# N

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29 Οκτ 2013 (πριν από 4 χρόνια και 7 μήνες)

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5
-
1

Chapter 5

Gases and the Kinetic
-
Molecular Theory

5
-
2

기체와

분자운동론

기체상태의

물질

기체의

압력

기체

법칙

보일의

법칙
,
샤를의

법칙
,
아보가드로의

법칙

분압

기체분자운동론

온도와

에너지
,
확산

실제기체

반데르발스

상태방정식

5
-
3

Gases and the Kinetic Molecular Theory

5.1
An Overview of the Physical States of Matter

5.2
Gas Pressure and Its Measurement

5.3
The Gas Laws and Their Experimental Foundations

5.4
Further Applications of the Ideal Gas Law

5.5
The Ideal Gas Law and Reaction Stoichiometry

5.6
The Kinetic
-
Molecular Theory: A Model for Gas Behavior

5.7
Real Gases: Deviations from Ideal Behavior

5
-
4

기체는

공부하는가
?

역사적인

배경과

의미

1.
Boyle’s Law

First Scientific Experiment, 1661

2.
Charles’s Law

Definition of Temperature, 1780s

3.

4.
Combined Ideal Gas Law and Kinetic Theories

First
Successful Scientific Law derived from purely
mathematical approach.

실용

배경과

의미

1.
기체는

열역학의

기초
,
열역학

1, 2
법칙을

설명

2.
화학

평형
,
화학적

퍼텐셜의

기초

3.
화학반응의

근본적

이해를

도움
-

반응동력학

5
-
5

Gases assume the volume and shape of their containers.

Gases are the most compressible state of matter.

Gases will mix evenly and completely when confined to the same
container.

Gases have much lower densities than liquids and solids.

Physical Characteristics of Gases

5
-
6

Barometer

Units of Pressure

1
pascal

(Pa) = 1 N/m
2

1
atm

= 760 mmHg = 760
torr

1
atm

= 101,325 Pa

bar = 10
5

Pa

psi =
lb
/in
2

= 6894.757 Pa

Pressure =

Force

Area

(
force

= mass x acceleration)

5
-
7

5
-
8

Pressure = Force/Area

SI Units

Force = mass
×

acceleration

Force = kg
-
m/s
2

= Newton

Pressure = Newton/m
2

= Pascal

Customary Units

Pressure =
atm
,
torr
, mmHg, bar, psi

Relate SI to customary

1.01325
×

10
5

Pascal = 1
atm

= 760
torr

bar = 10
5

Pascal

PRESSURE

Units and Measurement

5
-
9

Common
Units of Pressure

Atmospheric Pressure

Unit

Scientific Field

chemistry

atmosphere(
atm
)

1 atm*

pascal
(Pa
);

1.01325
×
10
5
Pa;

SI unit; physics, chemistry

mm
of mercury(Hg)

760 mm Hg*

chemistry, medicine, biology

torr

760 torr*

chemistry

pounds per square
inch (psi or lb/in
2
)

14.7 psi

engineering

bar

1.01325 bar

meteorology, chemistry,
physics

*This is an exact quantity; in calculations, we use as many significant figures as necessary.

5
-
10

Boyle’s Law(1662)

𝑝𝑉
=
𝑘

5
-
11

Charles’ Law

(1780s)

Definition of Temperature

V

=
V
0

+ a
t

V

=
a
T

0

273
.
15

Temperature(K)

T

(K) =
t

(
0
C) + 273.15

5
-
12

Equal volumes of gases contain the same
number of molecules at constant
T
,
P

22.414 L of any gas

contains 6.022
×
10
23

atoms (or molecules)

at 0

and 1 atm.

5
-
13

V

number of moles (
n
)

V

= constant
×

n

V
1
/
n
1

=
V
2
/
n
2

Constant temperature

Constant pressure

3 H
2
(
g
) + N
2
(
g
)

2 NH
3
(
g
)

3 volume + 1 volume

2 volume

3
mol

+ 1
mol

2
mol

3 molecules
+ 1
molecule

2
molecules

5
-
14

Ideal Gas Equation

Charles’ law:
V

T

(at constant
n

and
P
)

V

n

(at constant
P

and
T
)

Boyle’s law:
V

1
𝑃

(at constant
n

and
T
)

V

𝑛𝑇
𝑃

V

= constant
×
𝑛𝑇
𝑃

=
R

𝑛𝑇
𝑃

R

is the
gas constant

PV

=
nRT

5
-
15

Dalton’s Law of Partial Pressures

V

and
T

:
constant

P
1

P
2

P
total

=
P
1

+
P
2

5
-
16

Consider a case in which two gases,
A

and
B
, are in a
container of volume
V
.

