The kinetic theory of gases

2. GASES
•Gases are one of the most pervasive
aspects of our environment on the
Earth. We continually exist with
constant exposure to gases of all
forms.
•The steam formed in the air during a
hot shower is a gas.
•The Helium used to fill a birthday
balloon is a gas.
•The oxygen in the air is an essential
gas for life.

3. GASES
A windy day or a still day is a result of the difference in pressure of gases
in two different locations. A fresh breeze on a mountain peak is a study in
basic gas laws.

4. Important Characteristics of Gases
1) Gases are highly compressible
An external force compresses the gas sample and decreases its
volume, removing the external force allows the gas volume to
increase.
2) Gases are thermally expandable
When a gas sample is heated, its volume increases, and when it is
cooled its volume decreases.
3) Gases have high viscosity
Gases flow much easier than liquids or solids.
4) Most Gases have low densities
Gas densities are on the order of grams per liter whereas liquids
and solids are grams per cubic cm, 1000 times greater.
5) Gases are infinitely miscible
Gases mix in any proportion such as in air, a mixture of many gases.

5. •Helium He 4.0
•Neon Ne 20.2
•Argon Ar 39.9
•Hydrogen H
2
2.0
•Nitrogen N
2
28.0
•Nitrogen Monoxide NO 30.0
•Oxygen O
2
32.0
•Hydrogen Chloride HCl 36.5
•Ozone O
3
48.0
•Ammonia NH
3
17.0
•Methane CH
4
16.0
Substances That Are Gases under
Normal Conditions
Substance Formula MM(g/mol)

6. Kinetic Molecular Theory
•To fully understand the world around us
requires that we have a good understanding
of the behavior of gases. The description of
gases and their behavior can be approached
from several perspectives.
•The Gas Laws are a mathematical
interpretation of the behavior of gases.
• However, before understanding the
mathematics of gases, a chemist must have
an understanding of the conceptual
description of gases. That is the purpose of
the Kinetic Molecular Theory.

7. Kinetic Molecular Theory
•The Kinetic Molecular Theory is a single set of
descriptive characteristics of a substance known as
the Ideal Gas.
•All real gases require their own unique sets of
descriptive characteristics. Considering the large
number of known gases in the World, the task of
trying to describe each one of them individually
would be an awesome task.
•In order to simplify this task, the scientific
community has decided to create an imaginary gas
that approximates the behavior of all real gases. In
other words, the Ideal Gas is a substance that does
not exist.
•The Kinetic Molecular Theory describes that gas.
While the use of the Ideal Gas in describing all real
gases means that the descriptions of all real gases
will be wrong, the reality is that the descriptions of
real gases will be close enough to correct that any
errors can be overlooked.

8. The Nature of Gases
Three basic assumptions of the kinetic
theory as it applies to gases:
1. Gas is composed of particles- usually
molecules or atoms
–Small, hard spheres
–Insignificant volume; relatively far
apart from each other
–No attraction or repulsion between
particles

9. The Nature of Gases
2. Particles in a gas move rapidly in
constant random motion
–Move in straight paths, changing
direction only when colliding with one
another or other objects
–Average speed of O
2
in air at 20
o
C is
an amazing 1660 km/h!
(1.6km=1mile)

10. The Nature of Gases
3. Collisions are perfectly elastic-
meaning kinetic energy is transferred
without loss from one particle to
another- the total kinetic energy remains
constant
Newtonian Cradle-
Where the collisions between the balls elastic?
Yes, because kinetic energy was transferred
with each collision

11. •Why did the balls eventually stop
swinging? The collisions were not
perfectly elastic, some kinetic energy
was lost as heat during each collision.
•At constant temperatures and low to
moderate pressures, collisions between
gas particles are perfectly elastic

12. THE KINETIC THEORY OF GASES
•Gas consists of large number of particles
(atoms or molecules)
•Particles make elastic collisions with each
other and with walls of container
•There exist no external forces (density
constant)
•Particles, on average, separated by distances
large compared to their diameters
•No forces between particles except when
they collide
Remember the assumptions

13. What happens to a ball when it
drops?
The potential energy
of the ball
Which is converted to
kinetic energy in the
ball
Which is converted
to potential energy
in the ball
Is converted to kinetic
energy in the ball
Which is converted into
the potential energy of
the ball…………..
…..but in reality the ball
loses height and
eventually stops bouncing
Why does this
happen?

