3 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
4 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
5 Some Important GasesOxygen (O2): clear, breathable, supports combustion.Ozone (O3): poisonous, unstable form of oxygenNitrogen (N2): clear, low activity, most abundant gas in the Earth’s atmosphere.Hydrogen (H2): clear, lighter than air, flammable/explosiveCarbon 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
6 Some Important GasesCarbon 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 ammonia-water (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
7 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
8 Fun Gases (of no real importance) Nitrous Oxide (N2O)AKA: Laughing gas, Happy gas, Nitro, NOSOnce 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 HexafluorideOne of the densest gases in common use. Fun with Sulfur hexafluoride8
9 Match the gas with the problem it causes Gas ProblemCarbon Dioxide Ozone layer depletionCFCs Global WarmingMethane Toxic poisoningCarbon monoxide Noxious smellSulfur dioxide Acid Rain9Next slide: Summary
10 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 airBalloon drops slowly through airBalloon drops quickly through airExamples:Hydrogen (H2) 2Helium (He) 4Methane (CH4) 16Ammonia (NH3) 17Neon (Ne) 20Hydrogen Fluoride (HF) 21“Cyanide“ (HCN) 27Acetylene (C2H4) 28Nitrogen (N2) 28Carbon monoxide 28Ethane (C2H6) 30Oxygen (O2) 32Fluorine (F2) 38Argon (Ar) 40Carbon dioxide (CO2) 44Propane (C3H8) 44Butane (C4H10) 58Sulphur Hexafluoride (SF6) 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.
11 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”Glowing splint reignites, burning splint grows brighterBurning splint is extinguished, glowing splint is dimmedOther properties:Useful as fuelsCause metals and some other materials to corrode or oxidize. Can improve combustion.Can be used to preserve foods by slowing oxidationExamples:Hydrogen (H2)Methane (CH4)Propane (C3H8)Acetylene (C2H4)Oxygen (O2)Fluorine (F2)Chlorine (Cl2)Nitrous Oxide (NO2)Carbon dioxide (CO2)Nitrogen (N2)Argon (Ar)Helium (He)
12 Textbook Assignments Read Chapter 1: pp. 37 to 50 Do the exercises on pages 51 and 52Questions # 1 to 2212
13 Summary: Know the properties of gases Know the features of some important gases, esp:OxygenHydrogenCarbon dioxideKnow the environmental problems associated with some gases, eg.CFC’sSulfur dioxide13
14 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
15 2.1 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.
16 The Kinetic Theory of Gases (AKA: The Kinetic Molecular Theory) 2.1Page 54The 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
17 RThe Particle ModelNot in textThe 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
18 Kinetic Molecular Theory And TemperatureThe 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
19 Particle Motion and Phases of Matter 2.1.1Page 54Particle Motion and Phases of MatterRRecall that:In solids, the particles (molecules) are moving relatively slowly. They have low kinetic energyIn 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
20 Kinetic Theory Model of States LiquidParticles vibrate, move and “flow”, but cohesion (molecular attraction) keeps them close together.GasParticles move freely through container. The wide spacing means molecular attraction is negligible.SolidParticles vibrate but don’t “flow”. Strong molecular attractions keep them in place.20
21 Kinetic Motion of Particles 2.1.1Page 55Kinetic Motion of ParticlesParticles (ie. Molecules) can have 3 types of motion, giving them kinetic energyVibrational kinetic energy (vibrating)Rotational kinetic energy (tumbling)Translational kinetic energy (moving)21
22 Kinetic Theory and Solids & Liquids 2.1.1Page 56Kinetic Theory and Solids & LiquidsWhen it is cold, molecules move slowlyIn 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
23 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
24 Kinetic Theory and the Ideal Gas 2.1.3Page 61Kinetic Theory and the Ideal GasAs 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
25 2.1.3Page 61To 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 textbookOther textbooks contain additional assumptions associated with the kinetic theory.25
26 Kinetic Theory Hypotheses about an Ideal Gas 2.1.3Page 61Kinetic Theory Hypotheses about an Ideal GasThe particles of an ideal gas are infinitely small, so the size is negligible compared to the volume of the container holding the gas.The particles of an ideal gas are in constant motion, and move in straight lines (until they collide with other particles)The particles of an ideal gas do not exert any attraction or repulsion on each other.The average kinetic energy of the particles is proportional to the absolute temperature.26
27 No Gas is IdealSome 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
28 Other “Imaginary Features” of Ideal Gas 2.1.3Page 61Other “Imaginary Features” of Ideal GasAn ideal gas would obey the gas laws at all conditions of temperature and pressureAn 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
