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The Gas LawsThe Gas Laws

Boyle, Charles, Boyle, Charles, CombinedCombined, and , and IdealIdeal

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Kinetic TheoryKinetic Theory

Explains the states of matter in Explains the states of matter in terms ofterms of molecular compositionmolecular composition SpacingSpacing speedspeed

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According to the theory...According to the theory...

1. Matter composed of small particles1. Matter composed of small particles A. A. chemical properties-chemical properties- depend on depend on a. a. compositioncomposition b. b. typestypes of elements / molecules present. of elements / molecules present. B. B. physical properties-physical properties- depend on depend on a. a. forcesforces that particles exert on each that particles exert on each

otherother b. b. distancedistance separating the particles. separating the particles. 2. Particles are in constant motion.2. Particles are in constant motion. Degree of motion depends on Degree of motion depends on temperature.temperature. 3. 3. Total kinetic energy Total kinetic energy of colliding particles remains of colliding particles remains

constant.constant. elastic collisionselastic collisions - as indiv. particles - as indiv. particles

collide collide some gain Ek and some lose Ek. some gain Ek and some lose Ek. Overall Ek is constant.Overall Ek is constant.

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States States of of

MatteMatterr

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SolidsSolids

appear to vibrate around a fixed point appear to vibrate around a fixed point (Extremely short free mean path)(Extremely short free mean path)

have definite shapehave definite shape “ “ “ “ volumevolume noncompressablenoncompressable veryvery slow rate of diffusion slow rate of diffusion crystalline or amorphous in naturecrystalline or amorphous in nature

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LiquidsLiquids

particles are closer than those of particles are closer than those of gasesgases

forces of attraction between forces of attraction between particles stronger than those of particles stronger than those of gases, and weaker than those of gases, and weaker than those of solids.solids.

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GasesGases

The Kinetic Theory was developed by The Kinetic Theory was developed by studying an studying an ideal gasideal gas, , a mathematically a mathematically perfect gasperfect gas.. [Particles are treated as 1) [Particles are treated as 1) point point massesmasses; as having no volume, and 2) as ; as having no volume, and 2) as exerting no attractive forces on each other.exerting no attractive forces on each other.

Space occupied by gas depends on Space occupied by gas depends on temperaturetemperature and and pressure. pressure.

When describing a quantity of a gas When describing a quantity of a gas temperature and pressure MUST be specified.temperature and pressure MUST be specified.

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Standard Temperature & Standard Temperature & Pressure Pressure S.T.P.S.T.P.

Standard Standard TemperatureTemperature

00oo C C 273 K273 K

Standard PressureStandard Pressure 760 mm Hg760 mm Hg 760 n/m760 n/m22

760 Torr760 Torr 101.325 kPa101.325 kPa 1 atm1 atm

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Properties of GasesProperties of Gases

Particles in a gas are Particles in a gas are in rapid, constant in rapid, constant motion.motion.

Gas particles travel Gas particles travel in straight-line paths.in straight-line paths.

Gas particles fill Gas particles fill containers. containers.

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Properties of GasesProperties of Gases

Exerts PressureExerts Pressureincreases / decreases with a rise / fall increases / decreases with a rise / fall

in temperaturein temperature Have Low densityHave Low density

1000x less dense than liquid 1000x less dense than liquid counterpartcounterpart

Undergo DiffusionUndergo Diffusionspread out from area of spread out from area of greater to greater to

lesserlesser concentration until uniform concentration until uniform spacing existsspacing exists

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Properties of GasesProperties of Gases

Atmosphere is Atmosphere is denser as you denser as you move closer to move closer to Earth’s surface.Earth’s surface.

The weight of The weight of atmospheric gases atmospheric gases at any elevation at any elevation compress the compress the gases below. gases below. Very Dense

Less Dense

Compression

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At room temperature At room temperature gases...gases...

are molecularare molecular move independently of each othermove independently of each other travel at high speedstravel at high speeds

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At 0At 0ooCC travel at about 1000 m/sec.travel at about 1000 m/sec.

Goal to goal in .11 secGoal to goal in .11 sec undergo elastic collisionsundergo elastic collisions

alters individual speeds, but not overall alters individual speeds, but not overall EEkk..

collide nearly 5 BILLION times per collide nearly 5 BILLION times per SECOND!SECOND!

have different rates of diffusionhave different rates of diffusion Less concentrated - diffusion rate Less concentrated - diffusion rate More concentrated - diffusion rate More concentrated - diffusion rate

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Diffusion rate depends on...Diffusion rate depends on...

speed of gasesspeed of gases size of the moleculessize of the molecules attractive forces that may effect the attractive forces that may effect the

moleculesmolecules At the same temperature:At the same temperature:

the the averageaverage kinetic energy of all kinetic energy of all molecules is the same.molecules is the same.