14. How does the bouncing ball lose
energy?
•Through friction with the air (air
resistance)
•Through sound when it hits the floor
•Through deformation of the ball
•Through heat energy in the bounce

16. IDEAL GAS MODEL
•The gas consists of objects with a defined mass and zero volume.

•The gas particles travel randomly in straight-line motion where their movement can be described by the fundamental laws of mechanics.

•All collisions involving gas particles are elastic; the kinetic energy of the system is conserved even though the kinetic energy among the particles is redistributed.

•The gas particles do not interact with each other or the with the walls of any container.

•The gas phase system will have an average kinetic energy that is proportional to temperature; the kinetic energy will be distributed among the particles according to a Boltzmann type of distribution.

17. Boltzman Distribution. The behaviour of
the gas molecules under the action of
gravity.

18. Maxwell Distribution. Experiment with
Galton board demonstrates the
statistical sense of Maxwell distribution.

19. Ideal Gas Model
Kinetic Molecular Theory (KMT) for an ideal
gas states that all gas particles:
•are in random, constant, straight-line motion.
•are separated by great distances relative to
their size; the volume of the gas particles is
considered negligible.
•have no attractive forces between them.
•have collisions that may result in the transfer
of energy between gas particles, but the total
energy of the system remains constant.

20. Brownian motion. Chaotic motion of
minute particle suspended in a gas or
liquid

21. This animation illustrates the concept of
free path length of molecules in a gas.

22. Ideal vs. Non-Ideal Gases
•Kinetic Theory Assumptions
–Point Mass
–No Forces Between Molecules
–Molecules Exert Pressure Via Elastic
Collisions With Walls
xx
(courtesy F. Remer)

23. Ideal vs. Non-Ideal Gases
•Non-Ideal Gas
–Violates Assumptions
•Volume of molecules
•Attractive forces of molecules
(courtesy F. Remer)

24. Deviations from ideal behaviour
•A real gas is most like an ideal gas when the
real gas is at low pressure and high
temperature.
•At high pressures gas particles are close
therefore the volume of the gas particles is
considered.
•At low temperatures gas particles have low
kinetic energy therefore particles have some
attractive force
•Example
•Dry ice, liquid oxygen and nitrogen

25. Ideal Gases
Behave as described by the ideal gas
equation; no real gas is actually ideal
Within a few %, ideal gas equation describes
most real gases at room temperature and
pressures of 1 atm or less
In real gases, particles attract each other
reducing the pressure
Real gases behave more like ideal gases as
pressure approaches zero.

26. Atmospheric Pressure
•Weight of column of air above your head.
•We can measure the density of the
atmosphere by measuring the pressure it
exerts.

27. Effect of Atmospheric Pressure on
Objects at the Earth’s Surface

29. Atmospheric Pressure
Pressure = Force per Unit Area
Atmospheric Pressure is the weight of
the column of air above a unit area. For
example, the atmospheric pressure felt
by a man is the weight of the column of
air above his body divided by the area
the air is resting on
P = (Weight of column)/(Area of base)
Standard Atmospheric Pressure:
1 atmosphere (atm)
14.7 lbs/in
2
(psi)
760 Torr (mm Hg)
1013.25 KiloPascals or Millibars (kPa =
N/m
2
)

30. Pressure Measurement
Torricelli's Barometer
•Torricelli determined from this
experiment that the pressure of the
atmosphere is approximately 30
inches or 76 centimeters (one
centimeter of mercury is equal to 13.3
millibars. He also noticed that height
of the mercury varied with changes in
outside weather conditions.
For climatological and meteorological purposes, standard sea-level pressure
is said to be 76.0 cm or 29.92 inches or 1013 millibars

