrigerant . Very soluble in water, forms a basic solution called ammoniawater (NH4OH) which is found in some cleaners. Freon® or CFC: Non-toxic (safe-to-inhale in moderation) 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 (CH4): flammable gas, slightly lighter than air, produced by decomposition. Found in natural gas. Methane is also a “greenhouse” gas. Helium (He): inert, lighter than air. Used in balloons and in diver’s breathing mixtures. 6 Acetylene (C2H2): AKA ethene, it is used as a fuel in welding, lanterns and other devices. Propane (C3H8): used as a fuel in barbecues, stoves, lanterns and other devices. 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): 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% N2, 21% O2): 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 Fun Gases (of no real importance) Nitrous Oxide (N2O) – 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 engine’s horsepower. Sulfur Hexafluoride – One of the densest gases in common use. Fun with Sulfur hexafluoride 8 Match the gas with the problem it causes Gas Problem Ozone layer depletion Global Warming Toxic poisoning Noxious smell Acid Rain Carbon Dioxide CFCs Methane Carbon monoxide Sulfur dioxide Next slide: Summary 9 Some Gases Classified by Relative Density Low Density gases Neutral Density Gases High 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 (H2) 2 Helium (He) 4 Methane (CH4) 16 Ammonia (NH3) 17 Neon (Ne) 20 Hydrogen Fluoride (HF) 21 Examples: “Cyanide“ (HCN) Acetylene (C2H4) Nitrogen (N2) Carbon monoxide Ethane (C2H6) Oxygen (O2) Examples: Fluorine (F2) Argon (Ar) Carbon dioxide (CO2) Propane (C3H8) Butane (C4H10) Sulphur Hexafluoride (SF6) 27 28 28 28 30 32 38 40 44 44 58 146 *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. Some Gases Classified by Chemical Properties Combustible gases (combustion /explosion) Oxidizing (reactive) Gases (support combustion) Non-Reactive gases (don’t support combustion) 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 (H2) Methane (CH4) Propane (C3H8) Acetylene (C2H4) Examples: Oxygen (O2) Fluorine (F2) Chlorine (Cl2) Nitrous Oxide (NO2) Examples: Carbon dioxide (CO2) Nitrogen (N2) Argon (Ar) Helium (He) Textbook Assignments Read Chapter 1: pp. 37 to 50 Do the exercises on pages 51 and 52 – Questions # 1 to 22 12 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 • CFC’s • Sulfur dioxide 13 Chapter 2 Physical Properties of Gases Includes: The Kinetic Theory “Moving, moving, moving, Keep those atoms moving...” The Gas Laws. “Jumping Jack Flash, It’s a gas, gas, gas...” 14 2.1 Kinetic Theory • Overview: The kinetic theory of gases (AKA. kineticmolecular 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. 2.1 Page 54 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. 16 R Not in text The Particle Model • 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. - 17 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 2.1.1 Page 54 R 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. 19 Kinetic Theory Model of States Solid Particles vibrate but don’t “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 2.1.1 Page 55 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) 21 2.1.1 Page 56 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 don’t 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). 22 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 light—they glow. This glowing, gas-like substance is called “plasma” 23 2.1.3 Page 61 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.” 24 2.1.3 Page 61 • To make the physical laws (derived from kinetic equations from physics) work, they had to make assumptions about how molecules work. • Four of these assumptions are listed on page 61 of your textbook • Other textbooks contain additional assumptions associated with the kinetic theory. kinetic equation : E k 1 mv 2 2 25 2.1.3 Page 61 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. 