Embed Size (px)
Citation preview
Module 2Module 2
Gases and Their ApplicationsGases and Their Applications
Lesson 2-1Lesson 2-1
About GasesAbout Gases
Gas is one of the three main states of matterGas is one of the three main states of matter Gas particles may be Gas particles may be atomsatoms or or moleculesmolecules, ,
depending on the type of substance (ie, depending on the type of substance (ie, element or compound)element or compound)
Gas particles have much more space Gas particles have much more space between them than liquids or solids.between them than liquids or solids.
Gases are said to be an Gases are said to be an expandedexpanded form of form of matter, solids and liquids are matter, solids and liquids are condensed condensed forms of matter.forms of matter.
Gas is one of the three main states of matterGas is one of the three main states of matter Gas particles may be Gas particles may be atomsatoms or or moleculesmolecules, ,
depending on the type of substance (ie, depending on the type of substance (ie, element or compound)element or compound)
Gas particles have much more space Gas particles have much more space between them than liquids or solids.between them than liquids or solids.
Gases are said to be an Gases are said to be an expandedexpanded form of form of matter, solids and liquids are matter, solids and liquids are condensed condensed forms of matter.forms of matter.
General Properties of a GasGeneral Properties of a Gas
Gases do have mass (although it is Gases do have mass (although it is sometimes difficult to measure).sometimes difficult to measure).
Gases have no definite volume, Gases have no definite volume, Gases have no definite shape.Gases have no definite shape. Gases are compressible, meaning they can Gases are compressible, meaning they can
be squeezed into smaller containers, or can be squeezed into smaller containers, or can expand to fill larger containers.expand to fill larger containers.– Because gases compress, the density of gases Because gases compress, the density of gases
can only be compared under specific conditions.can only be compared under specific conditions.
Some Important GasesSome Important GasesSome Important GasesSome Important Gases
Oxygen (OOxygen (O22):): clear, breathable, supports combustion. clear, breathable, supports combustion. Ozone (OOzone (O33):): poisonous, unstable form of oxygen poisonous, unstable form of oxygen Nitrogen (NNitrogen (N22):): clear, low activity, most abundant gas in clear, low activity, most abundant gas in
the Earth’s atmosphere. the Earth’s atmosphere. Hydrogen (HHydrogen (H22):): clear, lighter than air, clear, lighter than air,
flammable/explosiveflammable/explosive Carbon dioxide (COCarbon dioxide (CO22):): clear, but turns limewater clear, but turns limewater
cloudy. Does not support respiration but low toxicity. cloudy. Does not support respiration but low toxicity. Heavier than air. Largely responsible for the Heavier than air. Largely responsible for the greenhouse effect (global warming)greenhouse effect (global warming)
Sulfur dioxide (SOSulfur dioxide (SO22):): smelly gas. When it combines smelly gas. When it combines with oxygen and water vapour it can form Hwith oxygen and water vapour it can form H22SOSO44, , responsible for acid rain.responsible for acid rain.
Oxygen (OOxygen (O22):): clear, breathable, supports combustion. clear, breathable, supports combustion. Ozone (OOzone (O33):): poisonous, unstable form of oxygen poisonous, unstable form of oxygen Nitrogen (NNitrogen (N22):): clear, low activity, most abundant gas in clear, low activity, most abundant gas in
the Earth’s atmosphere. the Earth’s atmosphere. Hydrogen (HHydrogen (H22):): clear, lighter than air, clear, lighter than air,
flammable/explosiveflammable/explosive Carbon dioxide (COCarbon dioxide (CO22):): clear, but turns limewater clear, but turns limewater
cloudy. Does not support respiration but low toxicity. cloudy. Does not support respiration but low toxicity. Heavier than air. Largely responsible for the Heavier than air. Largely responsible for the greenhouse effect (global warming)greenhouse effect (global warming)
Sulfur dioxide (SOSulfur dioxide (SO22):): smelly gas. When it combines smelly gas. When it combines with oxygen and water vapour it can form Hwith oxygen and water vapour it can form H22SOSO44, , responsible for acid rain.responsible for acid rain.
Carbon monoxide (CO):Carbon monoxide (CO): Clear, odourless, but Clear, odourless, but veryvery toxic. Destroys hemoglobin. About the same toxic. Destroys hemoglobin. About the same density as air.density as air.
Ammonia (NHAmmonia (NH33):): toxic, strong smell, refrigerant . toxic, strong smell, refrigerant . Very soluble in water, forms a basic solution called Very soluble in water, forms a basic solution called ammonia-water (NHammonia-water (NH44OH) which is found in some OH) which is found in some cleaners.cleaners.
FreonFreon®® or CFC: or CFC: Non-toxic refrigerant used in air- Non-toxic refrigerant used in air-conditioners & freezers. Freon may catalyze conditioners & freezers. Freon may catalyze ozone breakdown. The original Freon formula is ozone breakdown. The original Freon formula is now banned, but low chlorine versions are still in now banned, but low chlorine versions are still in use.use.
Methane (CHMethane (CH44):): flammable gas, slightly lighter than flammable gas, slightly lighter than air, produced by decomposition. Found in natural air, produced by decomposition. Found in natural gas. Methane is also a “greenhouse” gas. gas. Methane is also a “greenhouse” gas.
Helium (He):Helium (He): inert, lighter than air. Used in inert, lighter than air. Used in balloons and in diver’s breathing mixtures.balloons and in diver’s breathing mixtures.
Acetylene (CAcetylene (C22HH22): ): AKA ethene, it is used as a fuel in AKA ethene, it is used as a fuel in
welding, lanterns and other devices.welding, lanterns and other devices. Propane (CPropane (C33HH88): ): used as a fuel in barbecues, stoves, used as a fuel in barbecues, stoves,
lanterns and other devices.lanterns and other devices. Radon (Rn): Radon (Rn): A noble gas that is usually radioactive. It is A noble gas that is usually radioactive. It is
heavier than air, and sometimes found in poorly ventilated heavier than air, and sometimes found in poorly ventilated basements.basements.
Neon (Ne) Neon (Ne) and and Xenon (Xe)Xenon (Xe): Noble gases found in : Noble gases found in fluorescent light tubes, and as insulators inside windows. fluorescent light tubes, and as insulators inside windows. They glow more brightly than other gases when electrons They glow more brightly than other gases when electrons pass through them. Neon is slightly lighter than air, Xenon pass through them. Neon is slightly lighter than air, Xenon is quite a bit heavier.is quite a bit heavier.
Compressed Air (78% NCompressed Air (78% N22, 21% O, 21% O22): ): Not actually a pure Not actually a pure
gas, but a gas mixture that acts much like a pure gas. It is gas, but a gas mixture that acts much like a pure gas. It is used by scuba divers (at shallow depths), and to run used by scuba divers (at shallow depths), and to run pneumatic tools, and for producing foam materials.pneumatic tools, and for producing foam materials.
Fun GasesFun Gases(of no real importance)(of no real importance)
Nitrous OxideNitrous Oxide (N (N22O)O)– AKA: Laughing gas, Happy gas, Nitro, NOSAKA: Laughing gas, Happy gas, Nitro, NOS– Once used as an anaesthetic in dentist offices, this Once used as an anaesthetic in dentist offices, this
sweet-smelling gas reduces pain sensitivity and causes sweet-smelling gas reduces pain sensitivity and causes euphoric sensations. It is an excellent oxidizer, reigniting euphoric sensations. It is an excellent oxidizer, reigniting a glowing splint much like oxygen would. It is used in a glowing splint much like oxygen would. It is used in racing where it is injected into the carburetor to racing where it is injected into the carburetor to temporarily increase an engine’s horsepower. temporarily increase an engine’s horsepower.
Sulfur HexafluorideSulfur Hexafluoride– One of the densest gases in common use. One of the densest gases in common use.