31. The Nature of Gases
Atmospheric pressure results from
the collisions of air molecules with
objects
–Decreases as you climb a mountain
because the air layer thins out as
elevation increases
Barometer is the measuring
instrument for atmospheric
pressure; dependent upon weather

32. Common Units of Pressure
Unit Atmospheric Pressure Scientific Field
pascal (Pa); 1.01325 x 10
5
Pa SI unit; physics,
kilopascal(kPa) 101.325 kPa chemistry
atmosphere (atm) 1 atm* Chemistry

millimeters of mercury 760 mmHg* Chemistry, medicine,
( mm Hg ) biology
torr 760 torr* Chemistry
pounds per square inch 14.7 lb/in
2
Engineering
( psi or lb/in
2
)
bar 1.01325 bar Meteorology,
chemistry, physics

33. Converting Units of Pressure
Problem: A chemist collects a sample of carbon dioxide from the
decomposition of limestone (CaCO
3
) in a closed end manometer, the
height of the mercury is 341.6 mm Hg. Calculate the CO
2
pressure in
torr, atmospheres, and kilopascals.
Plan: The pressure is in mmHg, so we use the conversion factors from
Table 5.2(p.178) to find the pressure in the other units.
Solution:
P
CO2
(torr) = 341.6 mm Hg x = 341.6 torr
1 torr
1 mm Hg
converting from mmHg to torr:
converting from torr to atm:
P
CO2
( atm) = 341.6 torr x = 0.4495 atm
1 atm
760 torr
converting from atm to kPa:
P
CO2
(kPa) = 0.4495 atm x = 45.54 kPa
101.325 kPa
1 atm

34. Change in Pressure
Change in average
atmospheric pressure with
altitude.

35. The Nature of Gases
Gas Pressure – defined as the
force exerted by a gas per unit
surface area of an object
–Due to: a) force of collisions, and b)
number of collisions
–No particles present? Then there
cannot be any collisions, and thus no
pressure – called a vacuum

37. Manometers
Rules of thumb:
 When evaluating, start from the known
pressure end and work towards the
unknown end
 At equal elevations, pressure is
constant in the SAME fluid
 When moving down a manometer,
pressure increases
 When moving up a manometer,
pressure decreases
 Only include atmospheric pressure on
open ends
Manometers measure a pressure difference by balancing the
weight of a fluid column between the two pressures of interest

39. Manometers

40. Manometers
Find the pressure at
point A in this open u-
tube manometer with an
atmospheric pressure P
o

P
D
= γ
H2O
x h
E-D
+ P
o
P
c
= P
D
P
B
= P
C
- γ
Hg
x h
C-B
P
A
= P
B
Example 2
P = γ x h + P
O

41. The Gas Laws
•What would Polly
Parcel look like if she
had no gas molecules
inside?
zero molecules = zero pressure inside
zero pressure inside = zero force on the
inside

42. Gas Law Variables
• In order to describe gases, mathematically, it
is essential to be familiar with the variables
that are used. There are four commonly
accepted gas law variables
•Temperature
•Pressure
•Volume
•Moles

43. Temperature
•The temperature variable is always symbolized as T.
•It is critical to remember that all temperature values
used for describing gases must be in terms of
absolute kinetic energy content for the system.
•Consequently, T values must be converted to the
Kelvin Scale. To do so when having temperatures
given in the Celsius Scale remember the conversion
factor
•Kelvin = Celsius + 273
•According to the Kinetic Molecular Theory, every
particle in a gas phase system can have its own
kinetic energy. Therefore, when measuring the
temperature of the system, the average kinetic
energy of all the particles in the system is used.
•The temperature variable is representing the
position of the average kinetic energy as expressed
on the Boltzmann Distribution.

