Ch14.3Chem.ppt

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14.3 Ideal Gases >

Chapter 14 The Behavior of Gases

14.1 Properties of Gases

14.2 The Gas Laws

14.3 Ideal Gases

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14.3 Ideal Gases >

How can you blanket a stage with fog?

CHEMISTRY

&

YOU

CHEMISTRY

&

YOU

Solid carbon

dioxide, or dry ice,

can be used to

(3)

14.3 Ideal Gases >

How can you calculate the

amount of a contained gas when the

pressure, volume, and temperature

are specified?

Ideal Gas Law

(4)

14.3 Ideal Gases >

Suppose you want to calculate the number

of moles (

n

) of a gas in a fixed volume at a

known temperature and pressure.

Ideal Gas Law

(5)

14.3 Ideal Gases >

Suppose you want to calculate the number

of moles (

n

) of a gas in a fixed volume at a

known temperature and pressure.

• The volume occupied by a gas at a

specified temperature and pressure

depends on the number of particles.

Ideal Gas Law

(6)

14.3 Ideal Gases >

Suppose you want to calculate the number

of moles (

n

) of a gas in a fixed volume at a

known temperature and pressure.

• The volume occupied by a gas at a

specified temperature and pressure

depends on the number of particles.

• The number of moles of gas is directly

proportional to the number of particles.

Ideal Gas Law

(7)

14.3 Ideal Gases >

Suppose you want to calculate the number

of moles (

n

) of a gas in a fixed volume at a

known temperature and pressure.

• The volume occupied by a gas at a

specified temperature and pressure

depends on the number of particles.

• The number of moles of gas is directly

proportional to the number of particles.

Ideal Gas Law

(8)

14.3 Ideal Gases >

You can introduce moles into the

combined gas law by dividing each side of

the equation by

n

.

Ideal Gas Law

(9)

14.3 Ideal Gases >

You can introduce moles into the

combined gas law by dividing each side of

the equation by

n

.

• This equation shows that (

P



V

)/(

T



n

) is a

constant.

Ideal Gas Law

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14.3 Ideal Gases >

You can introduce moles into the

combined gas law by dividing each side of

the equation by

n

.

P

₁



V

₁

P

₂



V

₂

T

₁



n

₁

=

T

₂



n

₂

• This equation shows that (

P



V

)/(

T



n

) is a

constant.

• This constant holds for what are called ideal

gases—gases that conform to the gas laws.

Ideal Gas Law

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14.3 Ideal Gases >

If you know the values for

P

,

V

,

T

, and

n

for one set of conditions, you can calculate

a value for the

ideal gas constant

(R)

.

P



V

R

=

Ideal Gas Law

(12)

14.3 Ideal Gases >

If you know the values for

P

,

V

,

T

, and

n

for one set of conditions, you can calculate

a value for the

ideal gas constant

(R)

.

• Recall that 1 mol of every gas occupies

22.4 L at STP (101.3 kPa and 273 K).

P



V

T



n

R

=

Ideal Gas Law

(13)

14.3 Ideal Gases >

If you know the values for

P

,

V

,

T

, and

n

for one set of conditions, you can calculate

a value for the

ideal gas constant

(R)

.

• Recall that 1 mol of every gas occupies

22.4 L at STP (101.3 kPa and 273 K).

• Insert the values of

P

,

V

,

T

, and

n

into

(

P



V

)/(

T



n

).

P



V

T



n

R

=

101.3 kPa

_{273 K}

_

_{1 mol}



22.4 L

Ideal Gas Law

(14)

14.3 Ideal Gases >

If you know the values for

P

,

V

,

T

, and

n

for one set of conditions, you can calculate

a value for the

ideal gas constant

(R)

.

• Recall that 1 mol of every gas occupies

22.4 L at STP (101.3 kPa and 273 K).

• Insert the values of

P

,

V

,

T

, and

n

into

(

P



V

)/(

T



n

).