26 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 2.1.3 Page 61 Other “Imaginary Features” of Ideal Gas • An 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. • At absolute zero an ideal gas would occupy no space at all. 28 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 The mean & mode can help establish “average” molecules “Slow” molecules mean Most molecules mode Increasing # molecules The range of kinetic energies can be represented as a sort of “bell curve.” Maxwell’s Velocity Distribution Curve. “Average” molecules “Fast” Molecules Increasing kinetic energy Average kinetic energy 30 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 • Ek = mv2 kinetic energy of molecules 2 So, kinetic energy depends on both the speed (v) and on the mass (m) of the molecules. 31 Faster than average molecules Average kinetic energy of warmer molecules Slower than average molecules Average kinetic energy of molecules Average kinetic energy of colder molecules Number of molecules Distribution of Particles Around Average Kinetic Energies. Kinetic Energy of molecules (proportional to velocity of molecules) 32 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 1010 (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: • 722 400 000 000 000 000 000 000 000 – that’s more than there are stars in the universe! • The average distance air molecules travel between collisions is about 60nm. – 0.00000006m is about the width of a virus. 33 Videos • Kinetic Molecular Basketball – http://www.youtube.com/watch?v=t-Iz414g-ro&NR=1 • Average Kinetic Energies – http://www.youtube.com/watch?v=UNn_trajMFo&NR=1 • Thermo-chemistry lecture on kinetics 34 Assignments • Read pages 53 to 61 • Do Page 62 # 1-11 Chapter 2.2 • Behaviors of Gases – Compressibility – Expansion – Diffusion and Effusion – Graham’s Law • 2.2.1 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 • 2.2.2 Expansion: – Gases will expand to fill any container they occupy, due to the random motion of the molecules. 37 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. Effusion is the same process, but with the molecules passing through a small hole or barrier Next slide: 38 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? heavy particle light particle 39 Graham’s 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.” 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 Internet demo of effusion v1 v2 M2 M1 Where: v1= rate of gas 1 v2= rate of gas 2 M1= molar mass of gas1 M2=molar mass of gas 2 40 Graham’s Law Version #1, based on Effusion Rate • The relationship between the rate of effusion or diffusion and the molar masses is: v1 v2 Where: M 2 M1 Note: See the inversion of the 1 and 2 in the 2nd ratio! v1 is the rate of diffusion of gas 1, in any appropriate rate units* v2 is the rate of diffusion of gas 2, in the same units as gas 1 M1 is the molar mass of gas 1 M2 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) Thomas Graham (1805-1869) • Graham derived his law by treating gases as ideal, and applying the kinetic energy formula to them. • Ek = ½ mv2 • All gases have the same kinetic energy at the same temperature, • Therefore, mv2 for the first gas = mv2 for the second gas: m1v12 = m2v22. • 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 Graham’s Law Version #2, Based on Effusion Time • Sometimes it’s easier to measure the time it takes for a gas to effuse completely, rather than the rate. Graham’s law can be changed for this, but the relationship between time and molar mass is direct as the square root: t1 t2 Where: M1 M Note: In this variant law, the relationship is not inverted! 2 t1 is the time it takes for the first gas to effuse completely. t2 is the time it takes for an equal volume of the 2nd gas to effuse M1 is the molar mass of the first gas M2 is the molar mass of the second gas. Example of Graham’s Law: How much faster does He diffuse than N2? MN =2x14.0=28 g/mol Nitrogen (N2) has a molar MHe=1x4.0=4 g/mol mass of 28.0 g/mol 2 Helium (He) has a molar mass of 4.0 g/mol The difference between their diffusion rates is: Notice the reversal of order! So helium diffuses 2.6 times faster than nitrogen Next slide: 2.3 Pressure of Gases v He vN2 28 g / mol 4 g / mol M M N2 He 5 .3 2 .6 2 44 Assignments Read pages 63 to 67 Do Questions 1 to 10 on page 68 Outer Space (immeasurable) 100 km Spaceship 1 (2006) X15 (1963) < 0.003 kPa Edge of Space Chapter 2.3 • Pressure of Gases – What is Pressure – Atmospheric Pressure – Measuring Pressure 40 km 1 kPa 20 km 6 kPa 10 km 25 kPa 5 km 55 kPa 0 km 101 kPa Highest Jet 4 kPa Mt Everest 31 kPa Mr. Smith 46 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 gas’s 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: P F A Pressure = force divided by area 47 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 101.3 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 SP Pressure conversions P ( units given ) SP ( units given ) P ( units wanted ) SP ( units wanted ) 1.00 atm 760 mmHg 760 Torr 101.3 kPa 14.7 psi 1013 mB 29.9 inHg Example 1: convert 540 mmHg to kilopascals 540 mmHg 760 mmHg Divide P 101 . 