gas laws relationships between variables in the behaviour of gases

Gas lawsGas laws

Relationships between variables Relationships between variables in the behaviour of gasesin the behaviour of gases

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

Gas: no interactionsGas: no interactions

Not rigidNot rigid Completely fills containerCompletely fills container CompressibleCompressible Low densityLow density Energetic moleculesEnergetic molecules

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

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

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

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

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

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

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

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

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

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)

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

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

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

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?

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

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

Do’s and don’ts with Charles’ lawDo’s and don’ts with Charles’ law

1 2

1 2

V V

T T

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

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?

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

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

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 + … + …

Calculations with partial pressuresCalculations with partial pressures

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

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

Calculations with the ideal gas lawCalculations with the ideal gas law

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

Stoichiometry with the ideal gas lawStoichiometry with the ideal gas law

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

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

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