Kinetic Molecular Theory PowerPoint

Gases and Phases of Matter
The Kinetic Molecular
Theory

Kinetic Means “Moving”
• Kinetic = in motion
• Molecular = tiny particles
• Theory = our best model for how
things actually work

Kinetic Molecular Theory
• K
• M
• T
• Kinetic energy is perfectly maintained in “elastic”
molecular collisions. I.e., no energy is lost in collisions.
There is no attraction between particles.
• Molecules are in constant Motion.
– Vibrational motion (solid, liquid and gas molecules all
vibrate.)
– Translational motion (molecules free to move past
each other: liquids and gases only.)
• Tiny particles called “molecules” make up all matter.

Evidence That Gases Exist
• Many gases are
invisible, but not all.
• Iodine vapor is pink.
• Chlorine gas is
yellow-green.
• Smoke and clouds or
fog are NOT gases.

Evidence That Gases Exist
• Gases have mass.
• A balloon inflated
with air weighs more
than a non-inflated
one.
• Moving matter can do
work. Moving air can
do work. E. g. wind
farms and tornadoes.

Evidence That Gases Exist
• Many gases are odorless, but others are not.
• E. g. Hydrogen sulfide makes rotten eggs
and sulfur springs smell bad.
• And of course, we have all “passed wind” at
some point (although we usually won’t
admit it.)

Evidence That Gases Exist
• Gases occupy space,
or have volume.
• E. g. the inflated
balloon mentioned
earlier or the air in
your lungs or a
SCUBA tank.

Evidence That Gases Exist
• Gases exert pressure on
surfaces. Gas molecule
collisions put force on
surfaces.
• P = Force/area
• English system = lb/in 2
• Metric system = N/m 2
• 1N/m 2 = 1 Pascal
• You might be astounded
to learn how much force
(pounds) the atmosphere
around you puts on your
body. Try to find out the
total force on your skin
surface.
• Body Surface Area

Evidence That Gases Exist
• Finally, a scientist named Brown discovered
Brownian Motion.
• When smoke particles in a closed chamber
are examined under a microscope, they are
seen to vibrate.
• The explanation for their random movement
is that the particles are constantly
bombarded by moving air molecules.
• Java applet for Brownian motion.

Kinetic Molecular Theory
• An “ideal gas” is one in which molecular
collisions are perfectly elastic.
• Experimentation shows us that real gases do
not follow ideal behavior.
• We believe that the assumption that
molecular collisions are elastic is NOT
correct.

Kinetic Molecular Theory
• Hence, there are NO IDEAL GASES.
• In real gases, the molecules have some volume of
their own, and there is always some degree of
attraction between molecules.
• Small, non-polar molecules (e. g. He) at very low
pressure and high temperature approach ideal
behavior, but there is still deviation.
• This little applet shows how molecules might
behave and change state with attraction between
the particles. Phase changes with attraction between molecules.

The Gas Laws
• There are several important laws you will
need to know regarding gases.
• These laws involve the use of several
common variables.
• The main variables you will need are these:
– V, P, T, n, R, d and μ (Greek letter “mu”.)

Variables and Their Units
• V = volume in Liters
• T = temperature in Kelvins (°C + 273)
• P = pressure in atmospheres (atm), mmHg, or
kilopascals (kPa)
• n = number of moles of gas
• R = universal gas constant
• d = gas density in g/L
• μ = molar mass of the gas in g/mol

Boyle’s Law
• Robert Boyle discovered that (at constant temperature)
volume and pressure of a gas are inversely proportional.
• V 1 P 1 = V 2 P 2
• Simply put, as P↑, V↓ and vice versa.
• Can the volume of the gas be squeezed down to zero?
• No. The gas is composed of molecules and will always
have some volume and mass.
• As a large volume of atmospheric air is confined to the
small volume of a SCUBA tank, P increases inside the
tank. As V ↓, P ↑.

Charles’ Law
• Jacques Charles discovered that (at constant
pressure) gas volume and temperature are directly
proportional.
• V 1 /T 1 = V 2 /T 2
• Simply put, gases expand as they get warmer and
contract as they cool.
• As T↑, V ↑
• This is how hot air ballooning works.

Gay-Lussac’s Law
• Gay-Lussac discovered that (at constant
volume,) gas temperature and pressure are
directly proportional.
• P 1 /T 1 = P 2 /T 2
• Simply put, as T↑, P↑
• This is why aerosol cans say, “DO NOT
INCINERATE!”

