gas laws relationships between variables in the behaviour of gases
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Gas lawsGas laws
Relationships between variables Relationships between variables in the behaviour of gasesin the behaviour of gases
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Learning objectivesLearning objectives
Describe physical basis for pressure in a gasDescribe physical basis for pressure in a gas Describe the basic features of the kinetic theoryDescribe the basic features of the kinetic theory Distinguish among and convert common units of Distinguish among and convert common units of
pressurepressure Apply gas laws to simple problems in predicting Apply gas laws to simple problems in predicting
conditions of a gasconditions of a gas Apply ideal gas law to simple stoichiometry Apply ideal gas law to simple stoichiometry
problems in gasesproblems in gases
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Gas: no interactionsGas: no interactions
Not rigidNot rigid Completely fills containerCompletely fills container CompressibleCompressible Low densityLow density Energetic moleculesEnergetic molecules
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Kinetic theory and car tires – a case Kinetic theory and car tires – a case for atomsfor atoms
Molecules have energyMolecules have energy Energy increases with TEnergy increases with T Pressure is caused by energetic molecules Pressure is caused by energetic molecules
striking tire wallstriking tire wall Pumping up tire increases number of Pumping up tire increases number of
moleculesmolecules More molecules – higher pressureMore molecules – higher pressure Higher temperature – higher pressureHigher temperature – higher pressure
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Kinetic theory of gasesKinetic theory of gases
Gases consist of small atoms or molecules Gases consist of small atoms or molecules in constant random motionin constant random motion
Volume occupied by molecules is negligibleVolume occupied by molecules is negligible Molecules are independent of each other – Molecules are independent of each other –
no interactionsno interactions Collisions are perfectly elastic (no energy Collisions are perfectly elastic (no energy
loss)loss) Average energy is proportional to the Average energy is proportional to the
temperaturetemperature
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Under pressure: the atmosphereUnder pressure: the atmosphere
Gases exert pressure by virtue of motionGases exert pressure by virtue of motion Gravity makes the air density higher near Gravity makes the air density higher near
the earth’s surfacethe earth’s surface Pressure decreases with elevationPressure decreases with elevation
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Atmospheric pressureAtmospheric pressure
Pressure is force per unit areaPressure is force per unit area The weight of the air supports a column of The weight of the air supports a column of
mercury 760 mm highmercury 760 mm high BarometerBarometer is used for measuring is used for measuring
atmospheric pressureatmospheric pressure Atmospheric pressure changes with the Atmospheric pressure changes with the
weatherweather
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The atmosphere is layeredThe atmosphere is layered
TroposphereTroposphere Where the weather happensWhere the weather happens
StratosphereStratosphere Where the ozone isWhere the ozone is
MesosphereMesosphere IonosphereIonosphere
The brutal strength of solar radiation ionizes all The brutal strength of solar radiation ionizes all the components – permits transmission of radio the components – permits transmission of radio signals around the earth without need of mirrorssignals around the earth without need of mirrors
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Units of pressureUnits of pressure
AtmosphereAtmosphere Atmospheric pressure = 1 atmAtmospheric pressure = 1 atm
mm (or cm, or in) of mercury mm (or cm, or in) of mercury Atmospheric pressure = 760 mm (76 cm/29.9 in) HgAtmospheric pressure = 760 mm (76 cm/29.9 in) Hg
Pascal is SI unit for pressurePascal is SI unit for pressure Atmospheric pressure = 101 000 Pa (N/mAtmospheric pressure = 101 000 Pa (N/m22))
Pounds/square inchPounds/square inch Atmospheric pressure = 14.7 lb/inAtmospheric pressure = 14.7 lb/in22
Torr Torr Atmospheric pressure = 760 torrAtmospheric pressure = 760 torr
BarBar Atmospheric pressure = 1.01 barAtmospheric pressure = 1.01 bar