Fun with Sulfur hexafluoride
MatchMatchthe gas with the problem it causesthe gas with the problem it causes
GasGas ProblemProblem
Carbon DioxideCarbon Dioxide Ozone layer Ozone layer depletiondepletion
CFCsCFCs Global WarmingGlobal Warming MethaneMethane Toxic poisoningToxic poisoning Carbon monoxideCarbon monoxide Noxious smellNoxious smell Sulfur dioxideSulfur dioxide Acid RainAcid Rain
Next slide: SummaryNext slide: Summary
Textbook AssignmentsTextbook Assignments
Read Chapter 1: pp. 37 to 50Read Chapter 1: pp. 37 to 50
Do the exercises on pages 51 and 52Do the exercises on pages 51 and 52– Questions # 1 to 22Questions # 1 to 22
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
Chapter 2.1Chapter 2.1
• The Kinetic Theory– Moving, moving, moving,– Keep those atoms moving
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 “For simplicity, I usually call the gas particles “moleculesmolecules”, ”, although in truth, they could include atoms or ions.although in truth, they could include atoms or ions.
2.12.1
Page 54Page 54
The Particle Model
ReviewReview
Not in textNot in text
• The Kinetic Theory is part of the Particle Model of matter, which includes the following concepts:– All matter is composed of particles (ions, atoms or
molecules) which are extremely small and have a varying space between them, depending on their state or phase.
– Particles of matter may attract or repel each other, and the force of attraction or repulsion depends on the distance that separates them.
– Particles of matter are always moving.++
++
--
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!
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.
2.1.12.1.1
Page 54Page 54
Kinetic Theory Model of States
SolidSolidParticles vibrate Particles vibrate but don’t “flow”. but don’t “flow”. Strong molecular Strong molecular attractions keep attractions keep them in place.them in place.
LiquidLiquidParticles vibrate, move Particles vibrate, move and “flow”, but and “flow”, but cohesion (molecular cohesion (molecular attraction) keeps them attraction) keeps them close together.close together.
GasGasParticles move freely Particles move freely through container. The through container. The wide spacing means wide spacing means molecular attraction is molecular attraction is negligible. negligible.
Kinetic Motion of Particles
• Particles (ie. Molecules) can have 3 types of motion, giving them kinetic energy– Vibrational kinetic energy (vibrating)– Rotational kinetic energy (tumbling)– Translational kinetic energy (moving)
2.1.12.1.1
Page 55Page 55
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).
2.1.12.1.1
Page 56Page 56
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”
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.”
2.1.32.1.3
Page 61Page 61
• To make the physical laws (derived from kinetic equations) work, they had to make five assumptions about how molecules work.
• Four of these are listed on page 61 of your textbook
• The fifth one is not.
2.1.32.1.3
Page 61Page 61
Kinetic Theory Assumptions 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.
5. Collisions between particles are perfectly elastic, ie. No energy is lost in collisions.
2.1.32.1.3
Page 61Page 61
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 “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.
Other “Imaginary Features” Other “Imaginary Features” of Ideal Gasof Ideal Gas
• AnAn ideal gas would obey the gas ideal gas would obey the gas laws at all conditions of laws at all conditions of temperature and pressuretemperature and pressure
• An ideal gas would never An ideal gas would never condense into a liquid, or freeze condense into a liquid, or freeze into a solid.into a solid.
• At absolute zero an ideal gas At absolute zero an ideal gas would occupy no space at allwould occupy no space at all.
2.1.32.1.3
Page 61Page 61
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.
““Slow” Slow”
moleculesmolecules
The range of kinetic energies can be represented as a sort of “bell curve.” Maxwell’s Velocity Distribution Curve.
Increasing kinetic energyIncreasing kinetic energyAverage Average
kinetic energykinetic energy
Incr
easi
ng #
mole
cule
sIn
creasi
ng #
mole
cule
s
Most moleculesMost molecules
mod
em
od
e
mean
mean
““Average”Average”
moleculesmolecules
The mean & median The mean & median can help establish can help establish
“average” molecules“average” molecules
““Fast”Fast”
MoleculesMolecules
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
• KE = mv2 kinetic energy of molecules
2So, kinetic energy depends on both the speed
(v) and on the mass (m) of the molecules.
Distribution of Particles Around Average Kinetic Energies.
Kinetic Energy of moleculesKinetic Energy of molecules(proportional to velocity of molecules)(proportional to velocity of molecules)
Nu
mb
er
of
mole
cule
sN
um
ber
of
mole
cule
s
Avera
ge k
ineti
c e
nerg
y o
f m
ole
cu
les
Avera
ge k
ineti
c e
nerg
y o
f m
ole
cu
les
Avera
ge k
ineti
c e
nerg
y o
f w
arm
er
mole
cu
les
Avera
ge k
ineti
c e
nerg
y o
f w
arm
er
mole
cu
les
Faster Faster
than than
average moleculesaverage molecules
SlowerSlower
than than
average moleculesaverage molecules
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.
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
Chapter 2.2Chapter 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
2.2.3 Diffusion2.2.3 Diffusion
Diffusion is the tendency for molecules to Diffusion is the tendency for molecules to move from areas of high concentration to move from areas of high concentration to areas of lower concentration, until the areas of lower concentration, until the concentration is uniform. They do this concentration is uniform. They do this because of the random motion of the because of the random motion of the molecules.molecules.
Effusion is the same process, but with the Effusion is the same process, but with the molecules passing through a small hole or molecules passing through a small hole or barrierbarrier
Next slide:Next slide:
Rate or Diffusion or effusionRate or Diffusion or effusion
It has long been It has long been known that lighter known that lighter molecules tend to molecules tend to diffuse faster than diffuse faster than heavy ones, since heavy ones, since their average their average velocity is higher, velocity is higher, but how much but how much faster?faster?
Graham’s LawGraham’s Law Thomas Graham (c. 1840) studied Thomas Graham (c. 1840) studied
effusion (a type of diffusion effusion (a type of diffusion through a small hole) and through a small hole) and proposed the following law:proposed the following law:
““The rate of diffusion of a gas is The rate of diffusion of a gas is inversely proportional to the inversely proportional to the square root of its molar mass.”square root of its molar mass.” In other words, light gas particles will In other words, light gas particles will
diffuse faster than heavy gas diffuse faster than heavy gas molecules, and there is a math molecules, and there is a math formula to estimate how much faster.formula to estimate how much faster.
Next slide: ExampleNext slide: Example
1
2
2
1
M
M
v
v
Example of Graham’s Law: Example of Graham’s Law: How much faster does He diffuse than NHow much faster does He diffuse than N22??
Nitrogen (NNitrogen (N22) has a molar ) has a molar
mass of 28.0 g/molmass of 28.0 g/mol Helium (He) has a molar Helium (He) has a molar
mass of 4.0 g/molmass of 4.0 g/mol The difference between The difference between
their diffusion rates is:their diffusion rates is: Notice the reversal of Notice the reversal of
order!order! So helium diffuses 2.6 So helium diffuses 2.6
times faster than nitrogentimes faster than nitrogen Internet demo of effusionInternet demo of effusion
He
N
N
He
M
M
v
v 2
2
6.22
3.5
/4
/28
molg
molg
MMNN22=2x14.0=28 g/mol=2x14.0=28 g/mol
Next slide: AvogadroNext slide: Avogadro
MMHeHe=1x4.0=4 g/mol=1x4.0=4 g/mol
Chapter 2.3Chapter 2.3
• Pressure of Gases– What is Pressure– Atmospheric Pressure– Measuring Pressure– Graham’s Law
100 km 0 kPa100 km 0 kPa
40 km 1 kPa40 km 1 kPa
20 km 6 kPa20 km 6 kPa
10 km 25 kPa10 km 25 kPa
5 km 55 kPa5 km 55 kPa
0 km 101 kPa0 km 101 kPa
Mt Everest 30 kPaMt Everest 30 kPa
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:
Pressure = force divided by area
A
FP
Atmospheric Pressure
• This is the force of a 100 km column of air pushing down on us.
