GASESGASES

Chapter 10

Example: Air

78% nitrogen21% oxygen

Molecules only take up about 0.1% of total volume (the rest is empty space) extremely low density

Gases: easily compressible fluid no fixed volume or shape always form homogeneous mixtures with other

gases

PRESSUREPRESSURE Pressure is the force that acts on a given area.

A

FP

Units:

SI unit – Pascal = Pa (N.m-2)

Other units:

1 atm = 760 torr = 760 mm Hg = 101.325 kPa

1 bar = 100 kPa

Mercury Mercury BarometerBarometer Atmospheric pressure can be measured using a barometer.

If Pgas < Patm:

Pgas + Ph2 = Patm

If Pgas > Patm:

Pgas = Patm + Ph2

ManometerManometer

Measures the pressure of gases not open to the atmosphere.

THE IDEAL GAS LAWSTHE IDEAL GAS LAWS

Charle’s Law (T-V Relationship)

Boyle’s Law (P-V Relationship)

Avogadro’s Law (n-V Relationship)

BOYLE’S LAW (P-V RELATIONSHIP)BOYLE’S LAW (P-V RELATIONSHIP)

(T and n constant)

The volume of a fixed amount of gas maintained at constant temperature is inversely proportional to pressure.

P

1V

Demonstration of Boyle’s Law:

The volume of a fixed amount of gas maintained at constant pressure is directly proportional to it absolute temperature.

CHARLE’S LAW (T-V RELATIONSHIP)CHARLE’S LAW (T-V RELATIONSHIP)

(P and n constant)

TV

The volume of a gas maintained at constant temperature and pressure is directly proportional to the number of moles of gas.

AVOGADRO’S LAW (n-V RELATIONSHIP)AVOGADRO’S LAW (n-V RELATIONSHIP)

(T and P constant)

nV

(T and P constant)

IDEAL GAS EQUATIONIDEAL GAS EQUATION

P

1V (T and n constant)

TV (P and n constant)

nV

nRTPV

P

nTV Thus

P

nTRV or

R is the gas constant.

R = 0.08206 L.atm.mol-1.K-1

R = 8.314 m3.Pa.mol-1.K-1

R = 8.314 J.mol-1.K-1

nRTPV

If we have a gas under two sets of conditions, then

nT

PVR

22

22

11

11

Tn

VP

Tn

VP

See examples in textbook

constant

If 1 mole of ideal gas at 1 atm and 0oC (273.15 K), then:

P

nRTV

V = 22.41 L

STP for gases:

1 atm and 0oC (273.15 K)

V =(1 mol)(0.08206 L.atm.mol-1.K-1)(273.15 K)

(1 atm)

Comparison of an ideal gas to some real gases at STP

Rearrange:

V

n

RT

P

V

nM

RT

PM

RT

PM

DENSITY OF GASESDENSITY OF GASES

PV = nRT

E.g.: (CO2) > (O2) used in fire extinguishers

V

m

RT

PM

Gas Mixtures and Partial Gas Mixtures and Partial PressuresPressures

DALTON’S LAW OF PARTIAL PRESSURESDALTON’S LAW OF PARTIAL PRESSURES: In a gas mixture the total pressure is given by the sum of partial pressures of each component.

Since gas molecules are so far apart, we can assume they behave independently.

321total PPPP

Each gas in the mixture obeys the ideal gas equation:

V

RTnP ii

V

RTnnnP 321total

Consider one gas in a mixture of gases:

P1 = n1RT/V

Pt = ntRT/V t

1

t

1

n

n

P

P

tt

11 P

n

nP

t11 PXP

mole fraction

ExampleExample

A miniature volcano can be made in the lab with ammonium dichromate. When ignited it decomposes in a fiery display.

(NH4)2Cr2O7(s) N2(g) + 4H2O(g) + Cr2O3(s)

If 5.0 g of ammonium dichromate is used, and if the gases from this reaction are trapped in a 3.0 L flask at 23oC, what is the total pressure (in atm) of the gas in the flask? (Ignore the air in the flask)

Challenge: Do not ignore the air in the flask.

