Ch14.4Chem.ppt

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14.4 Gases: Mixtures and Movements >

Chapter 14 The Behavior of Gases

14.1 Properties of Gases

14.2 The Gas Laws

14.3 Ideal Gases

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14.4 Gases: Mixtures and Movements >

The surface of a latex

balloon has tiny pores

through which gas

particles can pass.

The rate at which the

balloon deflates

depends on the gas it

contains.

CHEMISTRY

&

YOU

CHEMISTRY

&

YOU

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

Gas pressure results from collisions of

particles in a gas with an object.

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

Gas pressure results from collisions of

particles in a gas with an object.

• If the number of particles increases in a

given volume, more collisions occur.

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

Gas pressure results from collisions of

particles in a gas with an object.

• If the number of particles increases in a

given volume, more collisions occur.

• If the average kinetic energy of the

particles increases, more collisions

occur.

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

Particles in a mixture of gases at the

same temperature have the same

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

• The kind of particle is not important.

Particles in a mixture of gases at the

same temperature have the same

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

Particles in a mixture of gases at the

same temperature have the same

kinetic energy.

• The kind of particle is not important.

• The contribution each gas in a mixture

makes to the total pressure is called the

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14.4 Gases: Mixtures and Movements >

The total pressure of dry air is the sum

of the partial pressures of the

component gases.

Interpret

Data

Interpret

Data

Composition of Dry Air

Component

Volume (%)

Partial pressure (kPa)

Nitrogen

78.08

79.11 Oxygen

20.95

21.22 Carbon dioxide

0.04

0.04 Argon and others

0.93

0.95

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

In a mixture of gases, the total pressure is

the sum of the partial pressures of the gases.

• The chemist John Dalton proposed a law to

explain this.

• Dalton’s law of partial pressures

states that,

at constant volume and temperature, the total

pressure exerted by a mixture of gases is equal

to the sum of the partial pressures of the

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

• The chemist John Dalton proposed a law to

explain this.

• Dalton’s law of partial pressures

states that,

at constant volume and temperature, the total

pressure exerted by a mixture of gases is equal

to the sum of the partial pressures of the

component gases.

In a mixture of gases, the total pressure is

the sum of the partial pressures of the gases.

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14.4 Gases: Mixtures and Movements >

Dalton’s Law

Each component gas exerts its own

pressure independent of the pressure

exerted by the other gases.

• The pressure in the container of heliox (500 kPa) is

the same as the sum of the pressures in the

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14.4 Gases: Mixtures and Movements >

Air contains oxygen, nitrogen, carbon

dioxide, and trace amounts of other

gases. What is the partial pressure of

oxygen

(P

_O

2 ) at 101.30 kPa of total

pressure if the partial pressures of

nitrogen, carbon dioxide, and other

gases are 79.10 kPa, 0.040 kPa, and

0.94 kPa, respectively?

Sample

Problem 14.7

Sample

Problem 14.7

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14.4 Gases: Mixtures and Movements >

Use the equation for Dalton’s law of partial pressures

(

P

_total

=

P

_O

2 +

P

N

2 +

P

CO

2 +

P

others

) to calculate the

unknown value (

P

_O

2 ).

KNOWNS

UNKNOWN

Analyze

List the knowns and the

unknown.

1 P

_N

2 = 79.10 kPa

P

_CO

2 = 0.040 kPa

P

_others

= 0.94 kPa

P

_total

= 101.30 kPa

P

_O

2 = ? kPa

Sample

Problem 14.7

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14.4 Gases: Mixtures and Movements >

Start with Dalton’s law of partial pressures.

Calculate

Solve for the unknown.

2 Rearrange Dalton’s law to isolate

P

_O

2 .

P

_total

=

P

_O

2

+

P

N

2

+

P

CO

2

+

P

others

P

_O

2

=

P

total

– (

P

N

2

+

P

CO

2

+

P

others

)

Sample

Problem 14.7

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14.4 Gases: Mixtures and Movements >

Substitute the values for the total pressure

and the known partial pressures, and solve

the equation.

Calculate

Solve for the unknown.

2 P

_O

2 = 101.30 kPa – (79.10 kPa + 0.040 kPa + 0.94 kPa)

= 21.22 kPa

Sample

Problem 14.7

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14.4 Gases: Mixtures and Movements >

• The partial pressure of oxygen must

be smaller than that of nitrogen

because

P

_total

is only 101.30 kPa.

• The other partial pressures are

small, so the calculated answer of

21.22 kPa seems reasonable.

Evaluate

Does this result make sense?

3 Sample

Problem 14.7

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14.4 Gases: Mixtures and Movements >

A tank used by scuba divers has a

P

_total

of

2.21 

10

4 kPa. If

P

N

₂

is 1.72



10

4 kPa and

P

_O

2 is 4.641



10

3 kPa, what is the partial

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14.4 Gases: Mixtures and Movements >

A tank used by scuba divers has a

P

_total

of

2.21 

10

4 kPa. If

P

N

₂

is 1.72



10

4 kPa and

P

_O

2 is 4.641



10

3 kPa, what is the partial

pressure of any other gases in the scuba tank

(

P

_other

)

?

P

_total

=

P

_O2

+

P

_N2

+

P

_others

P

_others

=

P

_total

– (

P

_N2

+

P

_O2

)

P

_others

= 2.21



10

4 kPa – (1.72



10

4 kPa + 4.641



10

3 kPa)

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14.4 Gases: Mixtures and Movements >

Graham’s Law

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14.4 Gases: Mixtures and Movements >

Graham’s Law

• If you open a perfume bottle in one

corner of a room, at some point, a

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14.4 Gases: Mixtures and Movements >

Graham’s Law

• If you open a perfume bottle in one

corner of a room, at some point, a

person standing in the opposite corner

will be able to smell the perfume.