P
A

=

n
A
R
T

V

P
B

=

n
B
R
T

V

n
A

is the number of moles of
A

n
B

is the number of moles of
B

P
T

=
P
A

+
P
B

X
A

=

n
A

n
A

+
n
B

X
B

=

n
B

n
A

+
n
B

P
A

=
X
A

P
T

P
B

=
X
B

P
T

P
i

=
x
i

P
T

mole fraction (x
i
) =

n
i

n
T

5
-
17

The Molar Mass of a Gas


=
𝑎𝑠𝑠
𝑀
=
𝑃𝑉
𝑅𝑇

𝑀
=
𝑅𝑇
𝑉𝑃

𝑑
=

𝑉

𝑀
=
𝑑𝑅𝑇
𝑃

5
-
18

Water Vapor Pressure Table

Temperature

Pressure

(
°
C)

(mmHg)

Temperature

Pressure

(
°
C) (mmHg)

Temperature

Pressure

(
°
C) (mmHg)

0.0 4.6

5.0 6.5

10.0 9.2

12.5 10.9

15.0 12.8

15.5 13.2

16.0 13.6

16.5 14.1

17.0 14.5

17.5 15.0

18.0 15.5

18.5 16.0

19.9
16.5

19.5 17.0

20.0 17.5

20.5 18.1

21.0 18.6

21.5 19.2

22.0 19.8

22.5 20.4

23.0 21.1

23.5 21.7

24.0 22.4

24.5 23.1

25.0 23.8

26.0
25.2

27.0 26.7

28.0 28.3

29.0 30.0

30.0 31.8

35.0 42.2

40.0 55.3

50.0 92.5

60.0 149.4

70.0 233.7

80.0 355.1

90.0 525.8

95.0 633.9

100.0
760.0

5
-
19

T

Pressure

T

Pressure

T

Pressure

T

Pressure

(
°
C
)

(mmHg)

(
°
C
)

(mmHg)

(
°
C
)

(mmHg)

(
°
C
)

(mmHg)

0

4.6

1

4.9

26

25.2

51

97.2

76

301.4

2

5.3

27

26.7

52

102.1

77

314.1

3

5.7

28

28.3

53

107.2

78

327.3

4

6.1

29

30.0

54

112.5

79

341.0

5

6.5

30

31.8

55

118.0

80

355.1

6

7.0

31

33.7

56

123.8

81

369.7

7

7.5

32

35.7

57

129.8

82

384.9

8

8.0

33

37.7

58

136.1

83

400.6

9

8.6

34

39.9

59

142.6

84

416.8

10

9.2

35

42.2

60

149.4

85

433.6

11

9.8

36

44.6

61

156.4

86

450.9

12

10.5

37

47.1

62

163.8

87

468.7

13

11.2

38

49.7

63

171.4

88

487.1

14

12.0

39

52.4

64

179.3

89

506.1

15

12.8

40

55.3

65

187.5

90

525.8

16

13.6

41

58.3

66

196.1

91

546.0

17

14.5

42

61.5

67

205.0

92

567.0

18

15.5

43

64.8

68

214.2

93

588.6

19

16.5

44

68.3

69

223.7

94

610.9

20

17.5

45

71.9

70

233.7

95

633.9

21

18.7

46

75.7

71

243.9

96

657.6

22

19.8

47

79.6

72

254.6

97

682.1

23

21.1

48

83.7

73

265.7

98

707.3

24

22.4

49

88.0

74

277.2

99

733.2

25

23.8

50

92.5

75

289.1

100

760.0

5
-
20

P,V,T

of gas A

amount
(mol)

of gas A

amount
(mol)

of gas B

P,V,T

of gas B

ideal
gas
law

ideal
gas
law

molar ratio from
balanced equation

stoichiometric
relationships among the amount
(
mol,
n
) of gaseous reactant or product and the
gas variables
P, V,
and
T.

3 H
2
(
g
) + N
2
(
g
)

2 NH
3
(
g
)

5
-
21

Kinetic Molecular Theory of Gases

1. A gas is composed of molecules that are separated from
each other by distances far greater than their own
dimensions. The molecules can be considered to be
points
;
that is, they
possess mass but have negligible volume
.

d(N
2
,
g
) = 0.00125 g/L (273
°
C)

d(N
2
,
liq
) = 0.808 g/mL (
-
195.8
°
C)

2. Gas molecules are in constant motion in
random directions
.
Collisions among molecules are
perfectly elastic
.

3. Gas molecules exert neither attractive nor repulsive forces
on one another
.(no

interaction)

5
-
22

V
a

n

E
k
= 1/2 mass x speed
2

E
k
= 1/2 mass x
u

2

u
2

is the root
-
mean
-
square speed

u
rms

=

3RT

M

R = 8.314Joule/mol*K

Graham’s Law of Effusion

The rate of effusion of a gas is inversely related to the square root of its molar mass.

rate of effusion

a

1

M

5
-
23

Applying Graham’s Law of Effusion

PROBLEM:

Calculate the ratio of the effusion rates of helium and methane (CH
4
).