44. Pressure
•The pressure variable is represented by the
symbol P.
•The pressure variable refers to the pressure
that the gas phase system produces on the
walls of the container that it occupies.
•If the gas is not in a container, then the
pressure variable refers to the pressure it
could produce on the walls of a container if it
were in one.
•The phenomenon of pressure is really a force
applied over a surface area. It can best be
expressed by the equation

45. Pressure
•Consider the Pressure equation and the impact of
variables on it.
•The force that is exerted is dependent upon the
kinetic energy of the particles in the system. If the
kinetic energy of the particles increases, for
example, then the force of the collisions with a given
surface area will increase. This would cause the
pressure to increase. Since the kinetic energy of the
particles is increased by raising the temperature,
then an increase in temperature will cause an
increase in pressure.
•If the walls of the container were reduced in total
surface area, there would be a change in the
pressure of the system. By allowing a given quantity
of gas to occupy a container with a smaller surface
area, the pressure of the system would increase.

46. Pressure
•As this container of gas
is heated, the
temperature increases.
As a result, the average
kinetic energy of the
particles in the system
increases.
•With the increase in
kinetic energy, the force
on the available amount
of surface area increases.
As a result, the pressure
of the system increases.
•Eventually,.........................
.Ka-Boom

47. Volume
•The Volume variable is represented by the symbol V.
It seems like this variable should either be very easy
to work with or nonexistent.
•Remember, according to the Kinetic Molecular
Theory, the volume of the gas particles is set at zero.
Therefore, the volume term V seems like it should be
zero.
•In this case, that is not true. The volume being
referred to here is the volume of the container, not
the volume of the gas particles.
•The actual variable used to describe a gas should be
the amount of volume available for the particles to
move around in. In other words

48. Volume
•Since the Kinetic Molecular Theory
states that the volume of the gas
particles is zero, then the equation
simplifies.
•As a result, the amount of available
space for the gas particles to move
around in is approximately equal to the
size of the container.
•Thus, as stated before, the variable V is
the volume of the container.

49. Moles
•The final gas law variable is the quantity of gas. This is always
expressed in terms of moles. The symbol that represents the
moles of gas is n. Notice that, unlike the other variables, it is in
lower case.
•Under most circumstances in chemistry, the quantity of a
substance is usually expressed in grams or some other unit of
mass. The mass units will not work in gas law mathematics.
Experience has shown that the number of objects in a system
is more descriptive than the mass of the objects.
• Since each different gas will have its own unique mass for the
gas particles, this would create major difficulties when working
with gas law mathematics.
•The whole concept of the Ideal Gas says that all gases can be
approximated has being the same. Considering the large
difference in mass of the many different gases available, using
mass as a measurement of quantity would cause major errors
in the Kinetic Molecular Theory.
•Therefore, the mole will standardize the mathematics for all
gases and minimize the chances for errors.

50. Conclusions
There are four variables used mathematically for describing a
gas phase system. While the units used for the variables may
differ from problem to problem, the conceptual aspects of the
variables remain unchanged.
1. T, or Temperature, is a measure of the average kinetic energy of
the particles in the system and MUST be expressed in the
Kelvin Scale.
2. P, or Pressure, is the measure of the amount of force per unit
of surface area. If the gas is not in a container, then P
represents the pressure it could exert if it were in a container.
3. V, or Volume, is a measure of the volume of the container that
the gas could occupy. It represents the amount of space
available for the gas particles to move around in.
4. n, or Moles, is the measure of the quantity of gas. This
expresses the number of objects in the system and does not
directly indicate their masses.

51. Gas Laws
•(1) When temperature is held constant, the density of a
gas is proportional to pressure, and volume is inversely
proportional to pressure. Accordingly, an increase in
pressure will cause an increase in density of the gas and
a decrease in its volume. – Boyles’s Law
•(2) If volume is kept constant, the pressure of a unit
mass of gas is proportional to temperature. If
temperature increase so will pressure, assuming no
change in the volume of the gas.
•(3) Holding pressure constant, causes the temperature of
a gas to be proportional to volume, and inversely
proportional to density. Thus, increasing temperature of
a unit mass of gas causes its volume to expand and its
density to decrease as long as there is no change in
pressure. - Charles’s Law

