5 - 1

GasesGases

PressurePressureBoyle’s LawBoyle’s LawCharles’ LawCharles’ Law

Gay-Lussac’s LawGay-Lussac’s LawAvogadro’s LawAvogadro’s Law

Ideal Gas EquationIdeal Gas EquationDalton’s LawDalton’s Law

Effusion and DiffusionEffusion and DiffusionKinetic-Molecular TheoryKinetic-Molecular Theory

Real GasesReal Gases

Elemental states at 25Elemental states at 25ooCC

He

Rn

XeI

KrBrSe

ArClS

NeFO

P

NC

H

Li

Na

Cs

Rb

K

TlHgAuHfLsBa

Fr

PtIrOsReWTa PoBiPb

Be

Mg

Sr

Ca

CdAgZrY PdRhRuTcMoNb

AcRa

ZnCuTiSc NiCoFeMnCrV

In SbSn

Ga Ge

Al

Gd

Cm

Tb

Bk

Sm

Pu

Eu

Am

Nd

U

Pm

Np

Ce

Th

Pr

Pa

Yb

No

Lu

Lr

Er

Fm

Tm

Md

Dy

Cf

Ho

Es

At

Te

As

Si

B

5 - 2

SolidLiquidGas

5 - 3

Observed propertiesObserved propertiesof matterof matter

StateProperty Solid Liquid Gas

Density High High Low (like solids)

Shape Fixed Takes shape Expands of lower part to fill

the of container

container

Compressibility Small Small Large

Thermal Very Small Moderateexpansion Small

5 - 4

The gaseous stateThe gaseous state

In this state, the particles have sufficient energy to overcome all forces that attract them to each other.

Each particle is completelyseparated from the others.

This results in low densitiesand the fact that gases completely fill the container that holds them.

5 - 5

Gas pressureGas pressure

Gases exhibit pressure on any container they are in.

Pressure is defined as a force per unit of area. Pressure = Force / Area

Several common unitsSeveral common units 1.00 atm = 760 torr

760 mm Hg 29.9 in Hg 14.7 lb/in2

1.01 x 105 Pa

force

area

5 - 6

BarometerBarometer

Device used to measure atmospheric pressure.

Oneatm

760 mmHg

29.9 inHg

vacuum

5 - 7

The gas lawsThe gas laws

Since gases are highly compressible and will expand when heated, these properties have been studied extensively.

The relationships between volume, pressure, temperature and moles are referred to as the gas lawsgas laws.

To understand the relationships, we must introduce a few concepts.

5 - 8

Units we will be usingUnits we will be using

VolumeVolume liters, although other units could be used.

TemperatureTemperature Must use an absolute scale. K - Kelvin is most often used.

PressurePressure Atm, torr, mmHg, lb/in2.- use what is appropriate.

MolesMoles We specify the amounts in molar quantities.

5 - 9

Gas lawsGas laws

Laws that show the relationship between volume and various properties of gases

Boyle’s LawBoyle’s LawCharles’ LawCharles’ Law

Gay-Lussac’s LawGay-Lussac’s LawAvogadro’s LawAvogadro’s Law

The Ideal Gas EquationIdeal Gas Equation combines several of these laws into a single relationship.

5 - 10

Boyle’s lawBoyle’s law

The volume of a gas is inversely proportional to its pressure.

PV = kor

P1 V1 = P2 V2

Temperature and number of moles must be held constant!

5 - 11

Boyle’s lawBoyle’s law

Increasing the pressureon a sample on gasdecreases it volume atconstant temperature.

Note the effect hereas weight is added.

5 - 12

Charles’ lawCharles’ law

The volume of a gas is directly proportional to the absolute temperature (K).

VT

= k

or V1 V2

T1 T2

Pressure and number of molesmust be held constant!

=

5 - 13

Charles’ lawCharles’ law

When you heat a sample of a gas, its volume increases.