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Standard temperature and pressure Standard temperature and pressure (STP)(STP)
Standard conditions allow direct comparison Standard conditions allow direct comparison of properties of different substancesof properties of different substances Standard temperature is 273 K (0Standard temperature is 273 K (0ºC)ºC) Standard pressure is 760 mm Hg or 1 Standard pressure is 760 mm Hg or 1
atmosphereatmosphere
At STP, 1 mole of At STP, 1 mole of anyany ideal gas occupies ideal gas occupies 22.414 L22.414 L
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Pressure changes (units)Pressure changes (units)
Convert 0.50 atm into a) mm Hg b) PaConvert 0.50 atm into a) mm Hg b) Pa
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Gas laws: experience in math formGas laws: experience in math form
The properties of gases can be described by The properties of gases can be described by a number of simple lawsa number of simple laws
The laws establish quantitative relationships The laws establish quantitative relationships between different variablesbetween different variables
They are largely intuitively obvious and They are largely intuitively obvious and familiarfamiliar
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The four variablesThe four variables
Pressure (P)Pressure (P) Volume (V)Volume (V) Temperature (T in Kelvin)Temperature (T in Kelvin) Number of molecules (n in moles)Number of molecules (n in moles)
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Variables and constantsVariables and constants
In the elementary gas laws two of the four In the elementary gas laws two of the four variables are kept constantvariables are kept constant
Each law describes how one variable reacts Each law describes how one variable reacts to changes in another variableto changes in another variable
All the simple laws can be integrated into All the simple laws can be integrated into one combined gas lawone combined gas law
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Boyle’s lawBoyle’s law
The first experimental gas The first experimental gas lawlaw
Pressure increases, volume Pressure increases, volume decreases (T, n constant)decreases (T, n constant)
1PV
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Boyle’s law problemsBoyle’s law problems
Initial conditions: PInitial conditions: P11 and V and V11
Final conditions: PFinal conditions: P22 and V and V22
Four variables: three given, one unknownFour variables: three given, one unknown Rearrange equation:Rearrange equation:
Units are not important provided same on both Units are not important provided same on both sidessides
1 1 1 12 2
2 2
;PV PV
P VV P
1 1 2 2PV PV
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Tank contains 12 L of gas at 4,500 mm Hg. What is Tank contains 12 L of gas at 4,500 mm Hg. What is volume when pressure = 750 mm Hg?volume when pressure = 750 mm Hg?
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Charles’ LawCharles’ Law
As temperature increases, As temperature increases, volume increases (P, n volume increases (P, n constant)constant) Temperature must be Temperature must be
measured in Kelvinmeasured in Kelvin
V T
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Absolute zeroAbsolute zero
Gay-Lussac observed V changed by 1/273 Gay-Lussac observed V changed by 1/273 of value at 0of value at 0ºCºC
Plotted as V = Plotted as V = kkT (T = ºC + 273):T (T = ºC + 273): V = 0 at T = 0V = 0 at T = 0
Does the gas actually occupy zero volume?Does the gas actually occupy zero volume? No, at lower T the law is not followedNo, at lower T the law is not followed
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Do’s and don’ts with Charles’ lawDo’s and don’ts with Charles’ law
1 2
1 2
V V
T T
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Combined gas lawCombined gas law
Fold together Boyle and Charles:Fold together Boyle and Charles:
Given five of the variables, find the sixthGiven five of the variables, find the sixth Units must be consistentUnits must be consistent Temperature in Temperature in KelvinKelvin
1 1 2 2
1 2
PV PV
T T
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Example of combined gas lawExample of combined gas law Gas at 27Gas at 27ºC and 2 atm pressure occupies 2 L. ºC and 2 atm pressure occupies 2 L.
What is new volume if pressure becomes 4 atm What is new volume if pressure becomes 4 atm and temperature is raised to 127ºC?and temperature is raised to 127ºC?