29 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
30 The mean & mode can help establish “average” molecules The range of kinetic energies can be represented as a sort of “bell curve.” Maxwell’s Velocity Distribution Curve.The mean & mode can help establish “average” moleculesMost molecules“Average”moleculesIncreasing # molecules“Slow”molecules“Fast”MoleculesmodemeanAveragekinetic energyIncreasing kinetic energy30
31 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 moleculesNot the mass of individual molecules.In fact, the lighter molecules will move fasterEk = mv2 kinetic energy of molecules2So, kinetic energy depends on both the speed (v) and on the mass (m) of the molecules.31
32 Distribution of Particles Around Average Kinetic Energies. Average kinetic energy of moleculesAverage kinetic energy of warmer moleculesAverage kinetic energy of colder moleculesNumber of moleculesSlowerthanaverage moleculesFasterthanaverage moleculesKinetic Energy of molecules(proportional to velocity of molecules)32
33 Kinetic Theory TriviaThe 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 second10 billion collisions every second means they bounce around a lot!The number of oxygen molecules in a classroom is about:that’s 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
34 Videos Kinetic Molecular Basketball Average Kinetic Energies Average Kinetic EnergiesThermo-chemistry lecture on kinetics34
35 AssignmentsRead pages 53 to 61Do Page 62 # 1-11
36 Chapter 2.2 Behaviors of Gases Compressibility Expansion Diffusion and EffusionGraham’s Law
37 2.2.1 Compressibility: 2.2.2 Expansion: 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 tanks2.2.2 Expansion:Gases will expand to fill any container they occupy, due to the random motion of the molecules.37
38 2.2.3 DiffusionDiffusion 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 barrier38Next slide:
39 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 particle39
40 Graham’s Law Internet demo of effusion 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.Where: v1= rate of gas 1v2= rate of gas 2M1= molar mass of gas1M2=molar mass of gas 240Next slide: Example
41 Graham’s Law Version #1, based on Effusion Rate The relationship between the rate of effusion or diffusion and the molar masses is:Note: See the inversion of the 1 and 2 in the 2nd ratio!Where: 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 1M1 is the molar mass of gas 1M2 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)
42 And in my spare time I invented dialysis, which has saved the lives of thousands of kidney patients Thomas Graham ( )Graham derived his law by treating gases as ideal, and applying the kinetic energy formula to them.Ek = ½ mv2All 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.
43 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:Note: In this variant law, the relationship is not inverted!Where: 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 effuseM1 is the molar mass of the first gasM2 is the molar mass of the second gas.
44 Example of Graham’s Law: How much faster does He diffuse than N2? MN2=2x14.0=28 g/molNitrogen (N2) has a molar mass of 28.0 g/molHelium (He) has a molar mass of 4.0 g/molThe difference between their diffusion rates is:Notice the reversal of order!So helium diffuses 2.6 times faster than nitrogenMHe=1x4.0=4 g/mol44Next slide: 2.3 Pressure of Gases
45 AssignmentsRead pages 63 to 67Do Questions 1 to 10 on page 68
46 Chapter 2.3 Pressure of Gases What is Pressure Atmospheric Pressure Outer Space (immeasurable)Spaceship 1 (2006)X15 (1963)100 km < kPaChapter 2.3Edge of SpacePressure of GasesWhat is PressureAtmospheric PressureMeasuring Pressure40 km 1 kPaHighest Jet 4 kPa20 km 6 kPa10 km 25 kPaMt Everest 31 kPa5 km 55 kPa46Mr. Smith0 km kPa
47 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 TheoryGas pressure is caused by billions of particles moving randomly, and striking the sides of the container.Pressure Formula:Pressure = force divided by area47
48 Atmospheric PressureThis is the force of a 100 km high column of air pushing down on us.Standard atmospheric pressure is1.00 atm (atmosphere), or101.3 kPa (kilopascals), or760 Torr (mmHg), or14.7 psi (pounds per square inch)Pressure varies with:Altitude. (lower at high altitude)Weather conditions. (lower on cloudy days)48
50 Measuring Pressure Barometer: measures atmospheric pressure. Two types:Mercury BarometerAneroid BarometerManometer: measures pressure in a container (AKA. Pressure guage)Dial Type: Similar to an aneroid barometerU-Tube: Similar to a mercury barometerPiston type: used in “tire guage”50
51 the Mercury BarometerA 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
52 The Aneroid BarometerIn an aneroid barometer, a chamber containing a partial vacuum will expand and contract in response to changes in air pressureA system of levers and springs converts this into the movement of a dial.