• Standard atmospheric pressure is• 1 atm (atmosphere) or• 101.3 kPa (kilopascals), or• 760 Torr (mmHg)• 14.7 psi (pounds per square inch)
• Pressure varies with:• Altitude• Weather conditions.
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
• A tube at least 800 mm long is filled with mercury (the densest liquid) and inverted over a dish that contains mercury.
• The mercury column will fall until the air pressure can support the mercury.
• On a sunny day at sea level, the air pressure will support a column of mercury 760 mm high.
• The column will rise and fall slightly as the weather changes.
• Mercury barometers are very accurate, but have lost popularity due to the toxicity of mercury.
the Mercury Barometer
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.
U-tube manometer Pressure gaugeU-tube manometer Pressure gauge
(mercury manometer) (aneroid)(mercury manometer) (aneroid)
Chapter 2.4Chapter 2.4
• The Simple Gas Laws– Boyle’s Law– Charles’ Law– Gay-Lussac’s Law
Lesson 2.4.1Lesson 2.4.1
Boyle’s LawBoyle’s LawRobert Boyle (1662)Robert Boyle (1662)
Lesson 2.4.1Lesson 2.4.1
Boyle’s LawBoyle’s LawRobert Boyle (1662)Robert Boyle (1662)
““For a given mass of gas at a For a given mass of gas at a constant temperature, the volume constant temperature, the volume
varies inversely with pressure.”varies inversely with pressure.”
““For a given mass of gas at a For a given mass of gas at a constant temperature, the volume constant temperature, the volume
varies inversely with pressure.”varies inversely with pressure.”
For Pressure and Volume
VP
1
Next slide: Air in SyringeNext slide: Air in Syringe
Robert BoyleRobert Boyle
BBorn: 25 January 1627orn: 25 January 1627Lismore, County Waterford, Ireland Died Lismore, County Waterford, Ireland Died 31 December 1691 (aged 64)31 December 1691 (aged 64)London, EnglandLondon, England
Fields: Physics, chemistry; Known for Fields: Physics, chemistry; Known for Boyle's Law. Considered to be the Boyle's Law. Considered to be the founder of modern chemistry founder of modern chemistry
Influences: Robert Carew, Galileo Influences: Robert Carew, Galileo Galilei, Otto von Guericke, Francis Galilei, Otto von Guericke, Francis Bacon Bacon
Influenced: Dalton, Lavoisier, Charles, Influenced: Dalton, Lavoisier, Charles, Gay-Lussack, Avogadro.Gay-Lussack, Avogadro.
Notable awards: Fellow of the Royal Notable awards: Fellow of the Royal SocietySociety
PressurePressure Gas pressure is the force placed on the sides of a Gas pressure is the force placed on the sides of a
container by the gas it holdscontainer by the gas it holds Pressure is caused by the collision of trillions of Pressure is caused by the collision of trillions of
gas particles against the sides of the containergas particles against the sides of the container Pressure can be measured many waysPressure can be measured many ways
Standard PressureStandard PressureAtmospheres (atm)Atmospheres (atm) 1 atm1 atmKilopascals (kPa)Kilopascals (kPa) 101.3 kPa 101.3 kPa Millibars (mB)Millibars (mB) 1013 mB1013 mBTorr (torr)Torr (torr) 760 torr760 torrMillimetres Hg (mmHg)Millimetres Hg (mmHg) 760 mmHg760 mmHgInches {Hg}Inches {Hg} 29.9 inHg29.9 inHgPounds per sq. in (psi)Pounds per sq. in (psi) 14.7 psi14.7 psi
Example of Boyle’s Law:Example of Boyle’s Law:Air trapped in a syringeAir trapped in a syringe
If some air is left in If some air is left in a syringe, and the a syringe, and the needle removed needle removed and sealed, you and sealed, you can measure the can measure the amount of force amount of force needed to needed to compress the gas compress the gas to a smaller to a smaller volume.volume.
Next slide: Inside syringeNext slide: Inside syringe
Inside the syringe…Inside the syringe…
The harder you press, the smaller The harder you press, the smaller the volume of air becomes. the volume of air becomes. Increasing the pressure makes the Increasing the pressure makes the volume smaller!volume smaller!
The original pressure was low, the The original pressure was low, the volume was large. The new volume was large. The new pressure is higher, so the volume is pressure is higher, so the volume is small.small. Click Here for an internet demo using Click Here for an internet demo using
psi (pounds per square inch) instead of psi (pounds per square inch) instead of kilopascals (1kPa=0.145psi)kilopascals (1kPa=0.145psi)
Next slide: PVNext slide: PV
lowlow
highhigh
This means that:This means that:
As the volume decreases, the pressure As the volume decreases, the pressure increasesincreases
As the volume increases, the pressure As the volume increases, the pressure decreasesdecreases
The formula for this is:The formula for this is:
PP11 V V11 = P = P22 V V22
Where Where PP11, V, V11 = pressure, volume before = pressure, volume before
PP22, V, V22 = pressure, volume after = pressure, volume after
As the volume decreases, the pressure As the volume decreases, the pressure increasesincreases
As the volume increases, the pressure As the volume increases, the pressure decreasesdecreases
The formula for this is:The formula for this is:
PP11 V V11 = P = P22 V V22
Where Where PP11, V, V11 = pressure, volume before = pressure, volume before
PP22, V, V22 = pressure, volume after = pressure, volume after
Next slide: ExampleNext slide: Example
Example 1Example 1
You have 30 mL of air in a syringe at 100 kPa. You have 30 mL of air in a syringe at 100 kPa. If you squeeze the syringe so that the air If you squeeze the syringe so that the air occupies only 10 mL, what will the pressure occupies only 10 mL, what will the pressure inside the syringe be?inside the syringe be?
PP11 ×× V V11 = P = P22 ×× V V22, so.. , so.. 100 kPa 100 kPa ×× 30 mL = 30 mL = ?? kPa kPa ×× 10 mL 10 mL 3000 mL3000 mL··kPa kPa ÷ ÷ 10 mL = 300 kPa 10 mL = 300 kPa The pressure inside the syringe will be 300 kPaThe pressure inside the syringe will be 300 kPa
Next slide: Graph of Boyle’s LawNext slide: Graph of Boyle’s Law
Graph of Boyle’s LawGraph of Boyle’s LawThe Pressure-Volume RelationshipThe Pressure-Volume Relationship
Pressure (kPa) Pressure (kPa)
Volu
me (
L)
Volu
me (
L)
100 200 300 400 500 600 700 800100 200 300 400 500 600 700 800
1
2
3
4
5
6
7
8
1
2
3
4
5
6
7
8
Boyle’s Law produces Boyle’s Law produces an inverse an inverse relationship graph.relationship graph.
100 x 8 = 800100 x 8 = 800
200 x 4 = 800200 x 4 = 800
400 x 2 = 800400 x 2 = 800
800 x 1 = 800800 x 1 = 800
P(kpa) x V(L)P(kpa) x V(L)
Next slide: Real Life DataNext slide: Real Life Data
300 x 2.66 = 800300 x 2.66 = 800
500 x 1.6 = 800500 x 1.6 = 800
600 x 1.33 = 800600 x 1.33 = 800700 x 1.14 = 800700 x 1.14 = 800
Example 2: Real Life DataExample 2: Real Life Data
2 4 6 8 10 12 14 16 182 4 6 8 10 12 14 16 18
5
10
15
2
0
25
30
35
40
5
10
15
2
0
25
30
35
40
In an experiment Mr. Taylor In an experiment Mr. Taylor and Tracy put weights and Tracy put weights onto a syringe of air. onto a syringe of air.