SOLUTION:

PLAN:

The effusion rate is inversely proportional to the square root of the
molar mass for each gas. Find the molar mass of both gases and find
the inverse square root of their masses.

M
of CH
4

= 16.04g/mol

M
of He = 4.003g/mol

CH
4

He

rate

rate

=

16.04

4.003

= 2.002

5
-
24

Figure 5.18

Diffusion of a gas particle through a
space filled with other particles.

distribution of molecular speeds

mean free path

collision frequency

5
-
25

Molar
Volume of Some Common Gases at
0
0
C
and 1
atm

Gas

Molar Volume

(L/mol)

Condensation Point

(
0
C)

He

H
2

Ne

Ideal gas

Ar

N
2

O
2

CO

Cl
2

NH
3

22.435

22.432

22.422

22.414

22.397

22.396

22.390

22.388

22.184

22.079

-
268.9

-
252.8

-
246.1

---

-
185.9

-
195.8

-
183.0

-
191.5

-
34.0

-
33.4

5
-
26

Figure 5.19

The behavior of several
real gases with increasing
external pressure.

5
-
27

Van
der Waals Constants for Some Common Gases

0.034

0.211

1.35

2.32

4.19

0.244

1.39

1.36

6.49

3.59

2.25

4.17

5.46

He

Ne

Ar

Kr

Xe

H
2

N
2

O
2

Cl
2

CO
2

CH
4

NH
3

H
2
O

0.0237

0.0171

0.0322

0.0398

0.0511

0.0266

0.0391

0.0318

0.0562

0.0427

0.0428

0.0371

0.0305

Gas

a

atm∙L
2

mol
2

b

L

mol

Van der Waals

equation for n

moles of a real gas

5
-
28

Collisions of Gas Particles

5
-
29

Collisions of Gas Particles

5
-
30

The gas molecules in the container are in random motion

5
-
31

압력과

기체분자

운동

운동량

변화

p =
mv
x

(

mv
x
)

= 2mv
x

분자의

왕복시간

t = 2a/
v
x

분자

개가

A

미치는

f =

p/

t= 2mv
x
/(2a/
v
x
)= mv
x
2
/a

N
개의

분자에

의해

A

가해지는

압력

P =
Σ
f/a
2

= m(v
x1
2
+ v
x2
2
+ ... + v
xN
2
)/a
3

=Nmv
x
2
/V

PV=Nmv
x
2

5
-
32

압력과

기체분자

운동

공간

상에서

무작위로

움직이는

분자는

특별한

방향에

대한

선호도가

없을

것이므로

분자당

평균운동에너지

Gas Pressure in the Kinetic Theory

5
-
33

운동에너지와

온도

이상

기체방정식

기체에

열이

가해지면

기체의

내부에너지와

온도가

증가
!

Boltzmann constant

Mean Kinetic Energy per particle

5
-
34

N
= number of molecules,

k
B

= Boltzmann constant, J K
-
1
,

n
= number of moles =
N
/
N
A
,

R

= gas constant, 0.08204 l
atm

mol
-
1

K
-
1

T =
temperature,

P

= gas pressure,

V

= volume,

N
A

PV

=
Nk
B
T

=
nRT

5
-
35

Maxwell
-
Boltzmann Distribution
for Molecular Speeds

f(u)

= speed distribution function,

m

= molecular mass,

k

= Boltzmann constant,

T

= temperature,
u

= speed

u~
u+du

사이의

속도를

가진

분자들의

5
-
36

분자속도와

에너지

분포

(Molecular velocity and energy distribution)

슈테른
(Otto

Stern)

분자속도

측정

노벨물리학상

수상자
(1943, w/ Gerlach)

Schematic diagram of a stern type experiment for determining the distribution

of molecular velocities

v ~ v+
∆v
사이의

분자개수

N
측정가능
!!

http://leifi.physik.uni
-
muenchen.de/web_ph12/ori ginal arbeiten/stern/molekularstr.htm

5
-
37

Molecular speed Distribution of N
2

gas

Maxwell Boltzmann distribution of molecular speeds in nitrogen gas at two
temperatures. The ordinate is the fractional number of molecules per unit
speed interval in (km/s)
-
1
.

