A GasA Gas

- Uniformly fills any container.

- Mixes completely with any other gas

- Exerts pressure on its surroundings.

PressurePressure

- is equal to force/unit area

- SI units = Newton/meter2 = 1 Pascal (Pa)

- 1 standard atmosphere = 101,325 Pa

- 1 standard atmosphere = 1 atm =

760 mm Hg = 760 torr

05_48

h h

Atmosphericpressure (Patm)

Atmosphericpressure (Patm)

Gaspressure (Pgas)less thanatmospheric pressure

Gaspressure (Pgas)greater thanatmospheric pressure

(Pgas) = (Patm) - h (Pgas) = (Patm) + h

(a) (b)

Boyle’s LawBoyle’s Law**

Pressure Volume = Constant (T = constant)

P1V1 = P2V2 (T = constant)

V 1/P (T = constant)

(*Holds precisely only at very low pressures.)

05_50P

(in

Hg)

0

V(in3)

20 40 60

50

100

PP2

V

2V

(a)

00

1/P (in Hg)

0.01 0.02 0.03

20

40slope = k

(b)

V(in

3 )

A gas that A gas that strictly obeys strictly obeys Boyle’s Law is called an Boyle’s Law is called an

ideal gasideal gas..

05_51

PV

(L

• at

m)

022.25

P (atm)

1.000.750.500.25

22.30

22.35

22.40

22.45Ne

O2

CO2

Ideal

Charles’s LawCharles’s Law

The volume of a gas is directly proportional to temperature, and extrapolates to zero at zero Kelvin.

V = bT (P = constant)

b = a proportionality constant

Charles’s LawCharles’s Law

VT

VT

P1

1

2

2 ( constant)

05_53

V(L

)

-300

T(ºC)

-200 -100 0 100 200

1

2

3

6

4

5

300

-273.2 ºC

N2O

H2

H2O

CH4

He

Avogadro’s LawAvogadro’s Law

For a gas at constant temperature and pressure, the volume is directly proportional to the number of moles of gas (at low pressures).

V = an

a = proportionality constant

V = volume of the gas

n = number of moles of gas

Ideal Gas LawIdeal Gas Law

- An equation of state for a gas.

- “state” is the condition of the gas at a given time.

PV = nRT

Ideal Gas LawIdeal Gas Law

PV = nRT

R = proportionality constant

= 0.08206 L atm mol

P = pressure in atm

V = volume in liters

n = moles

T = temperature in Kelvins

Holds closely at P < 1 atm

Standard Temperature Standard Temperature and Pressureand Pressure

“STP”

P = 1 atmosphere

T = C

The molar volume of an ideal gas is 22.42 liters at STP

Dalton’s Law of Dalton’s Law of Partial PressuresPartial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

Kinetic Molecular TheoryKinetic Molecular Theory

1. Volume of individual particles is zero.

2. Collisions of particles with container walls cause pressure exerted by gas.

3. Particles exert no forces on each other.

4. Average kinetic energy Kelvin temperature of a gas.

05_1541

Pext

Pext

Volume is decreased

05_1542

Pext

Pext

Temperature is increased

05_1543

Pext

Pext

Energy (heat) added

05_1544

Increase volume to return to originalpressure

Gas cylinder

Moles of gasincreases

Pext Pext

Pext

05_58

Rel

ativ

e nu

mbe

r of

O2

mol

ecu

les

with

giv

en

velo

city

0

Molecular velocity (m/s)

4 x 102 8 x102

05_59

Rel

ativ

e nu

mbe

r of

N2

mol

ecu

les

with

giv

en

velo

city

0Velocity (m/s)1000 2000 3000

273 K

1273 K

2273 K

The Meaning of The Meaning of TemperatureTemperature

Kelvin temperature is an index of the random motions of gas particles (higher T means greater motion.)

(KE)32avg RT

Effusion: describes the passage of gas into an evacuated chamber.

Diffusion: describes the mixing of gases. The rate of diffusion is the rate of gas mixing.

05_60

Gas

Vacuum

Pinhole

Rate of effusion for gas 1Rate of effusion for gas 2

2

1

MM

Distance traveled by gas 1Distance traveled by gas 2

2

1

MM

Effusion:Effusion:

Diffusion:Diffusion:

Real GasesReal Gases

Must correct ideal gas behavior when at high pressure (smaller volume) and low temperature (attractive forces become important).

05_62

00

P(atm)

200 400 600 800

1.0

2.0

PV

nRTCO2

H2

CH4N2

Ideal

gas

1000

05_63

00.6

200 400 600 800

1.0

1.4

1.8

P(atm)

PV

nRT

203 K

293 K

673 K

Idealgas

Real GasesReal Gases

[ ]P a V nb nRTobs2( / ) n V

corrected pressurecorrected pressure corrected volumecorrected volume

PPidealideal VVidealideal

Atmospheric CompositionAtmospheric Composition

The Big Three

Nitrogen (N2) = 78%

Oxygen (O2) = 21%

Argon (Ar) = 1%

05_68

Con

cent

ratio

n (p

pm

)

4:00

0

Time of day

0.1

0.2

0.3

0.4

0.5

6:00

8:00

10:0

0

Noo

n

2:00

4:00

6:00

NO

NO2

O3

Molecules of unburnedfuel (petroleum)

Otherpollutants