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GAS and PRESSUREGAS and PRESSURE

Gas molecules exert pressure by hitting Gas molecules exert pressure by hitting against the side of its container.against the side of its container.

Degree of pressure dependent on:Degree of pressure dependent on: 1. # of gas particles present*1. # of gas particles present* 2. volume [size] of the container*2. volume [size] of the container* 3. average Ek of the molecules *3. average Ek of the molecules * [temperature][temperature] Changing any of these conditions changes Changing any of these conditions changes

the pressure.the pressure.

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A A barometerbarometer is a device that is used is a device that is used to measure atmospheric pressure.to measure atmospheric pressure.

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GAS and PRESSUREGAS and PRESSURE

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VOLUME and PRESSUREVOLUME and PRESSURE

To test only ONE variable at a time, To test only ONE variable at a time, the following must be held constant.the following must be held constant.

1. # of gas particles present1. # of gas particles present 2. average Ek of the molecules2. average Ek of the molecules

[temperature][temperature]Boyle’s Law animation

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VOLUME and PRESSUREVOLUME and PRESSURE

2020

We can see that pressure is We can see that pressure is inversely proportional to inversely proportional to

volumevolumeP P 11

VVPV = kPV = k

PP11VV11 = k = k andand P P22VV22 = k = k

PP11VV11 = P = P22VV22

ororVV11 = = PP22

VV22 P P1 1 Boyle’s Boyle’s LawLaw

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How are the pressure, volume, and How are the pressure, volume, and temperature of a gas related?temperature of a gas related?

Boyle’s lawBoyle’s law states that for a given states that for a given mass of gas at constant temperature, mass of gas at constant temperature, the volume of the gas varies inversely the volume of the gas varies inversely with pressure.with pressure.

As pressure decreases, volume As pressure decreases, volume increasesincreases

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DALTON’S LAW of PARTIAL DALTON’S LAW of PARTIAL PRESSUREPRESSURE

The pressure of each gas in a mixture is The pressure of each gas in a mixture is called the called the partial pressurepartial pressure of that of that gas.gas.

John Dalton, the English chemist who John Dalton, the English chemist who proposed the atomic theory, discovered proposed the atomic theory, discovered that the pressure exerted by each gas that the pressure exerted by each gas in a mixture is independent of that in a mixture is independent of that exerted by other gases present. exerted by other gases present.

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Particle Model for a Gas Collected Over WaterParticle Model for a Gas Collected Over Water

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DALTON’S LAW of PARTIAL DALTON’S LAW of PARTIAL PRESSUREPRESSURE

Gases produced in the laboratory are often Gases produced in the laboratory are often collected over water. The gas produced by the collected over water. The gas produced by the reaction displaces the water in the reaction bottle.reaction displaces the water in the reaction bottle.

Dalton’s law of partial pressures can be applied to Dalton’s law of partial pressures can be applied to calculate the pressures of gases collected in this calculate the pressures of gases collected in this way. way.

Water molecules at the liquid surface evaporate Water molecules at the liquid surface evaporate and mix with the gas molecules. Water vapor, like and mix with the gas molecules. Water vapor, like other gases, exerts a pressure known as other gases, exerts a pressure known as vapor vapor pressure.pressure.

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DALTON’S LAW of PARTIAL DALTON’S LAW of PARTIAL PRESSUREPRESSURE

HgHg originally used to measure the originally used to measure the pressure of gasespressure of gases

Now known to be a carcinogenNow known to be a carcinogen ‘‘Mad as a hatter’Mad as a hatter’

HH22O replaced Hg O replaced Hg several problems existseveral problems exist Density is 13.6 x greater than mercuryDensity is 13.6 x greater than mercury Much more volatile. Much more volatile. Evaporates much faster.Evaporates much faster. Gases to be tested polluted with water’s vapor Gases to be tested polluted with water’s vapor

pressure.pressure.

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DALTON’S LAW of PARTIAL DALTON’S LAW of PARTIAL PRESSUREPRESSURE

In a mixture of gases [G1, G2, G3, ...] In a mixture of gases [G1, G2, G3, ...] the TOTAL pressure of the gas mixture the TOTAL pressure of the gas mixture is the SUM of the pressures of the is the SUM of the pressures of the individual gas pressures.individual gas pressures. Total Pressure = PressureGTotal Pressure = PressureG11 + PressureG + PressureG22 + Pressure G + Pressure G33 + +

... ...

