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Chapter 12: Gases and Their Chapter 12: Gases and Their PropertiesProperties

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Properties of GasesProperties of Gases

Gases form homogeneous mixtures Gases are compressible All gases have low densities

air 0.0013 g/mL water 1.00 g/mL iron 7.9 g/mL

Gases expand to fill their containers uniformly A gas exerts a pressure

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Kinetic Molecular TheoryKinetic Molecular Theory Gases consist of molecular particles moving in straight

lines at any given instant. Molecules collide with each other and the container

walls without any net loss of energy. Gas molecules behave independently --

attractive/repulsive forces between them are negligible. Gas molecules are widely spaced, the actual volume of

molecules is negligible compared to the space they occupy.

The average kinetic energy of the gas particles is proportional to the temperature.

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Kinetic GraphKinetic Graph

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Pressure, Volume, and Temperature Pressure, Volume, and Temperature RelationshipsRelationships

A. Pressure, volume, and temperature unitsB. Boyle's lawC. Charles' lawD. Gay-Lussac's lawE. Avogadro's law

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Pressure =

-measured with barometer or manometer

forceunit area

SI: 1 pascal (Pa) = 1 N/m2

common: 1 atm = 760 mm Hg= 760 torr= 14.7 lb/in2 (psi)= 101.325 kPa= 1.013 bar

Volume: mL, LTemperature: K

A. Pressure, Volume, and A. Pressure, Volume, and Temperature RelationshipsTemperature Relationships

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PressurePressure

Defined as force per unit area

skilopascalmsec

kg

m

)(kg)(m/sec

distance

onacceleratimass

Area

ForcePressure

22

2

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Atmospheric pressureAtmospheric pressure

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BarometerBarometer

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ManometersManometers

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Pressure UnitsPressure Units

101.325 kPa = 760 mmHg=760 torr=1 atm=30 in Hg=14.7 psi

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Robert Boyle, 1662: for a sample of gas at constant T, V 1/P

V = or PV = constant

P1V1 = P2V2 (at constant T)

constantP

B. Boyle’s lawB. Boyle’s law

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Boyles LawBoyles Law

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Jacques Charles, 1787: for a sample of gas at constant P, V T (K)

V = constant x T or = constant

VT

V1

T1

V2

T2

= (at constant P)

C. Charles’ lawC. Charles’ law

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Charles LawCharles Law

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Joseph Gay-Lussac, ~1800: for a sample of gas at constant V, P T (K)

P = constant x T or = constant

PT

P1

T1

P2

T2

= (at constant V)

D. Gay-Lussac’s lawD. Gay-Lussac’s law

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E. Avogadro’s lawE. Avogadro’s law

Amadeus Avogadro, 1811: at constant T and P, V n

V = constant x n or = constant

Vn

V1

n1

V2

n2

= (at constant T & P)

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Since PV = constant, P/T = constant, V/T = constant, and V/n = constant

= constant, R (universal gas constant)

or PV = nRT

PVnT

The Ideal gas lawsThe Ideal gas laws

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STP: 0ºC (273 K) and 1.00 atm (760 torr)molar volume = average volume occupied by one mole of gas at STP

= 22.4 L/mol

R = =

= 0.0821 L·atm/mol·K= 6.24 x 104 mL·torr/mol·K

PVnT

(1.00 atm)(22.4 L)(1.00 mol)(273 K)

STP and molar volumeSTP and molar volume

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mw =

since n = mw =

and since d = mw =

e.g., If one finds that a 0.108-g sample of gas occupies a volume of238 mL at 25ºC and 525 torr, what is the molecular weight of the gas?

mn

PVRT

mRTPV

mV

dRTP

Gas densities and molar massGas densities and molar mass

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partial pressure, p = pressure exerted by each gas in a mixture of gases

i

itotal pP

e.g., If 6.00 g of O2 and 9.00 g of CH4 are placed in a 15.0-L containerat 0º, what is the partial pressure of each gas and the total pressure inthe container.

Dalton’s law of partial pressuresDalton’s law of partial pressures 1. Dalton’s law1. Dalton’s law

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PT = p1 + p2 + p3…

1 gas offraction mole ,/

/1

T

1

T

1

T

1 Xn

n

VRTn

VRTn

P

p

p1 = X1PT

e.g., Air is 78 mol % N2 and 22 mol % O2. What is the partial pressureof each gas if the atmospheric pressure is 713 torr?

Dalton’s law of partial pressuresDalton’s law of partial pressures 2. mole fraction2. mole fraction

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vapor pressure = pressure exerted by evaporation of a liquid (or sublimation of a solid)

vacuum

liquidor solid

equilibriumat some T

pvap

pvap increases with T

e.g., H2O T pvap

0ºC 4.6 torr 25ºC 23.8 torr100ºC 760 torr (boils!)

Dalton’s law of partial pressuresDalton’s law of partial pressures3. collecting gases over water3. collecting gases over water

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Mixture of gas and water vapor.

PT = pgas + pvap(H2O)

Dalton’s law of partial pressuresDalton’s law of partial pressures3. collecting gases over water3. collecting gases over water

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Mole FractionMole Fraction

))(P(XP

andmoles total

component of moles(X)fraction Mole

total11