53 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.Tire gauge(piston manometer)U-tube manometer Pressure gauge(mercury manometer) (aneroid)You Tube manometer
54 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. Pgas(mmHg) = Patm(mmHg)+h(mm)Atm. pressureMust be in mmHg, not cm or kPa!After you finish, you can convert your answer to kPa, or atm. Or whatever.
55 Manometer Examples on a day when the air pressure is 763mmHg (101 Manometer Examples on a day when the air pressure is 763mmHg (101.7 kPa)Closed tube: Pgas(mm Hg)=h (mm Hg)Pgas = h = 4 cm = 40 mm HgPgas =h= 4 cm4 cmOpen: Pgas(mmHg)=P atm(mmHg) +h (mmHg)Pgas = mm Hg =823 mm HgPgas =6 cm Higher6Open: Pgas(mmHg)=P atm(mmHg) -h (mmHg)Pgas = mm Hg =703 mm HgPgas =96 cm Lower
56 AssignmentsRead pages 69 to 73.Do Page 74, Questions 1 to 4.
57 Chapter 2.4 The Simple Gas Laws Other Simple Laws that are a Gas: Boyle’s Law Relates volume & pressureCharles’ Law Relates volume & temperatureGay-Lussac’s Law Relates pressure & temperatureAvogadro’s Law Relates to the number of molesOther Simple Laws that are a Gas:Clarke’s Laws Relates possible and impossibleMurphy’s Law Anything that can go wrong willCole’s Law Relates thinly sliced cabbage to vinegar.57
58 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
59 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.”59
60 Robert BoyleBorn: 25 January 1627 Lismore, County Waterford, Ireland Died 31 December 1691 (aged 64) London, EnglandFields: Physics, chemistry; Known for Boyle's Law. Considered to be the founder of modern chemistryInfluences: Robert Carew, Galileo Galilei, Otto von Guericke, Francis BaconInfluenced: Dalton, Lavoisier, Charles, Gay-Lussack, Avogadro.Notable awards: Fellow of the Royal Society60
61 PressureGas pressure is the force placed on the sides of a container by the gas it holdsPressure is caused by the collision of trillions of gas particles against the sides of the containerPressure can be measured many waysStandard PressureAtmospheres (atm) 1 atmKilopascals (kPa)or(N/m2) kPa = N/m2Millibars (mB) mBTorr (torr) or mm mercury 760 torr = 760 mmHgCentimetres of mercury 76 cmHgInches of mercury (inHg) 29.9 inHg (USA only)Pounds per sq. in (psi) psi (USA only)61Next slide: Air in Syringe
62 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.62Next slide: Inside syringe
63 Inside the syringe… Read- don't copy 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)lowhigh63Next slide: PV
64 This means that:As the volume of a contained gas decreases, the pressure increasesAs the volume of a contained gas increases, the pressure decreasesThis assumes that:no more gas enters or leaves the container, andthat the temperature remains constant.The mathematical formula for this is given on the next slide64Next slide: Example
65 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: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 mLV2 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.
66 Example 1You 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 mL3000 mL·kPa ÷ 10 mL = 300 kPaThe pressure inside the syringe will be 300 kPa66Next slide: Graph of Boyle’s Law
67 Graph of Boyle’s Law The Pressure-Volume Relationship Boyle’s Law produces an inverse relationship graph.P(kpa) x V(L)100 x 8 = 800200 x 4 = 800Volume (L) 300 x 2.66 = 800400 x 2 = 800500 x 1.6 = 800600 x 1.33 = 800700 x 1.14 = 800800 x 1 = 80067Pressure (kPa) Next slide: Real Life Data
68 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)68Next slide: Boyle’s Law Experiment or skip to: Lesson 2.3 Charles’ Law:
69 Summary: Boyle’s law P1V1=P2V2 The volume of a gas is inversely proportional to its pressureFormula: P1V1=P2V2Graph: Boyle’s law is usually represented by an inverse relationship graph (a curve)P1V1=P2V2Volume (L) 69Pressure (kPa)
71 Assignments on Boyle’s Law Read pages 75 to 79Do questions 1 to 10 on page 97
72 Lesson Charles’ LawThe Relationship between Temperature and Volume.“Volume varies directly with Temperature”72Next slide: Jacques Charles
73 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.Born: November 12, 1746 ( ) Beaugency, OrléanaisDied: April 7, ( ) (aged 76), ParisNationality: FranceFields: physics, mathematics, hot air ballooningInstitutions: Conservatoire des Arts et MétiersNext slide: The Mathematical formula for this law
74 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: T1 is Temperature of the gas before it is heated, in kelvins.T2 is Temperature of the gas after it is heated, in kelvinsV1 is the volume of the gas before it was heated, in L or mLV2 is the volume of the gas after it was heated, in the same units.