If one of these gases is waterIf one of these gases is water Total Pressure = PressureGTotal Pressure = PressureG11 + PressureG + PressureG22 + Pressure + Pressure

Water + ...Water + ...

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To ‘dry out’ a gasTo ‘dry out’ a gas

Total Pressure = PressureGTotal Pressure = PressureG11 + PressureG + PressureG22 + Pressure + Pressure Water + ...Water + ...

- Pressure Water - Pressure Water

Pressure DRY gas = PressureGPressure DRY gas = PressureG11 + PressureG + PressureG22 + ... + ...

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Application of Dalton’s LawApplication of Dalton’s Law

A gas is collected A gas is collected by water displacementby water displacement. . It occupies 593 cm3 of space at 45 oC. It occupies 593 cm3 of space at 45 oC. The atmospheric [total] pressure is 101.1 The atmospheric [total] pressure is 101.1 kPa. What volume will the kPa. What volume will the drydry gas gas occupy at 45 oC and standard pressure?occupy at 45 oC and standard pressure?

V1 = 593 cm3 V1 = 593 cm3 V2 = ?V2 = ? P1[wet] = 101.1 kPaP1[wet] = 101.1 kPa P2 = 101.325 kPaP2 = 101.325 kPa

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PP11VV11 = P = P22VV22

[101.1kPa*][593 cm3] = [101.325 kPa] V[101.1kPa*][593 cm3] = [101.325 kPa] V22

At 45 At 45 ooC, PC, PH2OH2O = 71.9 mm Hg = 71.9 mm Hg Since 760 mm Hg = 101.325 kPaSince 760 mm Hg = 101.325 kPa

101.325 kPa101.325 kPa = ___ = ___x___x___ 760 mm Hg 71.9 mm Hg760 mm Hg 71.9 mm Hg 9.6 kPa = x9.6 kPa = x 101.1 kPa - 9.6 kPa = 91.5 kPa 101.1 kPa - 9.6 kPa = 91.5 kPa Pressure of the dry Pressure of the dry

gasgas

[91.5 kPa][593 cm3] = [101.325 kPa] V[91.5 kPa][593 cm3] = [101.325 kPa] V22 [91.5 kPa][593 cm3][91.5 kPa][593 cm3] = V = V22 [101.325 kPa][101.325 kPa]

535.5 cm3 = V535.5 cm3 = V22

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Example BExample B

Oxygen gas from the decomposition Oxygen gas from the decomposition of potassium chlorate, KClOof potassium chlorate, KClO33, was , was collected by water displacement. collected by water displacement. The barometric pressure and the The barometric pressure and the temperature during the experiment temperature during the experiment were 731.0 torr and 20.0°C. were 731.0 torr and 20.0°C. respectively. What was the partial respectively. What was the partial pressure of the oxygen collected?pressure of the oxygen collected?

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SolutionSolution

Given:Given: PPTT = = PPatmatm = 731.0 torr = 731.0 torr PPH2OH2O = 17.5 torr (vapor pressure of = 17.5 torr (vapor pressure of

water at 20.0°C) water at 20.0°C)

PPatmatm = P = PO2O2 + P + PH2OH2O

OP 2 731.0 torr 17. 7135 to .5 rr torr

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Diffusion and EffusionDiffusion and Effusion

The constant motion of gas molecules causes them to spread out to fill any container they are in.

The gradual mixing of two or more gases due to their spontaneous, random motion is known as diffusion.

Effusion is the process whereby the molecules of a gas confined in a container randomly pass through a tiny opening in the container.

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Diffusion and EffusionDiffusion and Effusion

Click here to view Click here to view diffusion animation

Click here to view Click here to view effusion animation

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Graham’s Law of EffusionGraham’s Law of Effusion

Rates of effusion and diffusion depend on the relative velocities of gas molecules. The velocity of a gas varies inversely with the square root of its molar mass.

Recall that the average kinetic energy of the molecules in any gas depends only the temperature.

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Graham’s Law of EffusionGraham’s Law of Effusion

• From the equation relating the kinetic energy of two From the equation relating the kinetic energy of two different gases at the same conditions, one can different gases at the same conditions, one can derive an derive an equationequation relating the rates of effuses of two gases with relating the rates of effuses of two gases with their molecular mass:their molecular mass:

AverageAverage kinetic energy = kinetic energy = temperaturetemperature

EEkk = 1/2mv = 1/2mv22

Molecule 1 has a EMolecule 1 has a Ekk1= 1/2mv1= 1/2mv22 Molecule 2 has a EMolecule 2 has a Ekk2 =1/2mv2 =1/2mv22