At the beginning, Mr. Taylor At the beginning, Mr. Taylor calculated the equivalent calculated the equivalent of 4 kgf of atmospheric of 4 kgf of atmospheric pressure were exerted pressure were exerted on the syringe.on the syringe.
0+4= 4kg : 29 mL (116)0+4= 4kg : 29 mL (116)
2+4= 6kg : 20 mL (120)2+4= 6kg : 20 mL (120)
4+4=8kg : 15 mL (120)4+4=8kg : 15 mL (120)
6+4=10kg: 12 mL (120)6+4=10kg: 12 mL (120)
8+4=12kg: 10.5 mL8+4=12kg: 10.5 mL (126)(126)
Next slide: Boyle’s Law Experiment or skip to: Lesson 2.3 Charles’ Law:Next slide: Boyle’s Law Experiment or skip to: Lesson 2.3 Charles’ Law:
Summary: Boyle’s law
• The volume of a gas is inversely proportional to its pressure
• Formula: P1V1=P2V2
• Graph: Boyle’s law is usually represented by an inverse relationship graph (a curve)
Volu
me (
L)
Volu
me (
L)
Pressure (kPa) Pressure (kPa)
VP
1
PP11VV11=P=P22VV22
Boyle’s Law Lab Activity• We will use the weight of a column of
mercury to compress and expand air (a gas) sealed in a glass tube.
• Read the handout for details of the procedure. (Note: You may shorten the procedure section in your report by including and referring to this handout as part of a complete sentence.)
• You should still write all other report sections (purpose, materials, diagram, observations etc.) in full, as normal.
Read,
Don
’t W
rite
Read,
Don
’t W
rite
#1. Horizontal#1. Horizontal
#2 Open end up#2 Open end up
#3 Open end down#3 Open end down
Diagram of Boyle’s Law Apparatus
Collecting Data
• You will need to find the length of the mercury column with the tube held horizontal:
• You also need this atmospheric information:
(a) Position of “right”side of mercury ___ mm
(b) Position of “left” of mercury column ___ mm
(c) Height of mercury column (a) – (b) (c) mm
(d) today’s temperature* ___ °C
(e) today’s barometric pressure (blackboard) (e) mmHg
*used to calibrate the barometer, not used in calculations*used to calibrate the barometer, not used in calculations
Collecting Data (continued)
(f) Position of “left” side of column mm
(g) Position of closure mm
(h) “volume” of gas (f) – (g) (h) Mm
Data set 2 - Open End Up:
(i) Position of bottom of column mm
(j) Position of closure should be same as (g) mm
(k) “volume” of gas (i) – (j) (k) mm
Data set 1 - Horizontal Tube:Data set 1 - Horizontal Tube:
Collecting Data (continued)
Data set 3 - Open End Down:
l) Position of Top of column mm
m) Position of closure should be same as (g) mm
n) “volume” of gas (l) – (m) mm
This concludes the collection of data, now This concludes the collection of data, now we must process it and calculate the PV we must process it and calculate the PV (pressure x volume) values at each of the (pressure x volume) values at each of the three conditions.three conditions.
Calculations
Barometric pressure
Item (e)
Column Height
Item (c)
“Pressure”
P
“Volume”
V
PV
PxV
Horizontal (e) (c) (e) (h)
Open End Up
(e) (c) (e)+(c) (k)
Open End Down
(e) (c) (e)- (c) (n)
Since we are using analogues for pressure & volume, the units don’t matter.
Conclusion and Discussion
• According to Boyle’s law, the PV values should all be identical. In the real world they will not be identical, but they should be very close.
• Analyze your results. While doing this you should find the percentage similarity between your largest and smallest result (smallest over largest x 100%). This can help you conclude if your results have supported Boyle’s Law or not.
• Discuss sources of error, and explain if they were significant in your results.
• Discuss the meaning of Boyle’s law as it relates to this activity.
Answers to Boyle’s Law Sheet
1. 1.00 L of a gas at standard temperature and pressure (101 kPa) is compressed to 473 mL. What is the new pressure of the gas?
formulaformula
PP11 • V • V11 =P =P22 • V • V22
KnownKnown
PP11= 101 kPa= 101 kPa
VV11= 1.00x10= 1.00x1033 mL mL
PP22= = unknownunknown
VV22= 473 mL= 473 mL
101kPa • 1000 mL = 101kPa • 1000 mL = PP22 kPa • 473 mL kPa • 473 mL
PP22 = = 101•1000 101•1000 kPa•mL = 213.53 kPakPa•mL = 213.53 kPa
473 mL473 mL
Answer: the pressure will be about 214 Answer: the pressure will be about 214 kilopascalskilopascals
1 mark 1 mark
1 mark
1 mark
2. In a thermonuclear device the pressure of 0.050 L of gas reaches 4.0x108kPa. When the bomb casing explodes, the gas is released into the atmosphere where it reaches a pressure of 1.00x102kPa. What is the volume of the gas after the explosion?
KnownKnown
PP11= 4.0x10= 4.0x1088kPakPa
VV11= 0.050 L= 0.050 L
PP22= 1x10= 1x1022kPakPa
VV22=unknown=unknown
formulaformula
PP11 • V • V11 =P =P22 • V • V22
4.0x104.0x1088kPa • 0.050L = 1x10kPa • 0.050L = 1x1022kPa • kPa • VV22LL
VV22 = = 4x104x1088•0.05 •0.05 kPa•L = 2.00x10kPa•L = 2.00x1055 L L
1x101x1022kPakPaAnswer: there will be 2.00x10Answer: there will be 2.00x1055Litres (or 200 000(or 200 000LL)) of gas of gas
1 mark
1 mark
1 mark
1 mark
3. synthetic diamonds can be manufactured at pressures of 6.00x104 atm. If we took 2.00L of gas at 1.00 atm and compressed it to 6.00x104 atm, what would the volume be?
KnownKnown
PP11= 1.00 atm= 1.00 atm
VV11= 2.00 L= 2.00 L
PP22= 6.0x10= 6.0x1044 atm atm
VV22= = unknownunknown
FormulaFormula
PP11VV11=P=P22VV22
1.00•2.00 = 6.0•101.00•2.00 = 6.0•1044 • • VV22 VV22 = 2.00 ÷ 6.0x10 = 2.00 ÷ 6.0x1044
V2 = 3.33 x10-5 L
1 mark1 mark
1 mark
orP1=1.01x102kPa,
P2=6.06x106kPa.
The volume would be 3.33x10The volume would be 3.33x10-5-5 LitresLitres1 mark
4. Divers get the bends if they come up too fast because gas in their blood expands, forming bubbles in their blood. If a diver has 0.0500L of gas in his blood at a depth of 50m where the pressure is 5.00x103 kPa, then rises to the surface where the pressure is 1.00x102kPa, what will the volume of gas in his blood be? Do you think this will harm the diver?
KnownKnown
PP11=5.00x10=5.00x1033 kPa kPa
VV11=0.0500 L=0.0500 L
PP22= 1.00x10= 1.00x1022 kPa kPa
VV22= = UnknownUnknown
FormulaFormula
PP11VV11=P=P22VV22
5.0x105.0x1033kPakPa • 0.0500 • 0.0500LL = 1x10 = 1x1022kPakPa • • VV22LL
VV22 = = 5x105x1033•0.05 •0.05 kPa•L = 2.50 LkPa•L = 2.50 L
1x101x1022kPakPaThe sudden appearance of 2½ The sudden appearance of 2½ litreslitres of gas in the of gas in the
diver’s bloodstream could be quite deadly.diver’s bloodstream could be quite deadly.