3 kPa =72.0 kPa Example 2: convert 155 kPa to atmospheres 155 kPa 101 . 3 kPa P 1 . 00 atm =1.53 atm 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 the Mercury Barometer • 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. 51 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. Manometers (Pressure Gauges) • 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. You Tube manometer Tire gauge (piston manometer) U-tube manometer (mercury manometer) Pressure gauge (aneroid) Reading U-tube manometers Atm. pressure Must be in mmHg, not cm or kPa! After you finish, you can convert your answer to kPa, or atm. Or whatever. • When reading a mercury Utube 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. Pgas(mmHg) = Patm(mmHg)+h(mm) Manometer Examples on a day when the air pressure is 763mmHg (101.7 kPa) 4 cm Closed tube: Pgas(mm Hg)=h (mm Hg) Pgas = h = 4 cm = 40 mm Hg Pgas = 40 mm Hg 101 . 3 kPa 5 . 3 kPa 760 mm Hg 6 Open: Pgas(mmHg)=P atm(mmHg) +h (mmHg) Pgas = 763 + 60mm Hg =823 mm Hg Pgas = 823 mm Hg 101 . 3 kPa 109 .7 kPa 760 mm Hg Open: Pgas(mmHg)=P atm(mmHg) -h (mmHg) Pgas = 763 - 60mm Hg =703 mm Hg Pgas = 703 mmHg 101 .3 kPa 93 .7 kPa 760 mmHg 9 Assignments • Read pages 69 to 73. • Do Page 74, Questions 1 to 4. Chapter 2.4 • The Simple Gas Laws – – – – Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’s Law Relates volume & pressure Relates volume & temperature Relates pressure & temperature Relates to the number of moles • Other Simple Laws that are a Gas: – Clarke’s Laws – Murphy’s Law – Cole’s Law Relates possible and impossible Anything that can go wrong will Relates thinly sliced cabbage to vinegar. 57 Clarke’s Laws of the impossible* Clarke’s 1st 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, he’s almost certainly wrong. Clarke’s 2nd Law: The only way to find the limits to what is possible is to go beyond them. Clarkes 3rd 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 Lesson 2.4.1 Boyle’s Law Robert Boyle (1662) For Pressure and Volume “For a given mass of gas at a constant temperature, the volume varies inversely with pressure.” P 1 V 59 Robert Boyle Born: 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 Influences: Robert Carew, Galileo Galilei, Otto von Guericke, Francis Bacon Influenced: Dalton, Lavoisier, Charles, Gay-Lussack, Avogadro. Notable awards: Fellow of the Royal Society 60 Pressure 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 can be measured many ways Atmospheres (atm) Kilopascals (kPa)or(N/m2) Millibars (mB) Torr (torr) or mm mercury Centimetres of mercury Inches of mercury (inHg) Pounds per sq. in (psi) Next slide: Air in Syringe Standard Pressure 1 atm 101.3 kPa = 101.3 N/m2 1013 mB 760 torr = 760 mmHg 76 cmHg 29.9 inHg (USA only) 14.7 psi (USA only) 61 Example of Boyle’s 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 Inside the syringe… 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. Click Here for an internet demo using psi (pounds per square inch) instead of kilopascals (1kPa=0.145psi) low high Next slide: PV 63 This means that: 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: 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 Boyle’s 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: P1V 1 P2V 2 Where: P1 is the pressure* of the gas before the container changes shape. P2 is the pressure after, in the same units as P1. V1 is the volume of the gas before the container changes, in L or mL V2 is the volume of the gas after, in the same units as V1 *appropriate pressure units include: kPa, mmHg, atm. Usable, but inappropriate units include psi, inHg. 