The Combined Gas Law
• To simplify life a bit, Boyle’s, Charles’ and
Gay-Lussac’s Laws are all put together into
one mathematical expression called the
Combined Gas Law.
• V 1 P 1 = V 2 P 2
T 1 T 2
• This is a very important law for you to
know.

Avogadro’s Principle
• Amedeo Avogadro proposed that at equal
temperature and pressure, equal volumes of
all gases contain the same number of
molecules.
• This important idea lead to the discovery of
Avogadro’s famous number (N). There are
6.02 x 10 23 molecules in 1 mole of any
substance.
• In a practical sense, more moles = more V
of gas.

The Ideal Gas Law
• One factor not considered by the combined
gas law is the amount (moles) of gas.
• The ideal gas law takes moles into account.
• PV = nRT
• This equation makes an automatic
correction to standard temperature and
pressure. This allows us to easily work
with systems that are not at STP.

Ideal Gases
• Earlier, we said that there were NO ideal gases.
So, what good is an ideal gas law?
• We can actually make pretty CLOSE predictions
using PV = nRT.
• Johannes Van der Waal developed a modified
version of the equation to compensate for real gas
behavior. You may research van der Waal’s
equation if you wish.

The Universal Gas Constant
• R is the universal gas constant that corrects
for systems not at STP.
• The value of R varies depending on which
units of pressure are being used.
• R = 0.0821 L • atm/mol • K
• R = 62.4 L • mmHg/mol • K
• R = 8.31 L • kPa/mol • K

V, P, T and n
• It is pointless to discuss the volume of a gas
without discussing the moles of gas and the
temperature and pressure at the same time.
• An change in any one of these 4 variables
affects the others. They are all interrelated.

Dalton’s Law
• Dalton’s Law of Partial Pressures says that
in a mixture of gases, each gas exerts its
own pressure as though the others were not
there.
• Mathematically, P T = P 1 + P 2 + P 3 + ...

The “Litter Box” Equation
• A useful version of the Ideal Gas Law
involves molar mass and gas density.
• μ = dRT/P
• If gas density (d in g/L) is known, molar
mass (μ in g/mol) can easily be calculated.
• We call it the “litter box” equation because
a kitty says “mu”, takes a “P”, and kicks
“dRT” over it. Easy to remember.

Barometers
• The barometer is a device
we use for measuring
atmospheric air pressure.
• It consists of a tube that is
sealed at one end and open
at the other.
• The tube is filled with
liquid mercury, tipped
upside down and the open
end placed in a dish of
mercury.

Barometers
Torricellian
Vacuum
Air
Glass Tube
Hg
760
mm
• Gravity pulls the mercury down
slightly in the tube, creating a
vacuum in the top, sealed end
of the tube.
• However, air pressure pushing
on the surface of the mercury in
the dish keeps the mercury
suspended in the tube.
• The higher the air pressure, the
higher the column in the tube.
• On a normal day at sea level,
the height of the mercury will
be 760mm above the level of
the mercury in the dish.

A Rising Barometer
• The next time the weather
forecaster says the barometer is
at 29.32 inches and rising, they
mean the mercury column is
going up in the tube.
• This indicates that the air
pressure is increasing.
• High pressure is usually
associated with cool, dry air and
sunny skies.
• Go ahead with your picnic
plans.

A Falling Barometer
• A falling barometer gets broken!
Just kidding.
• A falling barometer indicates low
air pressure. Air near the ground is
rising into the upper atmosphere.
• Air from near the ground usually
contains moisture (humidity). As
the air rises, it cools and the
moisture condenses.
• The result is clouds and perhaps
rain or snow.
• A falling barometer often indicates
stormy weather. You may want to
change your picnic plans.

Review
V
o
l
u
m
e
B
D
A
C
• Which line on the
graph at the left best
illustrates Boyle’s
Law of pressure and
volume?
• If you said “D”, you
are correct!
Pressure

Review
V
o
l
u
m
e
B
D
A
C
• Which line on the
graph shows Charles’
Law, the relationship
between temperature
and volume?
• If you said “A” you
are correct.
Temperature

Review
P
r
e
s
s
u
r
e
B
D
A
C
• Which line best
illustrates Gay-
Lussac’s law of
pressure vs.
temperature?
• If you said “A” again,
you are correct.
Temperature

Review
V
o
l
u
m
e
B
D
A
C
• Which line best shows
Avogadro’s principle
involving moles of gas
and volume.
• Once again, “A” is the
best answer.
• How did you do?
Moles