1 mark 1 mark
1 mark
1 mark
Lesson 2.4.2Lesson 2.4.2Charles’ LawCharles’ LawLesson 2.4.2Lesson 2.4.2Charles’ LawCharles’ Law
The Relationship between Temperature The Relationship between Temperature and Volume.and Volume.
““Volume varies directly with Temperature”Volume varies directly with Temperature”
Next slide: Jacques CharlesNext slide: Jacques Charles
TV
Jacques Charles (1787)Jacques Charles (1787)
““The volume of a fixed mass of The volume of a fixed mass of gas is directly proportional to gas is directly proportional to its temperature (in kelvins) if its temperature (in kelvins) if the pressure on the gas is kept the pressure on the gas is kept constant”constant”Formula for Charles’ Law:Formula for Charles’ Law:– Where:Where:
VV11= volume before change= volume before change
TT11= temperature before change= temperature before change
VV22= volume after change= volume after change
TT22 = temperature after change = temperature after change2
2
1
1
T
V
T
V
Next slide: The EvidenceNext slide: The Evidence
Charles Law EvidenceCharles Law Evidence
Charles used cylinders and pistons to Charles used cylinders and pistons to study and graph the expansion of study and graph the expansion of gases in response to heat.gases in response to heat.
See the next two slides for diagrams See the next two slides for diagrams of his apparatus and graphs.of his apparatus and graphs.
Lord Kelvin (William Thompson) used Lord Kelvin (William Thompson) used one of Charles’ graphs to discover one of Charles’ graphs to discover the value of absolute zero.the value of absolute zero.
Next slide: Diagram of Cylinder & PistonNext slide: Diagram of Cylinder & Piston
Charles Law ExamplePistonPiston
CylinderCylinder
Trapped GasTrapped Gas
Next slide: Graph of Charles’ LawNext slide: Graph of Charles’ Law
Click Here for a simulated Click Here for a simulated internet experimentinternet experiment
Graph of Charles Law
00°C°C 100100°C°C 200200°C°C150150°C°C5050°C°C 250250°C°C
1L1L
2L2L
3L3L
4L4L
5L5L
6L6L
-250-250°C°C -200-200°C°C -150-150°C°C -100-100°C°C -50-50°C°C
-273-273°C°C
Expansion of an “Ideal” Gas
Expansion of an “Ideal” Gas
Expansion of most real gases 2
73
27
3°° CC
Next slide: ExampleNext slide: Example
Liquid stateLiquid state
Solid stateSolid state condensa
tion
condensa
tion
freeze
freeze
Charles discovered the direct
relationship
Lord Kelvin traced it back
to absolute zero.
ExampleExample
If 2 Litres of gas at 27If 2 Litres of gas at 27°C are heated in a cylinder, °C are heated in a cylinder, and the piston is allowed to rise so that pressure is and the piston is allowed to rise so that pressure is kept constant, how much space will the gas take up kept constant, how much space will the gas take up at 327°C?at 327°C?
Convert temperatures to kelvins: 27°C =300k, Convert temperatures to kelvins: 27°C =300k, 327°C = 600k327°C = 600k
Use Charles’ Law: (see below)Use Charles’ Law: (see below) Answer: 4 LitresAnswer: 4 Litres
k
Litresx
k
Litresso
T
V
T
V
600300
2:,
2
2
1
1
Next slide: Lesson 2.4 Gay Lussac’s LawNext slide: Lesson 2.4 Gay Lussac’s Law
Summary: Charles’ law• The volume of a gas is
directly proportional to its temperature
• Formula:• Graph: Boyle’s law is
usually represented by an direct relationship graph (straight line)
• Video1
2
2
1
1
T
V
T
V
Absolute zeroAbsolute zero 00°°C=273KC=273K TempTempVolu
me (
L)
Volu
me (
L)
TV
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 0.5 litres, what will be the volume of the balloon when it is fully cooled?
KnownT1=22˚C
T2=4˚C
V1=0.5 L
V2= unknown
Temperatures must be converted to kelvinTemperatures must be converted to kelvin
=295K=295K
=277K=277K
2
2
1
1
T
V
T
V
So:V2=V1 x T2 ÷ T1
V2=0.5L x 277K ÷ 295K
V2=0.469 L
The balloon will have a volume of 0.47 litres
multiply
divide
Although only the answers are shown here, in order to get full marks you need to show all steps of the solution!
2. The balloon will have a volume of 0.71 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.
3. The bag will have a volume of 285mL
4. The volume of air in my lungs will be 2.35 litres
Gay-Lussac’s LawGay-Lussac’s LawFor Temperature-Pressure changes.For Temperature-Pressure changes.
““Pressure varies directly with Temperature”Pressure varies directly with Temperature”
Lesson 2.4.3Lesson 2.4.3
Next slide:’Next slide:’
TP
Joseph Gay-Lussac (1802)Joseph Gay-Lussac (1802)
““The pressure of a gas is The pressure of a gas is directly proportional to directly proportional to the temperature (in the temperature (in kelvins) if the volume is kelvins) if the volume is kept constant.”kept constant.”
Formula for Gay-Lussac’s Formula for Gay-Lussac’s Law:Law:
2
2
1
1
T
P
T
P
Next slide:’Next slide:’
Born Born 6 December 1778 6 December 1778
Saint-Léonard-de-NoblatSaint-Léonard-de-Noblat
Died Died 9 May 1850 @9 May 1850 @Saint-Léonard-de-NoblatSaint-Léonard-de-Noblat
NationalityNationalityFrenchFrench
FieldsFieldsChemistryChemistry
Known forKnown forGay-Lussac's lawGay-Lussac's law
Gay-Lussac’s LawGay-Lussac’s Law
As the gas in a As the gas in a sealed container is sealed container is heated, the pressure heated, the pressure increases.increases.
For calculations, you For calculations, you must use Kelvin must use Kelvin temperatures:temperatures: K=K=°°C+273C+273
pressurepressure
ExampleExample A sealed can contains 310 mL of air A sealed can contains 310 mL of air
at room temperature (20at room temperature (20°C)°C) and an and an internal pressure of 100 kPa. If the internal pressure of 100 kPa. If the can is heated to 606 can is heated to 606 °C what will the °C what will the internal pressure be?internal pressure be?
K
x
K
kPa
879293
100
2
2
1
1
T
P
T
P multiply
x x = 87900 = 87900 ÷ 293÷ 293
xx = 300 = 300Next slide: T vs P graphNext slide: T vs P graph
KnownP1= 100kPa
V1=310 mL
T1=20˚C
P2=unknown
T2=606˚C
˚Celsius must be converted to kelvins20˚C = 293 K 606˚C = 879 K
Answer: the pressure Answer: the pressure will be 300 kPawill be 300 kPa
Remove irrelevant factRemove irrelevant fact
=293K =879K
divide
Formula:
Temperature & Pressure GraphTemperature & Pressure Graph
The graph of temperature in Kelvin vs. The graph of temperature in Kelvin vs. pressure in kilopascals is a straight line. pressure in kilopascals is a straight line. Like the temperature vs. volume graph, it Like the temperature vs. volume graph, it can be used to find the value of absolute can be used to find the value of absolute zero.zero.
Graph of Pressure-Temperature Graph of Pressure-Temperature RelationshipRelationship
(Gay-Lussac’s Law)(Gay-Lussac’s Law)
Temperature (K) Temperature (K) Pre
ssure
(kP
a)
Pre
ssure
(kP
a)
273K273KNext slide:’Next slide:’
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)
2
2
1
1
T
P
T
P
Absolute zeroAbsolute zero 00°°C=273KC=273K TempTempPre
ssure
Pre
ssure
Avogadro’s HypothesisAvogadro’s HypothesisFor amount of gas.For amount of gas.