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? P1 × V1 = P2 × V2, so.. 100 kPa × 30 mL = ? kPa × 10 mL 3000 mL·kPa ÷ 10 mL = 300 kPa The pressure inside the syringe will be 300 kPa Next slide: Graph of Boyle’s Law 66 Graph of Boyle’s Law The Pressure-Volume Relationship 8 Boyle’s Law produces an inverse relationship graph. P(kpa) x V(L) 6 5 4 3 2 = 800 1.6 = 800 1.33 = 800 1.14 = 800 1 = 800 2 x x x x x 1 400 500 600 700 800 Volume (L) 200 x 4 = 800 300 x 2.66 = 800 7 100 x 8 = 800 Next slide: Real Life Data 100 200 300 400 500 600 700 800 Pressure (kPa) 67 Example 2: Real Life Data 30 35 2+4= 6kg : 20 mL (120) 4+4=8kg : 15 mL (120) 6+4=10kg: 12 mL (120) 10 25 (116) 8+4=12kg: 10.5 mL (126) 15 20 0+4= 4kg : 29 mL 5 At the beginning, Mr. Taylor calculated the equivalent of 4 kgf of atmospheric pressure were exerted on the syringe. 40 In an experiment Mr. Taylor and Tracy put weights onto a syringe of air. 2 4 6 8 10 12 14 16 Next slide: Boyle’s Law Experiment or skip to: Lesson 2.3 Charles’ Law: 18 68 Summary: Boyle’s law 1 • The volume of a gas is inversely proportional to its pressure P • Formula: P1V1=P2V2 P1V1=P2V2 Volume (L) • Graph: Boyle’s law is usually represented by an inverse relationship graph (a curve) V Pressure (kPa) 69 70 Assignments on Boyle’s Law • Read pages 75 to 79 • Do questions 1 to 10 on page 97 Lesson 2.4.2 Charles’ Law The Relationship between Temperature and Volume. “Volume varies directly with Temperature” V T Next slide: Jacques Charles 72 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 (1746-11-12) Beaugency, Orléanais Died: April 7, 1823 (1823-04-08) (aged 76), Paris Nationality: France Fields: physics, mathematics, hot air ballooning Institutions: Conservatoire des Arts et Métiers 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. V1 T1 Where: V2 T2 T1 is Temperature of the gas before it is heated, in kelvins. T2 is Temperature of the gas after it is heated, in kelvins V1 is the volume of the gas before it was heated, in L or mL V2 is the volume of the gas after it was heated, in the same units. 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 75 Charles Law Example Piston Cylinder Trapped Gas Click Here for a simulated internet experiment Next slide: Graph of Charles’ Law 76 Graph of Charles Law 6L Lord Kelvin traced it back to absolute zero. Charles discovered the direct relationship 5L 4L 3L Liquid state Solid state -250°C -200°C -150°C 1L Expansion of most real gases -100°C -50°C -273.15°C 0°C 50°C 100°C 273°C 2L 150°C 200°C 250°C Next slide: Example -273.15°C is called absolute zero. It is the coldest possible temperature. At absolute zero, molecules stop moving and even vibrating. Since temperature is based on the average kinetic energy of molecules, temperature cannot be said to exist if there is no kinetic energy (movement) William Thompson, The right honourable Lord Kelvin 1st Baron of Largs 1824-1907 Born in Belfast Ireland Died in Largs, Scotland Worked at the University of Glasgow Experimented in Thermodynamics. "There is nothing new to be discovered in physics now. All that remains is more and more precise measurement" Kelvin’s Scale In 1848 Lord Kelvin suggested using a temperature scale based on absolute zero, but with divisions exactly the same as the Celsius scale. For many years this was called the “absolute temperature scale” but long after his death it was renamed to honour Lord Kelvin To convert from Celsius to Kelvin, simply add 273 to the Celsius temperature. To convert back, subtract 273 Note: Temperature readings are always assumed to have at least 3 significant digits. For example, 6°C is assumed to mean 279 K with 3 sig.fig., even though the data only showed 1 sig.fig. 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? Convert temperatures to kelvins: 27°C =300k, 327°C = 600k Use Charles’ Law: (see below) Answer: 4 Litres V1 T1 V2 T2 , so : 2 Litres 300 K Next slide: Lesson 2.4 Gay Lussac’s Law x Litres 600 K Summary: Charles’ law • The volume of a gas is directly proportional to its temperature V T V1 T1 T2 Volume (L) • Formula: • Graph: Charles’ law is usually represented by a direct relationship graph (straight line) • Video1 V2 Absolute zero 0°C=273K Temp Charles’ Law Assignments • Read pages 80 to 84 • Do questions 11 to 21 on pages 97 and 98 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) Temperatures must be converted to kelvin