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14.4 Gases: Mixtures and Movements >

Graham’s Law

Diffusion

is the tendency of molecules to

move toward areas of lower concentration

until the concentration is uniform

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14.4 Gases: Mixtures and Movements >

Graham’s Law

A cylinder of air

and a cylinder of

bromine vapor

are sealed

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14.4 Gases: Mixtures and Movements >

Graham’s Law

A cylinder of air

and a cylinder of

bromine vapor

are sealed

together.

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14.4 Gases: Mixtures and Movements >

Graham’s Law

A cylinder of air

and a cylinder of

bromine vapor

are sealed

together.

Bromine vapor

diffuses upward

through the air.

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14.4 Gases: Mixtures and Movements >

Graham’s Law

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14.4 Gases: Mixtures and Movements >

Graham’s Law

During

effusion

, a gas escapes

through a tiny hole in its container.

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14.4 Gases: Mixtures and Movements >

Graham’s Law

Gases of lower molar mass

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14.4 Gases: Mixtures and Movements >

Graham’s Law

Thomas Graham’s Contribution

Graham’s law of effusion

states that

the rate of effusion of a gas is inversely

proportional to the square root of the

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14.4 Gases: Mixtures and Movements >

Graham’s Law

• This law can also be applied to the

diffusion of gases.

Thomas Graham’s Contribution

Graham’s law of effusion

states that

the rate of effusion of a gas is inversely

proportional to the square root of the

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14.4 Gases: Mixtures and Movements >

Graham’s Law

• This law can also be applied to the

diffusion of gases.

• If two objects with different masses have

the same kinetic energy, the lighter

object must move faster.

Thomas Graham’s Contribution

Graham’s law of effusion

states that

the rate of effusion of a gas is inversely

proportional to the square root of the

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14.4 Gases: Mixtures and Movements >

CHEMISTRY

&

YOU

Why do balloons filled with helium

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14.4 Gases: Mixtures and Movements >

Molecules of helium have a lower mass

than the average mass of air molecules,

so helium molecules effuse through the

tiny pores in a balloon faster than air

molecules do.

CHEMISTRY

&

YOU

CHEMISTRY

&

YOU

Why do balloons filled with helium

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14.4 Gases: Mixtures and Movements >

Graham’s Law

Comparing Effusion Rates

Suppose you have two balloons, one filled

with helium and the other filled with air.

• If the balloons are the same temperature, the

particles in each balloon have the same

average kinetic energy.

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14.4 Gases: Mixtures and Movements >

Graham’s Law

Comparing Effusion Rates

Suppose you have two balloons, one filled

with helium and the other filled with air.

• If the balloons are the same temperature, the

particles in each balloon have the same

average kinetic energy.

• But helium atoms are less massive than oxygen

or nitrogen molecules.

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14.4 Gases: Mixtures and Movements >

Graham’s Law

Rate

_A

Rate

_B

=

molar mass

_B

molar mass

_A

Because the rate of effusion is

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14.4 Gases: Mixtures and Movements >

How much faster does

helium (He) effuse than

nitrogen (N

₂

) at the same

temperature?

Sample

Problem 14.8

Sample

Problem 14.8

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14.4 Gases: Mixtures and Movements >

Use Graham’s law and the molar masses of the

two gases to calculate the ratio of effusion rates.

KNOWNS

UNKNOWN

Analyze

List the knowns and the

unknown.

1 molar mass

_He

= 4.0 g

molar mass

_N

2 = 28.0 g

ratio of effusion rates

= ?

Sample

Problem 14.8

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14.4 Gases: Mixtures and Movements >

Calculate

Solve for the unknown.

2

Start with the equation for Graham’s law

of effusion.

Rate

_H

_e

Rate

_N

2

=

molar mass

N

2

molar mass

_He

Sample

Problem 14.8

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14.4 Gases: Mixtures and Movements >

Calculate

Solve for the unknown.

2

Substitute the molar masses of nitrogen

and helium into the equation.

Rate

_H

_e

Rate

_N

₂

=

28.0 g

4.0 g

=

7.0 = 2.7

Sample

Problem 14.8

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14.4 Gases: Mixtures and Movements >

Helium atoms are less massive

than nitrogen molecules, so it

makes sense that helium effuses

faster than nitrogen.

Evaluate

Does this result make sense?

3 Sample

Problem 14.8

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14.4 Gases: Mixtures and Movements >

Which of the following gas particles

will diffuse fastest if all of these

gases are at the same temperature

and pressure?

A. SO

₂

C. N

₂

O

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14.4 Gases: Mixtures and Movements >

A. SO

₂

C. N

₂

O

B. Cl

₂

D. Hg

Which of the following gas particles

will diffuse fastest if all of these

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14.4 Gases: Mixtures and Movements >

Key Concepts

In a mixture of gases, the total pressure is

the sum of the partial pressures of the

gases.

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14.4 Gases: Mixtures and Movements >

Key Equations

Dalton’s Law:

Graham’s Law:

Rate

_A

Rate

_B

=

molar mass

_B

molar mass

_A

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14.4 Gases: Mixtures and Movements >

Glossary Terms

• partial pressure:

the contribution each gas in

a mixture of gases makes to the total

pressure

• Dalton’s law of partial pressures:

at

constant volume and temperature, the total

pressure exerted by a mixture of gases is

equal to the sum of the partial pressures of

the component gases

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14.4 Gases: Mixtures and Movements >

Glossary Terms

• effusion:

the process that occurs when a gas

escapes through a tiny hole in its container

• Graham’s law of effusion:

the rate of

effusion of a gas is inversely proportional to

the square root of its molar mass; this

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14.4 Gases: Mixtures and Movements >

END OF 14.4