To find the amount of gas produced by a reaction collect gas by displacing a volume of water.

watergastotal PPP

Note: there is water vapour mixed in with the gas.

To calculate the amount of gas produced, we need to correct for the partial pressure of the water vapour:

nRTPV E.g. 2KClO3(s) 2KCl(s) + 3O2(g)

Raise or lower container until the water levels inside and outside are the same.

Pwater = 0.031atm at 25oC

Kinetic Molecular TheoryKinetic Molecular TheoryWhy do gases behave as they do? Look at molecular level.

Assumptions:• Gases consist of a large number of molecules in

constant random motion.

• Volume of individual molecules negligible compared to volume of container.

• Intermolecular forces (forces between gas molecules) negligible.

• Energy can be transferred between molecules, but total kinetic energy is constant at constant

temperature.

• Average kinetic energy of molecules is proportional to temperature.

Magnitude of pressure given by how often and how hard the molecules strike the container.

Absolute temperature is a measure of the average kinetic energy of its molecules.

Molecules also collide with each other and can transfer energy between each other.

Ek = 1/2mu2

u = root mean square speedu average speed

EXERCISEEXERCISE

Using Kinetic Molecular Theory explain what happens when:

1) the volume of a gas increase at constant temperature?

2) the temperature of a gas increase at constant volume?

Different types of gas molecules of that have the same kinetic energy do not necessarily move at the same speed. Why?

M

RT3u

EffusionEffusion

The escape of gas molecules through a tiny hole into an evacuated space

When will a gas molecule move through the hole?

The faster molecules move, the greater the probability that they will effuse.

Graham’s Law of Effusion:

Consider two gases under identical PV-conditions with effusion rates r1 and r2, then:

1

2

2

1

2

1

2

1

M

M

MRT3

MRT3

u

u

r

r

i.e. rate of effusion is inversely proportional to the square root of its molar mass.

Two balloons are filled to the same volume. After 48 hours

Explain!

DiffusionDiffusion

The spread of a substance throughout a space or throughout a second substance.

A gas molecule will move in a straight line till it collides with the walls of the container or with other gas molecules results is a fairly random path.

Mean free path

The lower the mass of a molecule, the faster it can move and the faster it can diffuse

Real Real GasesGasesReal gases do not behave ideally under high pressure

RT

PVn

Consider 1 mol of gas

and low temperatures.

T ~ 300 K

N2

Why do we see these deviations?

Ideal gas molecules are assumed to occupy no space and have no intermolecular forces between them.

Real molecules do occupy space – the higher the pressure the more critical this becomes.

Intermolecular forces play a bigger role when molecules are closer together. Pressure appears lower.

Also at lower temperature, less kinetic energy to overcome these attractive forces.

Corrections for Non-ideal BehaviourCorrections for Non-ideal Behaviour

Van der Waals equation for real gases:

Ideal gas equation:V

nRTP

2

2

V

an

nbV

nRTP

Correction for Correction for volume of moleculesvolume of molecules

Van der Waals constant bb is a measure of the volume occupied by a mole of gas molecules.

Unit for bb: L/mol

2

2

V

an

nbV

nRTP

Correction for Correction for molecular attractionmolecular attraction

The pressure is reduced by the factor nn22a/Va/V22

Attractive forces between pairs of molecules increases as the square of the number of molecules per unit volume i.e. (n/V)(n/V)22

Van der Waals constant aa reflects how strongly gas molecules attract each other.

Unit for aa: L2 atm/mol2

nRTnbVV

anP 2

2

a and b generally increase with an increase in molecular mass

ExampleExample

Consider 1.00 mol of CO2(g) stored in a 3.00 L container at 0.0oC.

What will the pressure predicted by the ideal gas equation be?

And the van der Waals equation? Explain.