Data: T1=22˚C =295K So: T2=4˚C =277K 1 2 V2=V1 x T2 ÷ T1 V1=0.50 L V2=0.5L x 277K divide To find: 1 2 295K V2= unknown V =0.469 L V T V T 2 The balloon will have a volume of 0.47 litres 84 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. Convert temperatures to kelvin Data 20+273= 293K, 250+273=523k V1= 0.40L T1= 20°C =293 K Use Charles’ Law T2= 250°C =523 K V1 V2 0 .4 L V2 ... V2= ?0.7139L T1 T2 293 K 523 K 0.40L x 523 K ÷ 293 K = 0.7139L Answer: The balloon’s volume will be 0.71 litres 85 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? Convert temperatures to kelvin 19+273= 292K, 60+273=333K Data: V1=250 mL Use Charles’ Law T1= 19.0°C=292 K T2=60.0°C =333 K V V2 250 mL V2 1 ... V2= ?285.10 mL T1 T2 292 K 333 K 250mL x 333 K ÷ 292 K = 285.10mL Answer: The bag will have a volume of 285mL Although only the answers are shown here, in order to get full marks you need to show all steps of the solution! 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. 5. 6. The temperature is 279.7 K, which corresponds to 6.70 C. jacket or sweater would be appropriate clothing for this weather. A Lesson 2.4.3 Gay-Lussac’s Law For Temperature-Pressure changes. “Pressure varies directly with Temperature” PT Next slide:’ 88 Joseph Gay-Lussac (1802) “The pressure of a gas is directly proportional to the temperature (in kelvins) if the volume is kept constant.” Born 6 December 1778 Saint-Léonard-de-Noblat Died 9 May 1850 @ Saint-Léonard-de-Noblat Nationality: French Fields: Chemistry Known for Gay-Lussac's law Next slide:’ 89 Gay-Lussac’s Law Relating Pressure and Temperature of a Gas P1 T1 Where: P2 T2 P1 is the pressure* of the gas before the temperature change. P2 is the pressure after the temperature change, in the same units. T1 is the temperature of the gas before it changes, in kelvins. T2 is the temperature of the gas after it changes, in kelvins. *appropriate pressure units include: kPa, mmHg, atm. Gay-Lussac’s Law As the gas in a sealed container that cannot expand is heated, the pressure increases. pressure For calculations, you must use Kelvin temperatures: K=°C+273 91 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? Remove irrelevant fact Data: P1= 100kPa V1=310 mL T1=20˚C P2=unknown T2=606˚C Next slide: T vs P graph ˚Celsius must be converted to kelvins 20˚C ==293K 293 K 606˚C ==879K 879 K Formula: P1 T1 P2 100 kPa T2 divideK 293 x = 87900 ÷ 293 x = 300 x 879 K Answer: the pressure will be 300 kPa 92 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 also be used to find the value of absolute zero. 93 Pressure (kPa) Graph of Pressure-Temperature Relationship (Gay-Lussac’s Law) Temperature (K) Next slide:’ 273K 94 Summary: Gay-Lussac’s law • The pressure of a gas is directly proportional to its temperature • Formula: • Graph: Gay-Lussac’s law is usually represented by an direct relationship graph (straight line) P1 T2 Pressure T1 P2 Absolute zero 0°C=273K Temp Assignment on Gay-Lussac’s Law • Read pages 85 to 87 • Answer questions #22 to 30 on page 98 Lesson 2.4.4 Avogadro’s Law For amount of gas. “The volume of a gas is directly related to the number of moles of gas” V n Next slide: Lorenzo Romano Amedeo Carlo Avogadro di Quaregna 97 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 Avogadro’s hypothesis, Avogadro’s number. You already know most of the facts that relate to Avogadro’s Law: – That a mole contains a certain number of particles (6.02 x 1023) – 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. – 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). 99 It’s 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 container that can’t expand, then the pressure inside the container will increase. 