5
-
38

Apparatus for studying molecular speed distribution

Chopper method

gravitation method

5
-
39

Chemistry in Action: Super Cold Atoms

Gaseous
Rb

Atoms

1.7 x 10
-
7

K(170
nK
)

Bose
-
Einstein
Condensate

1995, Eric Cornell and Carl
Wieman

Three images showing formation of Bose
-
Einstein
condensate. picture from JILA

5
-
40

Gaseous Diffusion/Effusion

Diffusion of Ammonia and
HCl

Effusion enrichment of UF
6

Graham’s Law of Effusion

A bank of uranium gas
centrifuges

Uranium Information Centre

5
-
41

Gas diffusion

is the gradual mixing of molecules of one gas
with molecules of another by virtue of their kinetic properties.

NH
3

17 g/mol

HCl

36 g/mol

NH
4
Cl

5
-
42

Kinetic
-
Molecular Theory for
Gaseous Behavior

Principal Issues (
잠재적

문제점
)

Negligible Volume and No interaction

Hold only at low
P
, high
T
; for dilute gases

Elastic Collisions

Only in Newtonian mechanics is the reverse of an event as
likely as the event itself.

In the real world you cannot “unscramble” eggs because of
entropy effects resulting from large ensembles of molecules

5
-
43

Deviations from Ideal Behavior

1
mole of ideal gas

PV

=
RT

Z
=

PV

RT

= 1.0

Repulsive Forces

Attractive Forces

compression factor

5
-
44

Effect of intermolecular forces on
the pressure exerted by a gas.

Real Gas

Has volume

Has interaction(usually
attractive)

5
-
45

Van
der

Waals equation

nonideal

gas

P

+ (
V

nb
) =
nRT

an
2

V
2

(

)

}

corrected

pressure

}

corrected

volume

Gas

a

[(L
2

atm
)/mol
2
]

b

[10
-
2
L/
mol
]

He

0.03412

2.370

Ne

0.211

1.71

Ar

1.34

3.22

Kr

2.32

3.98

Xe

4.19

2.66

H
2

0.2444

2.661

N
2

1.390

3.913

O
2

1.360

3.183

CO
2

3.592

4.267

CH
4

2.25

4.28

CCl
4

20.4

13.8

C
2
H
2

4.390

5.136

Cl
2

6.493

5.622

C
4
H
10

14.47

12.26

C
8
H
18

37.32

23.68

Selected Values for a and b for the
van der Waals Equation

5
-
46

Hydrogen Economy & Fuel Cell

5
-
47

Chlorine Destroys Ozone

but is not consumed in the process

Ozone Depletion

5
-
48

5
-
49

Crutzen

Molina

Rowland

Holland (The
Netherlands)

Max
-
Planck
-
Institute
for Chemistry

Mainz, Germany

1933
-

USA (Mexico)

Department of Earth,

Atmospheric

and Planetary Sciences
and

Department of Chemistry,

MIT

Cambridge, MA, USA

1943
-

USA

Department of Chemistry,

University of California

Irvine, CA, USA

1927
-

5
-
50

Hindenberg

Crew:

40 to 61

Capacity:

50
-
72 passengers

Length:

245 m ,
Diameter:

41 m

Volume:

200,000 m³

Powerplant:

4
×

Daimler
-
Benz diesel
engines,

890 kW (1,200 hp)

each

기체
:
수소
(
헬륨으로

계획되었으나

수소로

대체
)

부력
:

5
-
51

Science of Hot Air Balloon

2008 National Balloon Classic in Indianola, Iowa.

부력

=

공기의

무게

공기의

무게

공기의

무게

=
공기의

밀도
(
ρ
(
T
hot
))
×

풍선의

부피
(V
)
×
g

공기의

무게

=
공기의

밀도
(
ρ
(
T
cold
))
×

풍선의

부피
(V
)
×
g

공기의

밀도

ρ
(
T
) =
w/V

=
Mp
/RT

부피
(m
3
)

600 ~ 2800 ~ 17,000

T
cold

~ 20

T
hot

~ 100

부력

~ 700kg

5
-
52

Lake Nyos, the killer Lake of
Cameroon

Clarke, T.,
Taming Africa’s killer lake
,
Nature
, V. 409,
p. 554
-
555, February 2001.

5
-
53

Lake Nyos, the killer Lake

Clarke, T.,
Taming Africa’s killer lake
,
Nature
, V. 409, p. 554
-
555, February 2001.

Test of the de
-
gassing operation in 1995

5
-
54

Air Bag Chemistry

5
-
55

Air Bag Chemistry

5
-
56

5
-
57

Air Bag Chemistry

5
-
58

Air Bag Chemistry

On ignition:

2 NaN
3

2Na + 3N
2

Secondary reactions:

10 Na + 2 KNO
3

K
2
O + 5 Na
2
O + N
2

K
2
O + Na
2
O + SiO
2

K
2
Na
2
SiO
4