75 Charles Law EvidenceCharles 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.75Next slide: Diagram of Cylinder & Piston
76 Charles Law Example Piston Cylinder Trapped Gas Click Here for a simulated internet experiment76Next slide: Graph of Charles’ Law
77 Graph of Charles Law Expansion of an “Ideal” Gas Charles discovered the direct relationship6LLord Kelvin traced it back to absolute zero.5LExpansion of an “Ideal” Gas4L3L2LExpansion of most real gasescondensationfreezeLiquid state1L273°CSolid state-250°C-200°C-150°C-100°C-50°C0°C50°C100°C150°C200°C250°C°CNext slide: Example
78 Absolute Zero is Real Cool! °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)Absolute Zero is Real Cool!
79 William Thompson, The right honourable Lord Kelvin 1st Baron of Largs Born in Belfast IrelandDied in Largs, ScotlandWorked at the University of GlasgowExperimented in Thermodynamics."There is nothing new to be discovered in physics now. All that remains is more and more precise measurement"
80 Kelvin’s ScaleIn 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 KelvinTo convert from Celsius to Kelvin, simply add 273 to the Celsius temperature. To convert back, subtract 273Note: 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.
81 ExampleIf 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 = 600kUse Charles’ Law: (see below)Answer: 4 LitresNext slide: Lesson 2.4 Gay Lussac’s Law
82 Summary: Charles’ lawThe volume of a gas is directly proportional to its temperatureFormula:Graph: Charles’ law is usually represented by a direct relationship graph (straight line)Video1Volume (L) Absolute zero0°C=273KTemp
83 Charles’ Law Assignments Read pages 80 to 84Do questions 11 to 21 on pages 97 and 98
84 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:T1=22˚CT2=4˚CV1=0.50 LTo find:V2= unknownTemperatures must be converted to kelvin=295K=277KSo:V2=V1 x T2 ÷ T1V2=0.5L x 277K295KV2=0.469 Lmultiplydivide84The balloon will have a volume of 0.47 litres
85 Answer: The balloon’s volume will be 0.71 litres 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.DataV1= 0.40LT1= 20°CT2= 250°CV2= ?Convert temperatures to kelvin20+273= 293K, =523k=293 KUse Charles’ Law=523 K0.7139L0.40L x 523 K ÷ 293 K = LAnswer: The balloon’s volume will be 0.71 litres85
86 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 kelvin19+273= 292K, =333KData:V1=250 mLT1= 19.0°CT2=60.0°CV2= ?Use Charles’ Law=292 K=333 KmL250mL x 333 K ÷ 292 K = mLAnswer: The bag will have a volume of 285mL
87 4. The volume of air in my lungs will be 2.35 litres 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 litresBe sure to show your known informationChange the temperature to Kelvins and show them.Show the formula you used and your calculationsState the answer clearly.5.6. The temperature is K, which corresponds to 6.70 C. A jacket or sweater would be appropriate clothing for this weather.
88 Gay-Lussac’s Law Lesson 2.4.3 For Temperature-Pressure changes. “Pressure varies directly with Temperature”88Next slide:’
89 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 1778Saint-Léonard-de-NoblatDied 9 May Saint-Léonard-de-NoblatNationality: FrenchFields: ChemistryKnown for Gay-Lussac's law89Next slide:’
90 Gay-Lussac’s Law Relating Pressure and Temperature of a Gas Where: 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.