100 Avogadro’s Laws Relating Moles of Gas to Volume or Pressure V1 n1 Where: V2 n2 or P1 n1 P2 n2 V1 = volume before, in appropriate volume units. V2 = volume after, in the same volume units P1=pressure before, in appropriate pressure units. P2=pressure after, in the same pressure units. n1 = #moles before n2 = #moles after 101 Assignments on Avogadro’s Law • Read pages 88 to 92 • Do Questions 31 to 36 on page 98 102 Lesson 2.45 Standard Conditions and Molar Volume Next slide: 103 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-held standard for comparing gases is called Standard Temperature and Pressure (STP) • Standard Temperature =0°C = 273 K • Standard Pressure =101.3 kPa 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 • Standard Pressure = 25°C = 298 K = 101.3 kPa Molar Volume • The volume of 1 mole of an ideal gas depends on the conditions: – At STP one mole of an ideal gas has a volume of 22.4 litres – AT SATP one mole of an ideal gas has a volume of 24.5 litres • Since all common gases are very near ideal at these temperatures, we can use these as standard molar volumes for ANY common gas. Comparison Standard and Ambient Conditions Pressure Temperature °C Temperature K Molar Volume Standard Temperature & Pressure Ambient Temperature & Pressure (STP) (SATP) 101.3 kPa 0 °C 273.15 K 22.4 L/mol 101.3 kPa 25 °C 298.15 K 24.5 L/mol Assignments on Molar Volume • Read pages 92 to 96 • Do Questions 37 to 52 on page 98 108 Lesson 2.5 & 2.6 The General Gas Law and the Ideal Gas Law Next slide: 109 The Combined or General Gas Law • The general (or combined) gas law replaces the four simple gas laws. It puts together: • • • • Boyle’s Law Charles’ Law Gay-Lussac’s Law Avogadro’s Law = General Gas 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) 110 The General Gas Law Relating all the Simple Laws Together P1V1 n1T1 Where: P2V 2 n 2T 2 P1 P2 are the pressure of the gas before and after changes. V1, V2 are the volume of the gas before and after changes. T1 T2 are the temperatures, in kelvins n 1, n2 is the number of moles of the gas. 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 don’t change, and you have the other laws: If the temperature is constant, then you have Boyle’s law. If, instead, pressure remains constant, you have Charles’ Law And the the Mostfinally, of the iftime, volume constant, number stays of moles stays then you have Gaythe same, so you can Lussac’s Law from the remove moles equation. P1V1 n1T1 P2V 2 n 2T 2 112 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) . P1V1 n1T1 Next slide: P2V 2 n 2T 2 Remember Standard Temperature & Pressure (STP) Standard Temperature is 0°C or more to the point, 273K (@SATP = 25°C = 298K) Standard Pressure is 101.3 kPa (one atmospheric pressure at sea level) At STP one mole of an ideal gas occupies exactly 22.4 Litres (@SATP = 24.5 L) The Ideal Gas Law: Calculating the Ideal Gas Constant. We are going to calculate a new constant by substituting in values for P2, V2, T2 and n2 At STP we know all the conditions of the gas. Substitute and solve to give us a constant P1V1 n1T1 P1V1 n1T1 P1V1 n1T1 Next slide: R-- The Ideal Gas Constant P2V 2 n 2T 2 101 . 3 kPa 22 . 4 L 1 mol 273 K 8 . 31 L kPa / K mol The Ideal Gas Constant is the proportionality constant that makes the ideal gas law work The Ideal Gas Constant has the symbol R R=8.31 L· kPa / K·mol The Ideal Gas constant is 8.31 litrekilopascals per kelvin-mole. Next slide: Ideal Gas Formula So, if P1V1 R n1T1 Then, by a bit of algebra: P1V1=n1RT1 Since we are only using one set of subscripts here, we might as well remove them: PV=nRT The Ideal Gas Law Relating Conditions to the Ideal Gas Constant PV nRT Where: P=Pressure, in kPa V=Volume, in Litres n= number of moles, in mol R= Ideal Gas constant, 8.31 T = Temperature, in kelvins LkPa/ Kmol The Ideal gas law is best to use when you don’t need a “before and after” situation. 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. Sample Problem 8.0 g of oxygen gas is at a pressure of 2.0x102 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 V=? (our unknown)= x n= 8.0g ÷ 32 g/mol =0.25 mol R=8.31 L·kPa/K·mol (ideal gas constant) T= 15°C + 273 = 288K 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.) 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) Data: P=200 kPa V=unknown = X n= not given 0.25 mol R=8.31 L·kPa/K·mol T= 15°C + 273 = 288K --m (O2) = 8g M (O2) = 32.0 g/mol Temperature has been converted to kelvins Calculate the value of n using the mole formula: n m M PV 8 .0 g 0 . 25 mol 32 . 0 g / mol nRT 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.) 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? (give answer to 2 significant digits) Data: P = 200 kPa R = 8.31 L·kPa/K·mol T = 15+273 = 288K m(O2)= 8.0 g M(O2)= 32.0 g/mol 8g n= 0 . 