P



V

T



n

R

=

101.3 kPa

_{273 K}

_

_{1 mol}



22.4 L

R

= 8.31 (L·kPa)/(K·mol)

Ideal Gas Law

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14.3 Ideal Gases >

The gas law that includes all four

variables—

P

,

V

,

T

,

n

—is called the

ideal

gas law

.

P



V

=

n



R

 T

PV

=

nR

T

or

Ideal Gas Law

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14.3 Ideal Gases >

When the pressure, volume, and

temperature of a contained gas are

known, you can use the ideal gas law

to calculate the number of moles of the

gas.

Ideal Gas Law

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14.3 Ideal Gases >

At 34

o

C, the pressure inside a

nitrogen-filled tennis ball with

a volume of 0.148 L is 212

kPa. How many moles of

nitrogen gas are in the tennis

ball?

Sample Problem 14.5

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14.3 Ideal Gases >

Use the ideal gas law (

PV

=

nRT

) to calculate

the number of moles (

n

).

KNOWNS

P

= 212 kPa

V

= 0.148 L

T

= 34

o

C

R

= 8.31 (L

·

kPa)/(K

·

mol)

UNKNOWN

n

= ? mol N

₂

Analyze

List the knowns and the

unknown.

1 Sample Problem 14.5

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14.3 Ideal Gases >

Convert degrees Celsius to kelvins.

Calculate

Solve for the unknown.

2

T

= 34

o

C + 273 = 307 K

Sample Problem 14.5

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14.3 Ideal Gases >

State the ideal gas law.

Calculate

Solve for the unknown.

2

P



V

=

n



R



T

Sample Problem 14.5

(21)

14.3 Ideal Gases >

Rearrange the equation to isolate

n

.

Calculate

Solve for the unknown.

2

n

=

_R

P



_

_T

V

Isolate

n

by dividing

both sides by (

R



T

)

:

=

R  T

n



R



T

P



V

R  T

P



V

=

n



R



T

Sample Problem 14.5

(22)

14.3 Ideal Gases >

Substitute the known values for

P

,

V

,

R

, and

T

into the equation and solve.

Calculate

Solve for the unknown.

2

n

= 1.23



10

–2

mol N

2

n

=

_{8.31 (L·kPa) / (K·mol)}

212 kPa



0.148 L

_

_{307 K}

n

=

P

_R



_

_T

V

Sample Problem 14.5

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14.3 Ideal Gases >

• A tennis ball has a small volume and

is not under great pressure.

• It is reasonable that the ball contains

a small amount of nitrogen.

Evaluate

Does the result make sense?

3 Sample Problem 14.5

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14.3 Ideal Gases >

A deep underground cavern

contains 2.24 x 10

6

L of

methane gas (CH

₄

) at a

pressure of 1.50 x 10

3

kPa and

a temperature of 315 K. How

many kilograms of CH

₄

does

the cavern contain?

Sample Problem 14.6

(25)

14.3 Ideal Gases >

Calculate the number of moles (

n

) using the ideal gas

law. Use the molar mass of methane to convert moles

to grams. Then convert grams to kilograms.

KNOWNS

P

= 1.50



10

3 kPa

V

= 2.24



10

3 L

T

= 315 K

UNKNOWN

m

= ? kg CH

₄

Analyze

List the knowns and the

unknown.

1 Sample Problem 14.6

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14.3 Ideal Gases >

State the ideal gas law.

Calculate

Solve for the unknown.

2

P



V

=

n



R



T

Rearrange the equation to isolate

n

.

n

=

P

_R



_

_T

V

Sample Problem 14.6

(27)

14.3 Ideal Gases >

Substitute the known quantities into the

equation and find the number of moles

of methane.

Calculate

Solve for the unknown.

2

n

=

8.31 (L·kPa)/(K·mol)



315 K

(1.50



10

6

kPa)



(2.24



10

6

L)

n

= 1.28



10

6

mol CH

4 Sample Problem 14.6

(28)

14.3 Ideal Gases >

Do a mole-mass conversion.

Calculate

Solve for the unknown.