91 Gay-Lussac’s LawAs the gas in a sealed container that cannot expand is heated, the pressure increases.For calculations, you must use Kelvin temperatures:K=°C+273pressure91
92 Remove irrelevant fact ExampleA 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 factData:P1= 100kPaV1=310 mLT1=20˚CP2=unknownT2=606˚C˚Celsius must be converted to kelvins20˚C = 293 K ˚C = 879 K=293K=879KFormula:multiplydividex = ÷ 293x = 300Answer: the pressure will be 300 kPa92Next slide: T vs P graph
93 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
95 Summary: Gay-Lussac’s law The pressure of a gas is directly proportional to its temperatureFormula:Graph: Gay-Lussac’s law is usually represented by an direct relationship graph (straight line)Pressure Absolute zero0°C=273KTemp
96 Assignment on Gay-Lussac’s Law Read pages 85 to 87Answer questions #22 to 30 on page 98
97 Avogadro’s Law Lesson 2.4.4 For amount of gas. “The volume of a gas is directly related to the number of moles of gas”97Next slide: Lorenzo Romano Amedeo Carlo Avogadro di Quaregna
98 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 AvogadroBorn: August 9, 1776Turin, ItalyDied: July 9, 1856Field: PhysicsUniversity of TurinKnown for Avogadro’s hypothesis, Avogadro’s number.
99 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
100 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
101 Avogadro’s Laws Relating Moles of Gas to Volume or Pressure Where: V1 = volume before, in appropriate volume units.V2 = volume after, in the same volume unitsP1=pressure before, in appropriate pressure units.P2=pressure after, in the same pressure units.n1 = #moles beforen2 = #moles after101
102 Assignments on Avogadro’s Law Read pages 88 to 92Do Questions 31 to 36 on page 98102
103 Standard Conditions and Molar Volume Lesson 2.45Standard Conditions andMolar Volume103Next slide:
104 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 KStandard Pressure =101.3 kPa
105 (SATP) Ambient Temperature Ambient Temperature = 25°C = 298 K 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 KStandard Pressure = kPa(SATP)
106 Molar VolumeThe 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 litresAT SATP one mole of an ideal gas has a volume of 24.5 litresSince all common gases are very near ideal at these temperatures, we can use these as standard molar volumes for ANY common gas.
107 Comparison Standard and Ambient Conditions Standard Temperature & Pressure(STP)Ambient Temperature & Pressure(SATP)Pressure101.3 kPaTemperature °C0 °C25 °CTemperature KKKMolar Volume22.4 L/mol24.5 L/mol
108 Assignments on Molar Volume Read pages 92 to 96Do Questions 37 to 52 on page 98108
109 The General Gas Law and the Ideal Gas Law Lesson 2.5 & 2.6The General Gas Law and the Ideal Gas Law109Next slide:
110 The Combined or General Gas Law The general (or combined) gas law replaces the four simple gas laws. It puts together:Boyle’s LawCharles’ LawGay-Lussac’s LawAvogadro’s LawAdvantages 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)= General Gas Law110
111 The General Gas Law Relating all the Simple Laws Together MemorizeWhere: 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 kelvinsn 1, n2 is the number of moles of the gas.
112 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’ LawAnd finally, if the volume stays constant, then you have Gay-Lussac’s LawMost of the time, the number of moles stays the same, so you can remove moles from the equation.112
113 FYI: Deriving a Formula, The Ideal Gas LawThe 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) .FYI: Deriving a Formula,no need to copy all of itNext slide:
114 Remember Standard Temperature & Pressure (STP) Standard Temperature is 0°C or more to the point, 273K = 25°C = 298K)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)OK, You should already know this part.If you don't, record it now!
115 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 n2At STP we know all the conditions of the gas.Substitute and solve to give us a constantNext slide: R-- The Ideal Gas Constant
116 The Ideal Gas Constant is the proportionality constant that makes the ideal gas law work The Ideal Gas Constant has the symbol RR=8.31 L· kPa / K·molThe Ideal Gas constant is 8.31 litre-kilopascals per kelvin-mole.MemorizeNext slide: Ideal Gas Formula
117 FYI: Deriving a Formula, no need to copy all of itSo, ifThen, by a bit of algebra: P1V1=n1RT1Since we are only using one set of subscripts here, we might as well remove them: PV=nRT
118 The Ideal Gas Law Relating Conditions to the Ideal Gas Constant Where: P=Pressure, in kPaV=Volume, in Litresn= number of moles, in molR= Ideal Gas constant, 8.31 LkPa/KmolT = Temperature, in kelvins
119 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.
