Chapter 10

Gases

A Gas

- Uniformly fills any container.

- Mixes completely with any other gas

- Exerts pressure on its surroundings.

Pressure

- 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)

Gas Laws

Boyle’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 strictly obeys Boyle’s Law is called an

ideal 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 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 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 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 Law

- An equation of state for a gas.

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

PV = nRT

Standard Temperature and Pressure

“STP”

P = 1 atmosphere

T = C

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

Ideal 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

Dalton’s Law of Partial Pressures

For a mixture of gases in a container,

PTotal = P1 + P2 + P3 + . . .

Partial Pressure

The partial pressure of a gas equals the mole fraction of the gas time the total pressure.

PA = χAPTotal

Kinetic 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

ecul

esw

ith g

iven

vel

ocity

0

Molecular velocity (m/s)

4 x 102 8 x102

05_59

Rel

ativ

e nu

mbe

r of

N2

mol

ecul

esw

ith g

iven

vel

ocity

0Velocity (m/s)1000 2000 3000

273 K

1273 K

2273 K

The Meaning of Temperature

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:

Diffusion:

Real Gases

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

Real Gases

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

corrected pressure corrected volume

Pideal Videal

END