25 mol 32 g / mol To find: V Next slide: Ideal vs. Real Formula: PV nRT Work: 200 kPa V 0 . 25 mol 8 . 31 0 . 25 mol 8 . 31 V V 2 . 99 L L kPa K mol 200 kPa L kPa K mol 288 K 288 K 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 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 don’t 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. 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? Convert to kelvins: 27°C+273=300K PV=nRT (ideal gas law formula) 100kPa25L=1molR300K, so… R=100kPa25L÷(300K1mol) R=8.33 kPaL /Kmol expected value: 8.31 kPaL /Kmol So the gas is not perfectly ideal, but it is very close to an ideal gas, ( 8 . 33 8 . 31 ) 100 % 0 . 24 % It varies from ideal by only 0.24% 8 . 31 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 Avogadro’s 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. Gas Laws: Summary Simple gas laws – Boyle’s Law: – Charles’ Law: – Gay-Lussac’s Law: – Combined gas law: P 1 V T PT V V1 V2 P1 T2 T1 P1V1 P2V 2 P1V1 n1T1 T1 P2 T2 P2V 2 n 2T 2 – Ideal gas law: PV nRT – The ideal gas constant: R=8.31 Lkpa/Kmol Video • Simple gas laws Assignments on the Ideal Gas Law • Read pages 100 to 104in textbook • Do Exercises p. 104 #1 to 16 Lesson 2.7 Stoichiometry of Gases Stoichiometry of Gases • When using stoichiometry with gases it is important to remember Avogadro’s hypothesis: that equal volumes of gas under the same conditions of temperature and pressure contain equal number of particles – Ie. At same pressure and temperature • Same volumes have same # moles • Volumes are proportional to numbers of moles Simple question 1 • How many litres of hydrogen will react with 3 Litres of oxygen to form water if both gases are at the same pressure and temperature? • 2 H2 + O2 2 H2O • 2 : 1 : 2 molar ratio • ?L : 3L : ?L volume ratio • 6L : 3L : XX proportion solution Answer: Six litres of hydrogen gas will react. In theory, this reaction would produce 6L of water vapour, but because the reaction is highly exothermic, the temperature would go up, so the result for water would be meaningless (hence the XX) Assignments on the Stoichiometry of Gases • Read pages 108 to 109 in textbook • Do Exercises p. 110 #1 to 9 Lesson 2.8 Dalton’s Law of partial pressures John Dalton Besides being the founder of modern atomic theory, John Dalton experimented Born on gases. He was the first to reasonably estimate the composition Died of the atmosphere at 21% Notable students oxygen, 79% Nitrogen Known for Influences 6 September 1766 Eaglesfield, Cumberland, England 27 July 1844 Manchester, England James Prescott Joule Atomic Theory, Law of Multiple Proportions, Dalton's Law of Partial Pressures, Daltonism John Gough 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 (Pair) = 79.1 kPa (N2)+ 21.2 kPa (O2) + 1.0 kPa(Other) Next slide: 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. Dalton’s Law The Law of Partial Pressures of Gases PT P1 P2 ... Where: PT is the total pressure of mixed gases P1 is the pressure of the 1st gas P2 is the pressure of the 2nd gas etc... Variant of Dalton’s Law (used for finding partial pressure of a gas in a mixture) PA nA nT PT Where: PA=Pressure of gas A nA = moles of gas A nT= total moles of all gases PT= Total Pressure of all gases Uses of Dalton’s 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 didn’t 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. 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. 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. Crew of Apollo 1 Gus Grissom, Ed White, Roger Chaffee Exercises : • Page 113 in new textbook, # 1 to 8 Extra practice (if you haven’t 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 Summary: • Dalton’s Law: The total pressure of a gas mixture is the sum of the partial pressures of each gas. PT = P1 + P2 + … • Graham’s Law: light molecules diffuse faster than heavy ones M2 Rate 1 • Avogadro’s hypothesis Rate 2 – A mole of gas occupies 22.4L at STP and contains 6.02x1023 particles M1 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 don’t 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. Pressure Gases are made of particles Particles move randomly! Energy of a particle: KE = ½ mV 2 Pressure is the result of particles colliding with the container walls. P = F /A • The end of module 2