““The volume of a gas is directly related to the The volume of a gas is directly related to the number of moles of gas”number of moles of gas”
Lesson 2.45Lesson 2.45
Next slide: Next slide: Lorenzo Romano Amedeo Carlo Avogadro di QuaregnaLorenzo Romano Amedeo Carlo Avogadro di Quaregna
nV
Lorenzo Romano Amedeo Carlo Lorenzo Romano Amedeo Carlo
Avogadro di QuaregnaAvogadro di Quaregna
““Equal volumes of gas at Equal volumes of gas at the same temperature the same temperature and pressure contain and pressure contain the same number of the same number of moles of particles.”moles of particles.” Amedeo AvogadroAmedeo Avogadro
Born: August 9, 1776 Born: August 9, 1776
Turin, ItalyTurin, Italy
Died: July 9, 1856Died: July 9, 1856
Field: PhysicsField: Physics
University of TurinUniversity of Turin
Known for Avogadro’s Known for Avogadro’s hypothesis, hypothesis, Avogadro’s number.Avogadro’s number.
You already know most of the facts that You already know most of the facts that relate to Avogadro’s hypothesis:relate to Avogadro’s hypothesis:– That a mole contains a certain number of That a mole contains a certain number of
particles (6.02 x 10particles (6.02 x 102323))– That a mole of gas at standard temperature and That a mole of gas at standard temperature and
pressure will occupy 22.4 Litrespressure will occupy 22.4 Litres The only new thing here, is how changing The only new thing here, is how changing
the amount of gas present will affect the amount of gas present will affect pressure or volume.pressure or volume.– Increasing the amount of gas present will Increasing the amount of gas present will
increase the volume of a gas (if it increase the volume of a gas (if it cancan expand), expand), – Increasing the amount of gas present will Increasing the amount of gas present will
increase the pressure of a gas (if it increase the pressure of a gas (if it is unable is unable to to expand).expand).
It’s mostly common sense…It’s mostly common sense…
If you pump more gas into a If you pump more gas into a balloon, and allow it to expand balloon, and allow it to expand freely, the volume of the balloon freely, the volume of the balloon will increase.will increase.
If you pump more gas into a If you pump more gas into a container that can’t expand, then container that can’t expand, then the pressure inside the container the pressure inside the container will increase.will increase.
Mathematical statements of Mathematical statements of Avogadro’s HypothesisAvogadro’s Hypothesis
2
2
1
1
n
P
n
P
2
2
1
1
n
V
n
V
WhereWhere
VV11 = volume before = volume before
VV22 = volume after = volume after
PP11=pressure before=pressure before
PP22=pressure after=pressure after
nn1 1 = #moles before= #moles before
nn22 = #moles after = #moles after
Reference & Assignment
• Reference: Textbook pp. 226 to 231
• Textbook Assignment: page 241 # 14 – 24– Do these in your assignments folder
Jump to next lesson: The combined gas lawsJump to next lesson: The combined gas laws
Next slide: answers to exercisesNext slide: answers to exercises
1. The Combined Gas Law1. The Combined Gas LawA.K.A. General Gas LawA.K.A. General Gas Law
or Universal Gas Lawor Universal Gas Law
2. The Ideal Gas Law2. The Ideal Gas Law
Created by combining Boyle’s Law, Created by combining Boyle’s Law, Charles’ Law and Gay-Lussac’s Law, Charles’ Law and Gay-Lussac’s Law, and adding Avogadro’s mole conceptand adding Avogadro’s mole concept
Next slide:Next slide:
Lesson 2.5Lesson 2.5
The Combined Gas Law Formula:The Combined Gas Law Formula:
22
22
11
11
Tn
VP
Tn
VP
Next slide: Ideal Gas LawNext slide: Ideal Gas Law
#moles before#moles before #moles after#moles after
The neat thing about the combined gas law is that The neat thing about the combined gas law is that it can replace the three original gas laws.it can replace the three original gas laws.
Just cross out or cover the parts that don’t change, Just cross out or cover the parts that don’t change, and you have the other laws:and you have the other laws:
22
22
11
11
Tn
VP
Tn
VP
Most of the time, the Most of the time, the number of moles stays number of moles stays the same, so you can the same, so you can remove moles from the remove moles from the equation.equation.
If the temperature is If the temperature is constant, then you have constant, then you have Boyle’s law.Boyle’s law.
If, instead, pressure If, instead, pressure remains constant, you remains constant, you have Charles’ Lawhave Charles’ Law
And finally, if the And finally, if the volume stays constant, volume stays constant, then you have Gay-then you have Gay-Lussac’s LawLussac’s Law
The Ideal Gas LawThe Ideal Gas Law
The The Ideal Gas Law Ideal Gas Law is derived from the is derived from the Combined Gas LawCombined Gas Law in several in several mathematical steps. mathematical steps. First, start with the combined gas law, First, start with the combined gas law, including P, V, T, and the amount of gas in including P, V, T, and the amount of gas in moles (n) .moles (n) .
Next slide:Next slide:
22
22
11
11
Tn
VP
Tn
VP
Remember Standard Temperature & PressureRemember Standard Temperature & Pressure(STP)(STP)
Standard Temperature is 0Standard Temperature is 0°°C (or more to C (or more to the point, 273K)the point, 273K)
Standard Pressure is 101.3 kPa (one Standard Pressure is 101.3 kPa (one atmospheric pressure at sea level)atmospheric pressure at sea level)
At STP one mole of an ideal gas occupies At STP one mole of an ideal gas occupies exactly 22.4 Litresexactly 22.4 Litres
The Ideal Gas Law: Calculating the The Ideal Gas Law: Calculating the Ideal Gas Constant.Ideal Gas Constant.
We are going to We are going to calculate a new constant calculate a new constant by substituting in values by substituting in values for Pfor P22, V, V22, T, T22 and n and n22
At STP we know all the At STP we know all the conditions of the gas.conditions of the gas.
Substitute and solve to Substitute and solve to give us a constantgive us a constant
Kmol
LkPa
Tn
VP
2731
4.223.101
11
11
molKkPaLTn
VP /31.8
11
11
Next slide: R-- The Ideal Gas ConstantNext slide: R-- The Ideal Gas Constant
22
22
11
11
Tn
VP
Tn
VP
The Ideal Gas ConstantThe Ideal Gas Constantis the proportionality constant that makes the ideal gas law workis the proportionality constant that makes the ideal gas law work
The Ideal Gas Constant has the symbol The Ideal Gas Constant has the symbol RR
R=8.31R=8.31 LL·· kPa / K kPa / K··molmol The Ideal Gas constant is 8.31 litre-The Ideal Gas constant is 8.31 litre-
kilopascals per kelvin-mole.kilopascals per kelvin-mole.
Next slide: Ideal Gas FormulaNext slide: Ideal Gas Formula
So, if So, if
Then, by a bit of algebra: PThen, by a bit of algebra: P11VV11=n=n11RTRT11
Since we are only using one set of Since we are only using one set of subscripts here, we might as well remove subscripts here, we might as well remove them: PV=nRTthem: PV=nRT
RTn
VP
11
11
The Ideal Gas LawThe Ideal Gas LawFormulaFormula
nRTPV Where P=Pressure (in kPa) Where P=Pressure (in kPa)
V=Volume (in Litres)V=Volume (in Litres)
n= number of molesn= number of moles
R= Ideal Gas constant (8.31 R= Ideal Gas constant (8.31 LLkPa/KkPa/Kmolmol))
T = Temperature (in Kelvins)T = Temperature (in Kelvins)Next slide: Sample ProblemNext slide: Sample Problem
The Ideal gas law is best to use when you The Ideal gas law is best to use when you don’t need a “before and after” situation.don’t need a “before and after” situation.