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Graham’s Law of EffusionGraham’s Law of Effusion

At the same temperatureAt the same temperatureEEk1k1= E= Ek2k2

1/2m1/2m11vv22 = 1/2m = 1/2m22vv22

mm11vv22 = m = m22vv22

mm11 = = vv2222

mm22 v v1122

√√mm11 = = vv22

mm22 v v11

OrOr√√mm11 = = rate of effusion of 2 rate of effusion of 2

mm22 = rate of effusion of 1 = rate of effusion of 1

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What are the relative effusion What are the relative effusion rates of krypton (Kr) and rates of krypton (Kr) and

bromine (Brbromine (Br22)?)? mmKrKr = = vvBr2Br2

mmBr2Br2 v vKrKr

8484 = =

160 160 .72 .72 = = vvBr2Br2

1 v1 vKrKr

Therefore, BrTherefore, Br22 diffuses slower than Kr, at diffuses slower than Kr, at about 72% of Kr’s speed.about 72% of Kr’s speed.

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GAS and TEMPERATUREGAS and TEMPERATURE

Jacques Charles studied the effect of Jacques Charles studied the effect of temperature on gasestemperature on gases

To test only ONE variable at a time, To test only ONE variable at a time, Charles held the following constant.Charles held the following constant.

1. # of gas particles present1. # of gas particles present 2. gas pressure2. gas pressure From his experiments he discovered that From his experiments he discovered that

all gasesall gases expand and contract to the same expand and contract to the same degree, with a set temperature change.degree, with a set temperature change.

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GAS and TEMPERATUREGAS and TEMPERATURE

Volume changes by 1/273 of the original volumeVolume changes by 1/273 of the original volume for each degree change in for each degree change in

temperature.temperature. At 0At 0ooC a gas has a volume of 1 m3. If the C a gas has a volume of 1 m3. If the

temperature is lowered to a -273temperature is lowered to a -27300C the gas C the gas volume would theoretically be reduced to volume would theoretically be reduced to zero!zero!

absolute zero- absolute zero- the temperature at the temperature at which a which a gas gas

1] has no volume1] has no volume 2] has no E2] has no Ekk Gas temperatures are ALWAYS measured in Gas temperatures are ALWAYS measured in

KELVINS.KELVINS. Charles Law animation

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Charles’ LawCharles’ Law

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GAS and TEMPERATUREGAS and TEMPERATUREV V T TVV = k = k

TT

VV11 = k = k VV22 = k = k

TT11 T T22

Charles’ LawCharles’ Law VV11 = = VV22

TT11 T T22

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Charles’ LawCharles’ Law Charles’s lawCharles’s law states that the volume of a states that the volume of a

fixed mass of gas is directly proportional to fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept its Kelvin temperature if the pressure is kept constant.constant.

Temperature in Kelvin (K)Temperature in Kelvin (K)

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Charles’ LawCharles’ Law As the temperature of the water As the temperature of the water

increases, the volume of the increases, the volume of the balloon increases.balloon increases.

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4747

V1 =V2

T1 T2

4.00L = V2

297K 331K

Cross multiply and solve for the missing variable, V2.

The answer is:

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Temperature and PressureTemperature and Pressure

Gay-Lussac’s LawGay-Lussac’s Law Joseph Louis Gay-Lussac in the early Joseph Louis Gay-Lussac in the early

1800's.1800's. To test only ONE variable at a time, To test only ONE variable at a time,

Gay-Lussac held the following constant.Gay-Lussac held the following constant. 1. # of gas particles present1. # of gas particles present 2. volume2. volume

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Temperature and PressureTemperature and Pressure

Pressure and Pressure and temperature are temperature are directly directly proportional to proportional to each other each other

5050

PP11 = k = k PP22 = k= k

TT1 1 TT22

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CHANGING MORE THAN ONE CHANGING MORE THAN ONE VARIABLEVARIABLE

It is highly possible that several It is highly possible that several environmental factors may change at environmental factors may change at the same time.the same time.

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The Combined Gas LawThe Combined Gas Law

The The combined gas lawcombined gas law describes the describes the relationship among the pressure, relationship among the pressure, temperature, and volume of an enclosed temperature, and volume of an enclosed gas.gas.

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(30.0L)(153kPa)(30.0L)(153kPa) = V = V22 (101.325kPa)(101.325kPa)

313K 273K313K 273K

Cross multiply and solve for VCross multiply and solve for V22..