2

1.28 

10

6 mol CH

4 

16.0 g CH

₄

1 mol CH

₄

= 20.5



10

6 g CH

4 = 2.05



10

7 g CH

4 Sample Problem 14.6

(29)

14.3 Ideal Gases >

Convert from grams to kilograms.

Calculate

Solve for the unknown.

2

2.05 

10

6 g CH

4 

1 kg

10

3 g

= 2.05



10

4 kg CH

4 Sample Problem 14.6

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14.3 Ideal Gases >

• Although the methane is

compressed, its volume is still very

large.

• So it is reasonable that the cavern

contains a large amount of methane.

Evaluate

Does the result make sense?

3 Sample Problem 14.6

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14.3 Ideal Gases >

How would you rearrange the ideal gas

law to isolate the temperature, T?

PV

n

R

T =

A

.

n

R

PV

T =

C

.

PR

n

V

T =

(32)

14.3 Ideal Gases >

How would you rearrange the ideal gas

law to isolate the temperature, T?

PV

n

R

T =

A

.

n

R

PV

T

=

C

.

PR

n

V

T =

(33)

14.3 Ideal Gases >

Ideal Gases and Real Gases

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14.3 Ideal Gases >

Ideal Gases and Real Gases

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14.3 Ideal Gases >

Ideal Gases and Real Gases

An ideal gas is one that follows the gas

laws at all conditions of pressure and

temperature.

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14.3 Ideal Gases >

Ideal Gases and Real Gases

An ideal gas is one that follows the gas

laws at all conditions of pressure and

temperature.

• Its particles could have no volume.

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14.3 Ideal Gases >

Ideal Gases and Real Gases

There is no gas for which these

assumptions are true.

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14.3 Ideal Gases >

Ideal Gases and Real Gases

(39)

14.3 Ideal Gases >

Ideal Gases and Real Gases

At many conditions of temperature and pressure,

a real gas behaves very much like an ideal gas.

(40)

14.3 Ideal Gases >

Ideal Gases and Real Gases

At many conditions of temperature and pressure,

a real gas behaves very much like an ideal gas.

• The particles in a real gas

have volume.

(41)

14.3 Ideal Gases >

Ideal Gases and Real Gases

At many conditions of temperature and pressure,

a real gas behaves very much like an ideal gas.

• The particles in a real gas

have volume.

• There are attractions

between the particles.

(42)

14.3 Ideal Gases >

Real gases differ most from an ideal

gas at low temperatures and high

pressures.

Ideal Gases and Real Gases

(43)

14.3 Ideal Gases >

Interpret Graphs

(44)

14.3 Ideal Gases >

(45)

14.3 Ideal Gases >

What are the characteristics of

an ideal gas?

The particles of an ideal gas have

no volume, and there is no

(46)

14.3 Ideal Gases >

Certain types of fog machines use dry ice

and water to create stage fog. What phase

changes occur when stage fog is made?

CHEMISTRY

&

YOU

(47)

14.3 Ideal Gases >

Certain types of fog machines use dry ice

and water to create stage fog. What phase

changes occur when stage fog is made?

CHEMISTRY

&

YOU

CHEMISTRY

&

YOU

(48)

14.3 Ideal Gases >

Key Concepts and Key Equation

When the pressure, volume, and temperature of a contained

gas are known, you can use the ideal gas law to calculate

the number of moles of the gas.

Real gases differ most from an ideal gas at

low temperatures and high pressures.

Key Equation: ideal gas law

(49)

14.3 Ideal Gases >

Glossary Terms

• ideal gas constant:

the constant in the

ideal gas law with the symbol

R

and the

value 8.31 (L·kPa)/(K·mol)

• ideal gas law:

the relationship

PV

=

nRT

,

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14.3 Ideal Gases >

Kinetic Theory

BIG IDEA

BIG

IDEA

• Ideal gases conform to the assumptions of

kinetic theory.

• The behavior of ideal gases can be predicted

by the gas laws.

• With the ideal gas law, the number of moles of

a gas in a fixed volume at a known

temperature and pressure can be calculated.

• Although an ideal gas does not exist, real

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14.3 Ideal Gases >

END OF 14.3