53. Boyle’s Law
•Hyperbolic Relation Between Pressure and
Volume
p
V
p – V Diagramp – V Diagram
isotherms
T
1T
2
T
3
T
3
>T
2
>T
1
(courtesy F. Remer)

55. Charles’ Law
•Linear Relation Between Temperature and
Pressure
P
T (K)
0 100 200 300
P – T DiagramP – T Diagram
isochorsisochorsV
1
V
2
V
3
V
1
<V
2
<V
3
(courtesy F. Remer)

56. Charles’ Law
Real data must be
obtained above
liquefaction
temperature.
Experimental curves for
different gasses,
different masses,
different pressures all
extrapolate to a
common zero.

57. Another version of Charles Law

58. Compression and expansion of
adiabatically isolated gas is
accompanied by its heating and cooling.

60. The Gas Laws
•What would Polly
Parcel look like if she
had a temperature of
absolute zero inside?
absolute zero = no molecular motion
no molecular motion = zero force on
the inside

61. Ideal Gas Law
The equality for the four variables involved
in Boyle’s Law, Charles’ Law, Gay-Lussac’s
Law and Avogadro’s law can be written
PV = nRT

R = ideal gas constant

62. PV = nRT
R is known as the universal gas constant
Using STP conditions
P V
R = PV = (1.00 atm)(22.4 L)
nT (1mol) (273K)
n T
= 0.0821 L-atm
mol-K

63. Learning Check
What is the value of R when the STP value
for P is 760 mmHg?

64. Solution
What is the value of R when the STP value
for P is 760 mmHg?
R = PV = (760 mm Hg) (22.4 L)
nT (1mol) (273K)
= 62.4 L-mm Hg
mol-K

65. Learning Check
Dinitrogen monoxide (N
2
O), laughing gas, is
used by dentists as an anesthetic. If 2.86
mol of gas occupies a 20.0 L tank at 23°C,
what is the pressure (mmHg) in the tank in
the dentist office?

66. Solution
Set up data for 3 of the 4 gas variables
Adjust to match the units of R

V = 20.0 L 20.0 L
T = 23°C + 273 296 K
n = 2.86 mol2.86 mol
P = ? ?

67. Rearrange ideal gas law for unknown P
P = nRT
V
Substitute values of n, R, T and V and
solve for P
P = (2.86 mol)(62.4L-mmHg)(296 K)
(20.0 L) (K-mol)
= 2.64 x 10
3
mm Hg

68. Learning Check
A 5.0 L cylinder contains oxygen gas
at 20.0°C and 735 mm Hg. How many
grams of oxygen are in the cylinder?

69. Solution
Solve ideal gas equation for n (moles)
n = PV
RT
= (735 mmHg)(5.0 L)(mol K)
(62.4 mmHg L)(293 K)
= 0. 20 mol O
2
x 32.0 g O
2
= 6.4 g O
2

1 mol O
2

70. Molar Mass of a gas
What is the molar mass of a gas if 0.250 g of
the gas occupy 215 mL at 0.813 atm and
30.0°C?
n = PV = (0.813 atm) (0.215 L) = 0.00703 mol
RT (0.0821 L-atm/molK) (303K)
Molar mass = g = 0.250 g = 35.6 g/mol
mol 0.00703 mol

71. Density of a Gas
Calculate the density in g/L of O
2
gas at STP.
From STP, we know the P and T.
P = 1.00 atm T = 273 K
Rearrange the ideal gas equation for moles/L
PV = nRT PV = nRT P = n
RTV RTV RT V

72. Substitute
(1.00 atm ) mol-K = 0.0446 mol O
2
/L
(0.0821 L-atm) (273 K)
Change moles/L to g/L
0.0446 mol O
2
x 32.0 g O
2
= 1.43 g/L
1 L 1 mol O
2
Therefore the density of O
2
gas at STP is
1.43 grams per liter

73. Formulas of Gases
A gas has a % composition by mass of
85.7% carbon and 14.3% hydrogen. At
STP the density of the gas is 2.50 g/L.
What is the molecular formula of the
gas?