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Gay-Lussac and law of combining Gay-Lussac and law of combining volumesvolumes
When gases react at constant temperature When gases react at constant temperature and pressure, they combine in volumes that and pressure, they combine in volumes that are related to each other as ratios of small are related to each other as ratios of small whole numberswhole numbers
His experiments with hydrogen and oxygen His experiments with hydrogen and oxygen had implications for the understanding of the had implications for the understanding of the atom and the structures of simple moleculesatom and the structures of simple molecules
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Avogadro’s LawAvogadro’s Law
As the number of moles of As the number of moles of gas increases, so does the gas increases, so does the volume (P, T constant)volume (P, T constant)
V n1 2
1 2
V V
n n
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Dalton’s law of partial pressuresDalton’s law of partial pressures
A mixture of gases exerts a pressure as if all A mixture of gases exerts a pressure as if all the gases were independent of one anotherthe gases were independent of one another
Total pressure is the sum of the pressures Total pressure is the sum of the pressures exerted by each oneexerted by each one
P = pP = p11 + p + p22 + p + p33 + … + …
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Calculations with partial pressuresCalculations with partial pressures
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Molar gas volumeMolar gas volume
The molar volume of a gas is the volume The molar volume of a gas is the volume occupied by 1 mole. At STP (standard occupied by 1 mole. At STP (standard temperature 273 K, and pressure 1 atm) temperature 273 K, and pressure 1 atm)
one mole of gas occupies 22.4 Lone mole of gas occupies 22.4 L Gas density is easily obtained from the Gas density is easily obtained from the
molar mass and molar volume – d = m/Vmolar mass and molar volume – d = m/V
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Ideal Gas LawIdeal Gas Law
The particles of an ideal gas have mass but no The particles of an ideal gas have mass but no volume - a fair approximation at low pressuresvolume - a fair approximation at low pressures
Collisions between the gas molecules are perfectly Collisions between the gas molecules are perfectly “elastic” – like superhard billiard balls. “elastic” – like superhard billiard balls. Reasonable for smaller molecules or noble gasesReasonable for smaller molecules or noble gases
R is the ideal gas constant = 0.0821 L-atmKR is the ideal gas constant = 0.0821 L-atmK-1-1molmol-1-1
Gases deviate from ideal behaviour as Gases deviate from ideal behaviour as pressure increases – closer proximity of moleculespressure increases – closer proximity of molecules molecules are more polar – stronger interactionsmolecules are more polar – stronger interactions
PV nRT
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Calculations with the ideal gas lawCalculations with the ideal gas law
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Chemical equations with gasesChemical equations with gases
Reactions with solids involve massesReactions with solids involve masses Reactions with gases involve volumesReactions with gases involve volumes
Volume Bn = PV/RT Mole:mole ratio V = nRT/PVolume A Moles A Moles B
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Stoichiometry with the ideal gas lawStoichiometry with the ideal gas law
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Gas laws and crash safetyGas laws and crash safety
The airbag represents a The airbag represents a fascinating study of fascinating study of chemistry applied in a very chemistry applied in a very practical areapractical area
Airbags have reduced Airbags have reduced serious injuries and serious injuries and fatalities by a significant fatalities by a significant margin compared with seat margin compared with seat belts onlybelts only
Chemistry plays a crucial Chemistry plays a crucial role in the performance of role in the performance of the airbagthe airbag
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Timing is everythingTiming is everything
The airbag must deploy within about 40 ms The airbag must deploy within about 40 ms of the impactof the impact
The airbag must not deploy unless there is The airbag must not deploy unless there is an impactan impact
Inflation depends upon a rapid chemical Inflation depends upon a rapid chemical reaction generating a quantity of gasreaction generating a quantity of gas
The bag, once inflated, must then deflate at The bag, once inflated, must then deflate at the point of impact with the driver to prevent the point of impact with the driver to prevent injuryinjury
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Chemistry is involved at many pointsChemistry is involved at many points
Chemical reaction to produce gas (nitrogen)Chemical reaction to produce gas (nitrogen) Strong NStrong N≡N bond provides driving force≡N bond provides driving force Reaction kinetics determine rate – must be Reaction kinetics determine rate – must be
fastfast Gas laws provide inflation – P proportional Gas laws provide inflation – P proportional
to Tto T