Just one set of data (one volume, one Just one set of data (one volume, one pressure, one temperature, one amount of pressure, one temperature, one amount of gas)gas)
If you know three of the data, you can find If you know three of the data, you can find the missing one.the missing one.
Sample ProblemSample Problem 8.0 g of oxygen gas is at a pressure of 8.0 g of oxygen gas is at a pressure of
2.0x102.0x1022 kPa kPa (ie: 200KPa)(ie: 200KPa) and a temperature of and a temperature of 15 15°°C. How many litres of oxygen are C. How many litres of oxygen are there? there? (assume 2 significant digits)(assume 2 significant digits)
Formula: Formula: PV = nRTPV = nRT Variables: Variables: P=P=20200 0 kPakPa V=V=?? (our unknown)= (our unknown)= xx n= 8.0n= 8.0gg ÷÷ 32 32 g/molg/mol = =0.25 0.25
molmol R=R=8.31 8.31 LL·kPa/K·mol ·kPa/K·mol (ideal gas (ideal gas
constant)constant)
T= 15T= 15°°C + 273 = C + 273 = 288288KK 200 200 xx = (0.25)(8.31)(288) , = (0.25)(8.31)(288) , thereforetherefore xx= (0.25)(8.31)(288) = (0.25)(8.31)(288) ÷ ÷ 200=200=2.92.99 L9 L There are 3.0 L of oxygen There are 3.0 L of oxygen (rounded to 2 S.D.)(rounded to 2 S.D.)Next slide: Ideal vs. RealNext slide: Ideal vs. Real
Sample problemSample problem
molmolg
g
M
mn 25.0
/32
8
8.0 g of oxygen gas is at a pressure of 2.0x102 kPa (ie: 8.0 g of oxygen gas is at a pressure of 2.0x102 kPa (ie: 200KPa) and a temperature of 15200KPa) and a temperature of 15°°C. How many litres C. How many litres of oxygen are there? (assume 2 significant digits)of oxygen are there? (assume 2 significant digits)
KnownKnown
P=P=20200 0 kPakPa
V=V=unknown = unknown = XX
n= not givenn= not given
R=R=8.31 8.31 LL·kPa/K·mol·kPa/K·mol
T= 15T= 15°°C + 273 = C + 273 = 288288KK
------
m (Om (O22) = 8g) = 8g
M (OM (O22) = 32.0 g/mol) = 32.0 g/mol
0.25 0.25 molmol
Temperature has been converted to Temperature has been converted to kelvinskelvins
Calculate the value of n using the mole Calculate the value of n using the mole formula:formula:
nRTPV 200 200 xx = (0.25)(8.31)(288) , = (0.25)(8.31)(288) , thereforetherefore
xx= (0.25)(8.31)(288) = (0.25)(8.31)(288) ÷ ÷ 200=200=2.92.99 L9 L
There are 3.0 L of oxygen There are 3.0 L of oxygen (rounded to 2 S.D.)(rounded to 2 S.D.)
Ideal vs. Real GasesIdeal vs. Real GasesThe gas laws were worked out by assuming that gases are The gas laws were worked out by assuming that gases are idealideal, that , that is, that they obey the gas laws at all temperatures and pressures. In 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 reality gases will condense or solidify at low temperatures and/or high pressures, at which point they stop behaving like gases. Also, pressures, at which point they stop behaving like gases. Also, attraction forces between molecules may cause a gas’ behavior to vary attraction forces between molecules may cause a gas’ behavior to vary slightly from ideal.slightly from ideal.
A gas is ideal if its particles are extremely small (true for most gases), 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 the distance between particles is relatively large (true for most gases near room temperature) and there are no forces of attraction between near room temperature) and there are no forces of attraction between the particles (not always true)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: SummaryNext slide: Summary
Testing if a gas is idealTesting if a gas is ideal
If you know all the important properties of a If you know all the important properties of a gas (its volume, pressure, temperature in gas (its volume, pressure, temperature in kelvin, and the number of moles) substitute kelvin, and the number of moles) substitute them into the ideal gas law, but don’t put in the them into the ideal gas law, but don’t put in the value of R. Instead, calculate to see if the value of R. Instead, calculate to see if the value of R is close to 8.31, if so, the gas is value of R is close to 8.31, if so, the gas is ideal, or very nearly so. If the calculated value ideal, or very nearly so. If the calculated value of R is quite different from 8.31 then the gas is of R is quite different from 8.31 then the gas is far from ideal.far from ideal.
ExampleExample
A sample of gas contains 1 mole of particles A sample of gas contains 1 mole of particles and occupies 25L., its pressure 100kPa is and and occupies 25L., its pressure 100kPa is and its temperature is 27its temperature is 27°°C. Is the gas ideal, nearly C. Is the gas ideal, nearly ideal, or not even close to ideal?ideal, or not even close to ideal?
Convert to kelvins: Convert to kelvins: 2727°°C+273=300KC+273=300K PV=nRTPV=nRT (ideal gas law formula)(ideal gas law formula) 100100kPakPa2525LL==11molmolRR300300KK, so…, so… R=R=100100kPakPa2525LL÷÷((300300KK11molmol)) R=R=8.338.33kPakPaL/KL/Kmolmol (actual value: R=8.31) (actual value: R=8.31) so the gas is very close to ideal (but not so the gas is very close to ideal (but not
perfectly ideal).perfectly ideal).
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: SummaryOriginal gas laws– Boyle’s Law: – Charles’ Law:– Gay-Lussac’s Law:
– Combined gas law:
– Ideal gas law:
– The ideal gas constant:
22
22
11
11
Tn
VP
Tn
VP
nRTPV
VP
1
2
2
1
1
T
V
T
V
2211 VPVP 2
2
1
1
T
P
T
P
TV TP
R=8.31 Lkpa/Kmol
Video
• Simple gas laws
References and Assignments
• References: – Textbook Chapter 10: pp. 221 to 240– Student Study Guide pp. 2-4 to 2-11
• Textbook: page 241 # 25 to 30– Do these in your assignments folder.
Extra practice:• Study guide: pp 2.12 to 2.17 # 1 to 22
– There is an answer key in the back for these– Do these on your own as review
Exercise Answers
14) The pressure will double, since there is twice as much gas occupying the same space. (I answered this using logic and Avagadro’s hypothesis rather than math. It stands to reason that twice as much gas in the same space will increase the pressure.)
15) The pressure will be four times as high, since the volume is one quarter what it was before: P1V1 = P2V2 so… P1V1 = 4P1 x ¼V1 (again, although you can do it with math, logic works better)
16) The pressure will be one third as great as it was before, since there is three times the volume: P1V1 = P2V2, so = 1/3 P1 x 3V1
17) The gas cannot expand, so it exerts force on its container. As the temperature increases, the gas particles move faster, hitting the container sides more frequently and with more force. This causes greater pressure. You can also explain this using Gay-Lussac’s law; P1/T1 = P2/T2
18) Make sure you use the KELVIN temperatures. The formula is P1/T1 = P2/T2 or 300 kpa/300K = xkPa/100K, so the pressure will be 100 kPa
19) An ideal gas obeys the gas laws at all temperatures and pressures (no real gas is perfectly ideal. More ideal properties will be discussed in the next section).