74. Formulas of Gases
Calculate Empirical formula
85.7 g C x 1 mol C = 7.14 mol C/7.14 = 1 C
12.0 g C
14.3 g H x 1 mol H = 14.3 mol H/ 7.14 = 2 H
1.0 g H
Empirical formula = CH
2
EF mass = 12.0 + 2(1.0) = 14.0 g/EF

75. Using STP and density ( 1 L = 2.50 g)
2.50 g x 22.4 L = 56.0 g/mol
1 L 1 mol
n = EF/ mol = 56.0 g/mol = 4
14.0 g/EF
molecular formula
CH
2
x 4 = C
4
H
8

76. Gases in Chemical Equations
On December 1, 1783, Charles used 1.00 x 10
3

lb of iron filings to make the first ascent in a
balloon filled with hydrogen
Fe(s) + H
2
SO
4
(aq) ¾® FeSO
4
(aq) + H
2
(g)
At STP, how many liters of hydrogen
gas were generated?

77. Solution
lb Fe ¾® g Fe ¾® mol Fe ¾® mol H
2
¾® L
H
2
1.00 x 10
3
lb x 453.6 g x 1 mol Fe x 1 mol H
2

1 lb 55.9 g 1 mol Fe
x 22.4 L H
2
= 1.82 x 10
5
L H
2
1 mol H
2
Charles generated 182,000 L of hydrogen to fill his
air balloon.

78. Learning Check
How many L of O
2
are need to react 28.0 g
NH
3
at

24°C and 0.950 atm?
4 NH
3
(g) + 5 O
2
(g) 4 NO(g) + 6 H
2
O(g)

79. Solution
Find mole of O
2

28.0 g NH
3
x 1 mol NH
3
x 5 mol O
2
17.0 g NH
3
4 mol NH
3

= 2.06 mol O
2
V = nRT = (2.06 mol)(0.0821)(297K) = 52.9 L
P

0.950 atm

80. Mixture of gases

81. Reacting mixture of gases

82. Learning Check
A.If the atmospheric pressure today is 745
mm Hg, what is the partial pressure (mm
Hg) of O
2
in the air?
1) 35.6 2) 156 3) 760
B. At an atmospheric pressure of 714, what is
the partial pressure (mm Hg) N
2
in the air?
1) 557 2) 9.14 3) 0.109

83. Solution
A.If the atmospheric pressure today is 745
mm Hg, what is the partial pressure (mm
Hg) of O
2
in the air?
2) 156
B. At an atmospheric pressure of 714, what is
the partial pressure (mm Hg) N
2
in the air?
1) 557

84. Partial Pressure
Partial Pressure
Pressure each gas in a mixture would exert
if it were the only gas in the container
Dalton's Law of Partial Pressures
The total pressure exerted by a gas mixture
is the sum of the partial pressures of the
gases in that mixture.
P
T
= P
1
+ P
2
+ P
3
+ .....

85. Partial Pressures
The total pressure of a gas mixture depends
on the total number of gas particles, not on
the types of particles.
STP
P = 1.00 atm P = 1.00 atm
1.0 mol He
0.50 mol O
2
+ 0.20 mol He
+ 0.30 mol N
2

86. Health Note
When a scuba diver is several hundred feet
under water, the high pressures cause N
2
from
the tank air to dissolve in the blood. If the
diver rises too fast, the dissolved N
2
will form
bubbles in the blood, a dangerous and painful
condition called "the bends". Helium, which is
inert, less dense, and does not dissolve in the
blood, is mixed with O
2
in scuba tanks used for
deep descents.

87. Learning Check
A 5.00 L scuba tank contains 1.05 mole of
O
2
and 0.418 mole He at 25°C. What is the
partial pressure of each gas, and what is
the total pressure in the tank?

88. Solution G20
P

= nRT P
T
= P
O
+ P
He
V
2
P
T


= 1.47 mol x 0.0821 L-atm x 298 K
5.00 L (K mol)
=7.19 atm

89. Micro Effusion

90. Macro Effusion