The pressure and numberof moles must be held constant.

5 - 14

Charles’ LawCharles’ Law

Placing an air filled balloon near liquid nitrogen (77 K)will cause the volume to be reduced. Pressure and the number of moles are constant.

5 - 15

Gay-Lussac’s LawGay-Lussac’s Law

Law of of Combining Volumes.Law of of Combining Volumes.At constant temperature and pressure, the volumes of gases involved in a chemical reaction are in the ratios of small whole numbers.

Studies by Joseph Gay-Lussac led to a better understanding of molecules and their reactions.

5 - 16

Gay-Lussac’s LawGay-Lussac’s Law

Example.Example.Reaction of hydrogen and oxygen gases.

Two ‘volumes’ of hydrogen will combine with one ‘volume’ of oxygen to produce two volumes of water.

We now know that the equation is:

2 H2 (g) + O2 (g) 2 H2O (g)

+H2 H2 O2 H2O H2O

5 - 17

Avogadro’s lawAvogadro’s law

Equal volumes of gas at the same temperature and pressure contain equal numbers of molecules.

V = k n

V1 V2

n1 n2

=

5 - 18

Avogadro’s lawAvogadro’s law

If you have more moles of a gas, it takes up morespace at the same temperature and pressure.

5 - 19

Standard conditions (STP)Standard conditions (STP)

Remember the following standard conditions.

Standard temperature = 273.15 K

Standard pressure = 1 atm

At these conditions:

One mole of a gas has a volume of 22.422.4 liters.

5 - 20

The ideal gas lawThe ideal gas law

A combination of Boyle’s, Charles’ and Avogadro’s Laws

PV = nRT

P = pressure, atm V = volume, L n = moles T = temperature, K R = 0.082 06 L atm/K mol

(gas law constant)

5 - 21

ExampleExample

What is the volume of 2.00 moles of gas at3.50 atm and 310.0 K?

PV = nRT

V = nRT / P

= (2.00 mol)(0.08206 L atm K-1mol-1)(310.0 K) (3.50 atm)

= 14.5 L

5 - 22

Ideal gas lawIdeal gas law

PVnT

( 1 atm ) ( 22.4 L )( 1 mol ) ( 273.15 K)

R =

= 0.08206 atm L mol-1 K-1

R =

R can be determined from standard conditions.

5 - 23

Ideal gas lawIdeal gas law

When you only allow volume and one other factor to vary, you end up with one of the other gas laws.

Just remember

Boyle Pressure

Charles Temperature

Avogadro Moles

5 - 24

Ideal gas lawIdeal gas law

P1V1

n1T1

= R =P2V2

n2T2

This one equationsays it all.

Anything held constant will“cancels out” of the equation

5 - 25

Ideal gas lawIdeal gas law

Example - if n and T are held constant

P1V1

n1T1

=P2V2

n2T2

This leaves us

P1V1 = P2V2 Boyle’s Law

5 - 26

ExampleExample

If a gas has a volume of 3.0 liters at 250 K,what volume will it have at 450 K ?

P1V1

n1T1

=P2V2

n2T2

Cancel P and nThey don’t change

V1

T1

=V2

T2

We end up withCharles’ Law

5 - 27

ExampleExample

If a gas has a volume of 3.0 liters at 250 K,what volume will it have at 450 K ?

V1

T1

=V2

T2

V2 = (3.0 l) (450 K)

(250 K)

= 5.4 L

P1V1

n1T1

=P2V2

n2T2

5 - 28

Dalton’s law of Dalton’s law of partial pressurespartial pressures

The total pressure of a gaseous mixture is the sum of the partial pressure of all the gases.

PT = P1 + P2 + P3 + .....

Air is a mixture of gases - each adds it own pressure to the total.

Pair = PN2 + PO2 + PAr + PCO2 + PH2O

5 - 29

Partial pressure examplePartial pressure example

Mixtures of helium and oxygen are used in scuba diving tanks to help prevent “the bends.”