20) PCO2 = 3.33 kPa, since all the partial pressures will add up to the total pressure (3.33+23.3+6.67=33.3)
21) Use Boyle’s law: P1V1=P2V2, therefore 91.2kpa4.0L=20.3kpaxL so therefore x=91.2x4÷20.3 the new volume is 17.9 L
22) Use Boyle’s law: P1V1=P2V2 ,so x=100kPa6L÷25.3kPa. The new volume will be 23.7L
• 23) Use Charles’Law: V1/T1=V2/T2, convert the temperature from °CK, so -50°C223K and 100 °C373K so… 5L/223K = x/373K so… x=5373÷223. The new volume will be about 8.36 L
• 24) Use Gay-Lussack’s law: P1/T1=P2/T2, don’t forget to change 27°C300K. So… 200kPa/300K=223kPa/x. The new temperature will be 61.5°C (converted from 334.5K)
ANSWERS
25) The combined gas laws:(this answer is straight from the lesson)
26) Convert the temperatures to kelvin, set up equation, leaving out n1 and n2 (moles don’t change), cross multiply:
Answer:
The new pressure is 127.8 kPa
22
22
11
11
Tn
VP
Tn
VP
K
LP
K
LkPa
373
7
223
5107 2
Multiply these togetherMultiply these together
Then divide by theseThen divide by these
27) Data given: need to find: m=12g(O2) M(O2)
P=52.7kPa V=x LR=8.31LkPa/Kmol n in molT= 25°C T in kelvin
Find the number of moles of O2: n=m/MM(O2)=32g/mol so: 12g ÷ 32g/mol = 0.375mol. Convert CK, 25°C+273=298K
formula: PV=nRTso: 52.7kPaxL=0.375mol8.31Lk•Pa/Kmol298K
so: x = (0.375 mol 8.31L•kPa 298 K) • __1_ K mol 52.7 kpa
Answer: The volume will be about 17.6 L
3232g/molg/mol
0.3750.375molmol298298KK
#28-30, answers (with brief explanation)(see me at lunch if you need more explanation)
28) Litres at STPa) 56 L b) 6.72 L c) 7.84 L(remember: each mole of gas @STP=22.4L)
29) Answer: The pressure will be 1714 kPa(use the formula PV=nRT)
30) Answer: The volume will be 16.8 L (use the formula PV=nRT)
Lesson 2.6Lesson 2.6Other laws dealing with gases:Other laws dealing with gases:
Dalton’s Law (partial pressure)Dalton’s Law (partial pressure)Graham’s Law (diffusion)Graham’s Law (diffusion)
Avogadro’s Hypothesis (moles of gas)Avogadro’s Hypothesis (moles of gas)
DaltonDalton’’s Laws LawThe Law of Partial PressuresThe Law of Partial Pressures
�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.
�P total = P1 + P2 + ...�The total pressure exerted by a mixture of gases is
equal to the sum of the partial pressures.�101.3 kPa (Pair) = 79.1 kPa (PN2)+ 21.2 kPa (PO2) + 1.0 kPa(P3)
Next slide:Next slide:
Uses of Dalton’s Law Uses of Dalton’s Law
In the 1960s NASA used the law of partial In the 1960s NASA used the law of partial pressures to reduce the launch weight of their pressures to reduce the launch weight of their spacecraft. Instead of using air at 101 kPa, they spacecraft. Instead of using air at 101 kPa, they used pure oxygen at 20kPa.used pure oxygen at 20kPa.
Breathing low-pressure pure oxygen gave the Breathing low-pressure pure oxygen gave the astronauts just as much “partial pressure” of astronauts just as much “partial pressure” of oxygen as in normal air.oxygen as in normal air.
Lower pressure spacecraft reduced the chances of Lower pressure spacecraft reduced the chances of explosive decompression, and it also meant explosive decompression, and it also meant their spacecraft didn’t have to be as strong or their spacecraft didn’t have to be as strong or heavy as those of the Russians (who used heavy as those of the Russians (who used normal air).. This is one of the main reasons the normal air).. This is one of the main reasons the Americans beat the Russians to the moon.Americans beat the Russians to the moon.
StoryStory
Don’t copy
Don’t copy
Carelessness with pure oxygen, however, Carelessness with pure oxygen, however, lead to the first major tragedy of the lead to the first major tragedy of the American space program…American space program…
At 20 kPa, pure oxygen is very safe to At 20 kPa, pure oxygen is very safe to handle, but at 101 kPa pure oxygen handle, but at 101 kPa pure oxygen makes everything around it extremely makes everything around it extremely flammable, and capable of burning five flammable, and capable of burning five times faster than normal.times faster than normal.
On January 27, 1967, during a pre-launch On January 27, 1967, during a pre-launch training exercise, the spacecraft Apollo-1 training exercise, the spacecraft Apollo-1 caught fire. The fire spread instantly, and caught fire. The fire spread instantly, and the crew died before they could open the the crew died before they could open the hatch. hatch.
Carelessness with pure oxygen, however, Carelessness with pure oxygen, however, lead to the first major tragedy of the lead to the first major tragedy of the American space program…American space program…
At 20 kPa, pure oxygen is very safe to At 20 kPa, pure oxygen is very safe to handle, but at 101 kPa pure oxygen handle, but at 101 kPa pure oxygen makes everything around it extremely makes everything around it extremely flammable, and capable of burning five flammable, and capable of burning five times faster than normal.times faster than normal.
On January 27, 1967, during a pre-launch On January 27, 1967, during a pre-launch training exercise, the spacecraft Apollo-1 training exercise, the spacecraft Apollo-1 caught fire. The fire spread instantly, and caught fire. The fire spread instantly, and the crew died before they could open the the crew died before they could open the hatch. hatch.
Gus Grissom, Ed White, Roger ChaffeeGus Grissom, Ed White, Roger ChaffeeGus Grissom, Ed White, Roger ChaffeeGus Grissom, Ed White, Roger Chaffee
Crew of Apollo 1Crew of Apollo 1Crew of Apollo 1Crew of Apollo 1
Avogadro’s HypothesisAvogadro’s Hypothesis
““At the same temperature and At the same temperature and pressure, equal volumes of gases pressure, equal volumes of gases contain the same number of contain the same number of particles (molecules)”particles (molecules)”
You already know some facts that came from You already know some facts that came from Avogadro’s hypothesis:Avogadro’s hypothesis:
Avogadro’s Number: Avogadro’s Number:
6.02 x 106.02 x 102323 particles per mole particles per mole
We now know that at STP a mole of gas will We now know that at STP a mole of gas will occupy 22.4 Loccupy 22.4 L
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
• Avogadro’s hypothesis– A mole of gas occupies 22.4L at STP and
contains 6.02x1023 particles
1
2
2
1
M
M
Rate
Rate
ExercisesAssignment, do in your assignment folder:
• Page 241 # 31-34– (If you have not shown me the previously
assigned exercises; p241 #14-30; hand them in at the same time.)
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 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.
Energy of a Energy of a particle:particle:
KE = ½ KE = ½ mV mV 22
Pressure is the Pressure is the result of result of particles particles colliding with colliding with the container the container walls.walls.
P = P = F /AF /A
Gases are made of particlesGases are made of particlesParticles move randomly!Particles move randomly!
PressurePressure
Assigned Activities
• References: – Read Textbook pp.197-203
• Practice problems: – Textbook: p199 #1-3– Student study guide: pp. 2-19 to 2-20(practice problems are for self-correction)
• Assignments (to be collected in your folder):– Page 241: all questions from 25 to 34– Handout #1: “combined gas law” #52-58– Handout #2: “gases & gas laws” 5 questions
(on the back.)
Answers (sheet 1)• 52: The volume of gas will be 36.5 L
• 53: The temperature will be 908K or 635C
• 54: The volume will be 250 mL or 0.25L
• 55: The pressure will be 251 kPa
• 56: The pressure will stay the same
• 57: The pressure will be 42.2 kPa
• 58: The volume will be 10.2 L
Answers (sheet 2)
• 1: The volume is about 32.5 L
• 2: The mass is about 1.53 x 10-7 g
• 3: The pressure is about 61909 kPa• 4: The pressure will increase by 168 kPa
(tricky: most students say 268kPa, but that’s what it ends at, NOT how much it changes!)
• 5: The total pressure is about 172kPa
• The end of module 2