VV22 = 39.5L = 39.5L

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IDEAL GASESIDEAL GASES REAL GASESREAL GASES * No volume* No volume * Has volume* Has volume * Not effected by attractive * Not effected by attractive * Some * Some

attraction attraction forces forces between particlesbetween particles

*mathematiclly perfect*mathematiclly perfect *variable in *variable in selectedselectedsituationssituations

Gas Laws Fail when:Gas Laws Fail when: 1. molecules are forced very close together 1. molecules are forced very close together

due to extremely HIGH due to extremely HIGH PRESSURE. [inter-PRESSURE. [inter-molecular attraction]molecular attraction]

2. molecules move too slowly to pull away 2. molecules move too slowly to pull away from the attraction from the attraction generated by other generated by other molecules. Molecules are displaying LOW kinetic molecules. Molecules are displaying LOW kinetic

energy; LOW TEMPERATURE.energy; LOW TEMPERATURE.

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EXPLOITING GAS EXPLOITING GAS TENDENCIESTENDENCIES

Joule-Thomas EffectJoule-Thomas Effect Highly compressed gas, allowed to escape Highly compressed gas, allowed to escape

through a small opening causes the temperature to through a small opening causes the temperature to drop.drop.

Explanation:Explanation: when molecules move apart from each other when molecules move apart from each other workwork must be must be

done.done. energy for the work comes from Eenergy for the work comes from Ekk

since Esince Ekk is the same as the temp, when it is used the temp is the same as the temp, when it is used the temp dropsdrops

aerosol cans cool as the gas escapesaerosol cans cool as the gas escapes refrigeratorsrefrigerators

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Low Pressure GasLow Pressure Gas High Pressure High Pressure GasGas

CompressorCompressor

Throttle ValveThrottle Valve

Low Pressure LiquidLow Pressure Liquid High High Pressure Pressure

LiquidLiquid

Very NarrowOpeningVery NarrowOpening

Condenser

Evaporator

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Gases and the MoleGases and the Mole

Two identical cubes filled with a gasTwo identical cubes filled with a gas Temperature for both cubes is constant Temperature for both cubes is constant

[the same][the same] Pressure is dependent on ... ?Pressure is dependent on ... ?

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Gases and the MoleGases and the Mole

Pressure is dependent on the amount Pressure is dependent on the amount gas in each box.gas in each box.

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Gases and the MoleGases and the Mole

If the pressure in the boxes are equal If the pressure in the boxes are equal and the amount gas in the boxes are and the amount gas in the boxes are equal, what can be said about the equal, what can be said about the number of gas molecules in each number of gas molecules in each box?box?

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The Mole–Volume The Mole–Volume RelationshipRelationship

Avogadro’s hypothesis states that equal Avogadro’s hypothesis states that equal volumes of gases at the same temperature and volumes of gases at the same temperature and pressure contain equal numbers of particles.pressure contain equal numbers of particles.

10.2

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Avagadro’s PrincipleAvagadro’s Principle

Under the same conditions of temperature Under the same conditions of temperature and pressure, the number of molecules of and pressure, the number of molecules of ANY GASANY GAS present in a specific volume is present in a specific volume is equal.equal.

At S.T.P.At S.T.P. 1 mole of 1 mole of any gasany gas occupies 22.4 L occupies 22.4 L 1 mole = 22.4 L 1 mole = 22.4 L

The quantity 22.4 L is called the The quantity 22.4 L is called the molar volumemolar volume of of a gas.a gas.

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Avagadro’s PrincipleAvagadro’s Principle

Remember 1 mole contains 6.02 X Remember 1 mole contains 6.02 X 10102323 particles. particles.

Therefore, at S.T.P.Therefore, at S.T.P. 1 mole = 22.4 L = 6.02 X 101 mole = 22.4 L = 6.02 X 102323

particles = gram formula wt.particles = gram formula wt.

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Ideal Gas LawIdeal Gas Law Relates Relates temperature temperature pressure pressure volume volume number of particles, or molesnumber of particles, or moles

PV = nRTPV = nRT

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Ideal Gas LawIdeal Gas Law

PP = pressure in either = pressure in either kPa, mm Hg or atmkPa, mm Hg or atm VV = volume in = volume in LL nn = number of = number of moles moles RR = gas law constant; = gas law constant; 8.3148.314 L L kPakPa, ,

K molK mol

62.462.4 L L mm Hgmm Hg , or , or .0821.0821 L L atmatm

K molK mol K mol K mol TT = temperature in = temperature in KelvinKelvin

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Which equation do I use???Which equation do I use???

Given conditions of temperature, Given conditions of temperature, pressure, and/or volume:pressure, and/or volume: Combine Gas LawCombine Gas Law

Amount [moles / grams]Amount [moles / grams]

is given or ask for:is given or ask for: Ideal Gas LawIdeal Gas Law