120 Sample Problem8.0 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 = nRTVariables: P=200 kPaV=? (our unknown)= xn= 8.0g ÷ 32 g/mol =0.25 molR=8.31 L·kPa/K·mol (ideal gas constant)T= 15°C = 288K200 x = (0.25)(8.31)(288) , thereforex= (0.25)(8.31)(288) ÷ 200=2.99 LThere are 3.0 L of oxygen (rounded to 2 S.D.)
121 Sample problem8.0 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)Temperature has been converted to kelvinsData:P=200 kPaV=unknown = Xn= not givenR=8.31 L·kPa/K·molT= 15°C = 288K---m (O2) = 8gM (O2) = 32.0 g/molCalculate the value of n using the mole formula:0.25 mol200 x = (0.25)(8.31)(288) , thereforex= (0.25)(8.31)(288) ÷ 200=2.99 LThere are 3.0 L of oxygen (rounded to 2 S.D.)
122 Sample Problem8.0 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 kPaR = 8.31 L·kPa/K·molT = = 288Km(O2)= 8.0 gM(O2)= 32.0 g/moln =To find:VFormula:Work:Next slide: Ideal vs. Real
123 Ideal vs. Real GasesThe 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
124 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.
125 ExampleA 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=300KPV=nRT (ideal gas law formula)100kPa25L=1molR300K, so…R=100kPa25L÷(300K1mol)R=8.33 kPaL /Kmol expected value: 8.31 kPaL /KmolSo the gas is not perfectly ideal, but it is very close to an ideal gas,It varies from ideal by only 0.24%
126 Gas Laws OverviewWhen using gas laws, remember that temperatures are given in Kelvins (K)Based on absolute zero: –273°CThe 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.
127 Gas Laws: Summary R=8.31 Lkpa/Kmol Simple gas laws Boyle’s Law: Charles’ Law:Gay-Lussac’s Law:Combined gas law:Ideal gas law:The ideal gas constant:R=8.31 Lkpa/Kmol
129 Assignments on the Ideal Gas Law Read pages 100 to 104in textbookDo Exercises p #1 to 16
130 Stoichiometry of Gases Lesson 2.7Stoichiometry of Gases
131 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 particlesIe. At same pressure and temperatureSame volumes have same # molesVolumes are proportional to numbers of moles
132 Simple question 1How 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 H2O2 : : 2 molar ratio?L : 3L : ?L volume ratio6L : 3L : XX proportion solutionAnswer: 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)
133 Assignments on the Stoichiometry of Gases Read pages 108 to 109 in textbookDo Exercises p #1 to 9
134 Dalton’s Law of partial pressures Lesson 2.8Dalton’s Law of partial pressures
135 John DaltonBesides 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% NitrogenBorn6 September Eaglesfield, Cumberland, EnglandDied27 July 1844 Manchester, EnglandNotable studentsJames Prescott JouleKnown forAtomic Theory, Law of Multiple Proportions, Dalton's Law of Partial Pressures, DaltonismInfluencesJohn Gough
136 Partial Pressure Many gases are mixtures, eg. Air is 78% nitrogen, 21% Oxygen, 1% other gasesEach 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) kPa (O2) kPa(Other)Next slide:
137 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.
138 Dalton’s Law The Law of Partial Pressures of Gases Where: PT is the total pressure of mixed gasesP1 is the pressure of the 1st gasP2 is the pressure of the 2nd gasetc...
139 Variant of Dalton’s Law (used for finding partial pressure of a gas in a mixture) Where: PA=Pressure of gas AnA = moles of gas AnT= total moles of all gasesPT= Total Pressure of all gases
140 Uses of Dalton’s Law Story Don’t copy 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.
141 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.
143 Crew of Apollo 1Gus Grissom, Ed White, Roger Chaffee
144 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 22There is an answer key in the back for theseDo these on your own as review
145 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 onesAvogadro’s hypothesisA mole of gas occupies 22.4L at STP and contains 6.02x1023 particles
146 Summary of Kinetic Theory Hypotheses (re. Behaviour of gas molecules):1. Gases are made of molecules moving randomly2. 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.
147 Gases are made of particles Particles move randomly! PressureEnergy of a particle:KE = ½ mV 2Pressure is the result of particles colliding with the container walls.P = F /A