For a particular dive, 46 liters of O2 and 12 liters of He were pumped in to a 5 liter tank. Both gases were added at 1.0 atm pressure at 25oC.

Determine the partial pressure for both gases in the scuba tank at 25oC.

5 - 30

Partial pressure examplePartial pressure example

First calculate the number of moles of each gas using PV = nRT.

nO2 = = 1.9 mol

nHe = = 0.49 mol

(1.0 atm) (46 l)(0.08206 l atm K-1 mol-1)(298.15K)

(1.0 atm) (12 l)(0.08206 l atm K-1 mol-1)(298.15K)

5 - 31

Partial pressure examplePartial pressure example

Now calculate the partial pressures of each.

PO2 = = 9.3 atm

PO2 = = 2.4 atm

Total pressure in the tank is 11.7 atm.

(1.9 mol) (298.15 K) (0.08206 l atm K-1 mol-1)(5.0 l)

(0.49 mol) (298.15 K) (0.08206 l atm K-1 mol-1)(5.0 l)

5 - 32

Relates the rates of effusion of two gases to their molar masses.

This law notes that larger molecules move more slowly.

Graham’s lawGraham’s law

Rate A MM BRate B MM A

=

DiffusionDiffusion

5 - 34

Diffusion and effusionDiffusion and effusion

DiffusionDiffusionThe random and spontaneous mixing of molecules.

EffusionEffusionThe escape ofmolecules throughsmall holes in abarrier.

5 - 35

Kinetic-molecular theoryKinetic-molecular theory

This theory explains the behavior of gases.

• Gases consist of very small particles (molecules) which are separated by large distances.

• Gas molecules move at very high speeds - hydrogen molecules travel at almost 4000 mph at 25oC.

• Pressure is the result of molecules hitting the container. At 25 oC and 1 atm, a molecule hits another molecule and average of 1010 times/sec.

5 - 36

Kinetic-molecular theoryKinetic-molecular theory

• No attractive forces exist between ideal gas molecules or the container they are in.

• Energy of motion is called kinetic energy.

Average kinetic energy = mv2

Because gas molecules hit each other frequently, their speed and direction is constantly changing.

The distribution of gas molecule speeds can be calculated for various temperatures.

12

5 - 37

Kinetic-molecular theoryKinetic-molecular theoryFr

act

ion

havin

g e

ach

sp

eed

0 500 1000 1500 2000 2500 3000Molecular speed (m/s)

O2 at 25oCO2 at 700oCH2 at 25oC

Average speed

5 - 38

We can plot the compressibility factor (PV/nRT)for gases. If the gas is ideal, it should alwaysgive a value of 1.

Obviously, none of these gases are ‘ideal.’

Real gasesReal gases

Com

pre

ssib

ility

fact

or

0 5 10Pressure, atm

H2

N2

CH4

C2H4

NH3

5 - 39

Real gasesReal gases

As pressure approaches zero, all gases approach ideal behavior.

At high pressure, gases deviate significantly from ideal behavior.

Why?Why?

• Attractive forces actually do exist between molecules.

• Molecules are not points -- they have volume.

5 - 40

Van der Waals equationVan der Waals equation

This equation is a modification of the ideal gas relationship. It accounts for attractive forces and molecular volume.

P +an2

V2 (V - nb) = nRT( )Correction for Molecular volume

Correction for attractiveforces between molecules

5 - 41

Van der Waals constantsVan der Waals constants

a bGas Formula L2 atm mol-2 L mol-1

Ammonia NH3 4.170 0.037 07Argon Ar 1.345 0.032 19Chlorine Cl2 6.493 0.056 22Helium He 0.034 12 0.023 70Hydrogen H2 0.244 4 0.026 61

Nitrogen N2 1.390 0.039 13

Water H2O 5.464 0.030 49Xenon Xe 4.194 0.051 05